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The British Expeditionary Force (BEF) was the contingent of the British Army sent to France in 1939 after Britain and France declared war on Nazi Germany on 3 September, beginning the Second World War. The BEF existed from 2 September 1939 when the BEF GHQ was formed until 31 May 1940, when GHQ closed down and its troops reverted to the command of Home Forces. During the 1930s, the British government had planned to deter war by abolishing the Ten Year Rule and rearming from the very low level of readiness of the early 1930s. The bulk of the extra money went to the Royal Navy and the Royal Air Force but plans were made to re-equip a small number of Army and Territorial Army divisions for service overseas.
General Lord Gort was appointed to the command of the BEF on 3 September 1939 and the BEF began moving to France on 4 September 1939. The BEF assembled along the Belgian–French border. The BEF took their post to the left of the French First Army under the command of the French 1st Army Group (fr:Groupe d'armées n° 1) of the North-Eastern Front (Front du Nord-est). Most of the BEF spent the Phoney War (3 September 1939 to 9 May 1940) digging field defences on the border. When the Battle of France (Fall Gelb) began on 10 May 1940, the BEF constituted 10 per cent of the Allied forces on the Western Front.
The BEF participated in the Dyle Plan, a rapid advance into Belgium to the line of the Dyle River, but the 1st Army Group had to retreat rapidly through Belgium and north-western France, after the German breakthrough further south at the Battle of Sedan (12–15 May). A local counter-attack at the Battle of Arras (1940) (21 May) was a considerable tactical success but the BEF, French and Belgian forces north of the Somme River retreated to Dunkirk on the French North Sea coast soon after, British and French troops being evacuated in Operation Dynamo (26 May – 4 June) to England after the capitulation of the Belgian army.
Saar Force, the 51st (Highland) Infantry Division and reinforcements, had taken over part of the Maginot Line for training. The force fought with local French units after 10 May, then joined the Tenth Army south of the Somme, along with the improvised Beauman Division and the 1st Armoured Division, to fight in the Battle of Abbeville (27 May – 4 June). The British tried to re-build the BEF with Home Forces divisions training in Britain, troops evacuated from France and lines-of-communications troops south of the Somme river (informally known as the 2nd BEF) but BEF GHQ was not reopened.
After the success of the second German offensive in France (Fall Rot), the 2nd BEF and Allied troops were evacuated from Le Havre in Operation Cycle (10–13 June) and the French Atlantic and Mediterranean ports in Operation Aerial (15–25 June, unofficially to 14 August). The Navy rescued 558,032 people, including 368,491 British troops but the BEF lost 66,426 men of whom 11,014 were killed or died of wounds, 14,074 wounded and 41,338 men missing or captured. About 700 tanks, 20,000 motor bikes, 45,000 cars and lorries, 880 field guns and 310 larger equipments, about 500 anti-aircraft guns, 850 anti-tank guns, 6,400 anti-tank rifles and 11,000 machine-guns were abandoned. As units arrived in Britain they reverted to the authority of the Commander-in-Chief, Home Forces.
== History ==
=== Background ===
==== 1918–1932 ====
After 1918, the prospect of war seemed so remote, that Government expenditure on the armed forces was determined by the assumption that no great war was likely. Spending varied from year to year and between the services but from July 1928 to March 1932, the formula of the Committee of Imperial Defence (CID) was
...that it should be assumed for the purpose of framing the estimates of the fighting services that at any given date there will be no major war for ten years.
and spending on equipment for the army varied from £1,500,000 to £2,600,000 per year from 1924 to 1933, averaging £2,000,000 or about 9 per cent of armaments spending a year. Until the early 1930s, the War Office intended to maintain a small, mobile and professional army and a start was made on motorising the cavalry and the artillery. By 1930, the Royal Army Service Corps (RASC) had been mechanised, some of the artillery could be moved by tractors, and a few engineer, signals and cavalry units had received lorries. From 1930–1934, the Territorial Army (TA) artillery, engineer, signals units were equipped with lorries and in 1938 the regular army gained its establishment of wheeled vehicles and half of its tracked vehicles, except for tanks. From 1923 to 1932, 5,000 motor vehicles were ordered at a rate of about 500 a year, just under half being six-wheeler lorries. By 1936, the army had 379 tanks, of which 209 were light tanks and 166 were mediums; 304 were considered obsolete; 69 of the light tanks were modern but did not begin to reach the army until 1935. The rule had reduced war spending from £766 million in 1920 to £102 million when it was abolished on 23 March 1932. The British army had fewer men than in 1914, no organisation or equipment for a war in Europe, and it would have taken the War Office three weeks to mobilise only an infantry division and a cavalry brigade.
==== Rearmament ====
===== Limited Liability =====
In March 1932, the Ten-Year Rule was abolished and in 1934, the Cabinet resolved to remedy equipment deficiencies in the armed forces over the next five years. The army was always the least favoured force but equipment spending increased from £6,900,000 from 1933–1934 financial year (1 April to 31 March), to £8,500,000 the following year and to more than £67,500,000 by 1938–1939 but the share of spending on army equipment only grew beyond 25 per cent of all military equipment spending in 1938. The relative neglect of the army led to a theory of "limited liability" until 1937, in which Britain would not send a great army to Europe in time of war. In 1934, the Defence Requirements Sub-Committee (DRC) of the CID assumed that a regular field army of five divisions was to be equipped as an expeditionary force, eventually to be supplemented by parts of the Territorial Army. The force and its air support would act as a deterrent greatly disproportionate to its size; plans were made to acquire sufficient equipment and training for the TA to provide a minimum of two extra divisions on the outbreak of war. It was expected that a British army in Europe would receive continuous reinforcement and in 1936, a TA commitment of twelve divisions was envisaged by Duff Cooper, the Secretary of State for War.
As rearmament of the navy and the air force continued, the nature of an army fit to participate in a European war was kept under review and in 1936, the Cabinet ordered the Chiefs of Staff Sub-Committee of the CID to provide a report on the role of an expeditionary force and the relative values of the army and the air force as deterrents for the same cost. The chiefs were in favour of a balanced rearmament but within financial limits, the air force should be favoured. In 1937, the Minister argued that a continental commitment was no longer feasible and that France did not now expect a big land army along with the navy and air force, Germany had guaranteed Belgian neutrality and that if the quantity of money was limited, defence against air attack, trade protection and the defence of overseas territories were more important and had to be secured before Britain could support allies in the defence of their territories. The "continental hypothesis" came fourth and the main role of the army was to protect the empire, which included the anti-aircraft defence of the United Kingdom (with the assistance of the TA). In 1938, "limited liability" reached its apogee, just as rearmament was maturing and the army was considering the "new conspectus", a much more ambitious rearmament plan.
In February 1938, the CID ruled that planning should be based on "limited liability"; between late 1937 and early 1939, equipment for the five-division field army was reduced to that necessary for colonial warfare in the Far East. In Europe, the field force could only conduct defensive warfare and would need a big increase in ammunition and the refurbishment of its tank forces. The field force continued to be the least-favoured part of the least-favoured military arm and in February 1938, the Secretary of State for War, Leslie Hore-Belisha, warned that possible allies should be left in no doubt about the effectiveness of the army. The re-armament plans for the field force remained deficiency plans, rather than plans for expansion. The July 1934 deficiency plan was estimated at £10,000,000 but cut by 50 per cent by the cabinet; by the first rearmament plan of 1936, the cost of the deficiency plan for the next five years had increased to £177,000,000. In the first version of the "new conspectus", spending was put at £347,000,000, although in 1938 this was cut to £276,000,000, still substantially more than the deficiency plan for 1936 but much of this sum was for anti-aircraft defence, a new duty imposed on the army.
===== Continental commitment =====
Obtaining equipment for the Field Force benefited from plans for the TA which, sometimes covertly, was used as a device to get more equipment which could be used by the regular army. At first it was admitted in the deficiency programmes of 1935–1936, in which an expansion of the TA in three stages to twelve divisions, was to complement the five regular divisions. The Cabinet postponed this plan for three years, during which the policy of limited liability precluded such developments, except for the purchase of the same training equipment for the TA as that used by the army, equivalent to that needed to equip two regular divisions, which was the maximum commitment promised to the French in 1938. The mobile division was split into two divisions and some extra equipment went to artillery and engineer units. By 1938 the deficiency programme was due to mature; in the wake of the Munich Crisis in September and the loss of the 35 divisions of the Czechoslovak Army, the Cabinet approved a plan for a ten-division army equipped for continental operations and a similar-sized TA, in early 1939. By reacting to events, the British Cabinet made it inevitable that
...the size of the Army was bound to be adjusted to what the French thought was the least they needed and the British the most that they could do.
The British made a commitment on 21 April 1939 to provide an army of six regular and 26 Territorial divisions, introduced equipment scales for war and began conscription to provide the manpower. In February 1939, the first four regular army divisions of the Field Force had been promised to the French, scheduled to reach the assembly area in France on the thirtieth day after mobilisation. Until this commitment, no staff work had been done, there was no information about French ports and railways and no modern maps.
=== Prelude ===
==== Despatch of the BEF ====
After the Invasion of Poland by Germany on 1 September 1939, the Cabinet appointed General John Vereker, 6th Viscount Gort (Lord Gort) to the command of the BEF on 3 September, subordinate to General Alphonse Georges, the French commander of the North-eastern Theatre of Operations, with the right of appeal to the British government. The BEF was to assemble on the Franco-Belgian border and advanced parties of troops left Portsmouth on 4 September under "Plan W4" and the first troop convoy left the ports on the Bristol Channel and Southampton on 9 September, disembarking at Cherbourg on 10 September and Nantes and Saint Nazaire on the French Atlantic coast two days later. German submarines had been held back by Hitler to avoid provoking the Allies and only a few mines were laid near Dover and Weymouth. By 27 September, 152,000 soldiers, 21,424 vehicles, 36,000 long tons (36,578 t) tons of ammunition, 25,000 long tons (25,401 t) of petrol and 60,000 long tons (60,963 t) of frozen meat had been landed in France.
On 3 October, I Corps with the 1st Infantry Division and 2nd Infantry Division began to take over the front line allocated to the BEF and II Corps with the 3rd Infantry Division and 4th Infantry Division followed on 12 October; the 5th Infantry Division arrived in December. By 19 October, the BEF had received 25,000 vehicles to complete the first wave. The majority of the troops were stationed along the Franco-Belgian border but British divisions took turns to serve with the French Third Army on the Maginot Line. In April 1940, the 51st Highland Infantry Division, reinforced by additional units and called Saar Force took over part of the French line. Belgium and the Netherlands were neutral and free of Allied or German military forces and for troops along the Maginot Line, inactivity and an undue reliance on the fortifications, which were believed to be impenetrable, led to "Tommy Rot" (portrayed in the song "Imagine Me in the Maginot Line"). Morale was high amongst the British troops but the limited extent of German actions by 9 May 1940, led many to assume that there would not be much chance of a big German attack in that area.
From January to April 1940, eight Territorial divisions arrived in France but the 12th (Eastern) Infantry Division, 23rd (Northumbrian) Division and 46th Infantry Division, informally called labour divisions, were not trained or equipped to fight. The labour divisions consisted of 26 new infantry battalions which had spent their first months guarding vulnerable points in England but had received very little training. Battalions and some engineers were formed into nominal brigades but lacked artillery, signals or transport. The divisions were used for labour from St Nazaire in Brittany to Saint-Pol-sur-Ternoise (St Pol) in French Flanders, on the understanding that they would not be called upon to fight before they had completed their training.
By May 1940 the BEF order of battle consisted of ten infantry divisions ready for field service, in I Corps, II Corps, III Corps and Saar Force. BEF GHQ commanded the Field Force and the BEF Air Component Royal Air Force (RAF) of about 500 aircraft but the Advanced Air Striking Force (AASF) long-range bomber force was under the control of RAF Bomber Command. GHQ consisted of men from Headquarters (HQ) Troops (consisting of the 1st Battalion, Welsh Guards, the 9th Battalion, West Yorkshire Regiment and the 14th Battalion, Royal Fusiliers), the 1st Army Tank Brigade, 1st Light Armoured Reconnaissance Brigade, HQ Royal Artillery and the 5th Infantry Division.
==== Phoney War ====
The period from September 1939 to 10 May 1940 was known as the Phoney War, the only Allied operation of any significance being the French Saar Offensive (7 September to 16 October 1939). The section of the Franco-Belgian border to be held by the BEF at that time stretched from Armentières westward towards Menin, then south to the junction of the border and the River Escaut (the French name for the Scheldt) at Maulde, forming a salient around Lille and Roubaix. The British began to dig trenches, weapons pits and pill boxes of the Gort Line. The first BEF fatality was 27-year-old Corporal Thomas Priday, from the 1st Battalion, King's Shropshire Light Infantry, attached to the 3rd Infantry Brigade of the 1st Infantry Division, killed on 9 December 1939, when his patrol set off a booby-trap and was fired upon by friendly troops. By November 1939, the French had decided that a defence along the Dyle Line in Belgium was feasible but the British were lukewarm about an advance into Belgium. Gamelin talked them round and on 9 November, the Dyle Plan/Plan D was adopted and on 17 November, Gamelin issued a directive detailing a line from Givet to Namur, the Gembloux Gap, Wavre, Louvain and Antwerp. For the next four months, the Dutch and Belgian armies laboured over their defences, the BEF expanded and the French army received more equipment and training.
==== Dyle plan, Breda variant ====
By May 1940, the 1st Army Group (Groupe d'armées n° 1) defended the Channel coast to the west end of the Maginot Line. The Seventh Army (Général d'armée Henri Giraud), BEF (General Lord Gort), First Army (Général d'armée Georges Maurice Jean Blanchard) and Ninth Army (Général d'armée André Corap) were ready to advance to the Dyle Line, by pivoting on the right (southern) Second Army. The Seventh Army would take over west of Antwerp, ready to move into Holland and the Belgians were expected to delay a German advance and then retire from the Albert Canal to the Dyle, between Antwerp to Louvain. The BEF was to defend about 12 mi (20 km) of the Dyle from Louvain to Wavre and the First Army on the right of the BEF was to hold 22 mi (35 km) from Wavre across the Gembloux Gap to Namur. The gap from the Dyle to Namur north of the Sambre, with Maastricht and Mons on either side, had few natural obstacles and led straight to Paris. The Ninth Army would take post south of Namur, along the Meuse to the left (northern) flank of the Second Army.
The Second and Ninth armies were dug in on the west bank of the Meuse on ground that was easily defended and behind the Ardennes, giving plenty of warning of a German attack. After the transfer of the Seventh Army, seven divisions remained behind the Second and Ninth armies and other divisions could be moved from behind the Maginot Line. All but one division were either side of the junction of the two armies, GQG being more concerned about a German attack past the north end of the Maginot Line and then south-east through the Stenay Gap, for which the divisions behind the Second Army were well placed. On 8 November, Gamelin added the Seventh Army, containing some of the best and most mobile French divisions, to the left flank of the 1st Army Group to move into Holland and protect the Scheldt estuary. In March, Gamelin ordered that the Seventh Army would advance to Breda to link with the Dutch. The Seventh Army, on the left flank of the Dyle manoeuvre, would be linked to it and if the Seventh Army crossed into the Netherlands, the left flank of the 1st Army Group was to advance to Tilburg if possible and certainly to Breda. The Seventh Army was to take post between the Belgian and Dutch armies turning east, a distance of 109 mi (175 km), against German armies only 56 mi (90 km) distant from Breda.
=== Battle ===
==== 10–21 May 1940 ====
At 4:35 a.m., the German invasion of France and the Low Countries commenced. The French Seventh Army drove forward on the northern flank and advanced elements reached Breda on 11 May. The French collided with the 9th Panzer Division and the advance of the 25e Division d'Infanterie Motorisée was stopped by German infantry, tanks and Ju 87 (Stuka) dive-bombers, as the 1re Division Légère Mécanisée was forced to retreat. (French heavy tanks were still on trains south of Antwerp.) The Seventh Army retired from the Bergen op Zoom–Turnhout Canal Line 20 mi (32 km) from Antwerp, to Lierre 10 mi (16 km) away on 12 May; on 14 May the Dutch surrendered.
In Belgium, German glider troops captured fort Eben-Emael by noon on 11 May; the disaster forced the Belgians to retreat to a line from Antwerp to Louvain on 12 May, far too soon for the French First Army to arrive and dig in. The Corps de Cavalerie fought the XVI Panzer Corps in the Battle of Hannut (12–14 May) the first ever tank-against-tank battle and the Corps de Cavalerie then withdrew behind the First Army, which had arrived at the Dyle Line. On 15 May, the Germans attacked the First Army along the Dyle, causing the meeting engagement that Gamelin had tried to avoid. The First Army repulsed the XVI Panzer Corps but during the Battle of Gembloux (14–15 May) GQG realised that the main German attack had come further south, through the Ardennes. The French success in Belgium contributed to the disaster on the Meuse at Sedan and on 16 May, Blanchard was ordered to retreat to the French border.
==== Operation David ====
The armoured cars of the 12th Royal Lancers crossed the border at 1:00 p.m. on 10 May, cheered on by Belgian civilians. The BEF sector ran along the Dyle about 22 mi (35 km) from Louvain, south-west to Wavre. The 3rd Division (II Corps) took the north with the 1st Division and 2nd Division (I Corps) the south, some battalions defending a frontage double that recommended in British manuals. The rest of the BEF formed a defence in depth back to the River Escaut. The Dyle north of Louvain was occupied by Belgian troops who refused to give way, even when Brooke appealed to the King of the Belgians and Georges ordered them out. The British infantry began to arrive on the Dyle on 11 May and dug in screened by light tanks and Bren carriers operating west of the river until 14 May, when the front line units were ready; the bridges were then blown. Later that day probes by reconnaissance troops of three German infantry divisions were dispersed. Next day, attacks on Louvain by the German 19th Division were repulsed by the 3rd Division. Further south, the river was only about 15 ft (4.6 m) wide, preventing tanks from crossing but passable by infantry. Richard Annand of the Durham Light Infantry in the southern sector was awarded a Victoria Cross. German bridgeheads across the Dyle were either eliminated or contained by British counter-attacks.
===== Ardennes =====
From 10–11 May, the XIX Panzer Corps engaged the two cavalry divisions of the Second Army, surprising them with a far larger force than expected and forced them back. The Ninth Army to the north had also sent its two cavalry divisions forward, which were withdrawn on 12 May, before they met German troops. The first German unit reached the Meuse in the afternoon but the local French commanders thought that they were far ahead of the main body and would wait before trying to cross the Meuse. From 10 May, Allied bombers had been sent to raid northern Belgium, to delay the German advance while the First Army moved up but attacks on the bridges at Maastricht had been costly failures, the 135 RAF day bombers being reduced to 72 operational aircraft by 12 May. At 7:00 a.m. on 13 May, the Luftwaffe began bombing the French defences around Sedan and continued for eight hours with about 1,000 aircraft in the biggest air attack in history.
Little material damage was done to the Second Army but morale collapsed. In the French 55e Division at Sedan, some troops began to straggle to the rear and in the evening panic spread through the division. German troops attacked across the river at 3:00 p.m. and had gained three footholds on the west bank by nightfall. The French and the RAF managed to fly 152 bomber and 250 fighter sorties on the Sedan bridges on 14 May but only in formations of 10–20 aircraft. The RAF lost 30 of 71 aircraft and the French were reduced to sending obsolete bombers to attack in the afternoon, also with many losses. On 16 May, the 1st Army Group was ordered to retreat from the Dyle Line, to avoid being trapped by the German breakthrough against the Second and Ninth armies but on 20 May, the Germans reached Abbeville on the Channel coast, cutting off the northern armies.
===== BEF retreat =====
The plan for the BEF withdrawal was that under cover of darkness, units would thin-out their front and make a phased and orderly withdrawal before the Germans realised what was happening. The objective for the night of 16/17 May was the Charleroi to Willebroek Canal (the Line of the Senne), the following night to the River Dendre from Maubeuge to Termonde and the Escaut to Antwerp (the Dendre Line), and finally on 18/19 May, to the Escaut from Oudenarde to Maulde on the French border (the Escaut Line). The order to withdraw was greeted with astonishment and frustration by the British troops who felt that they had held their own, but they were unaware of the deteriorating situation elsewhere. The withdrawal went mainly according to plan but required hard fighting from the corps rearguards. A communication breakdown caused a loss of co-ordination with the Belgian Army to the north-west of II Corps and a dangerous gap opened up between the two; fortunately it was covered by British light armour before the Germans could discover and exploit it.
===== Loss of the construction divisions =====
The three Territorial divisions, which had arrived in April equipped only with small arms, intended for construction and labouring tasks, were distributed across the path of the German spearhead. On 16 May, Georges realised that the Panzer divisions might reach the coast and outflank all the Allied armies to the north of them. He asked for the 23rd Division to defend the Canal du Nord at Arleux. The British Staff was of the opinion that the German breakthrough consisted of small detachments of light reconnaissance troops and that using these lightly armed and largely untrained troops against them did not seem unreasonable. The area was otherwise devoid of Allied units, so there was little alternative. The three divisions were grouped together in an improvised corps called Petreforce and on 18 and 19 May, the Territorials, lacking motor transport, began to march or entrain towards their defence positions.
The 70th Brigade of the 23rd Division dug in on the Canal Line but was ordered to withdraw towards Saulty on 20 May; in the process they were caught in the open by elements of 6th and 8th Panzer Divisions, from which only a few hundred survivors escaped. The 69th Brigade defended Arras and the 12th Division fought to delay 2nd Panzer Division on the Canal Line near Arras, at Doullens, Albert and Abbeville. The 138th Brigade of the 46th Division fought on the Canal Line but the 137th Brigade trains were attacked by the Luftwaffe en route; the survivors were able to withdraw to Dieppe and later fought on the Seine Crossings. The 139th Brigade fought on the River Scarpe and later defended the Dunkirk perimeter. By the end of 20 May, the divisions had ceased to exist, in most cases having only delayed the German advance by a few hours.
==== 21–26 May ====
The push by Army Group A towards the coast, combined with the approach of Army Group B from the north-east, left the BEF enveloped on three sides and by 21 May, the BEF had been cut off from its supply depots south of the Somme. The British counter-attacked at the Battle of Arras on the same day. This was well to the south of the main BEF force on the Escaut, where seven BEF divisions were placed in the front line. The British divisions were facing nine German infantry divisions, who began their attack on the morning of 21 May with a devastating artillery barrage. Shortly afterwards, infantry assaults started along the whole front, crossing the canalised river either by inflatable boats or by clambering across the wreckage of demolished bridges. Although the Escaut line was penetrated in numerous places, all the German bridgeheads were either thrown back or contained by vigorous but costly British counter-attacks and the remaining German troops were ordered to retire across the river by the night of 22 May. Later that same night, events further south prompted an order for the BEF to retire again, this time back to the Gort Line on the Franco-Belgian border. The Channel ports were at risk of capture. Fresh troops were rushed from England to defend Boulogne and Calais but after hard fighting, both ports were captured by 26 May in the Battle of Boulogne and Siege of Calais. On May 26, Gort ordered the BEF to withdraw to Dunkirk, the only port from which the BEF could still escape. In his biography of Bernard Montgomery, Nigel Hamilton described Gort's order as 'the greatest decision of his life'.
==== Retreat to Dunkirk ====
===== Le Paradis massacre =====
Detached rifle companies of the 2nd Battalion, Royal Norfolk Regiment of the 1st Battalion and Royal Scots of the 2nd Infantry Division provided rearguards during the evacuation of troops from Dunkirk. The 2nd Royal Norfolks held the line at La Bassée Canal with the 1/8th Lancashire Fusiliers, while the 2nd Royal Norfolks and 1st Royal Scots held the villages of Riez du Vinage and Le Cornet Malo, protecting the battalion headquarters at Le Paradis for as long as possible. After an engagement with German forces at dawn on 27 May in Le Cornet Malo, C Company and HQ Company of the 2nd Royal Norfolks fell back to the headquarters at the Cornet Farm outside Le Paradis. They were told by radio that their units were isolated and would not receive any assistance.
German forces attacked the farmhouse with tanks, mortars and artillery, which destroyed the building and forced the Norfolks to retreat to a nearby barn. The Royal Norfolks continued their defensive stand into the evening, by which point many had been wounded by the German bombardment. The last contact with Brigade Headquarters at L'Epinette occurred at 11:30 a.m. but despite the lack of support the Norfolks held on until 5:15 p.m. when they ran out of ammunition.
Cornered, outnumbered and with many wounded, 99 Royal Norfolks made a rush into the open but eventually, under the orders of their commander Major Lisle Ryder, the Norfolks surrendered. In the confusion of battle and in part due to battle fatigue, the Norfolks had surrendered not to the German company they had been fighting but rather to the 2nd Infantry Regiment of the SS Totenkopf Division (Death's Head) (SS-Hauptsturmführer and Obersturmbannführer Fritz Knöchlein), which had been fighting another isolated BEF unit, the Royal Scots, at an adjacent farm. The Knöchlein Totenkopt unit, notorious for their ruthlessness, had been engaged in mopping-up operations against Allied forces to the north and east of Cambrai. The 99 prisoners were marched to farm buildings on a nearby farm and lined up alongside a barn wall. They were then fired upon by two machine-guns; Knöchlein then armed his men with bayonets to kill the survivors. All but two of the Norfolks were killed and their bodies buried in a shallow pit. Privates Albert Pooley and William O'Callaghan, hiding in a pigsty, were discovered later by the farm's owner, Mme Creton and her son. The two soldiers were later captured by a Wehrmacht unit and spent the rest of the war as prisoners of war.
===== II Corps rearguard =====
The II Corps commander Lieutenant General Alan Brooke, was ordered to conduct a holding action with the 3rd, 4th, 5th and 50th Infantry Divisions along the Ypres–Comines canal as far as Yser, while the rest of the BEF fell back. At mid-day on 27 May, the Germans attacked south of Ypres with three divisions. German infantry infiltrated through the defenders and forced them back. On 27 May, Brooke ordered Major-General Bernard Montgomery to extend the 3rd Division line to the left, freeing the 10th and 11th Brigades of the 4th Division to join the 5th Division at Messines Ridge. The 10th and 11th Brigades managed to clear the ridge of Germans and by 28 May, the brigades were dug in east of Wytschaete. Brooke ordered a counter-attack led by the 3rd Battalion, Grenadier Guards and the 2nd Battalion, North Staffordshire Regiment of the 1st Division. The North Staffords advanced as far as the Kortekeer River, while the Grenadiers managed to reach the Ypres–Comines Canal but could not hold it. The counter-attack disrupted the Germans, holding them back a little longer while the BEF continued its retreat.
==== Dunkirk ====
The Germans failed to capture Dunkirk and on 31 May, General Georg von Küchler assumed command of the German forces on the Dunkirk perimeter and planned a bigger attack for 11:00 a.m. on 1 June. The French held the Germans back while the last troops were evacuated and just before midnight on 2 June, Admiral Bertram Ramsay, the officer commanding the evacuation, received the signal "BEF evacuated"; the French began to fall back slowly. By 3 June, the Germans were 2 mi (3.2 km) from Dunkirk and at 10:20 a.m. on 4 June, the Germans hoisted the swastika over the docks. Before Operation Dynamo, 27,936 men were embarked from Dunkirk; most of the remaining 198,315 men, a total of 224,320 British troops along with 139,097 French and some Belgian troops, were evacuated from Dunkirk between 26 May and 4 June, though having to abandon much of their equipment, vehicles and heavy weapons.
=== After Dunkirk ===
==== Lines-of-communication ====
Allied forces north of the Somme were cut off by the German advance on the night of 22/23 May, which isolated the BEF from its supply entrepôts of Cherbourg, Brittany and Nantes. Dieppe was the main BEF medical base and Le Havre the principal supply and ordnance source. The main BEF ammunition depot and its infantry, machine-gun and base depots were around Rouen, Évreux and Épinay. Three Territorial divisions and three lines-of-communication battalions had been moved north of the Seine on 17 May. Rail movements between these bases and the Somme was impeded by German bombing and trains arriving from the north full of Belgian and French troops; the roads also filled with retreating troops and refugees. Acting Brigadier Archibald Beauman lost contact with BEF GHQ.
Beauman improvised Beauforce from two infantry battalions, four machine-gun platoons and a company of Royal Engineers. Vicforce (Colonel C. E. Vickary) took over five provisional battalions from troops in base depots, who had few arms and little equipment. The Germans captured Amiens on 20 May, setting off panic and the spread of alarmist reports. Beauman ordered the digging of a defence line along the Andelle and Béthune to protect Dieppe and Rouen. From 1–3 June, the 51st Highland Division (formerly Saar Force) a Composite Regiment and the remnants of the 1st Support Group, 1st Armoured Division, relieved the French opposite the Abbeville–St Valery bridgehead. The Beauman Division held a 55 mi (89 km) line from Pont St Pierre, 11 mi (18 km) south-east of Rouen to Dieppe on the coast, which left the British units holding 18 mi (29 km) of the front line, 44 mi (71 km) of the Bresle and 55 mi (89 km) of the Andelle–Béthune line, with the rest of IX Corps on the right flank.
==== Second BEF ====
On 31 May, GHQ BEF closed and 2 June, Brooke visited the War Office and was given command of a new II Corps, comprising the 51st (Highland) Infantry Division and the 1st Armoured Division, with the 52nd (Lowland) Infantry Division and the 1st Canadian Infantry Division from Home Forces in Britain, then the 3rd Infantry Division as soon as it was ready. Brooke warned that the enterprise was futile, except as a political gesture. On 6 June, the Cabinet decided to reconstitute the BEF (Second BEF is an informal post-war term) with Gort remaining as commander in chief.
The 157th (Highland Light Infantry) Brigade (a brigade group) of the 52nd (Lowland) Division, departed for France on 7 June; Brooke returned five days later. On 9 June, the French port Admiral at Le Havre reported that Rouen had fallen and that the Germans were heading for the coast. Ihler and Fortune decided that their only hope of escape was via Le Havre. The port admiral requested British ships for 85,000 troops but this contradicted earlier plans for the IX Corps retirement and Dill hesitated, ignorant that the original plan was untenable. Karslake urged that the retirement be accelerated but had no authority to issue orders. Only after contacting the Howard-Vyse Military Mission at GQG and receiving a message that the 51st (Highland) Division was retreating with IX Corps towards Le Havre, did Dill learn the truth.
==== St Valery ====
The retreat to the coast began after dark and the last troops slipped away from the Béthune river at 11:00 p.m. Units were ordered to dump non-essential equipment and each gun were reduced to 100 rounds to make room on the RASC transport for the men. The night move was difficult as French troops, many horse-drawn, encroached on the British route and alarmist rumours spread. Fortune and Ihler set up at a road junction near Veules-les-Roses to direct troops to their positions and by the morning of 11 June, IX Corps had established a defence round St Valery. French transport continued to arrive at the perimeter and it was difficult in some places to recognise German troops following up, which inhibited defensive fire. That night, Fortune signalled that it was now or never. Troops not needed to hold the perimeter moved down to the beaches and the harbour. An armada of 67 merchant ships and 140 small craft had been assembled but few had wireless; thick fog ruined visual signalling and prevented the ships from moving inshore. Only at Veules-les-Roses at the east end of the perimeter, were many soldiers rescued, under fire from German artillery, which damaged the destroyers HMS Bulldog, Boadicea and Ambuscade; 2,137 British and 1,184 French troops were evacuated. Near dawn, the troops at the harbour were ordered back into the town and at 7:30 a.m., Fortune signalled that it might still be possible to escape the next night, then discovered that the local French commander had already surrendered.
==== Le Havre ====
Fortune had detached Arkforce comprising the 154th Infantry Brigade, A Brigade of the Beauman Division, two artillery regiments and engineers to guard Le Havre. Arkforce moved on the night of 9/10 June towards Fécamp, where most had passed through before the 7th Panzer Division arrived. A Brigade managed to force its way out but lost the wireless truck for liaison with the 51st (Highland) Division and Stanley-Clarke ordered Arkforce on to Le Havre. On 9 June, the Admiralty ordered Le Havre to be evacuated and the Commander-in-Chief, Portsmouth sent a flotilla leader, HMS Codrington across the channel, accompanied by six British and two Canadian destroyers, smaller craft and Dutch coasters (known as schuyts). On 10 June, HMS Vega escorted three blockships to Dieppe and two were sunk in the approach channel. Beach parties landed at Le Havre on 10 June and the evacuation began on 11 June, hindered somewhat by Luftwaffe bombing. The troopship SS Bruges was beached and the electric power was cut, rendering the cranes on the docks useless and improvised methods to embark heavy equipment were too slow. On 12 June, RAF fighters deterred more raids and the quartermaster of the 14th Royal Fusiliers got the transport away over the Seine via the ferry at Caudebec and ships at Quillebeuf at the river mouth. The Navy got 2,222 British troops from Le Havre to England and 8,837 were taken to Cherbourg to join the forces being assembled for the new II Corps (Second BEF).
==== Retreat from Normandy ====
By 13 June, the Germans were across the Seine and the Tenth Army (General Robert Altmayer) was isolated on the Channel coast. The AASF was ordered to retreat towards Nantes or Bordeaux while supporting the French armies, flying armed reconnaissance sorties over the Seine from dawn, which cost ten aircraft and crews; bad weather limited fighter sorties to the coast. On 14 June, attacks resumed against German units south of the Seine but the weather deteriorated and fewer sorties were flown. Seven Blenheims were shot down raiding Merville airfield but ten Fighter Command squadrons patrolled twice in squadron strength or provided bomber escorts, the biggest effort since Dunkirk, fighters of the AASF patrolling south of the Seine. The remnants of the 1st Armoured Division and two brigades of the Beauman Division had got south of the river, with thousands of lines-of-communication troops but only the 157th Infantry Brigade, 52nd (Lowland) Division was in contact with the Germans, occupying successive defensive positions. The French armies were forced into divergent retreats, with no obvious front line.
On 12 June, Weygand had recommended that the French government seek an armistice, which led to an abortive plan to create a defensive zone in Brittany. On 14 June, Brooke was able to prevent the rest of the 52nd (Lowland) Division being sent to join the 157th Infantry Brigade Group and during the night Brooke was told that he was no longer under French command and must prepare to withdraw the British forces from France. Marshall-Cornwall was ordered to take command of all British forces under the Tenth Army as Norman Force and while continuing to co-operate, to withdraw towards Cherbourg. The rest of the 52nd (Lowland) Division was ordered back to a line near Cherbourg to cover the evacuation on 15 June. The AASF was directed to send its remaining bomber squadrons back to Britain and use the fighters to cover the evacuations. The German advance began again during the day, with the 157th Infantry Brigade Group engaged east of Conches-en-Ouche with the Tenth Army, which was ordered back to a line from Verneuil to Argentan and the Dives river, where the British took over an 8 mi (13 km) front. German forces followed up quickly and on 16 June, Altmayer ordered the army to retreat into the Brittany peninsula.
==== Operation Aerial ====
From 15–25 June, British and Allied ships were covered by five RAF fighter squadrons in France, assisted by aircraft from England as they embarked British, Polish and Czech troops, civilians and equipment from the French Atlantic ports, particularly St Nazaire and Nantes. The Luftwaffe attacked the evacuation ships and on 17 June, sank the troopship RMS Lancastria in the Loire estuary. About 2,477 passengers and crew were saved but thousands of troops, RAF personnel and civilians were on board and at least 3,500 people died. Some equipment was embarked but ignorance about the progress of the German Army and alarmist reports, led some operations to be terminated early and much equipment needlessly was destroyed or left behind. About 700 tanks, 20,000 motor bikes, 45,000 cars and lorries, 880 field guns and 310 larger equipments, about 500 anti-aircraft guns, 850 anti-tank guns, 6,400 anti-tank rifles and 11,000 machine-guns were abandoned.
The official evacuation ended on 25 June, according to the terms of the Armistice of 22 June 1940 but informal departures continued from French Mediterranean ports until 14 August. From Operation Cycle at Le Havre, elsewhere along the Channel coast, to the termination of Operation Aerial, another 191,870 BEF troops were rescued, bringing the total of military and civilian personnel returned to Britain during the Battle of France to 558,032, including 368,491 British troops. Left behind in France was eight to ten divisions' worth of equipment and ammunition. As troops returned to Britain, they increased the manpower of the Commander-in-Chief, Home Forces (General Edmond Ironside 27 May to 20 July, then Brooke) but the trained and equipped units had been stripped from Home Forces and sent to France; only about two divisions' worth of equipment remained in the country. The equivalent of twelve divisions returned to Britain but these could only be re-equipped by the Ministry of Supply from production. Deliveries of 25-pounder field guns had increased to about 35 per month by June but the establishment of one infantry division was 72 guns.
== Aftermath ==
=== Analysis ===
In 1953, Lionel Ellis, the British official historian, wrote that by the end of the informal evacuations on 14 August, another 191,870 men had been evacuated after the 366,162 rescued by Operation Dynamo, a total of 558,032 people, 368,491 being British troops. In 2001, Brodhurst wrote that many civilians escaped from French Atlantic and Mediterranean ports to England via Gibraltar and that 22,656 more civilians left the Channel Islands, from 19–23 June. Much military equipment was lost but 322 guns, 4,739 vehicles, 533 motor cycles. 32,303 long tons (32,821 t) of ammunition, 33,060 long tons (33,591 t) of stores, 1,071 long tons (1,088 t) of petrol, 13 light tanks and 9 cruiser tanks were recovered. During the BEF evacuations 2,472 guns, anti-aircraft guns and anti-tank guns were destroyed or abandoned along with 63,879 vehicles consisting of 20,548 motor cycles and 45,000 cars and lorries, 76,697 long tons (77,928 t) of ammunition, 415,940 long tons (422,615 t) of supplies and equipment and 164,929 long tons (167,576 t) of petrol.
For every seven soldiers who escaped through Dunkirk, one man was left behind as a prisoner of war. The majority of these prisoners were sent on forced marches into Germany to towns such as Trier, the march taking as long as twenty days. Others were moved on foot to the river Scheldt and were sent by barge to the Ruhr. The prisoners were then sent by rail to POW camps in Germany. The majority (those below the rank of corporal) then worked in German industry and agriculture for five years. An intelligence report by the German IV Corps, which had been engaged against the BEF from the Dyle line to the coast, was circulated to the divisions training for Operation Sealion. The report said of the men of the BEF,
The English soldier was in excellent physical condition. He bore his own wounds with stoical calm. The losses of his own troops he discussed with complete equanimity. He did not complain of hardships. In battle he was tough and dogged. His conviction that England would conquer in the end was unshakeable.... The English soldier has always shown himself to be a fighter of high value. Certainly the Territorial divisions are inferior to the Regular troops in training but where morale is concerned they are their equal.... In defence the Englishman took any punishment that came his way.
=== Casualties ===
The BEF suffered 66,426 casualties, 11,014 killed or died of wounds, 14,074 wounded and 41,338 men missing or taken prisoner.
== Map gallery ==
German advances through The Netherlands, Belgium and France
=== Commemoration ===
No campaign medal was awarded for the Battle of France, but servicemen who had spent 180 days in France between 3 September 1939 and 9 May 1940, or "a single day, or part thereof" in France or Belgium between 10 May and 19 June 1940, qualified for the 1939–1945 Star.
== Notes ==
== Footnotes ==
== References ==
== Further reading ==
=== Books ===
Atkin, Ronald (1990). Pillar of Fire: Dunkirk 1940. Edinburgh: Birlinn. ISBN 978-1-84158-078-4.
Fantom, P. (2021). A Forgotten Campaign: The British Armed Forces in France 1940 – From Dunkirk to the Armistice. Warwick: Helion. ISBN 978-1-914059-01-8.
Forrester, C. (2018) [2015]. Monty's Functional Doctrine. Combined Arms Doctrine in British 21st Army Group in Northwest Europe 1944–45. Wolverhampton military studies (pbk. repr. ed.). Warwick: Helion. ISBN 978-1-912174-77-5.
Gibbs, N. H. (1976). Grand Strategy. History of the Second World War United Kingdom Military Series. Vol. I. London: HMSO. ISBN 978-0-11-630181-9.
Hinsley, F. H.; Thomas, E. E.; Ransom, C. F. G.; Knight, R. C. (1979). British Intelligence in the Second World War: Its Influence on Strategy and Operations. History of the Second World War United Kingdom Civil Series. Vol. I. London: HMSO. ISBN 978-0-11-630933-4.
Horne, A. (1982) [1969]. To Lose a Battle: France 1940 (Penguin repr. ed.). London: Macmillan. ISBN 978-0-14-005042-4.
May, Ernest R. (2000). Strange Victory: Hitler's Conquest of France. London: I.B.Tauris. ISBN 978-1-85043-329-3.
Postan, Michael Moissey; Hay, D.; Scott, J. D. (1964). Hancock, K. (ed.). Design and Development of Weapons: Studies in Government and Industrial Organisation. History of the Second World War. United Kingdom Civil Series. London: HMSO. OCLC 681432.
Richards, Denis (1974) [1953]. Royal Air Force 1939–1945: The Fight At Odds. Vol. I (pbk. ed.). London: HMSO. ISBN 978-0-11-771592-9. Retrieved 21 October 2016.
Warner, P. (2002) [1990]. The Battle of France, 1940: 10 May – 22 June (Cassell Military Paperbacks repr. ed.). London: Simon & Schuster. ISBN 978-0-304-35644-7.
Whelan, P. (2018). Useless Mouths: The British Army's Battles in France after Dunkirk May–June 1940. Solihull: Helion. ISBN 978-1-912390-90-8.
=== Reports ===
War Department (31 March 1942). The German Campaign in Poland September 1 to October 5, 1939 (Report). Digests and Lessons of Recent Military Operations. U. S. War Department, General Staff. OCLC 16723453. AG 062.11 (1–26–42). Retrieved 23 June 2018.
=== Theses ===
Harris, J. P. (1983). The War Office and Rearmament 1935–39 (PhD thesis). Registration. King's College London (University of London). OCLC 59260791. Docket uk.bl.ethos.289189. Retrieved 23 June 2018.
Nelsen II, J. T. (1987). Strength Against Weakness: The Campaign In Western Europe, May–June 1940 (Monograph). School of Advanced Military Studies US Army Command and General Staff College. OCLC 21094641. Docket ADA 184718. Archived from the original on 23 June 2018. Retrieved 23 June 2018.
Perry, F. W. (1982). Manpower and Organisational Problems in the Expansion of the British and other Commonwealth Armies during the Two World Wars (PhD thesis). London University. OCLC 557366960. Docket uk.bl.ethos.286414. Retrieved 23 June 2018.
Salmon, R. E. (2013). The Management of Change: Mechanizing the British Regular and Household Cavalry Regiments 1918–1942 (PhD thesis). University of Wolverhampton. OCLC 879390776. Docket uk.bl.ethos.596061. Retrieved 23 June 2018.
Stedman, A. D. (2007). 'Then what could Chamberlain do, other than what Chamberlain did'? A Synthesis and Analysis of the Alternatives to Chamberlain's Policy of Appeasing Germany, 1936–1939 (PhD thesis). Kingston University. OCLC 500402799. Docket uk.bl.ethos.440347. Retrieved 23 June 2018.
== External links ==
British Military History: France and Norway 1940
London Gazette Dispatches | Wikipedia/British_Expeditionary_Force_(World_War_II) |
The Force Research Unit (FRU) was a covert military intelligence unit of the British Army's Intelligence Corps. It was established in 1980 during the Troubles to obtain intelligence from terrorist organisations in Northern Ireland by recruiting and running agents and informants. From 1987 to 1991, it was commanded by Gordon Kerr. The FRU was renamed to the Joint Support Group (JSG) following the Stevens Inquiries into allegations of collusion between the security forces and Protestant paramilitary groups. The FRU was found to have colluded with loyalist paramilitaries by the Stevens Inquiries. This has been confirmed by some former members of the unit.
== Overview ==
Although the exact size of the unit was classified, former FRU operator Martin Ingram revealed in an interview that it consisted of 42 agent handlers and 26 support staff in the late 1980s. According to Ingram, their locations and staffing levels were:
The Force Research Unit worked alongside existing intelligence agencies including the Special Branch of the Royal Ulster Constabulary and MI5. In 1988, the All-Source Intelligence Cell was formed to improve the sharing of intelligence between the FRU, Special Branch and MI5. FRU operators were armed with cutting edge Heckler & Koch weapons normally reserved for elite counter terrorist units, such as the MP5K compact submachine gun and the HK53 carbine assault rifle. FRU operators worked closely on missions with elite units such as the Special Air Service and the 14th Intelligence Company, who were based out of a secure area of Aldergrove Flying Station at the time. They were also granted special privileges in the course of their work, such as the power to overrule senior officers in ordering an area to be cleared of regular security force patrols or by requesting immediate helicopter cover. The FRU likewise had the power to designate specific properties as "off limits" to RUC searches in order to protect agents or the intelligence documents the agents were in control of.
The British government has previously attempted to stop information about the FRU from becoming public, such as obtaining an injunction against The Sunday Times and arresting former FRU operatives who went public under suspicion of breaching the Official Secrets Act. Unsuccessful attempts were also made by an unknown "British Intelligence Agency" to pressure the ISP of the US based Cryptome website into removing an article naming former FRU operatives. In a 2000 interview with the Sunday Herald, an unnamed FRU operator denied accusations that they were a rogue unit, asserting that there was an unbroken chain of command from the agents on the ground all the way up to the highest levels of the Conservative Party-led government of the day (and ultimately Prime Minister Margaret Thatcher).
== List of former Force Research Unit personnel ==
Notable individuals who reportedly served in the Force Research Unit include:
Colin Parr
Peter Everson
Gordon Kerr (a.k.a Colonel 'J')
George Victor Williams
Ian Hurst (a.k.a Martin Ingram)
Margaret Walshaw BEM
Peter Charles Jones
David Moyles
Philip Campbell-Smith (a.k.a Rob Lewis)
Ronnie Anderson
== Covert agent handling ==
Agent handling by the FRU was primarily carried out via face-to-face meetings on a near weekly basis. Telephone contacts were discouraged, unless an urgent matter arose, as an agent could be overheard by family member's while using their house phone and the frequent use of phone boxes would raise suspicion.
Face-to-face meetings were tape-recorded and then transcribed on a Contact Form, after which the contents of the audio tape was erased. A copy of the Contact Form would be sent to FRU headquarters in Lisburn, who would then share any relative information with the RUC. A typical Contact Form consisted of the following sections:
== Collusion with loyalist paramilitaries ==
In the mid 1980s, the FRU recruited Brian Nelson as a double agent inside the Ulster Defence Association (UDA), and helped him to become the UDA's chief intelligence officer. Until it was proscribed in 1992, the UDA was a legal Ulster loyalist paramilitary group that had been involved in hundreds of attacks on Catholic and nationalist civilians as well as against republican paramilitaries. In the summer of 1985, Nelson traveled to South Africa in an unsuccessful attempt to procure weapons and debriefed his FRU handlers on his return. Nelson was also allegedly involved in the 1988 Ulster Resistance weapons importation from South Africa.
Through Nelson, the Force Research Unit helped the UDA to target people for assassination. In a March 2001 article for the Andersonstown News, Martin Ingram claimed that when Brian Nelson was appointed the UDA's intelligence chief in 1987, he handed over their entire cache of targeting files to the FRU, who then updated them with information taken from RUC Special Branch and Military Intelligence files before handing them back to Nelson for use in the planning of assassinations. In 1998, The Sunday Telegraph published a series of articles detailing the activities of the FRU and Brian Nelson's interactions with the unit. Secret documents examined by the newspaper suggested that the specific purpose of running Nelson in the UDA was to ensure that the Loyalist paramilitaries he sourced intelligence for would only target people actively involved in Republican
terrorism, instead of indiscriminately murdering Catholics at random. Evidence showed that Nelson was involved in at least 15 murders, 15 attempted murders, and 62 conspiracies
to murder during his time as an FRU agent.
In a 2000 interview with the Sunday Herald, an unnamed FRU operator identified Margaret Walshaw as being Nelson's primary FRU handler between 1986 and 1990, and accused her of colluding with him by sourcing maps, photos, and personal details of people to be targeted for assassination. The article further alleged that Walshaw even bought Nelson a personal computer so that information could be more effectively passed to him in floppy disk format, and the chances of him being arrested with incriminating documents could be reduced. Walshaw was also accused of failing to prevent murders she had advanced knowledge of, such as when Brian Robinson shot Patrick McKenna in a random attack. According to the source, Walshaw left Ireland in 1990 to become an FRU instructor with the Intelligence Corps.
In 2003, the BBC reported that FRU commanders aimed to make the UDA "more professional" by helping it to target and kill republican activists and prevent it from killing uninvolved Catholic civilians. If someone was under threat, agents like Nelson were to inform the FRU who were then to alert the police. Gordon Kerr, who ran the FRU from 1987 to 1991, claimed Nelson and the FRU saved over 200 lives in this way, and testified on Nelson's behalf for mitigation during his 1992 trial under the alias "Colonel J". Kerr defended the actions of the FRU regarding Nelson by asserting that the planning phase of assassinating a known PIRA activist took much longer than the usual ad hoc shooting of a random Catholic, which therefore allowed the FRU to warn RUC Special Branch to prepare "counter-measures", such as increasing the level of security forces in the area of the target's home. Kerr claimed that 730 intelligence reports had been forwarded to Special Branch in this manner, that identified threats to 217 individuals.
However, the Stevens Inquiries found evidence that only two lives were saved and said many loyalist attacks could have been prevented but were allowed to go ahead. The Stevens team believes that Nelson was responsible for at least 30 murders and many other attacks, including most prominently solicitor Pat Finucane, and that many of the victims were uninvolved civilians. The Cory Collusion Inquiry and a separate inquiry by Sir Desmond de Silva both also discovered evidence of collusion between the Brian Nelson and the FRU in the murder of Patrick Finucane. Although Nelson was imprisoned in 1992, FRU intelligence continued to help the UDA and other loyalist groups. From 1992 to 1994, loyalists were responsible for more deaths than republicans for the first time since the 1960s.
Allegations exist that the FRU sought restriction orders, a de-confliction agreement to restrict patrolling or surveillance in an area over a specified period, in advance of a number of loyalist paramilitary attacks in order to facilitate easy access to and escape from their target. This de-confliction activity was carried out at a weekly Tasking and Co-ordination Group which included representatives of the Royal Ulster Constabulary, MI5 and the British Army. It is claimed the FRU asked for restriction orders to be placed on areas where they knew loyalist paramilitaries were going to attack.
In a February 2025 podcast series for The Telegraph, former FRU operator Martin Ingram accused his former commanding officer at the Force Research Unit, Gordon Kerr, of being a proud Scottish Loyalist who let his own bigotry towards Irish Catholics cloud his judgement. Ingram also accused a former FRU colleague named Margaret Walshaw, who was Brian Nelson's handler, of passing information (such as photographs and vehicle registration numbers) to Nelson to help plan assassinations.
== Alleged infiltration of republican paramilitary groups ==
FRU are also alleged to have handled agents within republican paramilitary groups. A number of agents are suspected to have been handled by the FRU including IRA units who planted bombs and assassinated. Attacks are said to have taken place involving FRU-controlled agents highly placed within the IRA.
It is suspected that the FRU sought to influence the IRA primarily through an agent codenamed "Stakeknife", thought to have been a member of the IRA's Internal Security Unit (a unit responsible for counter-intelligence, interrogation and court martial of informers within the IRA). There is a debate as to whether this agent was IRA member Freddie Scappaticci or another, as of yet unidentified, IRA member. It is believed that "Stakeknife" was used by the FRU to influence the outcome of investigations conducted by the IRA's Internal Security Unit into the activities of IRA volunteers.
It is alleged that, in 1987, the UDA came into possession of details relating to the identity of the FRU-controlled IRA volunteer codenamed "Stakeknife" and that, unaware of this IRA volunteer's value to the FRU, they planned to assassinate him. Allegedly, after the FRU discovered "Stakeknife" was in danger from UDA assassination, they used Brian Nelson to persuade the UDA to assassinate Francisco Notarantonio instead, a Belfast pensioner who had been interned as an Irish republican in the 1940s. The killing of Notarantonio was claimed by the UFF at the time. Following the killing of Notarantonio, unaware of the involvement of the FRU, the IRA assassinated two UDA leaders in reprisal attacks. It has also been alleged that the FRU secretly passed details of the two UDA leaders to the IRA via "Stakeknife" in an effort to distract attention from him as a possible informer.
== FRU and the Stevens Inquiry ==
Former FRU operative Martin Ingram asserted that the arson attack which destroyed the offices of the Stevens Inquiry at RUC Headquarters in Carrickfergus in 1990 was carried out by the FRU to destroy evidence on operational activities collected by Stevens' regarding crimes
committed by one of its double agents (allegedly Brian Nelson). At the conclusion of the Stevens Inquiry in 2003, files on nine former members of the FRU were sent to the Director of Public Prosecutions in Northern Ireland in regards to illegal activity uncovered by the inquiry.
== See also ==
Stakeknife
== References ==
== External links ==
Relatives For Justice
Madden & Finucane
Brian Nelson
heavily redacted 1989 internal FRU report (Contact Form) of a meeting between Brian Nelson and his handlers
plea of mitigation by Colonel `J' (a.k.a Gordon Kerr) at Brian Nelson's 1992 trial
1999 British Irish Rights Watch report into FRU collusion with Loyalist paramilitaries
2004 Cory report regarding murder of Patrick Finucane
2012 de Silva report regarding murder of Patrick Finucane
2025 Daily Telegraph podcast (Bed of Lies, Series 3) on the Force Research Unit
BBC - Panorama: The Dirty War - 1993 documentary regarding Brian Nelson & the Force Research Unit (YouTube) | Wikipedia/Force_Research_Unit |
In cryptography, the clock was a method devised by Polish mathematician-cryptologist Jerzy Różycki, at the Polish General Staff's Cipher Bureau, to facilitate decrypting German Enigma ciphers. The method determined the rightmost rotor in the German Enigma by exploiting the different turnover positions. For the Poles, learning the rightmost rotor reduced the rotor-order search space by a factor of 3 (the number of rotors). The British improved the method, and it allowed them to use their limited number of bombes more effectively (the British confronted 5 to 8 rotors).
== Method ==
This method sometimes made it possible to determine which of the Enigma machine's rotors was at the far right, that is, in the position where the rotor always revolved at every depression of a key. The clock method was developed by Jerzy Różycki during 1933–1935.
Marian Rejewski's grill method could determine the right-hand rotor, but that involved trying each possible rotor permutation (there were three rotors at the time) at each of its 26 possible starting rotations. The grill method tests were also complicated by the plugboard settings. In contrast, the clock method involved simple tests that were unaffected by the plugboard.
In the early 1930s, determining the rotor order was not a significant burden because the Germans used the same rotor order for three months at a time. The rotor order could be determined once, and then that order could be used for the next three months. On 1 February 1936, the Germans changed the rotor order every month. On 1 November 1936, the Germans changed the rotor order every day.
Różycki's "clock" method was later elaborated by the British cryptologist Alan Turing at Bletchley Park in the development of a cryptological technique called "Banburismus."
=== Background ===
The Cipher Bureau received German radio intercepts enciphered by the Enigma machine. With about 60 messages, the Bureau could determine Marian Rejewski's characteristic structure for the message key encoding. By exploiting poor message keys, the Bureau could determine the message key encoding. At that point, the cryptanalysts may know only the message keys and their ciphertext. They may not know the other secrets of the daily key such as the plugboard setting, the ring settings, the rotor order, or the initial setting. With such little information and some luck, the Poles could still determine which rotor was the rightmost.
In the daily traffic, there might be about a dozen message pairs whose message key starts with the same two letters. That means the left and middle rotors are in the same position.
There are two ways to align the ciphertexts of the message pair. Both alignments are tried; one of the alignments will use an identical polyalphabetic substitution. From that, the cryptanalyst can determine the rotor turnover happened within a particular range of letters.
The rotors had different turnover positions. The British used the mnemonic "Royal Flags Wave Kings Above", which meant Rotor I turned over at R, Rotor II turned over at F, Rotor III turned over at W, Rotor IV turned over at K, and all other rotors turned over at A.
If the message pairs cooperated, the Poles could narrow the window where the turnover happens to include only one rotor. One message pair might say the turnover happened in the window B to U; that meant rotors I (R), II (F), and IV (K) were viable. A second message pair might produce a window of M to C; that meant rotors I (R), III (W), V+ (A) were viable. Only Rotor I satisfies both message pairs, so Rotor I is the right-hand rotor.
=== Machine settings ===
The Enigma cipher machine relied on the users having some shared secrets. Here are the secret daily settings from a 1930 Enigma manual:
Daily settings (shared secret):
Rotor Order : II I III
Ringstellung : 24 13 22 (XMV)
Reflector : A
Plugboard : A-M, F-I, N-V, P-S, T-U, W-Z
Grundstellung: 06 15 12 (FOL)
The daily settings told the code clerks how to configure the machine so message could be exchanged. Initially, the machine had three rotors that could be arranged in any order (the wheel order or rotor order). Each rotor had a ring with numbers or letters on it, and that ring could be in any of 26 positions. A plugboard interchanged additional characters.
For each message, the operator would choose a three-letter message key to encrypt the body of the message. The intention was for this key to be random, and using a random key for each message was a good security practice. The message key needed to be communicated to the recipient so the recipient could decrypt the message.
Instead of sending the message keys in the clear, the message keys would be encrypted with the Grundstellung (ground setting). In a grave procedural mistake, the Germans encrypted the message key twice. If the message key were "ABL", then the Germans would encrypt the doubled key "ABLABL" and send the result ("PKPJXI"). Sending the message key twice allowed keys garbled in transmission to be recovered, but the cryptographic mistake was encrypting the doubled key rather than sending the encrypted key twice (e.g., "PKPPKP"). The doubled key gave the Poles an attack. If there were sufficient message traffic using the same daily key (about 70 messages) and the code clerks used weak keys (such as "CCC" or "WER"), then the Poles could use Rejewski's method of characteristics to determine all the day's message keys. Surprisingly, the Poles cracked the message keys without learning the substantial secrets of the daily machine settings: the plugboard settings, the rotor order, the rotor positions, or the ring settings.
The Poles had to use other techniques to get those remaining secrets; the clock method helped determine the rotor order.
=== Different rotors have different turnover positions ===
The clock method exploited the three rotors (I, II, III) having different turnover positions. The rightmost rotor moved as each character was enciphered. At a certain position on the ring, enciphering the character would also cause the next rotor to the left to move one position (a turnover). The ring position that caused the next rotor to move was different for each rotor: rotor I advanced at the Q-R transition ("royal"); rotor II advanced at E-F ("flags"); rotor III advanced at V-W ("wave"). If the turnover could be detected, then the rightmost rotor might be identified.
The Poles, because they cracked the message key, knew the ring positions for each message because the ring positions were the message key.
With sufficient traffic, the Poles would find message keys that started with the same two characters. Say the Poles received messages with keys "AAA" and "AAT".
Message Key AAA: BQWBOCKUQFPQDJTMFTYSRDDQEQJWLPTNMHJENUTPYULNPRTCKG
Message Key AAT: SRDDQEQJWLPTNMHJENUTPYULNPRTCKGFHWQJTVQROVULGDMNMX
=== Index of coincidence ===
Using the index of coincidence on a long enough message, the Poles could determine where the rotor settings coincide. That determination is statistical, but it is also subtle. It exploits the nonuniform letter frequency in a language. Consider two sentences with their letters aligned. If letters had the same frequency, then a letter in the first sentence would match the letter in the same position of the second sentence with probability 1/26 (0.038). For natural languages, characters such as "e" are much more likely, so the chance of coincidence much higher. Here's a case where there are six coincidences in the first 28 characters (much more than the expected 1.73 matches per 26 characters):
WEHOLDTHESETRUTHSTOBESELFEVIDENT
WHENINTHECOURSEOFHUMANEVENTS
* *** * *
The index of coincidence also holds true if the two strings being compared are encrypted under the same polyalphabetic key; if the characters are equal, then their encryptions are also equal. Conversely, if the strings are encrypted under a different polyalphabetic key, the strings will be randomized and the index of coincidence will show only random matches (1 out of 26 characters will match).
If the two strings are long enough (say 260 characters), then the index of coincidence will give an indication whether the strings were encrypted under the same polyalphabetic key (i.e., the same rotor configuration).
=== Rotor position and coincidence ===
To emphasize the index of coincidence to an absurd level, the two example messages above consist entirely of the letter "A", so the coincidences occur at every position that shares the same rotor positions (something that would not happen for normal messages). That allows the coincidence to be starkly obvious even in a short message. In practice, long messages are needed to get a good statistical indication.
The Poles searched the daily traffic to find a pair of messages whose keys started the same two letters. Example key pairs would be ("UIB", "UIW") or ("GCE", "GCX"). The chance that first two letters of a message key match another message's key is small (1/(26×26)=1/576), but finding such a pair in a set of messages can be likely; finding such a match is an example of the birthday problem.
The Poles wanted the first two letters to match because that meant the left and middle rotors were at identical rotations and would produce the same permutation. The Poles could also align the two messages to account for the differing third letter of the key. Given the ("AAA", "AAT") example pair from above, the Poles knew there were two possible ways the messages could be aligned so that the messages shared a common key (common rotor rotations). The two cases reflect whether the turnover (movement of the middle rotor) happens between "A" and "T" or between "T" and "A".
A T
right rotor pos: ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
Message Key AAA: BQWBOCKUQFPQDJTMFTYSRDDQEQJWLPTNMHJENUTPYULNPRTCKG
Message Key AAT: SRDDQEQJWLPTNMHJENUTPYULNPRTCKGFHWQJTVQROVULGDMNMX
Coincidence: ===============================
Conclusion: same key, so no turnover in A-T.
T A
right rotor pos: TUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRS
Message Key AAT: SRDDQEQJWLPTNMHJENUTPYULNPRTCKGFHWQJTVQROVULGDMNMX
Message Key AAA: BQWBOCKUQFPQDJTMFTYSRDDQEQJWLPTNMHJENUTPYULNPRTCKG
Coincidence:
Conclusion: different key, so turnover in T-A
The middle rotor will turnover at different positions depending upon which rotor is in the rightmost (fast) position. The change points for rotors I, II, and III are indicated by 1, 2, and 3. The position of the middle rotor is given assuming the right rotor is I, II, or III.
Message Key AAA: BQWBOCKUQFPQDJTMFTYSRDDQEQJWLPTNMHJENUTPYULNPRTCKG
turnover 2 1 3 2 1 3
Right ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXY
Middle(I) AAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCC
Middle(II) AAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCC
Middle(III) AAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCC
Message Key AAT: SRDDQEQJWLPTNMHJENUTPYULNPRTCKGFHWQJTVQROVULGDMNMX
turnover 3 2 1 3
Right TUVWXYZABCDEFGHIJKLMNOPQRSTUVWXY
Middle(I) AAAAAAAAAAAAAAAAAAAAAAAABBBBBBBB
Middle(II) AAAAAAAAAAAABBBBBBBBBBBBBBBBBBBB
Middle(III) AAABBBBBBBBBBBBBBBBBBBBBBBBBBCCC
For the language-based coincidences to occur, all three rotors must be in sync. If they are not, then the plaintext would be randomly scrambled and the language properties would not show through. Looking at the region where the coincidence occurs, some observations can be made. If rotor I was on the right, then the middle rotor never matches and the index of coincidence would not indicate a coincidence. If rotor II was on the right, then the middle rotor would also never match. Rotor III shows complete agreement. Consequently, the rightmost rotor would be rotor III.
At this point, the Poles would know the right rotor is III and the rotor order is either (I, II, III) or (II, I, III). Although they knew the message key, they did not know the ring settings, so they did not know the absolute positions of the rotors. They also did not know the plugboard settings. The Poles could use other methods to learn that information, but those methods would be simplified by knowing the right rotor.
== Utility ==
Early on, the clock method was not very important. In 1932, the Germans kept the same rotor order for three months at a time. On 1 February 1936, the Germans changed the rotor order every month. Daily wheel order changes started 1 November 1936.
In October 1936, the Germans increased the number of plugs from six to eight, and that complicated the grill method. The Poles developed the cyclometer and card catalog. Although the new method was not ready for a year, it identified the entire rotor order (not just the right rotor) with little work. Unfortunately, the catalog was rendered useless on 2 November 1937 when the Germans changed the reflector; a new catalog needed to be made.
On 15 September 1938, the Germans changed their procedures so that the messages on a network did not use the same Grundstellung. The change would complicate the clock method because the message key was no longer easily known.
The British codebreakers extended the clock method; see Banburismus. German naval Enigma messages used the same Grundstellung, and the British codebreakers could determine the encrypted message keys. If all but the final letter of the encrypted keys matched, then they would have the same rotor positions except for the right rotor. The problem was the British were not matching plaintext message keys (as the Poles) but rather encrypted message keys, so the last letter of the encrypted message key did not have a natural "ABCDE...WXYZ" ordering but rather an arbitrary order. Rather than looking at just two offset, the British had to look at all the possible offsets and infer enough of the third wheel order before they could determine the right rotor. Correctly guessing the last rotor could save the British a lot of valuable Bombe time.
== Notes ==
== References ==
Kozaczuk, Władysław (1984), Kasparek, Christopher (ed.), Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, Frederick, Maryland: University Publications of America, ISBN 978-0-89093-547-7 A revised and augmented translation of W kręgu enigmy, Warsaw, Książka i Wiedza, 1979, supplemented with appendices by Marian Rejewski
Rejewski, Marian (July 1981), "How Polish Mathematicians Deciphered the Enigma", Annals of the History of Computing, 3 (3), IEEE: 213–234, doi:10.1109/MAHC.1981.10033, S2CID 15748167
Rejewski, Marian (1984), "The Mathematical Solution of the Enigma Cipher", in Kasparek, Christopher (ed.), Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, pp. Appendix E: 272–291, ISBN 978-0-89093-547-7
Good, Jack (1993), "Enigma and Fish", in Hinsley, F. H.; Stripp, Alan (eds.), Codebreakers: The inside story of Bletchley Park, Oxford: Oxford University Press, pp. 149–166, ISBN 978-0-19-280132-6 | Wikipedia/Clock_(cryptography) |
Magic was an Allied cryptanalysis project during World War II. It involved the United States Army's Signals Intelligence Service (SIS) and the United States Navy's Communication Special Unit.
== Codebreaking ==
Magic was set up to combine the US government's cryptologic capabilities in one organization dubbed the Research Bureau. Intelligence officers from the Army and Navy (and later civilian experts and technicians) were all under one roof. Although they worked on a series of codes and cyphers, their most important successes involved RED, BLUE, and PURPLE.
=== RED ===
In 1923, a US Navy officer acquired a stolen copy of the Secret Operating Code codebook used by the Imperial Japanese Navy during World War I. Photographs of the codebook were given to the cryptanalysts at the Research Desk and the processed code was kept in red-colored folders (to indicate its Top Secret classification). This code was called "RED".
=== BLUE ===
In 1930, the Japanese government created a more complex code that was codenamed BLUE, although RED was still being used for low-level communications. It was quickly broken by the Research Desk no later than 1932. US Military Intelligence COMINT listening stations began monitoring command-to-fleet, ship-to-ship, and land-based communications.
=== PURPLE ===
After Japan's ally Germany declared war in the fall of 1939, the German government began sending technical assistance to upgrade their communications and cryptography capabilities. One part was to send them modified Enigma machines to secure Japan's high-level communications with Germany. The new code, codenamed PURPLE (from the color obtained by mixing red and blue), was baffling.
PURPLE, like Enigma, began its communications with the same line of code but then became an unfathomable jumble. Codebreakers tried to break PURPLE communiques by hand but found they could not. Then the codebreakers realized that it was not a manual additive or substitution code like RED and BLUE, but a machine-generated code similar to Germany's Enigma cipher. Decoding was slow and much of the traffic was still hard to break. By the time the traffic was decoded and translated, the contents were often out of date.
A reverse-engineered machine created in 1939 by a team of technicians led by William Friedman and Frank Rowlett could decrypt some of the PURPLE code by replicating some of the settings of the Japanese Enigma machines. This accelerated decoding and the addition of more translators on staff in 1942 made it easier and quicker to decipher the traffic intercepted.
== PURPLE traffic ==
The Japanese Foreign Office used a cipher machine to encrypt its diplomatic messages. The machine was called "PURPLE" by U.S. cryptographers. A message was typed into the machine, which enciphered and sent it to an identical machine. The receiving machine could decipher the message only if set to the correct settings, or keys. American cryptographers built a machine that could decrypt these messages.
The PURPLE machine itself was first used by Japan in 1940. U.S. and British cryptographers had broken some PURPLE traffic well before the attack on Pearl Harbor. However, the PURPLE machines were used only by the Foreign Office to carry diplomatic traffic to its embassies. The Japanese Navy used a completely different crypto-system, known as JN-25.
U.S. analysts discovered no hint in PURPLE of the impending Japanese attack on Pearl Harbor. Nor could they, as the Japanese were very careful not to discuss their plan in Foreign Office communications. No detailed information about the planned attack was even available to the Japanese Foreign Office, as that agency was regarded by the military, particularly its more nationalist members, as insufficiently "reliable".
U.S. access to private Japanese diplomatic communications (even the most secret ones) was less useful than it might otherwise have been because policy in prewar Japan was controlled largely by military groups like the Imperial Way Faction, and not by the Foreign Office. The Foreign Office itself deliberately withheld from its embassies and consulates much of the information it did have, so the ability to read PURPLE messages was less than definitive regarding Japanese tactical or strategic military intentions.
U.S. cryptographers (see Station HYPO) had decrypted and translated the 14-part Japanese diplomatic message breaking off ongoing negotiations with the U.S. at 1 p.m. Washington time on 7 December 1941, even before the Japanese Embassy in Washington could do so. As a result of the deciphering and typing difficulties at the embassy, the note was delivered late to American Secretary of State Cordell Hull. When the two Japanese diplomats finally delivered the note, Hull had to pretend to be reading it for the first time, even though he already knew about the attack on Pearl Harbor.
Throughout the war, the Allies routinely read both German and Japanese cryptography. The Japanese Ambassador to Germany, General Hiroshi Ōshima, often sent priceless German military information to Tokyo. This information was routinely intercepted and read by Roosevelt, Churchill and Eisenhower. According to Lowman, "The Japanese considered the PURPLE system absolutely unbreakable… Most went to their graves refusing to believe the [cipher] had been broken by analytic means… They believed someone had betrayed their system."
== Distribution prior to Pearl Harbor ==
Even so, the diplomatic information was of limited value to the U.S. because of its manner and its description. "Magic" was distributed in such a way that many policy-makers who had need of the information in it knew nothing of it, and those to whom it actually was distributed (at least before Pearl Harbor) saw each message only briefly, as the courier stood by to take it back, and in isolation from other messages (no copies or notes being permitted). Before Pearl Harbor, they saw only those decrypts thought "important enough" by the distributing Army or Navy officers.
Nonetheless, being able to read PURPLE messages gave the Allies a great advantage in the war. For instance, the Japanese ambassador to Germany, Baron Hiroshi Ōshima, produced long reports for Tokyo which were enciphered on the PURPLE machine. They included reports on personal discussions with Adolf Hitler and a report on a tour of the invasion defenses in Northern France (including the D-Day invasion beaches). General Marshall said that Ōshima was "our main basis of... information regarding Hitler's intentions in Europe".
== Dewey and Marshall ==
During the 1944 election, Thomas Dewey threatened to make Pearl Harbor a campaign issue, until General Marshall sent him a personal letter which said, in part:
To explain the critical nature of this set-up, which would be wiped out in an instant if the least suspicion were aroused regarding it, the Battle of Coral Sea was based on deciphered messages and therefore our few ships were in the right place at the right time. Further, we were able to concentrate our limited forces to meet their naval advance on Midway when otherwise we almost certainly would have been some 3,000 miles [4,800 km] out of place. We had full information on the strength of their forces.
Dewey promised not to raise the issue, and kept his word.
== Post-war debates ==
The break into the PURPLE system, and into Japanese messages generally, was the subject of acrimonious hearings in Congress post-World War II in connection with an attempt to decide who, if anyone, had allowed the disaster at Pearl Harbor to happen and who therefore should be blamed. During those hearings the Japanese learned, for the first time, the PURPLE cypher system had been broken. They had been continuing to use it, even after the War, with the encouragement of the American Occupation Government.
Much confusion over who in Washington or Hawaii knew what and when, especially as "we were decrypting their messages," has led some to conclude "someone in Washington" knew about the Pearl Harbor attack before it happened, and, since Pearl Harbor was not expecting to be attacked, the "failure to warn Hawaii one was coming must have been deliberate, since it could hardly have been mere oversight". However, PURPLE was a diplomatic, not a military code. Thus, only inferences could be drawn from PURPLE as to specific Japanese military actions.
== History ==
When PURPLE was broken by the U.S. Army's Signals Intelligence Service (SIS), several problems arose for the Americans: who would get the decrypts, which decrypts, how often, under what circumstances, and crucially (given interservice rivalries) who would do the delivering. Both the U.S. Navy and Army were insistent they alone handle all decrypted traffic delivery, especially to highly placed policy makers in the U.S. Eventually, after much to-ing and fro-ing, a compromise was reached: the Army would be responsible for the decrypts on one day, and the Navy the next.
The distribution list eventually included some—but not all—military intelligence leaders in Washington and elsewhere, and some—but, again, not all—civilian policy leaders in Washington. The eventual routine for distribution included the following steps:
the duty officer (Army or Navy, depending on the day) would decide which decrypts were significant or interesting enough to distribute
they would be collected, locked into a briefcase, and turned over to a relatively junior officer (not always cleared to read the decrypts) who would 'make the rounds' to the appropriate offices.
no copies of any decrypts were left with anyone on the list. The recipient would be allowed to read the translated decrypt, in the presence of the distributing officer, and was required to return it immediately upon finishing. Before the beginning of the second week in December 1941, that was the last time anyone on the list saw that particular decrypt.
== Decryption process ==
There were several prior steps needed before any decrypt was ready for distribution:
Interception. The Japanese Foreign Office used both wireless transmission and cables to communicate with its off shore units. Wireless transmission was intercepted (if possible) at any of several listening stations (Hawaii, Guam, Bainbridge Island in Washington state, Dutch Harbor on an Alaska island, etc.) and the raw cypher groups were forwarded to Washington, D.C. Eventually, there were decryption stations (including a copy of the Army's PURPLE machine) in the Philippines as well. Cable traffic was (for many years before late 1941) collected at cable company offices by a military officer who made copies and started them to Washington. Cable traffic in Hawaii was not intercepted due to legal concerns until David Sarnoff of RCA agreed to allow it during a visit to Hawaii the first week of December 1941. At one point, intercepts were being mailed to (Army or Navy) Intelligence from the field.
Deciphering. The raw intercept was deciphered by either the Army or the Navy (depending on the day). Deciphering was usually successful as the cipher had been broken.
Translation. Having obtained the plain text, in Latin letters, it was translated. Because the Navy had more Japanese-speaking officers, much of the burden of translation fell onto the Navy. And because Japanese is a difficult language, with meaning highly dependent upon context, effective translation required not only fluent Japanese, but considerable knowledge of the context within which the message was sent.
Evaluation. The translated decrypt had to be evaluated for its intelligence content. For example, is the ostensible content of the message meaningful? If it is, for instance, part of a power contest within the Foreign Office or some other part of the Japanese government, its meaning and implications would be quite different from a simple informational or instructional message to an embassy. Or, might it be another message in a series whose meaning, taken together, is more than the meaning of any individual message. Thus, the fourteenth message to an embassy instructing that embassy to instruct Japanese merchant ships calling at that country to return to home waters before, say, the end of November would be more significant than a single such message meant for a single ship or port. Only after having evaluated a translated decrypt for its intelligence value could anyone decide whether it deserved to be distributed.
In the period before the attack on Pearl Harbor, the material was handled awkwardly and inefficiently, and was distributed even more awkwardly. Nevertheless, the extraordinary experience of reading a foreign government's most closely held communications, sometimes even before the intended recipient, was astonishing. It was so astonishing, someone (possibly President Roosevelt) called it magic. The name stuck.
== Executive Order 9066 ==
One aspect of Magic remains controversial to this day—the amount of involvement the intercepts played in the issuing of United States Executive Order 9066 on February 19, 1942, and subsequent Executive Order 9102 on March 18, which led to the creation of the Wartime Relocation Authority (WRA). This is often confused with the issue of internment, which was actually handled by the Justice Department's Immigration and Naturalization Service (INS) and affected all citizens of countries at war with the United States in any location.
Internment of "enemy aliens" by the U.S. government began two months prior to Executive Order 9066 on December 8, 1941, immediately after the attack at Pearl Harbor and included Germans and Italians, and not just the Japanese living on the U.S. West Coast.
David Lowman in his book MAGIC: the Untold Story reports that the primary justification for the Japanese-American relocations and internments was to protect against espionage and sabotage, because Magic could not be mentioned during the war. Those defending the decision to evacuate and relocate when seen in context, notably blogger and investigative reporter Michelle Malkin, point to Magic intercepts as partial justification for EO 9066. Malkin cites 1984 testimony of the Undersecretary with the most Magic knowledge, who stated that Magic "was a very important factor" in their considerations.
Extensive additional primary source documents are cited in Malkin's book In Defense of Internment to argue that Magic intercepts discuss the development of a spy ring among Japanese Americans by the Japanese consulates, provide the type of espionage data being sent to Japan, and much more which raised a suspicion that many thousands in the Japanese American community were an espionage risk, including members of Kibei, Issei and Nisei.
In 1988, Congress passed and President Ronald Reagan signed legislation that apologized for the internment on behalf of the U.S. government. The legislation said that government actions were based on "race prejudice, war hysteria, and a failure of political leadership". The hearings that produced this decision did not take into account the Magic intercepts.
The following is the actual text of several Magic intercepts translated into English before and during the war and declassified and made public in 1978 by the U.S. government (The Magic Background of Pearl Harbor, Government Printing Office, 8 volumes)
=== Tokyo to Washington ===
Magic intercept Tokyo to Washington #44 – Jan 30, 1941
Intercept dated January 30, 1941 and noted as translated 2-7-41
Numbered #44
FROM: Tokyo (Matsuoka)
TO: Washington (Koshi)
(In two parts – complete).
(Foreign Office secret).
(1) Establish an intelligence organ in the Embassy which will maintain liaison with private and semi-official intelligence organs (see my message to Washington #591 and #732 from New York to Tokyo, both of last year's series).
With regard to this, we are holding discussions with the various circles involved at the present time.
(2) The focal point of our investigations shall be the determination of the total strength of the U.S. Our investigations shall be divided into three general classifications: political, economic, and military, and definite course of action shall be mapped out.
(3) Make a survey of all persons or organizations which either openly or secretly oppose participation in the war.
(4) Make investigations of all antisemitism, communism, movements of Negroes, and labor movements.
(5) Utilization of U.S. citizens of foreign extraction (other than Japanese), aliens (other than Japanese), communists, Negroes, labor union members, and anti-Semites, in carrying out the investigations described in the preceding paragraph would undoubtedly bear the best results.
These men, moreover, should have access to governmental establishments, (laboratories?), governmental organizations of various characters, factories, and transportation facilities.
(6) Utilization of our "Second Generations" and our resident nationals. (In view of the fact that if there is any slip in this phase, our people in the U.S. will be subjected to considerable persecution, and the utmost caution must be exercised).
(7) In the event of U.S. participation in the war, our intelligence set-up will be moved to Mexico, making that country the nerve center of our intelligence net. Therefore, will you bear this in mind and in anticipation of such an eventuality, set up facilities for a U.S.-Mexico international intelligence route. This net which will cover Brazil, Argentina, Chile, and Peru will also be centered in Mexico.
(8) We shall cooperate with the German and Italian intelligence organs in the U.S. This phase has been discussed with the Germans and Italians in Tokyo, and it has been approved.
Please get the details from Secretary Terasaki upon his assuming his duties there.
Please send copies to those offices which were on the distribution list of No. 43.
=== Japanese U.S. consulates to Tokyo ===
Throughout the rest of 1941, some of the messages between Tokyo and its embassies and consulates continued to be intercepted.
In response to the ordered shift from propaganda efforts to espionage collection, the Japanese consulates throughout the western hemisphere reported their information normally through the use of diplomatic channels, but when time-sensitive through the use of PURPLE encoded messages. This provided vital clues to their progress directly to the U.S. President and his top advisers.
Intercepts in May 1941 from the consulates in Los Angeles and Seattle report that the Japanese were having success in obtaining information and cooperation from "second generation" Japanese Americans and others.
Magic intercept LA to Tokyo #067 – May 9, 1941
Intercept dated May 9, 1941 and translated 5-19-41
Numbered #067
FROM: Los Angeles (Nakauchi)
TO: Tokyo (Gaimudaijin)
(In 2 parts – complete).
Strictly Secret.
Re your message # 180 to Washington.
We are doing everything in our power to establish outside contacts in connection with our efforts to gather intelligence material. In this regard, we have decided to make use of white persons and Negroes, through Japanese persons whom we cannot trust completely. (It not only would be very difficult to hire U.S. (military?) experts for this work at present time, but the expenses would be exceedingly high.) We shall, furthermore, maintain close connections with the Japanese Association, the Chamber of Commerce, and the newspapers.
With regard to airplane manufacturing plants and other military establishments in other parts, we plan to establish very close relations with various organizations and in strict secrecy have them keep these military establishments under close surveillance. Through such means, we hope to be able to obtain accurate and detailed intelligence reports. We have already established contacts with absolutely reliable Japanese in the San Pedro and San Diego area, who will keep a close watch on all shipments of airplanes and other war materials, and report the amounts and destinations of such shipments. The same steps have been taken with regards to traffic across the U.S.-Mexico border.
We shall maintain connection with our second generations who are at present in the (U.S.) Army, to keep us informed of various developments in the Army. We also have connections with our second generations working in airplane plants for intelligence purposes.
With regard to the Navy, we are cooperating with our Naval Attache's office, and are submitting reports as accurately and speedily as possible.
We are having Nakazawa investigate and summarize information gathered through first hand and newspaper reports, with regard to military movements, labor disputes, communistic activities and other similar matters. With regard to anti-Jewish movements, we are having investigations made by both prominent Americans and Japanese who are connected with the movie industry which is centered in this area. We have already established connections with very influential Negroes to keep us informed with regard to the Negro movement.
Magic intercept Seattle to Tokyo #45 – May 11, 1941
Intercept dated May 11, 1941 and translated 6-9-41
Numbered # 45
FROM: Seattle (Sato)
TO: Tokyo
(3 parts – complete)
Re your # 180 to Washington
1. Political Contacts
We are collecting intelligences revolving around political questions, and also the questions of American participation in the war which has to do with the whole country and this local area.
2. Economic Contacts
We are using foreign company employees, as well as employees in our own companies here, for the collection of intelligence having to do with economics along the lines of the construction of ships, the number of airplanes produced and their various types, the production of copper, zinc and aluminum, the yield of tin for cans, and lumber. We are now exerting our best efforts toward the acquisition of such intelligences through competent Americans. From an American, whom we contacted recently, we have received a private report on machinists of German origin who are Communists and members of the labor organizations in the Bremerton Naval Yard and Boeing airplane factory. Second generation Japanese ----- ----- ----- [three words missing].
3. Military Contacts
We are securing intelligences concerning the concentration of warships within the Bremerton Naval Yard, information with regard to mercantile shipping and airplane manufacturing, movements of military forces, as well as that which concerns troop maneuvers.
With this as a basis, men are sent out into the field who will contact Lt. Comdr. OKADA, and such intelligences will be wired to you in accordance with past practice. KANEKO is in charge of this. Recently we have on two occasions made investigations on the spot of various military establishments and concentration points in various areas. For the future we have made arrangements to collect intelligences from second generation Japanese draftees on matters dealing with the troops, as well as troop speech and behavior. ----- ---- -----. [three words missing]
4. Contacts with Labor Unions
The local labor unions A.F. of L. and C.I.O. have considerable influence. The (Socialist?) Party maintains an office here (its political sphere of influence extends over twelve zones.) The C.I.O., especially, has been very active here. We have had a first generation Japanese, who is a member of the labor movement and a committee chairman, contact the organizer, and we have received a report, though it is but a resume, on the use of American members of the (Socialist ?) Party. ------ OKAMARU is in charge of this.
5. In order to contact Americans of foreign extraction and foreigners, in addition to third parties, for the collection of intelligences with regard to anti-participation organizations and the anti-Jewish movement, we are making use of a second generation Japanese lawyer.
This intelligence ---- ----- -----.
=== Access by Roosevelt's cabinet ===
These intercepts plus other reports from the FBI and the Office of Naval Intelligence counter-espionage efforts, the TACHIBANA espionage case during summer 1941, FBI efforts against Japanese yakuza throughout the 1930s along the West Coast (the TOKOYO and TOYO CLUBs) were all available only to the most senior leaders in the Roosevelt cabinet. Even J. Edgar Hoover, Director of the FBI, was not privy to the existence of Magic intelligence.
=== Opposing viewpoint ===
Those who consider that Executive Order 9066 regarding Japanese American internment was not based on Magic intercepts, argue:
the commanding officer on the West coast, Lt. Gen. J. L. DeWitt, was not on the Magic intercept list,
his superior, Secretary of War Henry Stimson, was on the intercept list, and
Stimson requested justification for the relocation program from DeWitt.
If Magic intercepts provided justification, why ask DeWitt for further justification?
One theory is that Stimson wanted DeWitt to provide justifications that could be made public, because the Magic intercepts could not be made public.
The issue was inflamed due to the release of Malkin's 2004 book, In Defense of Internment, in which the Magic intercepts play a major role in the defense of her thesis.
== Other Japanese ciphers ==
PURPLE was an enticing, but quite tactically limited, window into Japanese planning and policy because of the peculiar nature of Japanese policy making prior to the War (see above). Early on, a better tactical window was the Japanese Fleet Code (an encoded cypher), called JN-25 by U.S. Navy cryptanalysts. Breaking into the version in use in the months after December 7, 1941 provided enough information to lead to U.S. naval victories in the battles of the Coral Sea and Midway, stopping the initial Japanese advances to the south and eliminating the bulk of Japanese naval air power.
Later, broken JN-25 traffic provided the schedule and routing of the plane Admiral Isoroku Yamamoto would be flying in during an inspection tour in the southwest Pacific, giving USAAF pilots a chance to ambush the officer who had conceived the Pearl Harbor attack. Later still, access to Japanese Army messages from decrypts of Army communications traffic assisted in planning the island hopping campaign to the Philippines and beyond.
Another source of information was the Japanese Military Attaché code (known as JMA to the Allies) introduced in 1941. This was a fractionating transposition system based on two-letter code groups which stood for common words and phrases. The groups were written in a square grid according to an irregular pattern and read off vertically, similar to a disrupted columnar transposition. Then the letters were superenciphered using a pre-arranged table of alphabets. This system was broken by John Tiltman at Bletchley Park in 1942.
== Other claimed breaks into PURPLE ==
The 1992 book The Sword and the Shield: The Mitrokhin Archive and the Secret History of the KGB, by Christopher Andrew, based on the Mitrokhin Archive smuggled out of Russia in the early 1990s by a KGB archivist, contains information about wartime Soviet knowledge of Japanese enciphered transmissions. It claims that the Soviets independently broke into Japanese PURPLE traffic (as well as the Red predecessor machine).
It claims that decrypted PURPLE messages contributed to the decision by Stalin to move troops from Far Eastern Asia to the area around Moscow for the counterattack against Germany in December 1941, as the messages convinced the Soviet government that there would not be a Japanese attack.
== How secret was Magic? ==
Public notice had actually been served that Japanese cryptography was dangerously inadequate by the Chicago Tribune, which published a series of stories just after Midway, starting on 7 June 1942, which claimed (correctly) that victory was due in large part to the U.S. breaking into Japanese crypto systems (in this case, the JN-25 cypher, though which system(s) had been broken was not mentioned in the newspaper stories). The Tribune claimed the story was written by Stanley Johnston from his own knowledge (and Jane's).
Ronald Lewin points out that the story repeats the layout and errors of a signal from Admiral Nimitz which Johnston saw while on the transport Barnett. Nimitz was reprimanded by Admiral King for sending the dispatch to Task Force commanders on a channel available to nearly all ships. The Lexington's executive officer, Commander Morton T. Seligman was assigned to shore duty and retired early.
However, neither the Japanese nor anyone who might have told them seem to have noticed either the Tribune coverage, or the stories based on the Tribune account published in other U.S. papers. Nor did they notice announcements made on the floor of the United States Congress to the same effect. There were no changes in Japanese cryptography connected with those newspaper accounts or Congressional disclosures.
Alvin Kernan was an aviation ordnanceman on board the aircraft carriers Enterprise and the Hornet during the war. During that time, he was awarded the Navy Cross. In his book Crossing the Line, he states that when the carrier returned to Pearl Harbor to resupply before the Battle of Midway, the crew knew that the Japanese code had been broken and that U.S. naval forces were preparing to engage the Japanese fleet at Midway. He insists that he "…exactly remembers the occasion on which I was told, with full details about ships and dates…" despite the later insistence that the breaking of the code was kept secret.
U.S. Navy Commander I.J. Galantin, who retired as an Admiral, refers several times to Magic in his 1988 book about his Pacific theater war patrols as captain of the U.S. submarine Halibut. However, Galantin refers to Magic as "Ultra" which was actually the name given to the breaking of the German code. Upon receiving one message from Pacific Fleet command, directing him off normal station to intercept Japanese vessels due to a Magic message, Galantin writes. "I had written my night orders carefully. I made no reference to Ultra and stressed only the need to be very alert for targets in this fruitful area". Galantin had previously mentioned in his book that all submarine captains were aware of "Ultra" (Magic).
In addition, Army Chief of Staff George C. Marshall discovered early in the war that Magic documents were being widely read at the White House, and that "…at one time over 500 people were reading messages we had intercepted from the Japanese… Everyone seemed to be reading them" .
== Fiction ==
Neal Stephenson's novel Cryptonomicon includes a fictionalized version of Magic, with the Japanese cryptosystem being named "Indigo" rather than "PURPLE".
James Bond is given the products of the fictionalized "MAGIC 44" decryption programme in You Only Live Twice as a bargaining chip when he is deployed to negotiate for intelligence concessions from Tiger Tanaka, head of Japanese intelligence.
The W.E.B. Griffin series The Corps is a fictionalized account of United States Navy and Marine Corps intelligence operations in the Pacific Theater during World War II. Many of the main characters in the novels, both fictional and historical, have access to and use intelligence from Magic.
== See also ==
Japanese army and diplomatic codes
Japanese naval codes
Ultra (cryptography)
== Footnotes ==
== Sources ==
== Further reading == | Wikipedia/Magic_(cryptography) |
The bomba, or bomba kryptologiczna (Polish for "bomb" or "cryptologic bomb"), was a special-purpose machine designed around October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma-machine ciphers.
== Etymology ==
How the machine came to be called a "bomb" has been an object of fascination and speculation. One theory, most likely apocryphal, originated with Polish engineer and army officer Tadeusz Lisicki (who knew Rejewski and his colleague Henryk Zygalski in wartime Britain but was never associated with the Cipher Bureau). He claimed that Jerzy Różycki (the youngest of the three Enigma cryptologists, and who had died in a Mediterranean passenger-ship sinking in January 1942) named the "bomb" after an ice-cream dessert of that name. This story seems implausible, since Lisicki had not known Różycki.
Rejewski himself stated that the device had been dubbed a "bomb" "for lack of a better idea".
Perhaps the most credible explanation is given by a Cipher Bureau technician, Czesław Betlewski: workers at B.S.-4, the Cipher Bureau's German section, christened the machine a "bomb" (also, alternatively, a "washing machine" or a "mangle") because of the characteristic muffled noise that it produced when operating.
A top-secret U.S. Army report dated 15 June 1945 stated:
A machine called the "bombe" is used to expedite the solution. The first machine was built by the Poles and was a hand operated multiple enigma machine. When a possible solution was reached a part would fall off the machine onto the floor with a loud noise. Hence the name "bombe".
The U.S. Army's above description of the Polish bomba is both vague and inaccurate, as is clear from the device's description at the end of the second paragraph of the "History" section, below: "Each bomb... essentially constituted an electrically powered aggregate of six Enigmas..." Determination of a solution involved no disassembly ("a part... fall[ing] off") of the device.
== Background ==
The German Enigma used a combination key to control the operation of the machine: rotor order, which rotors to install, which ring setting for each rotor, which initial setting for each rotor, and the settings of the stecker plugboard. The rotor settings were trigrams (for example, "NJR") to indicate the way the operator was to set the machine. German Enigma operators were issued lists of these keys, one key for each day. For added security, however, each individual message was encrypted using an additional key modification. The operator randomly selected a trigram rotor setting for each message (for example, "PDN"). This message key would be typed twice ("PDNPDN") and encrypted, using the daily key (all the rest of those settings). At this point each operator would reset his machine to the message key, which would then be used for the rest of the message. Because the configuration of the Enigma's rotor set changed with each depression of a key, the repetition would not be obvious in the ciphertext since the same plaintext letters would encrypt to different ciphertext letters. (For example, "PDNPDN" might become "ZRSJVL.")
This procedure, which seemed reasonably secure to the Germans, was nonetheless a cryptographic malpractice, since the first insights into Enigma encryption could be inferred from seeing how the same character string was encrypted differently two times in a row.
== History ==
Using the knowledge that the first three letters of a message were the same as the second three, Polish mathematician–cryptologist Marian Rejewski was able to determine the internal wiring of the Enigma machine and thus to reconstruct the logical structure of the device. Only general traits of the machine were suspected, from the example of the commercial Enigma variant, which the Germans were known to have been using for diplomatic communications. The military versions were sufficiently different to present an entirely new problem. Having done that much, it was still necessary to check each of the potential daily keys to break an encrypted message (i.e., a "ciphertext"). With many thousands of such possible keys, and with the growing complexity of the Enigma machine and its keying procedures, this was becoming an increasingly daunting task.
In order to mechanize and speed up the process, Rejewski, a civilian mathematician working at the Polish General Staff's Cipher Bureau in Warsaw, invented the "bomba kryptologiczna" (cryptologic bomb), probably in October 1938. Each bomb (six were built in Warsaw for the Cipher Bureau before September 1939) essentially constituted an electrically powered aggregate of six Enigmas and took the place of some one hundred workers.
The bomb method was based, like the Poles' earlier "grill" method, on the fact that the plug connections in the commutator ("plugboard") did not change all the letters. But while the grill method required unchanged pairs of letters, the bomb method required only unchanged letters. Hence it could be applied even though the number of plug connections in this period was between five and eight. In mid-November 1938, the bombs were ready, and the reconstructing of daily keys now took about two hours.
Up to July 25, 1939, the Poles had been breaking Enigma messages for over six and a half years without telling their French and British allies. On December 15, 1938, two new rotors, IV and V, were introduced (three of the now five rotors being selected for use in the machine at a time). As Rejewski wrote in a 1979 critique of appendix 1, volume 1 (1979), of the official history of British Intelligence in the Second World War, "we quickly found the [wirings] within the [new rotors], but [their] introduction [...] raised the number of possible sequences of drums from 6 to 60 [...] and hence also raised tenfold the work of finding the keys. Thus the change was not qualitative but quantitative. We would have had to markedly increase the personnel to operate the bombs, to produce the perforated sheets (60 series of 26 sheets each were now needed, whereas up to the meeting on July 25, 1939, we had only two such series ready) and to manipulate the sheets."
Harry Hinsley suggested in British Intelligence in the Second World War that the Poles decided to share their Enigma-breaking techniques and equipment with the French and British in July 1939 because they had encountered insuperable technical difficulties. Rejewski rejected this: "No, it was not [cryptologic] difficulties [...] that prompted us to work with the British and French, but only the deteriorating political situation. If we had had no difficulties at all we would still, or even the more so, have shared our achievements with our allies as our contribution to the struggle against Germany."
== See also ==
Cryptanalysis of the Enigma – Decryption of the cipher of the Enigma machine
Zygalski sheets – Cryptologic technique used in World War II
== Notes ==
=== Works cited ===
Kozaczuk, Władysław (1984). Kasparek, Christopher (ed.). Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two. Translated by Christopher Kasparek. Frederick, Maryland: University Publications of America. ISBN 0-89093-547-5.
== Further reading ==
Momsen, Bill (2007). "Codebreaking and Secret Weapons in World War II". Archived from the original on 2013-09-13.
Rejewski, Marian (July 1981). "How Polish Mathematicians Deciphered the Enigma". Annals of the History of Computing. 3 (3): 213–234.
== External links ==
Bomba Kryptologiczna Simulator, David Link | Wikipedia/Bomba_(cryptography) |
The native resolution of a liquid crystal display (LCD), liquid crystal on silicon (LCoS) or other flat panel display refers to its single fixed resolution. As an LCD consists of a fixed raster, it cannot change the resolution to match the signal being displayed as a cathode-ray tube (CRT) monitor can, meaning that optimal display quality can be reached only when the signal input matches the native resolution. An image where the number of pixels is the same as in the image source and where the pixels are perfectly aligned to the pixels in the source is said to be pixel perfect.
While CRT monitors can usually display images at various resolutions, an LCD monitor has to rely on interpolation (scaling of the image), which causes a loss of image quality. An LCD has to scale up a smaller image to fit into the area of the native resolution. This is the same principle as taking a smaller image in an image editing program and enlarging it; the smaller image loses its sharpness when it is expanded. This is especially problematic as most resolutions are in a 4:3 aspect ratio (640×480, 800×600, 1024×768, 1280×960, 1600×1200) but there are odd resolutions that are not, notably 1280×1024. If a user were to map 1024×768 to a 1280×1024 screen there would be distortion as well as some image errors, as there is not a one-to-one mapping with regard to pixels. This results in noticeable quality loss and the image is much less sharp.
In theory, some resolutions could work well, if they are exact multiples of smaller image sizes. For example, a 1600×1200 LCD could display an 800×600 image well, as each of the pixels in the image could be represented by a block of four on the larger display, without interpolation. Since 800×600 is an integer factor of 1600×1200, scaling should not adversely affect the image. But in practice, most monitors apply a smoothing algorithm to all smaller resolutions, so the quality still suffers for these "half" modes.
Most LCD monitors are able to inform the PC of their native resolution using Extended display identification data (EDID); however, some LCD TVs, especially those with 1366x768 pixels, fail to provide their native resolution and only provide a set of lower resolutions, resulting in a less than pixel perfect output.
Some widescreen LCD monitors optionally display lower resolutions without scaling or stretching an image, so the image will always be in full sharpness. However, it will not occupy the full screen. This is most often recognizable upon close inspection, as there will typically be black edges visible on either side of the panel horizon.
== See also ==
1:1 pixel mapping
Resolution independence
== References ==
Gaming issues with TFT LCD Displays
(Wayback Machine copy) | Wikipedia/Native_resolution |
2K resolution is a generic term for display devices or content having a horizontal resolution of approximately 2,000 pixels. In the movie projection industry, Digital Cinema Initiatives is the dominant standard for 2K output and defines a 2K format with a resolution of 2048 × 1080. For television and consumer media, the dominant resolution in the same class is 1920 × 1080, but in the cinema industry this is generally referred to as HD and distinguished from the various 2K cinema formats.: 71,685
== Resolutions ==
== Standards and terminology ==
In the cinematography industry, 2K resolution traditionally refers to a digital scan of 35 mm film with a resolution around 2000 pixels wide. Typically this is done at 2048 × 1556, but the exact dimensions vary based on the aspect ratio and size of the scan area.: 714
In modern cinema, another common 2K resolution is 2048 × 1080. This is the resolution of the 2K container format standardized by DCI in their Digital Cinema System Specification in 2005. The resolution of the encapsulated video content follows the SMPTE 428-1 standard,: §3.2.1 which establishes the following resolutions for a 2K distribution:: 6
2048 × 1080 (full frame, 256∶135 or ≈1.90∶1 aspect ratio)
1998 × 1080 (flat crop, 1.85∶1 aspect ratio)
2048 × 858 (CinemaScope crop, ≈2.39∶1 aspect ratio)
However, the term 2K itself is generic, was not coined by DCI, and does not refer specifically to the DCI 2K standard. Usage of the term 2K predates the publication of the DCI standard. The resolution 1920 × 1080 has also been referred to as a 2K resolution by other standards organizations like NHK Science & Technology Research Laboratories and ITU Radiocommunication Sector (which were involved in the standardization of 1080p HDTV and 4K UHDTV). In consumer products, 2560 × 1440 (1440p) is sometimes referred to as 2K, but it and similar formats are more traditionally categorized as 2.5K resolutions.: 102
== See also ==
21:9 aspect ratio
== References == | Wikipedia/2K_resolution |
Resolution independence is where elements on a computer screen are rendered at sizes independent from the pixel grid, resulting in a graphical user interface that is displayed at a consistent physical size, regardless of the resolution of the screen.
== Concept ==
As early as 1978, the typesetting system TeX due to Donald Knuth introduced resolution independence into the world of computers. The intended view can be rendered beyond the atomic resolution without any artifacts, and the automatic typesetting decisions are guaranteed to be identical on any computer up to an error less than the diameter of an atom. This pioneering system has a corresponding font system, Metafont, which provides suitable fonts of the same high standards of resolution independence.
The terminology device independent file format (DVI) is the file format of Donald Knuth's pioneering TeX system. The content of such a file can be interpreted at any resolution without any artifacts, even at very high resolutions not currently in use.
== Implementation ==
=== macOS ===
Apple included some support for resolution independence in early versions of macOS, which could be demonstrated with the developer tool Quartz Debug that included a feature allowing the user to scale the interface. However, the feature was incomplete, as some icons did not show (such as in System Preferences), user interface elements were displayed at odd positions and certain bitmap GUI elements were not scaled smoothly. Because the scaling feature was never completed, macOS's user interface remained resolution-dependent.
On June 11, 2012, Apple introduced the 2012 MacBook Pro with a resolution of 2880×1800 or 5.2 megapixels – doubling the pixel density in both dimensions. The laptop shipped with a version of macOS that provided support to scale the user interface twice as big as it has previously been. This feature is called HighDPI mode in macOS and it uses a fixed scaling factor of 2 to increase the size of the user interface for high-DPI screens. Apple also introduced support for scaling the UI by rendering the user interface on higher or smaller resolution that the laptop's built-in native resolution and scaling the output to the laptop screen. One obvious downside of this approach is either a decreased performance on rendering the UI on a higher than native resolution or increased blurriness when rendering lower than native resolution. Thus, while the macOS's user interface can be scaled using this approach, the UI itself is not resolution-independent.
=== Microsoft Windows ===
The GDI system in Windows is pixel-based and thus not resolution-independent. To scale up the UI, Microsoft Windows has supported specifying a custom DPI from the Control Panel since Windows 95. (In Windows 3.1, the DPI setting is tied to the screen resolution, depending on the driver information file.) When a custom system DPI is specified, the built-in UI in the operating system scales up. Windows also includes APIs for application developers to design applications that will scale properly.
GDI+ in Windows XP adds resolution-independent text rendering however, the UI in Windows versions up to Windows XP is not completely high-DPI aware as displays with very high resolutions and high pixel densities were not available in that time frame. Windows Vista and Windows 7 scale better at higher DPIs.
Windows Vista also adds support for programs to declare themselves to the OS that they are high-DPI aware via a manifest file or using an API. For programs that do not declare themselves as DPI-aware, Windows Vista supports a compatibility feature called DPI virtualization so system metrics and UI elements are presented to applications as if they are running at 96 DPI and the Desktop Window Manager then scales the resulting application window to match the DPI setting. Windows Vista retains the Windows XP style scaling option which when enabled turns off DPI virtualization (blurry text) for all applications globally.
Windows Vista also introduces Windows Presentation Foundation. WPF applications are vector-based, not pixel-based and are designed to be resolution-independent.
Windows 7 adds the ability to change the DPI by doing only a log off, not a full reboot and makes it a per-user setting. Additionally, Windows 7 reads the monitor DPI from the EDID and automatically sets the DPI value to match the monitor's physical pixel density, unless the effective resolution is less than 1024 x 768.
In Windows 8, only the DPI scaling percentage is shown in the DPI changing dialog and the display of the raw DPI value has been removed. In Windows 8.1, the global setting to disable DPI virtualization (only use XP-style scaling) is removed. At pixel densities higher than 120 PPI (125%), DPI virtualization is enabled for all applications without a DPI aware flag (manifest) set inside the EXE. Windows 8.1 retains a per-application option to disable DPI virtualization of an app. Windows 8.1 also adds the ability for each display to use an independent DPI setting, although it calculates this automatically for each display. Windows 8.1 prevents a user from forcibly enabling DPI virtualization of an application. Therefore, if an application wrongly claims to be DPI-aware, it will look too small on high-DPI displays in 8.1, and a user cannot correct that.
Windows 10 adds manual control over DPI for individual monitors. In addition, Windows 10 version 1703 brings back the XP-style GDI scaling under a "System (Enhanced)" option. This option combines GDI+'s text rendering at a higher resolution with the usual scaling of other elements, so that text appears crisper than in the normal "System" virtualization mode.
=== Android ===
Since Android 1.6 "Donut" (September 2009) Android has provided support for multiple screen sizes and densities. Android expresses layout dimensions and position via the density-independent pixel or "dp" which is defined as one physical pixel on a 160 dpi screen. At runtime, the system transparently handles any scaling of the dp units, as necessary, based on the actual density of the screen in use.
To aid in the creation of underlying bitmaps, Android categorizes resources based on screen size and density:
=== X Window System ===
The Xft library, the font rendering library for the X11 system, has a dpi setting that defaults to 75. This is simply a wrapper around the FC_DPI system in fontconfig, but it suffices for scaling the text in Xft-based applications. The mechanism is also detected by desktop environments to set its own DPI, usually in conjunction with the EDID-based DisplayWidthMM family of Xlib functions. The latter has been rendered ineffective in Xorg Server 1.7; since then EDID information is only exposed to XRandR.
In 2013, the GNOME desktop environment began efforts to bring resolution independence ("hi-DPI" support) for various parts of the graphics stack. Developer Alexander Larsson initially wrote about changes required in GTK+, Cairo, Wayland and the GNOME themes. At the end of the BoF sessions at GUADEC 2013, GTK+ developer Matthias Clasen mentioned that hi-DPI support would be "pretty complete" in GTK 3.10 once work on Cairo would be completed. As of January 2014, hi-DPI support for Clutter and GNOME Shell is ongoing work.
Gtk supports scaling all UI elements by integer factors, and all text by any non-negative real number factors. As of 2019, Fractional scaling of the UI by scaling up and then down is experimental.
=== Other ===
Although not related to true resolution independence, some other operating systems use GUIs that are able to adapt to changed font sizes. Microsoft Windows 95 onwards used the Marlett TrueType font in order to scale some window controls (close, maximize, minimize, resize handles) to arbitrary sizes. AmigaOS from version 2.04 (1991) was able to adapt its window controls to any font size.
Video games are often resolution-independent; an early example is Another World for DOS, which used polygons to draw its 2D content and was later remade using the same polygons at a much higher resolution. 3D games are resolution-independent since the perspective is calculated every frame and so it can vary its resolution.
== See also ==
Adobe Illustrator
CorelDRAW
Direct2D
Display PostScript
Himetric
Inkscape
Page zooming
Responsive Web Design
Retina display
Scalable Vector Graphics
Synfig
Twips
Vector-based graphical user interface
Vector graphics
Video scaler
== References ==
== External links ==
Declaration of resolution-independence by John Siracusa | Wikipedia/Resolution_independence |
Tandy Graphics Adapter (TGA, also Tandy graphics) is a computer display standard for the Tandy 1000 series of IBM PC compatibles, which has compatibility with the video subsystem of the IBM PCjr but became a standard in its own right.
== PCjr graphics ==
The Tandy 1000 series began in 1984 as a clone of the IBM PCjr, offering support for existing PCjr software. As a result, its graphics subsystem is largely compatible.
The PCjr, released in 1983, has a graphics subsystem built around IBM's Video Gate Array (not to be confused with the later Video Graphics Array) and an MC6845 CRTC and extends on the capabilities of the Color Graphics Adapter (CGA), increasing the number of colors in each screen mode. CGA's 2-color mode can be displayed with four colors, and its 4-color mode can be displayed with all 16 colors.
Since the Tandy 1000 was much more successful than PCjr, their shared hardware capabilities became more associated with the Tandy brand than with IBM.
While there is no specific name for the Tandy graphics subsystem (Tandy's documentation calls it the "Video System Logic"), common parlance referred to it as TGA. Where not otherwise stated, information in this article that describes the TGA also applies to the PCjr video subsystem.
While EGA would eventually deliver a superset of TGA graphics on IBM compatibles, software written for TGA is not compatible with EGA cards.
== Output capabilities ==
=== Tandy Video I / PCjr ===
Tandy 1000 systems before the Tandy 1000 SL, and the PCjr, have this type of video. It offers several CGA-compatible modes and enhanced modes.
CGA compatible modes:
320 × 200 in 4 colors from a 16 color (4-bit RGBI) hardware palette. Pixel aspect ratio of 1:1.2.
640 × 200 in 2 colors from 16. Pixel aspect ratio of 1:2.4
40 × 25 with 8 × 8 pixel font text mode (effective resolution of 320 × 200)
80 × 25 with 8 × 8 pixel font text mode (effective resolution of 640 × 200)
Both text modes could themselves be set to display in monochrome, or in 16 colors.
In addition to the CGA modes, it offers:
160 × 200 with 16 colors (equivalent to the graphical quality of many contemporary 8-bit home computers and games consoles, using the same 16 KB memory size and machine bandwidth as the original CGA modes, and analogous to/somewhat able to share graphics assets with CGA's "composite color" mode whilst remaining displayable on RGB monitors)
320 × 200 with 16 colors
640 × 200 with 4 colors (from 16)
Some games detect the Tandy hardware and display enhanced graphics in Tandy mode even when their CGA display mode is selected, while others offer the option to select "Tandy" graphics.
=== Tandy Video II / ETGA ===
Tandy 1000 SL-series, TL-series, and RL-series models have this type of video.
It offers the same modes as Tandy Video I, plus one more non-CGA mode:
640 × 200 with 16 colors
== Popularity ==
With built-in joystick ports, 16-color graphics and multichannel sound, the Tandy 1000 was considered the best platform for IBM PC-compatible games before the VGA era, and the combination of its graphics and sound became a de facto standard, "Tandy compatible".
By 1988 games mentioning "Tandy" on packaging was common. Doing so reportedly caused Radio Shack to very likely sell them in stores. 28 of 66 games that Computer Gaming World tested in 1989 supported Tandy graphics. Titles such as Cisco Heat, Indiana Jones and the Last Crusade, Loom, Magic Pockets, Oh No! More Lemmings, Out of This World, OverKill, Prince of Persia, The Secret of Monkey Island and SimCity are indicated as supporting PCjr/Tandy graphics.
A display driver for Tandy graphics hardware was supplied with Windows 2.0, and could be used on Windows 3.0.
== Hardware design ==
TGA graphics are built into the motherboards of Tandy computers. The PCjr uses a custom monitor with a unique 18-pin plug, but an adapter (with the same DE-9 connector and pinout as IBM's CGA/EGA) can connect it to the IBM Color Display or similar 4-bit digital (TTL) RGBI monitor. The Tandy 1000 provides the DE-9 connector directly.
The monitor is responsible for translating the 4-bit digital levels into 16 colors, as shown it the following table (actual colors could vary somewhat between monitors):
The later Tandy 1000 SL and TL models offered an enhanced version of the TGA, still limited to displaying 16 colors but at an improved resolution of 640 × 200.
=== Programmable palette ===
When operating in the CGA video modes which use 1 or 2 bits per pixel, TGA allows remapping of the 2 or 4 palette entries to any of the 16 colors in the CGA gamut via programmable palette control registers. This allows software to use the CGA modes without being constrained to the three hardwired palettes of the actual CGA.
The following improvements in color choice are available in the CGA graphics modes:
320 × 200 in 4 colors: The three foreground colors can be freely chosen, in addition to the background color which could already be set on the CGA
640 × 200 in 2 colors: The background color can be freely chosen, rather than always being black, in addition to the foreground color which could already be set on the CGA.
The palette mapping logic is always active, even in text modes, so it is possible to cause certain text to change in appearance (appear, disappear, cycle colors, etc.) just by changing the palette, without making any changes to the character attribute bytes in RAM.
The PCjr/TGA programmable palette was carried over to the IBM EGA, where it was extended to 6-bit entries for 64 colors. VGA retained this 16 x 6-bit "internal palette" and added another, cascaded 256 x 18-bit RAMDAC "external palette".
=== Shared RAM ===
Unlike every other IBM-designed PC video standard, TGA uses some of the main system RAM as video RAM. The PCjr had 64 KB of built-in RAM on the mainboard, and an additional 64 KB can be installed via a special card that plugs into a dedicated slot on the PCjr mainboard. This 64 KB or 128 KB of base RAM is special in that it is shared with the PCjr video subsystem.
TGA video modes use either 16 KB or 32 KB of RAM. Text modes use 16 KB divided into 4 or 8 pages, for 80×25 or 40×25 text formats respectively; any part of the 16 KB not used for text display pages can be used as general RAM.
In graphical modes, the base 128 KB of RAM is divided into eight 16 KB banks. The PCjr can use any bank for video generation, in a video mode that uses 16 KB. In a mode that uses 32 KB, it can use any even bank concatenated with the next higher odd bank. The PCjr can also independently map any 16 KB bank of base RAM to address 0xB8000 for CPU access, for CGA compatibility.
Apart from address 0xB8000, the CPU can access any bank at any time via its native address in the first 128 KB of the address space. The first bank overlaps the interrupt vector table of the x86 CPU and the data area used by the BIOS, so it is generally not usable for graphics.
Using system memory has advantages: It saves the cost of dedicated video RAM, and the dynamic RAM is refreshed by the 6845 CRT controller as long as the video is running, so there is no need for separate DRAM refresh circuitry. In the IBM PC XT upon which the PCjr is based, DRAM refresh is performed by one channel of the 8237 DMA controller, triggered by one channel of the 8253 programmable timer, while in the PCjr the 8237 is eliminated and the timer channel is repurposed (to work around a complication of other cost-cutting in the keyboard interface).
Up to almost 128 KB of RAM can be used for video (if software is mostly in ROM—e.g. on PCjr cartridges—or in RAM above the first 128 KB), and the displayed video banks can be switched instantaneously to implement double-buffering (or triple-buffering, or up to 7-fold buffering in 16 KB video modes) for smooth full-screen animation, something the CGA cannot do.
The Tandy 1000 computers do not incorporate the PCjr's cost-cutting measures (most of them have an 8237 DMA controller), but for compatibility with PCjr video, they use the same RAM-sharing scheme.
== Incompatibilities ==
The PCjr video and Tandy 1000 graphics subsystems are not identical. One difference is in the size of the video memory aperture at address 0xB8000. While the PCjr video hardware can use up to 32 KB of RAM for the video buffer, it emulates the CGA precisely by making only 16 KB of this available at address 0xB8000. Like the true CGA, the 16 KB of RAM at 0xB8000 is aliased at address 0xBC000.
The Tandy hardware, in contrast, makes the full 32 KB of selected video RAM available at 0xB8000. This difference causes some software written for Tandy graphics not to work correctly on a PCjr, displaying images in 320 × 200 16-color or 640 × 200 with periodic black horizontal lines: a "venetian-blinds" effect.
It is possible that software for the PCjr that relies on the memory wrap-around at address 0xBC000 will not work correctly on a Tandy 1000.
== See also ==
Plantronics Colorplus, a graphic board with similar capabilities
List of 8-bit computer hardware palettes
List of defunct graphics chips and card companies
== References == | Wikipedia/Tandy_Graphics_Adapter |
Extended Video Graphics Array (or EVGA) is a standard created by VESA in 1991 (VBE 1.2) denoting a non-interlaced resolution of 1024x768 at a maximum of 70 Hz refresh rate.
EVGA is similar to (but is not the same as) the IBM XGA standard. The 1990s were a period of evolving standards and EVGA did not achieve wide adoption.
== See also ==
Display resolution standards
Super VGA
IBM 8514
Extended Graphics Array
Expanded Graphics Adapter (IBM 3270 PC peripheral, also referred as XGA)
== References ==
== External links ==
VESA standards:
Video Electronics Standards Association home page
VESA Standards Page | Wikipedia/Extended_Video_Graphics_Array |
The eXtended Graphics Array (usually called XGA) is a graphics card manufactured by IBM and introduced for the IBM PS/2 line of personal computers in 1990 as a successor to the 8514/A. It supports, among other modes, a display resolution of 1024 × 768 pixels with 256 colors at 43.5 Hz (interlaced), or 640 × 480 at 60 Hz (non-interlaced) with up to 65,536 colors. The XGA-2 added an 800 × 600 65,536 color mode and 1024 × 768 60 Hz non-interlaced.
The XGA was introduced at $1095 with 512K VRAM and additional $350 for the 512 KB memory expansion (equivalent to $2600 and $840, respectively, in 2024). As with the 8514/A, XGA required a Micro Channel architecture bus at a time when ISA systems were standard, however due to more extensive documentation and licensing ISA clones of XGA were made. XGA was integrated into the motherboard of the PS/2 Model 95 XP 486.
An improved version called XGA-2 was introduced in 1992 at $360, worth $810 in 2024 dollars.
XGA gives its name to the resolution 1024 × 768, as IBM's VGA gave its name to 640 × 480, despite the IBM 8514/A and PGC cards respectively supporting those resolutions prior to the eponyms.
== Features ==
The 8514 had used a standardised API called the "Adapter Interface" or AI. This interface is also used by XGA, IBM Image Adapter/A, and clones of the 8514/A and XGA such as the ATI Technologies Mach 32 and IIT AGX. The interface allows computer software to offload common 2D-drawing operations (line-draw, color-fill, and block copies via a blitter) onto the hardware. This frees the host CPU for other tasks, and greatly improves the speed of redrawing a graphics visual (such as a pie-chart or CAD-illustration). Hardware-level documentation of the XGA was also made, which had not been available for the 8514/A.
XGA introduced a 64x64 hardware sprite which was typically used for the mouse pointer.
=== Differences from 8514/A ===
Register-compatible with VGA
Adds a 132 column text mode and high color in 640 × 480
Requires a minimum of 80386 host CPU
Provides a 3-dimensional drawing space called a "bitmap" which may reside anywhere in system memory
Adds a sprite for a hardware cursor
The Adapter Interface driver is moved to a .SYS file instead of TSR program
Provisions made for multitasking environment
XGA can act as bus master and access system memory directly
Hardware level documentation has been provided by IBM
=== XGA-2 ===
XGA-2 added support for non-interlaced 1024 × 768 and made 1MB VRAM standard. It had a programmable PLL circuit and pixel clocks up to 90 MHz, enabling a 75 Hz refresh rate at 1024 × 768. The 800 × 600 resolution was added with 16 bit high color support. The DAC was increased to 8 bits per channel, and the accelerated functions were enabled at 16 bit color depth. Faster VRAM also improved performance.
== Output capabilities ==
The XGA offered:
640 × 480:
graphics mode with 256 colors at once (8-bit) out of 262,144 (18-bit RGB palette);
graphics with 65,536 colors at once (16-bit "high color");
text mode with 80×34 characters
1024 × 768:
graphics with 256 colors out of 262,144;
text with 85×38 or 146×51 characters
XGA-2 introduced:
640 × 480 graphics with 256 colors out of 16.7M (24-bit palette);
800 × 600 graphics with 65,536 colors at once;
1024 × 768 graphics with 256 colors out of 16.7M
Later clone boards offered additional resolutions:
640 × 480 graphics with 16.7M accessible colors at once (if it were possible with 640 × 480 pixels) (24-bit "true color");
800 × 600 graphics with 16.7M colors at once;
1280 × 1024 graphics with 65,536 and 16.7M colors at once
== Clones ==
Unlike with the 8514/A, IBM fully documented the hardware interface to XGA. Further, IBM licensed the XGA design to SGS-Thomson (inmos) and Intel. The IIT AGX014 was largely compatible with the XGA-2 and offered some enhancements.
The VESA Group introduced a common standardized way to access features like hardware cursors, Bit Block transfers (Bit Blt), off screen sprites, hardware panning, drawing and other functions with VBE/accelerator functions (VBE/AF) in August 1996. This, along with standardised device drivers for operating systems such as Microsoft Windows, eliminated the need for a hardware standard for graphics.
== See also ==
List of IBM products
List of defunct graphics chips and card companies
== References ==
== Further reading ==
Jake Richter (1992). Power Programming the IBM XGA. MIS Press. ISBN 9781558281271.
Richard F. Ferraro (1994). Programmer's Guide to the EGA, VGA, and Super VGA Cards. Addison-Wesley. ISBN 9780201624908. | Wikipedia/Extended_Graphics_Array |
The Color Graphics Adapter (CGA), originally also called the Color/Graphics Adapter or IBM Color/Graphics Monitor Adapter, introduced in 1981, was IBM's first color graphics card for the IBM PC and established a de facto computer display standard.
== Hardware design ==
The original IBM CGA graphics card was built around the Motorola 6845 display controller, came with 16 kilobytes of video memory built in, and featured several graphics and text modes. The highest display resolution of any mode was 640 × 200, and the highest color depth supported was 4-bit (16 colors).
The CGA card could be connected either to a direct-drive CRT monitor using a 4-bit digital (TTL) RGBI interface, such as the IBM 5153 color display, or to an NTSC-compatible television or composite video monitor via an RCA connector. The RCA connector provided only baseband video, so to connect the CGA card to a television set without a composite video input required a separate RF modulator.
IBM produced the 5153 Personal Computer Color Display for use with the CGA, but this was not available at release and would not be released until March 1983.
Although IBM's own color display was not available, customers could either use the composite output (with an RF modulator if needed), or the direct-drive output with available third-party monitors that supported the RGBI format and scan rate. Some third-party displays lacked the intensity input, reducing the number of available colors to eight, and many also lacked IBM's unique circuitry which rendered the dark-yellow color as brown, so any software which used brown would be displayed incorrectly.
== Output capabilities ==
CGA offered several video modes.
Graphics modes:
160 × 100 in 16 colors, chosen from a 16-color palette, utilizing a specific configuration of the 80 × 25 text mode.
This used 4 bits per pixel, with a total memory use of (160 * 100 * 4) / 8 = 8 kilobytes.
320 × 200 in 4 colors, chosen from 3 fixed palettes, with high- and low-intensity variants, with color 1 chosen from a 16-color palette.
This used 2 bits per pixel, with a total memory use of (320 * 200 * 2) / 8 = 16 kilobytes.
640 × 200 in 2 colors, one black, one chosen from a 16-color palette.
This used 1 bit per pixel, with a total memory use of (640 * 200) / 8 = 16 kilobytes.
Some software achieved greater color depth by utilizing artifact color when connected to a composite monitor.
Text modes:
40 × 25 with 8 × 8 pixel font (effective resolution of 320 × 200)
80 × 25 with 8 × 8 pixel font (effective resolution of 640 × 200)
IBM intended that CGA be compatible with a home television set. The 40 × 25 text and 320 × 200 graphics modes are usable with a television, and the 80 × 25 text and 640 × 200 graphics modes are intended for a monitor.
CGA graphics modes comparison
CGA software images
== Color palette ==
CGA uses a 4-bit RGBI 16-color gamut, but not all colors are available at all times, depending on which graphics mode is being used. In the medium- and high-resolution modes, colors are stored at a lower bit depth and selected by fixed palette indexes, not direct selection from the full 16-color palette.
When four bits are used (for low-resolution mode, or for programming color registers) they are arranged according to the RGBI color model:
The lower three bits represent red, green, and blue color components
The fourth "intensifier" bit, when set, increases the brightness of all three color components (red, green, and blue).
These four colour bits are then interpreted internally by the monitor, or converted to NTSC colours (see below).
=== With an RGBI monitor ===
When using a direct-drive monitor, the four color bits are output directly to the DE-9 connector at the back of the card.
Within the monitor, the four signals are interpreted to drive the red, green and blue color guns. With respect to the RGBI color model described above, the monitor would translate the digital four-bit color number to some seven distinctive analog voltages in the range from 0.0 to 1.0 for each gun.
Color 6 is treated specially; normally, color 6 would become dark yellow, as seen to the left, but in order to achieve a more pleasing brown tone, special circuitry in most RGBI monitors, starting with the IBM 5153 color display, makes an exception for color 6 and changes its hue from dark yellow to brown by reducing the analogue green signal's amplitude. The exact amount of reduction differed between monitor models: the original IBM 5153 Personal Computer Color Display reduces the green signal's amplitude by about one third, while the IBM 5154 Enhanced Color Display internally converts all 4-bit RGBI color numbers to 6-bit ECD color numbers, which amounts to halving the green signal's amplitude. The Tandy CM-2, CM-4 and CM-11 monitors provide a potentiometer labelled "BROWN ADJ." to adjust the amount of green signal reduction.
This "RGBI with tweaked brown" palette was retained as the default palette of later PC graphics standards such as EGA and VGA, which can select colors from much larger gamuts, but default to these until reprogrammed.
Later video cards/monitors in CGA emulation modes would approximate the colors with the following formula:
red := 2/3×(colorNumber & 4)/4 + 1/3×(colorNumber & 8)/8
green := 2/3×(colorNumber & 2)/2 + 1/3×(colorNumber & 8)/8
blue := 2/3×(colorNumber & 1)/1 + 1/3×(colorNumber & 8)/8
if (color == 6)
green := green * 2/3
which yields the canonical CGA palette:
=== With a composite color monitor/television set ===
For the composite output, these four-bit color numbers are encoded by the CGA's onboard hardware into an NTSC-compatible signal fed to the card's RCA output jack. For cost reasons, this is not done using an RGB-to-YIQ converter as called for by the NTSC standard, but by a series of flip-flops and delay lines.
Consequently, the hues seen are lacking in purity; notably, both cyan and yellow have a greenish tint, and color 6 again looks dark yellow instead of brown.
The relative luminances of the colors produced by the composite color-generating circuit differ between CGA revisions: they are identical for colors 1-6 and 9-14 with early CGAs produced until 1983, and are different for later CGAs due to the addition of additional resistors.
== Standard text modes ==
CGA offers four BIOS text modes (Modes 0 to 3, called alphanumeric or A/N modes in IBM's documentation). In these modes, individual pixels on the screen cannot be addressed directly. Instead, the screen is divided into a grid of character cells, each displaying a character defined in one of two bitmap fonts, "normal" and "thin," included in the card's ROM. The fonts are fixed and cannot be modified or selected from software, only by a jumper on the board itself.
Fonts are stored as bitmaps at a color depth of 1-bit, with a "1" representing the character and a "0" representing the background. These colors can be chosen independently, for each character on the screen, from the full 16-color CGA palette. The character set is defined by hardware code page 437.
The font bitmap data is only available to the card itself, it cannot be read by the CPU. In graphics modes, text output by the BIOS operates by copying text from the font ROM bit-by-bit to video memory.
=== 40 × 25 mode ===
BIOS Modes 0 and 1 are both 40 columns by 25 rows text modes, with each character a pattern of 8×8 dots. The effective screen resolution in this mode is 320 × 200 pixels (a pixel aspect ratio of 1:1.2.) The card has sufficient video RAM for eight different text pages in this mode.
The difference between these two modes can only be seen on a composite monitor, where mode 0 disables the color burst, making all text appear in grayscale. Mode 1 enables the color burst, allowing for color. Mode 0 and Mode 1 are functionally identical on RGB monitors and on later adapters that emulate CGA without supporting composite color output.
=== 80 × 25 mode ===
BIOS Modes 2 and 3 select 80 columns by 25 rows text modes, with each character still an 8×8 dot pattern, but displayed at a higher scan rate. The effective screen resolution of this mode is 640 × 200 pixels. In this mode, the card has enough video RAM for four different text pages.
As with the 40-column text modes, Mode 2 disables the color burst in the composite signal and Mode 3 enables it.
=== Textmode color ===
Each character cell stored four bits for foreground and background color. However, in the card's default configuration, the fourth bit of the background color does not set intensity, but sets the blink attribute for the cell. All characters on the screen with this bit set will periodically blink, meaning their foreground color will be changed to their background color so the character becomes invisible. All characters blink in unison.
By setting a hardware register, the blink feature can be disabled, restoring access to high-intensity background colors.
All blinking characters on the screen blink in sync. The blinking attribute effect is enabled by default and the high-intensity background effect is disabled; disabling blinking is the only way to freely choose the latter eight-color indexes (8-15) for the background color.
Notably, the GW-BASIC and Microsoft QBASIC programming languages included with MS-DOS supported all the text modes of the CGA with full color control, but did not provide a normal means through the BASIC language to switch the CGA from blink mode to 16-background-color mode. This was still possible however by directly programming the hardware registers using the OUT statement of the BASIC language.
== Standard graphics modes ==
CGA offers graphics modes at three resolutions: 160 × 100, 320 × 200 and 640 × 200. In all modes every pixel on the screen can be set directly, but the color depth for the higher modes does not permit selecting freely from the full 16-color palette.
=== 320 × 200 ===
In the medium-resolution 320 × 200 modes (Modes 4 and 5), each pixel is two bits, which select colors from a four-color palette. In mode 4, there are two palettes, and in mode 5 there is a single palette.
Several choices can be made by programming hardware registers. First, the selected palette. Second, the intensity – which is defined for the entire screen, not on a per-pixel basis. Third, color 0 (the "background" color) can be set to any of the 16 colors.
The specific BIOS graphics mode influences which palettes are available. BIOS Mode 4 offers two palettes: green/red/brown and cyan/magenta/white.
As with the text modes 0 and 2, Mode 5 disables the color burst to allow colors to appear in grayscale on composite monitor. However, unlike the text modes, this also affects the colors displayed on an RGBI monitor, altering them to the cyan/red/white palette seen above. This palette is not documented by IBM, but was used in some software.
=== 640 × 200 ===
In the high-resolution 640 × 200 mode (Mode 6), each pixel is one bit, providing two colors which can be chosen from the 16-color palette by programming hardware registers.
In this mode, the video picture is stored as a simple bitmap, with one bit per pixel setting the color to "foreground" or "background". By default the colors are black and bright white, but the foreground color can be changed to any entry in the 16-color CGA palette. The background color cannot be changed from black on an original IBM CGA card.
This mode disables the composite color burst signal by default. The BIOS does not provide an option to turn the color burst on in 640 × 200 mode, and the user must write directly to the mode control register to enable it.
== Further graphics modes and tweaks ==
A number of official and unofficial features exist that can be exploited to achieve special effects.
In 320 × 200 graphics mode, the background color (which also affects the border color), which defaults to black on mode initialization, can be changed to any of the other 15 colors of the CGA palette. This allows for some variation, as well as flashing effects, as the background color can be changed without having to redraw the screen (i.e. without changing the contents of the video RAM).
In text mode, the border color (displayed outside the regular display area and including the overscan area) can be changed from the default black to any of the other 15 colors.
Through precision timing, it is possible to switch to another palette while the video is being output, allowing the use of any one of the six palettes per scanline. An example of this is California Games, when run on a stock 4.77 MHz 8088. Running on a faster computer does not produce the effect, as the method the programmers used to switch palettes at predetermined locations is extremely sensitive to machine speed. The same can be done with the background color, as is used to create the river and road in Frogger. Another documented example of the technique is in Atarisoft's port of Jungle Hunt to the PC.
Additional colors can be approximated using dithering.
Using palette 0 at low intensity and dark blue as the background color provides the three primary RGB colors, as well as brown.
Some of these above tweaks can be combined. Examples can be found in several games.
=== 160 × 100 16 color mode ===
Technically, this mode is not a graphics mode, but a tweak of the 80 × 25 text mode. The character cell height register is changed to display only two lines per character cell instead of the normal eight lines. This quadruples the number of text rows displayed from 25 to 100. These "tightly squeezed" text characters are not full characters. The system only displays their top two lines of pixels (eight each) before moving on to the next row.
Character 221 of the CGA character set consists of a box occupying the entire left half of the character matrix. (Character 222 consists of a box occupying the entire right half.)
Because each character can be assigned different foreground and background colors, it can be colored (for example) blue on the left (foreground color) and bright red on the right (background color). This can be reversed by swapping the foreground and background colors.
Using either character 221 or 222, each half of each truncated character cell can thus be treated as an individual pixel—making 160 horizontal pixels available per line. Thus, 160 × 100 pixels at 16 colors, with an aspect ratio of 1:1.2, are possible.
Although a roundabout way of achieving a 16-color graphics display, this works quite well and the mode is even mentioned (although not explained) in IBM's official hardware documentation. This mode was used as early as 1983 on the game Moon Bugs.
More detail can be achieved in this mode by using other characters, combining ASCII art with the aforesaid technique. This was explored by Macrocom, Inc on two games: Icon: Quest for the Ring (released in 1984) and The Seven Spirits of Ra (released in 1987).
The same text cell height reduction technique can also be used with the 40 × 25 text mode, yielding a resolution of 80 × 100.
== Composite output ==
Using the composite output instead of an RGBI monitor produced lower-quality video, due to NTSC's inferior separation between luminance and chrominance. This is especially a problem with 80-column text:
For this reason, each of the text and graphics modes has a duplicate mode which disables the composite colorburst, resulting in a black-and-white picture, but also eliminating color bleeding to produce a sharper picture. On RGBI monitors, the two versions of each mode are usually identical, with the exception of the 320 × 200 graphics mode, where the "monochrome" version produces a third palette.
=== Extended artifact colors ===
Programmers discovered that this flaw could be turned into an asset, as distinct patterns of high-resolution dots would turn into consistent areas of solid colors, thus allowing the display of completely new artifact colors. Both the standard 320 × 200 four-color and the 640 × 200 color-on-black graphics modes could be used with this technique.
==== Internal operation ====
Direct colors are the normal 16 colors as described above under "The CGA color palette".
Artifact colors are seen because the composite monitor's NTSC chroma decoder misinterprets some of the luminance information as color. By carefully placing pixels in appropriate patterns, a programmer can produce specific cross-color artifacts yielding a desired new color; either from purely black-and-white pixels in 640 × 200 mode, or resulting from a combination of direct and artifact colors in 320 × 200 mode, as seen on the following pictures:
CGA composite artifact color generation: pixels as displayed on a RGBI (left) or composite (right) monitor.
Thus, with the choice between 320 × 200 vs. 640 × 200 mode, the choice between the two palettes, and one freely-selectable color (the background in 320 × 200 modes and the foreground in 640 × 200 mode), it is possible to use many different sets of artifact colors, making for a total gamut of over 100 colors.
Later demonstrations by enthusiasts have increased the maximum number of colors the CGA can display at the same time to 1024. This technique involves a text mode tweak which quadruples the number of text rows. Certain ASCII characters such as U and ‼ are then used to produce the necessary patterns, which result in non-dithered images with an effective resolution of 80 × 100 on a composite monitor.
160 cycles of the NTSC color clock occur during each line's output, so in 40 column mode each pixel occupies half a cycle and in 80 column mode each pixel uses a quarter of a cycle. Limiting the character display to the upper one or two scanlines, and taking advantage of the pixel arrangement in certain characters of the codepage 437, it is possible to display up to 1024 colors. This technique was used in 8088 MPH.
==== Availability and caveats ====
The 320 × 200 variant of this technique (see above) is how the standard BIOS-supported graphics mode looks on a composite color monitor. The 640 × 200 variant, however, requires modifying a bit (color burst disable) directly in the CGA's hardware registers. As a result, it is usually referred to as a separate "mode."
Being completely dependent on the NTSC encoding/decoding process, composite color artifacting is not available on an RGBI monitor, nor is it emulated by EGA, VGA or contemporary graphics adapters.
The modern, games-centric PC emulator DOSBox supports a CGA mode, which can emulate a composite monitor's color artifacting. Both 640 × 200 composite mode and the more complex 320 × 200 variant are supported.
==== Resolution and usage ====
Composite artifacting, whether used intentionally or as an unwanted artifact, reduces the effective horizontal resolution to a maximum of 160 pixels, more for black-on-white or white-on-black text, without changing the vertical resolution. The resulting composite video display with "artifacted" colors is sometimes described as a 160 × 200 / 16-color "mode", though technically it was a technique using a standard mode.
The low resolution of this composite color artifacting method led to it being used almost exclusively in games. Many high-profile titles offered graphics optimized for composite color monitors. Ultima II, the first game in the game series to be ported to IBM PC, used CGA composite graphics. King's Quest I also offered 16-color graphics on the PC, PCjr and Tandy 1000, but provided a 'RGB mode' at the title screen which would utilize only the ordinary CGA graphics mode, limited to 4 colors.
Examples of CGA games on RGBI and composite monitors
== Limitations, bugs and errata ==
Video timing on the CGA is provided by the Motorola 6845 video controller. This integrated circuit was originally designed only for character-based alphanumeric (text) displays and can address a maximum of 128 character rows.
To realize graphics modes with 200 scanlines on the CGA, the MC6845 is programmed with 100 character rows per picture and two scanlines per character row. Because the video memory address output by the MC6845 is identical for each scanline within a character row, the CGA must use the MC6845's "row address" output (i.e. the scanline within the character row) as an additional address bit to fetch raster data from video memory.
This implies that unless the size of a single scanline's raster data is a power of two, raster data cannot be laid out continuously in video memory. Instead, graphics modes on the CGA store the even-numbered scanlines contiguously in memory, followed by a second block of odd-numbered scanlines starting at video memory position 8,192. This arrangement results in additional overhead in graphics modes for software that manipulates video memory.
Even though the MC6845 video controller can provide the timing for interlaced video, the CGA's circuitry aligns the synchronization signals in such a way that scanning is always progressive. Consequently, it is impossible to double the vertical resolution to 400 scanlines using a standard 15 kHz monitor.
The higher bandwidth used by 80-column text mode results in random short horizontal lines appearing onscreen (known as "snow") if a program writes directly to video memory during screen drawing. The BIOS avoids the problem by only accessing the memory during horizontal retrace, or by temporarily turning off the output during scrolling. While this causes the display to flicker, IBM decided that doing so was better than snow. The "snow" problem does not occur on any other video adapter, or on most CGA clones.
In the 80-column text mode, the pixel clock frequency is doubled, and all synchronization signals are output for twice the number of clock cycles in order to last for their proper duration. The composite output's color burst signal circuit is an exception: because it still outputs the same number of cycles, now at the doubled clock rate, the color burst signal produced is too short for most monitors, yielding no or unstable color. Hence, IBM documentation lists the 80-column text mode as a "feature" only for RGBI and black-and-white composite monitors. Stable color can still be achieved by setting the border color to brown, which happens to produce a phase identical to the correct color burst signal and serves as a substitute for it.
== Dual-head support ==
The CGA was released alongside the IBM MDA, and can be installed alongside the MDA in the same computer. A command included with PC DOS permits switching the display output between the CGA and MDA cards. Some programs like Lotus 1-2-3 and AutoCAD support using both displays concurrently.
== Software support ==
CGA was widely supported in PC software up until the 1990s. Some of the software that supported the board was:
Visi On (an early GUI, used the 640x200 monochrome mode)
Windows 3.0 (and earlier versions, supported the 640x200 monochrome mode)
OS/2 1.1 (and earlier versions)
Graphics Environment Manager (GEM)
== Competing adapters ==
BYTE in January 1982 described the output from CGA as "very good—slightly better than color graphics on existing microcomputers". PC Magazine disagreed, reporting in June 1983 that "the IBM monochrome display is absolutely beautiful for text and wonderfully easy on the eyes, but is limited to simple character graphics. Text quality on displays connected to the color/graphics adapter ... is at best of medium quality and is conducive to eyestrain over the long haul".
In a retrospective commentary, Next Generation also took a negative view on the CGA, stating, "Even for the time (early 1980s), these graphics were terrible, paling in comparison to other color machines available on the market."
CGA had several competitors:
For business and word processing use, IBM provided the Monochrome Display Adapter (MDA) at the same time as CGA. MDA was much more popular than CGA at first. Since a great many PCs were sold to businesses, the sharp, high-resolution monochrome text was more desirable for running applications.
In 1982, the non-IBM Hercules Graphics Card (HGC) was introduced, the first third-party video card for the PC. In addition to an MDA-compatible text mode, it offered a monochrome graphics mode with a resolution of 720×348 pixels, higher than the CGA.
Also in 1982 the Plantronics Colorplus board was introduced, with twice the memory of a standard CGA board (32k, compared to 16k). The additional memory can be used in graphics modes to double the color depth, giving two additional graphics modes—16 colors at 320 × 200 resolution, or 4 colors at 640 × 200 resolution.
The IBM PCjr (1984) and compatible Tandy 1000 (1985) featured onboard "extended CGA" video hardware that extended video RAM beyond 16 kB, allowing 16 colors at 320 × 200 resolution and four colors at 640 × 200 resolution. Because the Tandy 1000 long outlived the PCjr, the video modes became known as "Tandy Graphics Adapter" or "TGA", and were very popular for games during the 1980s. Similar but less widely used was the Plantronics Colorplus.
In 1984, IBM also introduced the Professional Graphics Controller, a high-end graphics solution intended for e.g. CAD applications. It was mostly backwards compatible with CGA. The PGC did not see widespread adoption due to its $4,000 price tag, and was discontinued in 1987.
Other alternatives:
Paradise Systems introduced in 1984 the first successful CGA-compatible card for MDA monitors. It displayed CGA's 16 colors in shades of monochrome. Because it was hardware-compatible with CGA, the Paradise card did not need special software support or additional drivers.
Another extension in some CGA-compatible chipsets (including those in the Olivetti M24 / AT&T 6300, the DEC VAXmate, and some Compaq and Toshiba portables) is a doubled vertical resolution. This gives a higher quality 8 × 16 text display and an additional 640 × 400 graphics mode.
The CGA card was succeeded in the consumer space by IBM's Enhanced Graphics Adapter (EGA) card, which supports most of CGA's modes and adds an additional resolution (640 × 350) as well as a software-selectable palette of 16 colors out of 64 in both text and graphics modes.
== Specifications ==
=== DE-9 connector for RGBI monitor ===
The Color Graphics Adapter uses a standard DE-9 connector for direct-drive video (to an RGBI monitor). The connector on the card is female and the one on the monitor cable is male.
=== RCA connector for composite monitor or television ===
The Color Graphics Adapter uses a standard RCA connector for connection to an NTSC-compatible television or composite video monitor. The connector on the card is female and the one on the monitor cable is male.
== See also ==
RGB color model
Graphics card
Graphic display resolutions
Graphics processing unit
Light pen
List of display interfaces
List of 8-bit computer hardware palettes – CGA section
Code page 437
List of defunct graphics chips and card companies
== References ==
Notes
== External links ==
Colour Graphics Adapter Notes
Games with CGA Graphics
Representative screenshots of CGA games
User Friendly thread on the use of CGA | Wikipedia/Color_Graphics_Adapter |
An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning "without" and στίγμα (stigma), "a mark, spot, puncture".
== Forms of astigmatism ==
There are two distinct forms of astigmatism. The first is a third-order aberration, which occurs for objects (or parts of objects) away from the optical axis. This form of aberration occurs even when the optical system is perfectly symmetrical. This is often referred to as a "monochromatic aberration", because it occurs even for light of a single wavelength. This terminology may be misleading, however, as the amount of aberration can vary strongly with wavelength in an optical system.
The second form of astigmatism occurs when the optical system is not symmetric about the optical axis. This may be by design (as in the case of a cylindrical lens), or due to manufacturing error in the surfaces of the components or misalignment of the components. In this case, astigmatism is observed even for rays from on-axis object points. This form of astigmatism is extremely important in vision science and eye care, since the human eye often exhibits this aberration due to imperfections in the shape of the cornea or the lens.
=== Third-order astigmatism ===
In the analysis of this form of astigmatism that occurs only in off-axis object point imaging, it is most common to consider rays from a given point on the object, which propagate in two particular planes. The first plane is the tangential plane. This is the plane including both the object point under consideration and the axis of symmetry (optical axis). Rays that propagate in this plane are called tangential rays. Planes that include the optical axis are meridional planes. It is common to simplify problems in radially-symmetric optical systems by choosing object points in the vertical ("y") plane only. This plane is then sometimes referred to as the meridional plane.
The second plane used in the analysis is the sagittal plane, defined as the plane orthogonal to the tangential plane and containing the chief ray before refraction (so along the original chief ray direction). This plane intersects the optical axis at the entrance pupil of the optical system. This plane is not a tangential plane so is a skew plane, in other words not a meridional plane. Rays propagating in this plane are called sagittal rays.
In third-order astigmatism, the tangential rays (in the tangential plane) and sagittal rays (in the sagittal plane) form foci at different distances along the optic axis. These foci are called the tangent focus and sagittal focus, respectively. In the presence of astigmatism, an off-axis point on the object is not sharply imaged by the optical system. Instead, sharp lines are formed at the tangential and sagittal foci. The image at the tangent focus is a short line, oriented in the direction of the sagittal plane; images of circles centered on the optic axis, or small lines tangential to such circles, will be sharp in this focal plane. The image at the sagittal focus is a short line, oriented in the direction of the tangential plane; images of spokes radiating from the center are sharp at this focus. In between these two foci, a round but "blurry" image is formed. This is called the medial focus or circle of least confusion. This plane often represents the best compromise image location in a system with astigmatism.
The amount of aberration due to astigmatism is proportional to the square of the angle between the rays from the object and the optical axis of the system. With care, an optical system can be designed to reduce or eliminate astigmatism. Such systems are called anastigmats.
=== Astigmatism in systems that are not rotationally symmetric ===
If an optical system is not axisymmetric, either due to an error in the shape of the optical surfaces or due to misalignment of the components, astigmatism can occur even for on-axis object points. This effect is often used deliberately in complex optical systems, especially certain types of telescope. Some telescopes deliberately use non-spherical optics to overcome this phenomenon.
In the analysis of these systems, it is common to consider tangential rays (a plane including an object point being considered and the optical axis), and rays in a meridional plane (a plane containing the optical axis) perpendicular to the tangential plane. This plane is called either the sagittal meridional plane or, confusingly, just the sagittal plane.
==== Ophthalmic astigmatism ====
In optometry and ophthalmology, the vertical and horizontal planes are identified as tangential and sagittal meridians, respectively. Ophthalmic astigmatism is a refraction error of the eye in which there is a difference in degree of refraction in different meridians. It is typically characterized by an aspherical, non-figure of revolution cornea in which the corneal profile slope and refractive power in one meridian is less than that of the perpendicular axis.
Astigmatism causes difficulties in seeing fine detail. Astigmatism can be often corrected by glasses with a lens that has different radii of curvature in different planes (a cylindrical lens), contact lenses, or refractive surgery.
Astigmatism is quite common. Studies have shown that about one in three people suffers from it. The prevalence of astigmatism increases with age. Although a person may not notice mild astigmatism, higher amounts of astigmatism may cause blurry vision, squinting, asthenopia, fatigue, or headaches.
There are a number of tests that are used by ophthalmologists and optometrists during eye examinations to determine the presence of astigmatism and to quantify the amount and axis of the astigmatism. A Snellen chart or other eye chart may initially reveal reduced visual acuity. A keratometer may be used to measure the curvature of the steepest and flattest meridians in the cornea's front surface. Corneal topography may also be used to obtain a more accurate representation of the cornea's shape. An autorefractor or retinoscopy may provide an objective estimate of the eye's refractive error and the use of Jackson cross cylinders in a phoropter may be used to subjectively refine those measurements. An alternative technique with the phoropter requires the use of a "clock dial" or "sunburst" chart to determine the astigmatic axis and power.
Astigmatism may be corrected with eyeglasses, contact lenses, or refractive surgery. Various considerations involving ocular health, refractive status, and lifestyle frequently determine whether one option may be better than another. In those with keratoconus, toric contact lenses often enable patients to achieve better visual acuities than eyeglasses. If the astigmatism is caused by a problem such as deformation of the eyeball due to a chalazion, treating the underlying cause will resolve the astigmatism.
==== Misaligned or malformed lenses and mirrors ====
Grinding and polishing of precision optical parts, either by hand or machine, typically employs significant downward pressure, which in turn creates significant frictional side pressures during polishing strokes that can combine to locally flex and distort the parts. These distortions generally do not possess figure-of-revolution symmetry and are thus astigmatic, and slowly become permanently polished into the surface if the problems causing the distortion are not corrected. Astigmatic, distorted surfaces potentially introduce serious degradations in optical system performance.
Surface distortion due to grinding or polishing increases with the aspect ratio of the part (diameter to thickness ratio). To a first order, glass strength increases as the cube of the thickness. Thick lenses at 4:1 to 6:1 aspect ratios will flex much less than high aspect ratio parts, such as optical windows, which can have aspect ratios of 15:1 or higher. The combination of surface or wavefront error precision requirements and part aspect ratio drives the degree of back support uniformity required, especially during the higher down pressures and side forces during polishing. Optical working typically involves a degree of randomness that helps greatly in preserving figure-of-revolution surfaces, provided the part is not flexing during the grind/polish process.
==== Deliberate astigmatism in optical systems ====
Compact disc players use an astigmatic lens for focusing. When one axis is more in focus than the other, dot-like features on the disc project to oval shapes. The orientation of the oval indicates which axis is more in focus, and thus which direction the lens needs to move. A square arrangement of only four sensors can observe this bias and use it to bring the read lens to best focus, without being fooled by oblong pits or other features on the disc surface.
In 3D PALM/STORM, a type of optical super-resolution microscopy, a cylindrical lens can be introduced into the imaging system to create astigmatism, which allows measurement of the Z position of a diffraction-limited light source.
Laser line levels use a cylindrical lens to spread a laser beam from a point into a line.
== See also ==
Anastigmat (lens type)
Stigmatism
== References ==
Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. ISBN 978-0-8194-5294-8.
Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. ISBN 978-0-201-11609-0.
== External links ==
Astigmatism Articles www.hfhut.com
Paul van Walree's Astigmatism and field curvature. Archived on 2017-07-20. | Wikipedia/Astigmatism_(optical_systems) |
A display resolution standard is a commonly used width and height dimension (display resolution) of an electronic visual display device, measured in pixels. This information is used for electronic devices such as a computer monitor. Certain combinations of width and height are standardized (e.g. by VESA) and typically given a name and an initialism which is descriptive of its dimensions.
The graphics display resolution is also known as the display mode or the video mode, although these terms usually include further specifications such as the image refresh rate and the color depth.
The resolution itself only indicates the number of distinct pixels that can be displayed on a screen, which affects the sharpness and clarity of the image. It can be controlled by various factors, such as the type of display device, the signal format, the aspect ratio, and the refresh rate.
Some graphics display resolutions are frequently referenced with a single number (e.g. in "1080p" or "4K"), which represents the number of horizontal or vertical pixels. More generally, any resolution can be expressed as two numbers separated by a multiplication sign (e.g. "1920×1080"), which represent the width and height in pixels. Since most screens have a landscape format to accommodate the human field of view, the first number for the width (in columns) is larger than the second for the height (in lines), and this conventionally holds true for handheld devices that are predominantly or even exclusively used in portrait orientation.
The graphics display resolution is influenced by the aspect ratio, which is the ratio of the width to the height of the display. The aspect ratio determines how the image is scaled and stretched or cropped to fit the screen. The most common aspect ratios for graphics displays are 4:3, 16:10 (equal to 8:5), 16:9, and 21:9. The aspect ratio also affects the perceived size of objects on the screen.
The native screen resolution together with the physical dimensions of the graphics display can be used to calculate its pixel density. An increase in the pixel density often correlates with a decrease in the size of individual pixels on a display.
Some graphics displays support multiple resolutions and aspect ratios, which can be changed by the user or by the software. In particular, some devices use a hardware/native resolution that is a simple multiple of the recommended software/virtual resolutions in order to show finer details; marketing terms for this include "Retina display".
== Table of display resolution standards ==
== Aspect ratio ==
The favored aspect ratio of mass-market display industry products has changed gradually from 4:3, then to 16:10, then to 16:9, and has now changed to 18:9 for smartphones. The 4:3 aspect ratio generally reflects older products, especially the era of the cathode ray tube (CRT). The 16:10 aspect ratio had its largest use in the 1995–2010 period, and the 16:9 aspect ratio tends to reflect post-2010 mass-market computer monitor, laptop, and entertainment products displays. On CRTs, there was often a difference between the aspect ratio of the computer resolution and the aspect ratio of the display causing non-square pixels (e.g. 320 × 200 or 1280 × 1024 on a 4:3 display).
The 4:3 aspect ratio was common in older television cathode ray tube (CRT) displays, which were not easily adaptable to a wider aspect ratio. When good quality alternate technologies (i.e., liquid crystal displays (LCDs) and plasma displays) became more available and less costly, around the year 2000, the common computer displays and entertainment products moved to a wider aspect ratio, first to the 16:10 ratio. The 16:10 ratio allowed some compromise between showing older 4:3 aspect ratio broadcast TV shows, but also allowing better viewing of widescreen movies. However, around the year 2005, home entertainment displays (i.e., TV sets) gradually moved from 16:10 to the 16:9 aspect ratio, for further improvement of viewing widescreen movies. By about 2007, virtually all mass-market entertainment displays were 16:9. In 2011, 1920 × 1080 (Full HD, the native resolution of Blu-ray) was the favored resolution in the most heavily marketed entertainment market displays. The next standard, 3840 × 2160 (4K UHD), was first sold in 2013.
Also in 2013, displays with 2560 × 1080 (aspect ratio 64:27 or 2.370, however commonly referred to as "21:9" for easy comparison with 16:9) appeared, which closely approximate the common CinemaScope movie standard aspect ratio of 2.35–2.40. In 2014, "21:9" screens with pixel dimensions of 3440 × 1440 (actual aspect ratio 43:18 or 2.38) became available as well.
The computer display industry maintained the 16:10 aspect ratio longer than the entertainment industry, but in the 2005–2010 period, computers were increasingly marketed as dual-use products, with uses in the traditional computer applications, but also as means of viewing entertainment content. In this time frame, with the notable exception of Apple, almost all desktop, laptop, and display manufacturers gradually moved to promoting only 16:9 aspect ratio displays. By 2011, the 16:10 aspect ratio had virtually disappeared from the Windows laptop display market (although Mac laptops are still mostly 16:10, including the 2880 × 1800 15" Retina MacBook Pro and the 2560 × 1600 13" Retina MacBook Pro). One consequence of this transition was that the highest available resolutions moved generally downward (i.e., the move from 1920 × 1200 laptop displays to 1920 × 1080 displays).
In response to usability flaws of now common 16:9 displays in office/professional applications, Microsoft and Huawei started to offer notebooks with a 3:2 aspect ratio. By 2021, Huawei also offers a monitor display offering this aspect ratio, targeted towards professional uses.
== High-definition ==
All standard HD resolutions share a 16∶9 aspect ratio, although some derived resolutions with smaller or larger ratios also exist, e.g. 4∶3 and 64∶27, respectively. Most of the narrower resolutions are only used for storing, not for displaying videos, while the wider resolutions are often available as physical displays. YouTube, for instance, recommends users upload videos in a 16:9 format with 240, 360, 480 (SD), 720, 1080 (HD), 1440, 2160 (4K) or 4320 (8K) lines.
While the monikers for those resolutions originally all used a letter prefix with "HD" for the multiplier, and possibly a "+" suffix for intermediate or taller formats, the newer, larger formats tend to be used with "K" notation for thousands of pixels of horizontal resolution, but may be disambiguated by a system qualifier that includes "HD", e.g. "8K UHD" instead of just "8K".
=== 960 × 540 (qHD) ===
Note: qHD is quarter HD; QHD is quad HD
qHD is a display resolution of 960 × 540 pixels, which is exactly one-quarter of a Full HD (1080p) frame, in a 16:9 aspect ratio. Notably, it is neither "qFHD" nor 640 × 360 which would be quarter of "HD" resolution (720p).
Some of the few tabletop TVs to use this as its native resolution from around 2005 were the Sony XEL-1 and the Sharp Aquos P50. Sharp marketed its ED TV sets with this resolution as PAL optimal.
Similar to DVGA, this resolution became popular for high-end smartphone displays in early 2011. Mobile phones including the Jolla, Sony Xperia C, HTC Sensation, Motorola Droid RAZR, LG Optimus L9, Microsoft Lumia 535, and Samsung Galaxy S4 Mini have displays with the qHD resolution, as does the PlayStation Vita portable game system.
=== 1280 × 720 (HD) ===
The HD or 720p resolution of 1280 × 720 pixels stems from high-definition television (HDTV), where it originally used 50 or 60 frames per second. With its 16:9 aspect ratio, it is exactly 2 times the width and 1+1/2 times the height of 4:3 VGA (640 × 480), which shares its aspect ratio and 480 line count with NTSC. HD, therefore, has exactly 3 times as many pixels as VGA, i.e. almost 1 megapixel.
In the mid-2000s, when the digital HD technology and standard debuted on the market, this type of resolution was often referred to by the branded name "HD ready" or "HDr" for short, which had specified it as a minimum resolution for devices to qualify for the certification. However, few screens have been built that use this resolution natively. Most employ 16:9 panels with 768 lines instead (WXGA), which resulted in odd numbers of pixels per line, i.e. 13651/3 are rounded to 1360, 1364, 1366 or even 1376, the next multiple of 16.
=== 1600 × 900 (HD+) ===
The HD+ resolution of 1600 × 900 pixels in a 16:9 aspect ratio is often referred to as "900p".
=== 1920 × 1080 (FHD) ===
FHD (Full HD) is the resolution 1920 × 1080 used by the 1080p and 1080i HDTV video formats. It has a 16:9 aspect ratio and 2,073,600 total pixels, i.e. very close to 2 megapixels, and is exactly 50% larger than 720p HD (1280 × 720) in each dimension for a total of 2.25 times as many pixels. When using interlacing, the uncompressed bandwidth requirements are similar to those of 720p at the same field rate (a 12.5% increase, as one field of 1080i video is 1,036,800 pixels, and one frame of 720p video is 921,600 pixels). Although the number of pixels is the same for 1080p and 1080i, the effective resolution is somewhat lower for the interlaced format, as it is necessary to use some vertical low-pass filtering to reduce temporal artifacts such as interline twitter.
Sometimes, this resolution is referred to simply as HD, as is evident from derived terms like qHD (quarter), which have a half of the lines and columns of their common base 1920 × 1080, whereas QHD (quadruple) has double the dimensions of 1280 × 720 instead.
When set in relation to higher resolutions, 1920 × 1080 is also referred to as 2K because it has roughly 2000 pixels of horizontal resolution.
The next bigger resolution from 1920 × 1080 in vertical direction is 1920 × 1200 (16∶10), which is hence called FHD+ by some producers, but is elsewhere known as WUXGA, the wider variant of 1600 × 1200 UXGA.
=== 2048 × 1080 (DCI 2K) ===
DCI 2K is a standardized format established by the Digital Cinema Initiatives consortium in 2005 for 2K video projection. This format has a resolution of 2048 × 1080 (2.2 megapixels) with an aspect ratio of 256∶135 (1.8962) or roughly "17∶9". This is the native resolution for DCI-compliant 2K digital projectors – active displays with this resolution are rare. The display aspect ratio is frequently wider than the native one, requiring non-square pixels.
=== 2560 × 1080 (UWFHD) ===
The resolution 2560 × 1080 is equivalent to Full HD (1920 × 1080) extended in width by one third, with an aspect ratio of 64:27 (2.370, or 21.3:9). Monitors at this resolution usually contain built-in firmware to divide the screen into two 1280 × 1080 screens.
There are other, non-standard display resolutions with 1080 lines whose aspect ratios fall between the usual 16∶9 and the ultra-wide 64∶27, e.g. 18∶9, 18.5∶9, 19∶9 and 19.5∶9. They are mostly used in smartphones or phablets and do not have established names, but may be subsumed under the umbrella term ultra-wide (full) HD.
=== 2560 × 1440 (QHD) ===
Note: qHD is quarter HD; QHD is quad HD
QHD (Quad HD) or 1440p is a display resolution of 2560 × 1440 pixels. The name "QHD" reflects the fact that it has four times as many pixels as HD (720p). It is also sometimes called "WQHD" to distinguish it from qHD (960 × 540), otherwise it is technically redundant since the HD resolutions are all widescreen.
This resolution was under consideration by the ATSC in the late 1980s to become the standard HDTV format, because it is exactly 3 times the height of SDTV NTSC television signals, with a wider aspect ratio. Pragmatic technical constraints made them choose the now well-known 16:9 formats of 1280 × 720 (1.5x NTSC/VGA height) and 1920 × 1080 (2x PAL height of 540 lines) instead.
In October 2006, Chi Mei Optoelectronics (CMO) announced a 47-inch 1440p LCD panel to be released in Q2 2007; the panel was planned to finally debut at FPD International 2008 in a form of autostereoscopic 3D display. As of the end of 2013, monitors with this resolution were becoming more common.
The 27-inch version of the Apple Cinema Display monitor introduced in July 2010 has a native resolution of 2560 × 1440, as did its successor, the 27-inch Apple Thunderbolt Display.
The resolution is also used in portable devices. In September 2012, Samsung announced the Series 9 WQHD laptop with a 13-inch 2560 × 1440 display. In August 2013, LG announced a 5.5-inch QHD smartphone display, which was used in the LG G3. In October 2013 Vivo announced a smartphone with a 2560 × 1440 display.
Other phone manufacturers followed in 2014, such as Samsung with the Galaxy Note 4, and Google and Motorola with the Nexus 6 smartphone. By the mid-2010s, it was a common resolution among flagship phones such as the HTC 10, the Lumia 950, and the Galaxy S6 and S7.
==== 5120 × 1440 DQHD ====
Ultrawide (curved) monitors with a 32:9 aspect ratio and a 5120 × 1440 resolution have been referred to as Dual QHD or DQHD for short. It is sometimes also called "Super-Ultrawide" for marketing purposes.
=== 3200 × 1800 (QHD+) ===
The resolution 3200 × 1800 has a 16:9 aspect ratio and is exactly four times as many pixels as the 1600 × 900 HD+ resolution, and is therefore referred to as "QHD+" (Quad HD+). It has also been referred to as simply "QHD" by some companies.
The first products announced to use this resolution were the 2013 HP Envy 14 TouchSmart Ultrabook and the 13.3-inch Samsung Ativ Q.
=== 3440 × 1440 (UWQHD) ===
The resolution 3440 × 1440 is equivalent to QHD (2560 × 1440) extended in width by 34%, giving it an aspect ratio of 43:18 (2.38:1, or 21.5:9; commonly marketed as simply "21:9"). The first monitor to support this resolution was the 34-inch LG 34UM95-P. This monitor was first released in Germany in late December 2013, before being officially announced at CES 2014.
=== 3840 × 1080 ===
The resolution 3840 × 1080 is equivalent to two Full HD (1920 × 1080) displays side by side or one vertical half of a 4K UHD (3840 × 2160) display. It has an aspect ratio of 32:9 (3.5:1), close to the 3.6:1 ratio of IMAX UltraWideScreen 3.6. Samsung monitors at this resolution contain built-in firmware to divide the screen into two 1920 × 1080 screens, or one 2560 × 1080 and one 1280 × 1080 screen.
=== 3840 × 1600 ===
The resolution 3840 × 1600 has a 12:5 aspect ratio, i.e. 2.4 or 21.6:9, which is commonly marketed as simply "21:9". It is equivalent to WQXGA (2560 × 1600) extended in width by 50%, or 4K UHD (3840 × 2160) reduced in height by 26%. This resolution is commonly encountered in cinematic 4K content that has been cropped vertically to a widescreen aspect ratio. The first monitor to support this resolution was the 37.5-inch LG 38UC99-W. Other vendors followed, with Dell U3818DW, HP Z38c, and Acer XR382CQK.
This resolution has been referred to as UW4K, WQHD+, UWQHD+ or QHD+, though no single name is agreed upon.
=== 3840 × 2160 (4K UHD) ===
The resolution 3840 × 2160, sometimes referred to as 4K UHD or 4K × 2K, has a 16:9 aspect ratio and 8,294,400 pixels. It is double the size of Full HD (1920 × 1080) in both dimensions for a total of four times as many pixels, and triple the size of HD (1280 × 720) in both dimensions for a total of nine times as many pixels. It is the lowest common multiple of the HDTV resolutions.
3840 × 2160 was chosen as the resolution of the UHDTV1 format defined in SMPTE ST 2036-1, as well as the 4K UHDTV system defined in ITU-R BT.2020 and the UHD-1 broadcast standard from DVB. It is also the minimum resolution requirement for CEA's definition of an Ultra HD display. Before the publication of these standards, it was sometimes casually referred to as "QFHD" (Quad Full HD).
The first commercial displays capable of this resolution include an 82-inch LCD TV revealed by Samsung in early 2008, the Sony SRM-L560, a 56-inch LCD reference monitor announced in October 2009, an 84-inch display demonstrated by LG in mid-2010, and a 27.84-inch 158 PPI 4K IPS monitor for medical purposes launched by Innolux in November 2010. In October 2011 Toshiba announced the REGZA 55x3, which is claimed to be the first 4K glasses-free 3D TV.
DisplayPort supports 3840 × 2160 at 30 Hz in version 1.1 and added support for up to 75 Hz in version 1.2 (2009) and 120 Hz in version 1.3 (2014), while HDMI added support for 3840 × 2160 at 30 Hz in version 1.4 (2009) and 60 Hz in version 2.0 (2013).
When support for 4K at 60 Hz was added in DisplayPort 1.2, no DisplayPort timing controllers (TCONs) existed which were capable of processing the necessary amount of data from a single video stream. As a result, the first 4K monitors from 2013 and early 2014, such as the Sharp PN-K321, Asus PQ321Q, and Dell UP2414Q and UP3214Q, were addressed internally as two 1920 × 2160 monitors side by side instead of a single display and made use of DisplayPort's Multi-Stream Transport (MST) feature to multiplex a separate signal for each half over the connection, splitting the data between two timing controllers. Newer timing controllers became available in 2014, and after mid-2014 new 4K monitors such as the Asus PB287Q no longer rely on MST tiling technique to achieve 4K at 60 Hz, instead, using the standard SST (Single-Stream Transport) approach.
In 2015, Sony announced the Xperia Z5 Premium, the first smartphone with a 4K display, and in 2017 Sony announced the Xperia XZ Premium, the first smartphone with a 4K HDR display.
=== 4096 × 2160 (DCI 4K) ===
4096 × 2160, referred to as DCI 4K, Cinema 4K or 4K × 2K, is the resolution used by the 4K container format defined by the Digital Cinema Initiatives Digital Cinema System Specification, a prominent standard in the cinema industry. This resolution has an aspect ratio of 256:135 (1.8962:1), and 8,847,360 total pixels. This is the native resolution for DCI 4K digital projectors and displays.
HDMI added support for 4096 × 2160 at 24 Hz in version 1.4 and 60 Hz in version 2.0.
=== 5120 × 2160 ===
The resolution 5120 × 2160 is equivalent to 4K UHD (3840 × 2160) extended in width by one third, giving it a 64:27 aspect ratio (2.370 or 21.3:9, commonly marketed as simply "21:9") and 11,059,200 total pixels. It is exactly double the size of 2560 × 1080 in both dimensions, for a total of four times as many pixels. The first displays to support this resolution were 105-inch televisions, the LG 105UC9 and the Samsung UN105S9W. In December 2017, LG announced a 34-inch 5120 × 2160 monitor, the 34WK95U, and in January 2021 the 40-inch 40WP95C. LG refers to this resolution as "5K2K WUHD".
=== 5120 × 2880 (5K) ===
The resolution 5120 × 2880, commonly referred to as 5K or 5K × 3K, has a 16:9 aspect ratio and 14,745,600 pixels. Although it is not established by any of the UHDTV standards, some manufacturers such as Dell have referred to it as "UHD+". It is exactly double the pixel count of QHD (2560 × 1440) in both dimensions for a total of four times as many pixels, and is one third larger than 4K UHD (3840 × 2160) in both dimensions for a total of 1.77 times as many pixels. The line count of 2880 is also the least common multiple of 480 and 576, the scanline count of NTSC and PAL, respectively. Such a resolution can vertically scale SD content to fit by natural numbers (6 for NTSC and 5 for PAL). Horizontal scaling of SD is always fractional (non-anamorphic: 5.33...5.47, anamorphic: 7.11...7.29).
The first display with this resolution was the Dell UltraSharp UP2715K, announced on September 5, 2014. On October 16, 2014, Apple announced the iMac with Retina 5K display.
DisplayPort version 1.3 added support for 5K at 60 Hz over a single cable, whereas version 1.2 was only capable of 5K at 30 Hz. Early 5K 60 Hz displays such as the Dell UltraSharp UP2715K and HP DreamColor Z27q that lacked DisplayPort 1.3 support required two DisplayPort 1.2 connections to operate at 60 Hz, in a tiled display mode similar to early 4K displays using DP MST.
=== 7680 × 4320 (8K UHD) ===
The resolution 7680 × 4320, sometimes referred to as 8K UHD, has a 16:9 aspect ratio and 33,177,600 pixels. It is exactly double the size of 4K UHD (3840 × 2160) in each dimension for a total of four times as many pixels, and Quadruple the size of Full HD (1920 × 1080) in each dimension for a total of sixteen times as many pixels. 7680 × 4320 was chosen as the resolution of the UHDTV2 format defined in SMPTE ST 2036-1, as well as the 8K UHDTV system defined in ITU-R BT.2020 and the UHD-2 broadcast standard from DVB.
DisplayPort 1.3, finalized by VESA in late 2014, added support for 7680 × 4320 at 30 Hz (or 60 Hz with Y′CBCR 4:2:0 subsampling). VESA's Display Stream Compression (DSC), which was part of early DisplayPort 1.3 drafts and would have enabled 8K at 60 Hz without subsampling, was cut from the specification prior to publication of the final draft.
DSC support was reintroduced with the publication of DisplayPort 1.4 in March 2016. Using DSC, a "visually lossless" form of compression, formats up to 7680 × 4320 (8K UHD) at 60 Hz with HDR and 30 bit/px color depth are possible without subsampling.
== Video Graphics Array (VGA and derivatives) ==
=== 160 × 120 (QQVGA) ===
Quarter-QVGA (QQVGA or qqVGA) denotes a resolution of 160 × 120 (4:3 storage aspect ratio) or 120 × 160 pixels, usually used in displays of handheld devices. The term Quarter-QVGA signifies a resolution of one fourth the number of pixels in a QVGA display (half the number of vertical and half the number of horizontal pixels) which itself has one fourth the number of pixels in a VGA display. There are also devices with QQVGA 160 × 128 (5:4 storage aspect ratio).
The abbreviation qqVGA may be used to distinguish quarter from quad, just like qVGA.
=== 240 × 160 ===
HQVGA (or Half-QVGA) denotes a display screen resolution of 240 × 160 or 160 × 240 pixels, as seen on the Game Boy Advance. This resolution is half of QVGA, which is itself a quarter of VGA, which is 640 × 480 pixels.
=== 320 × 240 (QVGA) ===
Quarter VGA (QVGA or qVGA) is a popular term for a computer display with 320 × 240 display resolution. QVGA displays were most often used in mobile phones, personal digital assistants (PDA), and some handheld game consoles. Often the displays are in a "portrait" orientation (i.e., taller than they are wide, as opposed to "landscape") and are referred to as 240 × 320.
The name comes from having a quarter of the 640 × 480 maximum resolution of the original IBM Video Graphics Array display technology, which became a de facto industry standard in the late 1980s. QVGA is not a standard mode offered by the VGA BIOS, even though VGA and compatible chipsets support a QVGA-sized Mode X. The term refers only to the display's resolution and thus the abbreviated term QVGA or Quarter VGA is more appropriate to use.
QVGA resolution is also used in digital video recording equipment as a low-resolution mode requiring less data storage capacity than higher resolutions, typically in still digital cameras with video recording capability, and some mobile phones. Each frame is an image of 320 × 240 pixels. QVGA video is typically recorded at 15 or 30 frames per second. QVGA mode describes the size of an image in pixels, commonly called the resolution; numerous video file formats support this resolution.
While QVGA is a lower resolution than VGA, at higher resolutions the "Q" prefix commonly means quad(ruple) or four times higher display resolution (e.g., QXGA is four times higher resolution than XGA). To distinguish quarter from quad, lowercase "q" is sometimes used for "quarter" and uppercase "Q" for "Quad", by analogy with SI prefixes like m/M and p/P, but this is not a consistent usage.
Some examples of devices that use QVGA display resolution include the iPod Classic, Samsung i5500, LG Optimus L3-E400, Galaxy Fit, Y and Pocket, HTC Wildfire, Sony Ericsson Xperia X10 Mini and Mini pro and Nintendo 3DS' bottom screen.
=== 400 × 240 (WQVGA) ===
Wide QVGA or WQVGA are some display resolutions having the same height in pixels as QVGA, but wider.
Since QVGA is 320 pixels wide and 240 pixels high (aspect ratio of 4:3), the resolution of a WQVGA screen might be 360 × 240 (3:2 aspect ratio), 384 × 240 (16:10 aspect ratio), 400 × 240 (5:3 – such as the Nintendo 3DS screen), 426 × 240, 428 × 240 (≈16:9 ratio) or 432 × 240 (18:10 aspect ratio). As with WVGA, exact ratios of n:9 are difficult because of the way VGA controllers internally deal with pixels. For instance, when using graphical combinatorial operations on pixels, VGA controllers will use 1 bit per pixel. Since bits cannot be accessed individually but by chunks of 16 or an even higher power of 2, this limits the horizontal resolution to a 16-pixel granularity, i.e., the horizontal resolution must be divisible by 16. In the case of the 16:9 ratio, with 240 pixels high, the horizontal resolution should be 240 / 9 × 16 = 426.6 (4262⁄3), the closest multiple of 16 is 432.
WQVGA has also been used to describe displays that are not 240 pixels high, for example, Sixteenth HD1080 displays which are 480 pixels wide and 270 or 272 pixels high. This may be due to WQVGA having the nearest screen height.
WQVGA resolutions were commonly used in touchscreen mobile phones, such as 400 × 240, 432 × 240, and 480 × 240. For example, the Hyundai MB 490i, Sony Ericsson Aino and the Samsung Instinct have WQVGA screen resolutions – 240 × 432. Other devices such as the Apple iPod Nano also use a WQVGA screen, 240 × 376 pixels. The Nintendo 3DS line is probably the most famous device to have a WQVGA screen.
=== 480 × 320 (HVGA) ===
HVGA (Half-size VGA) screens have 480 × 320 pixels (3:2 aspect ratio), 480 × 360 pixels (4:3 aspect ratio), 480 × 272 (≈16:9 aspect ratio), or 640 × 240 pixels (8:3 aspect ratio). The former is used by a variety of PDA devices, starting with the Sony CLIÉ PEG-NR70 in 2002, and standalone PDAs by Palm. The latter was used by a variety of handheld PC devices. VGA resolution is 640 × 480.
Examples of devices that use HVGA include the Apple iPhone (1st generation through 3GS), iPod Touch (1st Generation through 3rd), BlackBerry Bold 9000, HTC Dream, Hero, Wildfire S, LG GW620 Eve, MyTouch 3G Slide, Nokia 6260 Slide, Palm Pre, Samsung M900 Moment, Sony Ericsson Xperia X8, mini, mini pro, active and live and the Sony PlayStation Portable.
Texas Instruments produces the DLP pico projector which supports HVGA resolution.
HVGA was the only resolution supported in the first versions of Google Android, up to release 1.5. Other higher and lower resolutions became available starting on release 1.6, like the popular WVGA resolution on the Motorola Droid or the QVGA resolution on the HTC Tattoo.
Three-dimensional computer graphics common on television throughout the 1980s were mostly rendered at this resolution, causing objects to have jagged edges on the top and bottom when edges were not anti-aliased.
=== 640 × 480 (VGA) ===
Video Graphics Array (VGA) refers specifically to the display hardware first introduced with the IBM PS/2 line of computers in 1987. Through its widespread adoption, VGA has also come to mean either an analog computer display standard, the 15-pin D-subminiature VGA connector, or the 640 × 480 resolution itself. While the VGA resolution was superseded in the personal computer market in the 1990s and the SEGA Dreamcast in 1998, it became a popular resolution on mobile devices in the 2000s. VGA is still the universal fallback troubleshooting mode in the case of trouble with graphic device drivers in operating systems.
In the field of video, the resolution of 480i supports 640 samples per line (corresponding to 640x480) corresponding to Standard Definition (SD), in contrast to high-definition (HD) resolutions like 1280 × 720 and 1920 × 1080.
=== 800 × 480 (WVGA) ===
Wide VGA or WVGA, sometimes just WGA are some display resolutions with the same 480-pixel height as VGA but wider, such as 720 × 480 (3:2 aspect ratio), 800 × 480 (5:3), 848 × 480, 852 × 480, 853 × 480, or 854 × 480 (≈16:9).
It was a common resolution among LCD projectors and later portable and hand-held internet-enabled devices (such as MID and Netbooks) as it is capable of rendering websites designed for an 800 wide window in full page-width. Examples of hand-held internet devices, without phone capability, with this resolution include: Spice stellar nhance mi-435, ASUS Eee PC 700 series, Dell XCD35, Nokia 770, N800, and N810.
=== 854 × 480 (FWVGA) ===
FWVGA is an abbreviation for Full Wide Video Graphics Array which refers to a display resolution of 854 × 480 pixels. 854 × 480 is approximately the 16:9 aspect ratio of anamorphically "un-squeezed" NTSC DVD widescreen video and is considered a "safe" resolution that does not crop any of the image. It is called Full WVGA to distinguish it from other, narrower WVGA resolutions which require cropping 16:9 aspect ratio high-definition video (i.e. it is full width, albeit with a considerable reduction in size).
The 854 pixel width is rounded up from 853.3:
480 × 16⁄9 = 7680⁄9 = 853+1⁄3.
Since a pixel must be a whole number, rounding up to 854 ensures inclusion of the entire image. 853 × 480 is the 16:9 equivalent for NTSC (480 lines) on a display with square pixels. Plasma and other digital TV sets with this resolution were marketed as enhanced-definition television (EDTV) at the time.
In 2010, mobile phones with FWVGA display resolution started to become more common. (See also: list of mobile phones with FWVGA display.) In addition, the Wii U GamePad for Nintendo's Wii U gaming console includes a 6.2-inch FWVGA display.
=== 800 × 600 (SVGA) ===
Super Video Graphics Array, abbreviated to Super VGA or SVGA, also known as Ultra Video Graphics Array early on, abbreviated to Ultra VGA or UVGA, is a broad term that covers a wide range of computer display standards.
Originally, it was an extension to the VGA standard first released by IBM in 1987. Unlike VGA – a purely IBM-defined standard – Super VGA was defined by the Video Electronics Standards Association (VESA), an open consortium set up to promote interoperability and define standards. When used as a resolution specification, in contrast to VGA or XGA for example, the term SVGA normally refers to a resolution of 800 × 600 pixels.
The marginally higher resolution 832 × 624 is the highest 4:3 resolution not greater than 219 pixels, with its horizontal dimension a multiple of 32 pixels. This enables it to fit within a framebuffer of 512 KB (512 × 210 bytes), and the common multiple of 32 pixels constraint is related to alignment. For these reasons, this resolution was available on the Macintosh LC III and other systems.
=== 1024 × 576, 1024 × 600 (WSVGA) ===
The wide version of SVGA is known as WSVGA (Wide Super VGA or Wide SVGA), featured on Ultra-Mobile PCs, netbooks, and tablet computers. The resolution is either 1024 × 576 (aspect ratio 16:9) or 1024 × 600 (128:75) with screen sizes normally ranging from 7 to 10 inches. It has full XGA width of 1024 pixels.
Although digital broadcast content in former PAL/SECAM regions has 576 active lines, several mobile TV sets with a DVB-T2 tuner use the 600-line variant with a diameter of 7, 9 or 10 inches (18 to 26 cm).
1024 × 576 is the 16:9 equivalent for PAL (576 lines) on a display with square pixels, resulting in a pixel aspect ratio of 16∶11 or 64∶45 depending on the native resolution of PAL.
=== 960 × 640 ===
DVGA (DoubleVGA) screens have 960 × 640 pixels (3:2 aspect ratio). Both dimensions are double that of HVGA, hence the pixel count is quadrupled.
Examples of devices that use DVGA include the Meizu MX mobile phone and the Apple iPhone 4 and 4S with the iPod Touch 4, where the screen is called the "Retina Display".
iPhone 5 introduced a wide, 16:9 variant at 1136 × 640 pixels, which also has no official acronym.
=== 1280 × 960 (QuadVGA) ===
QuadVGA (also labelled as Quad VGA or Quad-VGA) is a non-standard term used to refer to a resolution of 1280 × 960, since both sides are doubled from VGA. However, it is usually not as the abbreviation QVGA because this is strongly associated with the alternate meaning Quarter VGA (QVGA 320 × 240).
It is sometimes unofficially called SXGA− to avoid confusion with the SXGA standard (1280 × 1024). Elsewhere, this 4:3 resolution was supposedly also called UVGA (Ultra VGA), or SXVGA (Super eXtended VGA).
== Extended Graphics Array (XGA and derivatives) ==
=== 1024 × 768 (XGA) ===
The Extended Graphics Array (XGA) or originally Extended Video Graphics Array (Extended-VGA, EVGA) is an IBM display standard introduced in 1990. Later it became the most common appellation of the 1024 × 768 pixels display resolution.
The initial version of XGA expanded upon IBM's older VGA by adding support for four new screen modes, including one new resolution:
640 × 480 pixels in direct 16 bits-per-pixel (65,536 color) RGB hi-color and 8 bit/px (256 color) palette-indexed mode.
1024 × 768 pixels with a 16- or 256-color (4 or 8 bit/px) palette, using a low frequency interlaced refresh rate.
XGA-2 added a 24-bit DAC, but this was used only to extend the available master palette in 256-color mode, e.g. to allow true 256-greyscale output. Other improvements included the provision of the previously missing 800 × 600 resolution in up to 65,536 colors, faster screen refresh rates in all modes (including non-interlace, flicker-free output for 1024 × 768), and improved accelerator performance and versatility.
All standard XGA modes have a 4:3 aspect ratio with square pixels, although this does not hold for certain standard VGA and third-party extended modes (640 × 400, 1280 × 1024).
=== WXGA ===
Wide XGA (WXGA) is a set of non-standard resolutions derived from XGA (1024 × 768) by widening it to 1366 × 768 with a widescreen aspect ratio of nearly 16:9 or to 1280 × 800 with an aspect ratio of 16:10. WXGA is commonly used for low-end LCD TVs and LCD computer monitors for widescreen presentation. The exact resolution offered by a device described as "WXGA" can be somewhat variable owing to a proliferation of several closely related timings optimised for different uses and derived from different bases.
In Microsoft Windows operating system specifically, the larger taskbar of Windows 7 occupies an additional 16-pixel lines by default, which may compromise the usability of programs that already demanded a full 1024 × 768 (instead of, e.g. 800 × 600) unless it is specifically set to use small icons; an "oddball" 784-line resolution would compensate for this, but 1280 × 800 has a simpler aspect and also gives the slight bonus of 16 more usable lines. Also, the Windows Sidebar in Windows Vista and 7 can use the additional 256 or 336 horizontal pixels to display informational "widgets" without compromising the display width of other programs, and Windows 8 is specifically designed around a "two-pane" concept where the full 16:9 or 16:10 screen is not required. Typically, this consists of a 4:3 main program area (typically 1024 × 768, 1000 × 800 or 1440 × 1080) plus a narrow sidebar running a second program, showing a toolbox for the main program or a pop-out OS shortcut panel taking up the remainder.
==== 1366 × 768 (WXGA) ====
When referring to televisions and other monitors intended for consumer entertainment use, WXGA is often understood to refer to a resolution of 1366 × 768, with an aspect ratio of very nearly 16:9. The basis for this otherwise odd seeming resolution is similar to that of other "wide" standards – the line scan (refresh) rate of the well-established "XGA" standard (1024 × 768 pixels, 4:3 aspect ratio) extended to give square pixels on the increasingly popular 16:9 widescreen display ratio without having to effect major signalling changes other than a faster pixel clock, or manufacturing changes other than extending panel width by one third. As 768 is not divisible by 9, the aspect ratio is not quite 16:9 – this would require a width of 13651⁄3 (1365.3) pixels. However, at only 0.05%, the resulting error is insignificant. It is also occasionally referred to as FWXGA (Full Wide XGA), so it can be distinguished from other, narrower WXGA resolutions.
Following the introduction of the European HD ready logo in 2005, a year later 1366 × 768 was the most popular resolution for liquid crystal display televisions (versus XGA for Plasma TVs flat panel displays);
By 2013, even this was relegated to only being used in smaller or cheaper displays (e.g. "bedroom" LCD TVs, or low-cost, large-format plasmas), cheaper laptop and mobile tablet computers, and midrange home cinema projectors, having otherwise been overtaken by higher "full HD" resolutions such as 1920 × 1080.
A common variant on this resolution is also 1360 × 768 (unnamed or named FWXGA), which confers several technical benefits, most significantly a reduction in memory requirements from just over to just under 1 MB per 8-bit channel (1366 × 768 needs 1024.5 KB per channel; 1360 × 768 needs 1020 KB; 1 MB is equal to 1024 KB), which simplifies architecture and can significantly reduce the amount–and speed–of VRAM required with only a very minor change in available resolution, as memory chips are usually only available in fixed megabyte capacities. For example, at 32-bit color, a 1360 × 768 framebuffer would require only 4 MB, whilst a 1366 × 768 one may need 5, 6, or even 8 MB depending on the exact display circuitry architecture and available chip capacities. The 6-pixel reduction also means each line's width is divisible by 8 pixels, simplifying numerous routines used in both computer and broadcast/theatrical video processing, which operate on 8-pixel blocks. Historically, many video cards also mandated screen widths divisible by 8 for their lower-color, planar modes to accelerate memory accesses and simplify pixel position calculations (e.g. fetching 4-bit pixels from 32-bit memory is much faster when performed 8 pixels at a time, and calculating exactly where a particular pixel is within a memory block is much easier when lines do not end partway through a memory word), and this convention persisted in low-end hardware even into the early days of widescreen, LCD HDTVs; thus, most 1366-width displays also quietly support display of 1360-width material, with a thin border of unused pixel columns at each side. This narrower mode is even further removed from the 16:9 ideal, but the error is still less than 0.5% (technically, the mode is either 15.94:9.00 or 16.00:9.04) and should be imperceptible.
==== 1280 × 800 (WXGA) ====
When referring to laptop displays or independent displays and projectors intended primarily for use with computers, WXGA is also used to describe a resolution of 1280 × 800 pixels, with an aspect ratio of 16:10. This was once particularly popular for laptop screens, usually with a diagonal screen size of between 12 and 15 inches, as it provided a useful compromise between 4:3 XGA and 16:9 WXGA, with improved resolution in both dimensions vs. the old standard (especially useful in portrait mode, or for displaying two standard pages of text side by side), a perceptibly "wider" appearance and the ability to display 720p HD video "native" with only very thin letterbox borders (usable for on-screen playback controls) and no stretching. Additionally, it required only 1000 KB (just under 1 MB) of memory per 8-bit channel; thus, a typical double-buffered 32-bit color screen could fit within 8 MB, limiting everyday demands on the complexity (and cost, energy use) of integrated graphics chipsets and their shared use of typically sparse system memory (generally allocated to the video system in relatively large blocks), at least when only the internal display was in use (external monitors generally being supported in "extended desktop" mode to at least 1600 × 1200 resolution). 16:10 (or 8:5) is itself a rather "classic" computer aspect ratio, harking back to early 320 × 200 modes (and their derivatives) as seen in the Commodore 64, IBM CGA card and others. However, as of mid-2013, this standard is becoming increasingly rare, crowded out by the more standardized and thus more economical-to-produce 1366 × 768 panels, as its previously beneficial features become less important with improvements to hardware, gradual loss of general backwards software compatibility, and changes in interface layout. As of February 2024, the market availability of panels with 1280 × 800 native resolution had been generally relegated to handheld gaming computers 1280 × 800 is used by Valve's Steam Deck, as well as several other handheld gaming computers.
==== Other WXGA ====
Additionally, at least three other resolutions are sometimes labelled as WXGA:
The first variant, 1280 × 768, can be seen as a compromise resolution that addressed this problem, as well as a halfway point between the older 1024 × 768 and 1280 × 1024 resolutions, and a stepping stone to 1366 × 768 (being one-quarter wider than 1024, not one-third) and 1280 × 800, that never quite caught on in the same way as either of its arguably derivative successors. Its square-pixel aspect ratio is 15:9 (or 5:3), in contrast to HDTV's 16:9 and 1280 × 800's 16:10. It is also the lowest resolution that might be found in an "Ultrabook" standard laptop, as it satisfies the minimum horizontal and vertical pixel resolutions required to officially qualify for the designation.
Second, the HDTV-standard 1280 × 720 (otherwise commonly described as "720p"), which offers an exact 16:9 aspect ratio with square pixels; naturally, it displays standard 720p HD video material without stretching or letterboxing and 1080i/1080p with a simple 2:3 downscale. This resolution has found some use in tablets and modern, high-pixel-density mobile phones, as well as small-format "netbook" or "ultralight" laptop computers. However, its use is uncommon in larger, mainstream devices as it has an insufficient vertical resolution for the proper use of modern operating systems such as Windows 7 whose UI design assumes a minimum of 768 lines. For certain uses such as word processing, it can even be considered a slight downgrade (reducing the number of simultaneously visible lines of text without granting any significant benefit as even 640 pixels is sufficient horizontal resolution to legibly render a full page width, especially with the addition of subpixel anti-aliasing).
Another mentionable resolution is 1152 × 768 with a 3:2 aspect ratio.
Likewise, 1344 × 768 with a 7:4 aspect ratio (similar to 16:9) is used sometimes.
Some 1440 × 900 resolution displays have also been found labeled as WXGA; however, the "correct" label is WXGA+.
=== 1152 × 864 (XGA+) ===
XGA+ stands for Extended Graphics Array Plus and is a computer display standard, usually understood to refer to the 1152 × 864 resolution with an aspect ratio of 4:3. Until the advent of widescreen LCDs, XGA+ was often used on 17-inch desktop CRT monitors. It is the highest 4:3 resolution not greater than 220 pixels (≈1.05 megapixels), with its horizontal dimension a multiple of 32 pixels. This enables it to fit closely into a video memory or framebuffer of 1 MB (1 × 220 bytes), assuming the use of one byte per pixel. The common multiple of 32 pixels constraint is related to alignment.
Historically, the resolution also relates to the earlier standard of 1152 × 900 pixels, which was adopted by Sun Microsystems for the Sun-2 workstation in the early 1980s. A decade later, Apple Computer selected the resolution of 1152 × 870 for their 21-inch CRT monitors, intended for use as two-page displays on the Macintosh II computer. These resolutions are even closer to the limit of a 1 MB framebuffer, but their aspect ratios differ slightly from the common 4:3.
XGA+ is the next step after XGA (1024 × 768), although it is not approved by any standard organizations. The next step with an aspect ratio of 4:3 is 1280 × 960 (QuadVGA) or 1400 × 1050 (SXGA+).
=== 1440 × 900 (WXGA+, WSXGA) ===
WXGA+ and WSXGA are terms referring to a computer display resolution of 1440 × 900. Occasionally manufacturers use other terms to refer to this resolution. The Standard Panels Working Group refers to the 1440 × 900 resolution as WXGA (but refers also WXGA to 1280 × 800).
WXGA+ can be considered enhanced versions of WXGA with more pixels. The aspect ratio is 16:10 (widescreen). WXGA+ resolution is common in 19-inch widescreen desktop monitors (a very small number of such monitors use WSXGA+), and is also optional, although less common, in laptop LCDs, in sizes ranging from 12.1 to 17 inches.
==== 1600 × 1024 ====
The name WSXGA is also used to describe a resolution of 1600 × 1024, which has an aspect ratio of 25:16 (52:42 = 1.5625, which is between 14:9 and 16:10).
==== 1280 × 854 ====
WXGA+ has also been used to refer to a resolution of 1280 × 854, which has an aspect ratio very close to 3:2 (1.5).
=== 1280 × 1024 (SXGA) ===
Super XGA (SXGA) is a standard monitor resolution of 1280 × 1024 pixels. This display resolution is the "next step" above the XGA resolution that IBM developed in 1990.
The 1280 × 1024 resolution is not the standard 4:3 aspect ratio, instead it is a 5:4 aspect ratio (1.25:1 instead of 1.3:1). A standard 4:3 monitor using this resolution will have rectangular rather than square pixels, meaning that unless the software compensates for this the picture will be distorted, causing circles to appear elliptical.
SXGA is the most common native resolution of 17-inch and 19-inch LCD monitors. An LCD monitor with SXGA native resolution will typically have a physical 5:4 aspect ratio, preserving a 1:1 pixel aspect ratio.
Sony manufactured a 17-inch CRT monitor with a 5:4 aspect ratio designed for this resolution. It was sold under the Apple brand name.
SXGA is also a popular resolution for cell phone cameras, such as the Motorola Razr and most Samsung and LG phones. Although having been taken over by newer UXGA (2.0-megapixel) cameras, the 1.3-megapixel was the most common around 2007.
Any CRT that can run 1280 × 1024 can also run 1280 × 960 (QuadVGA or sometimes SXGA-), which has the standard 4:3 ratio. A flat panel TFT screen, including one designed for 1280 × 1024, will show stretching distortion when set to display any resolution other than its native one, as the image needs to be interpolated to fit in the fixed grid display. Some TFT displays do not allow a user to disable this, and will prevent the upper and lower portions of the screen from being used forcing a "letterbox" format when set to a 4:3 ratio.
The 1280 × 1024 resolution became popular because at 24 bit/px color depth it fits well into 4 megabytes of video RAM. At the time, memory was extremely expensive. Using 1280 × 1024 at 24-bit color depth allowed using 3.75 MB of video RAM, fitting nicely with VRAM chip sizes which were available at the time (4 MB):
(1280 × 1024) px × 24 bit/px ÷ 8 bit/byte ÷ 220 byte/MB = 3.75 MB
=== 1400 × 1050 (SXGA+) ===
SXGA+ stands for Super Extended Graphics Array Plus and is a computer display standard. An SXGA+ display is commonly used on 14-inch or 15-inch laptop LCD screens with a resolution of 1400 × 1050 pixels. An SXGA+ display is used on a few 12-inch laptop screens such as the ThinkPad X60 and X61 (both only as tablet) as well as the Toshiba Portégé M200 and M400, but those are far less common. At 14.1 inches, Dell offered SXGA+ on many of the Latitude C-Series laptops, such as the C640, and IBM since the ThinkPad T21. Sony also used SXGA+ in their Z1 series, but no longer produces them as widescreen has become more predominant.
In desktop LCDs, SXGA+ is used on some low-end 20-inch monitors, whereas most of the 20-inch LCDs use UXGA (standard screen ratio), or WSXGA+ (widescreen ratio).
A rare resolution of 2800 × 2100, i.e. with double the pixels horizontally and vertically, is known as QSXGA+.
=== 1680 × 1050 (WSXGA+) ===
WSXGA+ stands for Widescreen Super Extended Graphics Array Plus. WSXGA+ displays were commonly used on Widescreen 20-, 21-, and 22-inch LCD monitors from numerous manufacturers (and a very small number of 19-inch widescreen monitors), as well as widescreen 15.4-inch and 17-inch laptop LCD screens like the Thinkpad T61p, the late 17" Apple PowerBook G4 and the unibody Apple 15" MacBook Pro. The resolution is 1680 × 1050 pixels (1,764,000 pixels) with a 16:10 aspect ratio.
WSXGA+ is the widescreen version of SXGA+. The next highest resolution (for widescreen) after it is WUXGA, which is 1920 × 1200 pixels.
=== 1600 × 1200 (UXGA) ===
UXGA (sometimes UGA) is an abbreviation for Ultra Extended Graphics Array referring to a standard monitor resolution of 1600 × 1200 pixels (totaling 1,920,000 pixels), which is exactly four times the default image resolution of SVGA (800 × 600) (totaling 480,000 pixels). Dell Inc. refers to the same resolution of 1,920,000 pixels as UGA. It is generally considered to be the next step above SXGA (1280 × 960 or 1280 × 1024), but some resolutions (such as the unnamed 1366 × 1024 and SXGA+ at 1400 × 1050) fit between the two.
UXGA has been the native resolution of many fullscreen monitors of 15 inches or more, including laptop LCDs such as the ones in the IBM ThinkPad A21p, A30p, A31p, T42p, T43p, T60p, Dell Inspiron 8000/8100/8200 and Latitude/Precision equivalents; some Panasonic Toughbook CF-51 models; and the original Alienware Area 51M gaming laptop. However, in more recent times, UXGA is not used in laptops at all but rather in desktop monitors that have been made in sizes of 20 inches and 21.3 inches. Some 14-inch laptop LCDs with UXGA have also existed (such as the Dell Inspiron 4100), but these are very rare.
There are two different widescreen cousins of UXGA, one called UWXGA with 1600 × 768 (750) and one called WUXGA with 1920 × 1200 resolution.
=== 1920 × 1200 (WUXGA) ===
WUXGA stands for Widescreen Ultra Extended Graphics Array and is a display resolution of 1920 × 1200 pixels (2,304,000 pixels) with a 16:10 screen aspect ratio. It is a wide version of UXGA. By some producers it is called FHD+ because it is the next bigger resolution in vertical direction after FHD (1920 × 1080). WUXGA/FHD+ can be used for viewing high-definition television (HDTV) content, which uses a 16:9 aspect ratio and a 1280 × 720 (720p) or 1920 × 1080 (1080i or 1080p) resolution.
The 16:10 aspect ratio (as opposed to the 16:9 used in widescreen televisions) was chosen because this aspect ratio is appropriate for displaying two full pages of text side by side.
WUXGA resolution has a total of 2,304,000 pixels. One frame of uncompressed 8 BPC RGB WUXGA is 6.75 MiB (6.912 MB). Initially, it was available in widescreen CRTs such as the Sony GDM-FW900 and the Hewlett-Packard A7217A (introduced in 2003), and in 17-inch laptops. Most QXGA displays support 1920 × 1200. WUXGA is also available in some mobile phablet devices such as the Huawei Honor X2 Gem.
The next lower standard resolution (for widescreen) before it is WSXGA+, which is 1680 × 1050 pixels (1,764,000 pixels, or 30.61% fewer than WUXGA); the next higher resolution widescreen is an unnamed 2304 × 1440 resolution (supported by the above GDM-FW900 and A7217A) and then the more common WQXGA, which has 2560 × 1600 pixels (4,096,000 pixels, or 77.78% more than WUXGA).
=== 2048 × 1152 (QWXGA) ===
QWXGA (for Quad-WXGA or Quad Wide Extended Graphics Array) is a display resolution of 2048 × 1152 pixels with a 16:9 aspect ratio.
If taken as a starting point that WXGA has a display resolution of 1366 × 768 or 1280 × 800 a display with a size 4-times of WXGA should have 2732 × 1536 or 2560 × 1600 pixels, but the first is non-existent and the latter is named WQXGA. Conversely, the quarter of QWXGA (2048 × 1152) would have 1024 × 576 pixels but this is named WSVGA.
A few QWXGA LCD monitors were available in 2009 with 23- and 27-inch displays, such as the Acer B233HU (23-inch) and B273HU (27-inch), the Dell SP2309W, and the Samsung 2343BWX. As of 2011, most 2048 × 1152 monitors have been discontinued, and as of 2013, no major manufacturer produces monitors with this resolution.
=== 2048 × 1536 (QXGA) ===
QXGA (for Quad-XGA or Quad Extended Graphics Array) is a display resolution of 2048 × 1536 pixels with a 4:3 aspect ratio as XGA. The name comes from it having four times as many pixels as an XGA display of 1024 × 768.
Examples of LCDs with this resolution are the IBM T210 and the Eizo G33 and R31 screens, but in CRT monitors this resolution is much more common; some examples include the Sony F520, ViewSonic G225fB, NEC FP2141SB or Mitsubishi DP2070SB, Iiyama Vision Master Pro 514, and Dell and HP P1230. Of these monitors, none are still in production.
A related display size is WQXGA, which is a widescreen version.
IDTech manufactured a 15-inch QXGA IPS panel, used in the IBM ThinkPad R50p. NEC sold laptops with QXGA screens in 2002–05 for the Japanese market.
The iPad (from 3rd through 6th generation and Mini 2) also have a QXGA display.
=== 2560 × 1600 (WQXGA) ===
WQXGA (Wide Quad Extended Graphics Array) is a display resolution of 2560 × 1600 pixels with a 16:10 aspect ratio. The name implies a "wide QXGA" (QXGA 2048 × 1536) but it's not. Instead, WQXGA has exactly four times as many pixels as a WXGA (1280 × 800) hence the name "Quad-WXGA" would fit but QWXGA is defined as 2048 × 1152 pixels.
By some producers it is called QHD+ referring to QHD (2560 × 1440). (QHD+ is sometimes also used for the resolution 3200 × 1800 (QHD+).)
To obtain a vertical refresh rate higher than 40 Hz with DVI, this resolution requires dual-link DVI cables and devices. To avoid cable problems monitors are sometimes shipped with an appropriate dual link cable already plugged in. Many video cards support this resolution. One feature that was unique to the 30-inch WQXGA monitors is the ability to function as the centerpiece and main display of a three-monitor array of complementary aspect ratios, with two UXGA (1600 × 1200) 20-inch monitors turned vertically on either side. The resolutions are equal, and the size of the 1600 resolution edges is within a tenth of an inch (16-inch vs. 15.89999"), presenting a "picture window view" without the extreme lateral dimensions, small central panel, asymmetry, resolution differences, or dimensional difference of other three-monitor combinations. The resulting 4960 × 1600 composite image has a 3.1:1 aspect ratio. This also means one UXGA 20-inch monitor in portrait orientation can also be flanked by two 30-inch WQXGA monitors for a 6320 × 1600 composite image with an 11.85:3 (79:20, 3.95:1) aspect ratio.
An early consumer WQXGA monitor was the 30-inch Apple Cinema Display, unveiled by Apple in June 2004. At the time, dual-link DVI was uncommon on consumer hardware, so Apple partnered with Nvidia to develop a special graphics card that had two dual-link DVI ports, allowing simultaneous use of two 30-inch Apple Cinema Displays. The nature of this graphics card, being an add-in AGP card, meant that the monitors could only be used in a desktop computer, like the Power Mac G5, that could have the add-in card installed, and could not be immediately used with laptop computers that lacked this expansion capability.
In March 2009, Apple updated several Macintosh computers with a Mini DisplayPort adapter, such as the Mac mini and iMac. These allow an external connection to a 2560 × 1600 display.
In 2010, WQXGA made its debut in a handful of home theater projectors targeted at the Constant Height Screen application market. Both Digital Projection Inc and projectiondesign released models based on a Texas Instruments DLP chip with a native WQXGA resolution, alleviating the need for an anamorphic lens to achieve 1:2.35 image projection. Many manufacturers have 27–30-inch models that are capable of WQXGA, albeit at a much higher price than lower resolution monitors of the same size. Several mainstream WQXGA monitors are or were available with 30-inch displays, such as the Dell 3007WFP-HC, 3008WFP, U3011, U3014, UP3017, the Hewlett-Packard LP3065, the Gateway XHD3000, LG W3000H, and the Samsung 305T. Specialist manufacturers like NEC, Eizo, Planar Systems, Barco (LC-3001), and possibly others offer similar models. As of 2016, LG Display make a 10-bit 30-inch AH-IPS panel, with wide color gamut, used in monitors from Dell, NEC, HP, Lenovo and Iiyama.
Released in November 2012, Google's Nexus 10 is the first consumer tablet to feature WQXGA resolution. Before its release, the highest resolution available on a tablet was QXGA (2048 × 1536), available on the Apple iPad 3rd and 4th generations devices. Several Samsung Galaxy tablets, including the Note 10.1 (2014 Edition), Tab S 8.4, 10.5 and TabPRO 8.4, 10.1 and Note Pro 12.2, as well as the Gigaset QV1030, also feature a WQXGA resolution display.
In 2012, Apple released the 13 inch MacBook Pro with Retina Display that features a WQXGA display, and the new MacBook Air in 2018.
The LG Gram 17 introduced in 2019 uses a 17-inch WQXGA display.
=== 2560 × 2048 (QSXGA) ===
QSXGA (Quad Super Extended Graphics Array) is a display resolution of 2560 × 2048 pixels with a 5:4 aspect ratio. Grayscale monitors with a 2560 × 2048 resolution, primarily for medical use, are available from Planar Systems (Dome E5), Eizo (Radiforce G51), Barco (Nio 5, MP), WIDE (IF2105MP), IDTech (IAQS80F), and possibly others.
Recent medical displays such as Barco Coronis Fusion 10MP or NDS Dome S10 have a native panel resolution of 4096 × 2560. These are driven by two dual-link DVI or DisplayPort outputs. They can be considered to be two seamless virtual QSXGA displays as they have to be driven simultaneously by both dual-link DVI or DisplayPort since one dual-link DVI or DisplayPort cannot single-handedly display 10 megapixels. A similar resolution of 2560 × 1920 (4:3) was supported by a small number of CRT displays via VGA such as the Viewsonic P225f when paired with the right graphics card.
=== 2880 × 1800 (WQXGA+) ===
Doubling the width and height of WXGA+ 1440 × 900 for a higher pixel density yields WQXGA+.
=== 3200 × 2048 (WQSXGA) ===
WQSXGA (Wide Quad Super Extended Graphics Array) describes a display standard that can support a resolution up to 3200 × 2048 pixels, assuming a 25:16 (1.5625:1) aspect ratio. The Coronis Fusion 6MP DL by Barco supports a slightly wider 3280 × 2048 (approximately 16:10).
=== 3200 × 2400 (QUXGA) ===
QUXGA (Quad Ultra Extended Graphics Array) describes a display standard that can support a resolution up to 3200 × 2400 pixels, assuming a 4:3 aspect ratio.
=== 3840 × 2400 (WQUXGA) ===
WQUXGA (Wide Quad Ultra Extended Graphics Array) describes a display standard that supports a resolution of 3840 × 2400 pixels, which provides a 16:10 aspect ratio. This resolution is exactly four times 1920 × 1200 pixels (WUXGA).
Some manufacturers refer to this resolution as UHD+ because it has some additional lines compared to UHD (3840 × 2160).
Most display cards with a DVI connector are capable of supporting the 3840 × 2400 resolution. However, the maximum refresh rate will be limited by the number of DVI links connected to the monitor. 1, 2, or 4 DVI connectors are used to drive the monitor using various tile configurations. Only the IBM T221-DG5 and IDTech MD22292B5 support the use of dual-link DVI ports through an external converter box. Many systems using these monitors use at least two DVI connectors to send video to the monitor. These DVI connectors can be from the same graphics card, different graphics cards, or even different computers. Motion across the tile boundary(ies) can show tearing if the DVI links are not synchronized. The display panel can be updated at a speed between 0 Hz and 41 Hz (48 Hz for the IBM T221-DG5, -DGP, and IDTech MD22292B5). The refresh rate of the video signal can be higher than 41 Hz (or 48 Hz) but the monitor will not update the display any faster even if graphics card(s) do so.
In June 2001, WQUXGA was introduced in the IBM T220 LCD monitor using a LCD panel built by IDTech. LCD displays that support WQUXGA resolution include: IBM T220, IBM T221, Iiyama AQU5611DTBK, ViewSonic VP2290, ADTX MD22292B, and IDTech MD22292 (models B0, B1, B2, B5, C0, C2). IDTech was the original equipment manufacturer which sold these monitors to ADTX, IBM, Iiyama, and ViewSonic. However, none of the WQUXGA monitors (IBM, ViewSonic, Iiyama, ADTX) are in production anymore: they had prices that were well above even the higher end displays used by graphic professionals, and the lower refresh rates, 41 Hz and 48 Hz, made them less attractive for many applications.
== Unsystematic resolutions ==
Some hardware devices, smartphones in particular, use non-standard resolutions for their displays. Still, their aspect ratio or one of the dimensions is often derived from one of the standards. Many of them have bend edges, rounded corners, notches or islands for sensors, which may make some pixels invisible or unused.
After having used VGA-based 3∶2 resolutions HVGA (480 × 320) and "Retina" DVGA (960 × 640) for several years in their iPhone and iPod products with a screen diagonal of 9 cm or 3.5 inches, Apple started using more exotic variants when they adopted the 16∶9 aspect ratio to provide a consistent pixel density across screen sizes: first 1136 × 640 with the iPhone 5(c/s) and SE 1st for 10 cm or 4 inch screens, and later the 1-megapixel resolution of 1334 × 750 with the iPhone 6(s)/7/8 and SE 2nd/3rd for 12 cm or 4.7 inch screens, while devices with 14 cm or 5.5 inch screens used standard 1920 × 1080 with the iPhone 6(s)/7/8 Plus.
Keeping the pixel density of previous models, the iPhone X(s) and 11 Pro introduced a 2436 × 1125 resolution for 15 cm or 5.8 inch screens, while the iPhone XS Max and 11 Pro Max introduced a 2688 × 1242 resolution for 17 cm or 6.5 inch screens (with a notch) all at an aspect ratio of roughly 13∶6 or, for marketing, 19.5∶9.
Subsequent Apple smartphones and phablets stayed with that aspect ratio but increased screen size slightly with approximately constant pixel density. The resulting resolutions have longer sides divisible by 6 and hardly rounded shorter sides:
1792 × 828 (iPhone 11, Xr),
2532 × 1170 (12/13 (Pro), 14),
2556 × 1179 (14(Pro), 15 Pro),
2778 × 1284 (12/13 Pro Max, 14 Plus),
2796 × 1290 (14/15 Pro Max, 15 Plus).
The only Apple smartphone models that shared an ultra-wide 19½∶9 resolution with Android phones were the iPhone 12/13 Mini with 2340 × 1080.
Other manufacturers have also introduced phones with irregular display resolutions and aspect ratios, such as Samsung's various "Infinity" displays with 37∶18 = 18½∶9 aspect ratios (Galaxy S8/S9 and A8/A9) at resolutions of 2960 × 1440 and 2220 × 1080.
2160 × 1080 is a resolution used by many smartphones since 2018. It has an aspect ratio of 18:9, matching that of the Univisium film format.
Other phones feature an 19∶9 aspect ratio with resolutions like 3040 × 1440 (e.g. S10) and 2280 × 1080 (S10e).
Even wider resolutions with the same aspect ratio of 19½∶9 as iPhones are 3120 × 1440 (e.g. S24+) or 2340 × 1080 (Poco M3).
Some phones have an aspect ratio of ca. 20∶9 at resolutions like 2400 × 1080 (e.g. S10 Lite) and 3200 × 1440 (e.g. S20).
Phones with foldable displays, e.g. Samsung Galaxy Z series, usually have non-systematic resolutions and aspect ratios, which are either roughly square when folded along the longer edge (Fold) or extremely tall when folded along the smaller edge (Flip).
Some air traffic control monitors use displays with a resolution of 2048 × 2048, with an aspect ratio of 1:1, and similar consumer monitors at resolution of 1920 × 1920 are also available aimed primarily at productivity tasks.
== See also ==
Dot pitch
List of common display resolutions
Pixel density
Ultrawide formats for history and comparison of video formats and displays, which are growing wider
== References == | Wikipedia/Display_resolution_standards |
Professional Graphics Controller (PGC, often called Professional Graphics Adapter and sometimes Professional Graphics Array) is a graphics card manufactured by IBM for PCs. It consists of three interconnected PCBs, and contains its own processor and memory. The PGC was, at the time of its release, the most advanced graphics card for the IBM XT and aimed for tasks such as CAD.
Introduced in 1984, the Professional Graphics Controller offered a maximum resolution of 640 × 480 with 256 colors on an analog RGB monitor, at a refresh rate of 60 hertz—a higher resolution and color depth than CGA and EGA supported. This mode is not BIOS-supported. It was intended for the computer-aided design market and included 320 KB of display RAM and an on-board Intel 8088 microprocessor. The 8088 ran software routines such as "draw polygon" and "fill area" from an on-board 64 KB ROM so that the host CPU didn't need to load and run these routines itself. While never widespread in consumer-class personal computers, its US$2,995 (equivalent to $9,100 in 2024) list price, plus $1,295 display, compared favorably to US$50,000 dedicated CAD workstations of the time (even when the $4,995 price of a PC XT Model 87 was included). It was discontinued in 1987 with the arrival of VGA and 8514.
== Software support ==
The board was targeted at the CAD market, therefore limited software support is to be expected. The only software systems known to support the PGC are IBM's Graphical Kernel System, P-CAD 4.5, Canyon State Systems CompuShow and AutoCAD 2.5.
== Output capabilities ==
PGC supports:
640 × 480 with 256 colors from a palette of 4,096 (12-bit RGB palette, or 4 bits per color component).
Color Graphics Adapter text and graphics modes. Text modes use a font with 8×16-pixel character cells and have 400 rows of pixels.
There are six possible color arrangements:
Default 256-colour palette - Low 4 bits intensity, high 4 bits colour;
16-colour palette - Makes the PGC behave as two 16-colour planes. If high 4 bits are 0, low 4 bits are colour; otherwise, high 4 bits are colour;
2-3-3 palette (Palette 2) - Bits 6-7 red, bits 3-5 green, bits 0-2 blue;
3-2-3 palette (Palette 3) - Bits 5-7 red, bits 3-4 green, bits 0-2 blue;
3-3-2 palette (Palette 4) - Bits 5-7 red, bits 2-4 green; bits 0-1 blue;
6x6x6 colour cube - six equally spaced shades of red, green, and blue.
== Operation ==
The display adapter was composed of three physical circuit boards (one with the on-board microprocessor, firmware ROMs and video output connector, one providing CGA emulation, and the third mostly carrying RAM) and occupied two adjacent expansion slots on the XT or AT motherboard or the Expansion Unit; the third card was located in between the two slots. The PGC could not be used in the original IBM PC without the 5161 Expansion Unit due to the different spacing of its slots.
In addition to its native 640 × 480 mode, the PGC optionally supported the documented text and graphics modes of the Color Graphics Adapter, which could be enabled using an onboard jumper. However, it was only partly register-compatible with CGA.
== Related monitor ==
The PGC's matching display was the IBM 5175, an analog RGB monitor that is unique to it and not compatible with any other video card without modification. With hardware modification, the 5175 can be used with VGA, Macintosh, and various other analog RGB video sources. Some surplus 5175s in VGA-converted form were still sold by catalog retailers such as COMB (Close Out Merchant Buyers) as late as the early 1990s.
== Hardware clones ==
Matrox PG-640, PG-1280 and QG-640 (for the DEC MicroVAX)
Dell NEC MVA-1024 card
Everex EPGA
Orchid Technology TurboPGA
Vermont Microsystems IM-640, IM-1024
== See also ==
PC/GX
List of defunct graphics chips and card companies
== References ==
Notes
== External links ==
Professional Graphics Controller: Notes - Pictures and programming information | Wikipedia/Professional_Graphics_Controller |
The Hercules Graphics Card (HGC) is a computer graphics controller formerly made by Hercules Computer Technology, Inc. that combines IBM's text-only MDA display standard with a bitmapped graphics mode, also offering a parallel printer port. This allows the HGC to offer both high-quality text and graphics from a single card.
The HGC was very popular and became a widely supported de facto display standard on IBM PC compatibles. The HGC standard was used long after more technically capable systems had entered the market, especially on dual-monitor setups.
== History ==
The Hercules Graphics Card was released to fill a gap in the IBM video product lineup. When the IBM Personal Computer was launched in 1981, it had two graphics cards available: the Color Graphics Adapter (CGA) and the Monochrome Display And Printer Adapter (MDA). CGA offered low-resolution (320 × 200) color graphics and medium-resolution (640 × 200) monochrome graphics, while MDA offers a sharper text mode (equivalent to 720 × 350) but has no per-pixel addressing modes and is limited to a fixed character set.
These adapters were quickly found to be inadequate by the market, creating a demand for a card that offers high-resolution graphics and text. The founder of Hercules Computer Technology, Van Suwannukul, created the Hercules Graphics Card so that he could work on his doctoral thesis on an IBM PC using the Thai alphabet, impossible with the low resolution of CGA or the fixed character set of MDA. It initially retailed in 1982 for $499.
== Hardware design ==
The original HGC is an 8-bit ISA card with 64 KB of RAM, visible on the board as eight 4164 RAM chips, and a DE-9 output compatible with the IBM monochrome monitor used with the MDA. Like the MDA, it includes a parallel interface for attaching a printer.
The video output is 5 V TTL, as with the MDA card. Nominally, the Hercules card provides a horizontal scanning frequency of 18.425 ± 0.500 kHz and 50 Hz vertical. It runs at two slightly different sets of frequencies depending on whether in text or graphics mode, providing a different vertical refresh rate and a different aspect ratio via a different pixel clock and number of scanlines.
== Capabilities ==
The Hercules card provides two modes:
80 × 25 text mode with 9 × 14 pixel font (effective resolution of 720 × 350, MDA-compatible)
720 × 348 graphics mode (pixel-addressable graphics)
The text mode of the Hercules card uses the same signal timing as the MDA text mode.
The Hercules graphics mode is similar to the CGA high-resolution (640 × 200) two-color mode; the video buffer contains a packed-pixel bitmap (eight pixels per byte, one bit per pixel) with the same byte format—including the pixel-to-bit mapping and byte order—as the CGA two-color graphics mode, and the video buffer is also split into interleaved banks, each 8 KB in size.
However, because in the Hercules graphics mode there are more than 256 scanlines and the display buffer size is nearly 32 KB (instead of 16 KB as in all CGA graphics modes), four interleaved banks are used in the Hercules mode instead of two as in the CGA modes. Also, to represent 720 pixels per line instead of 640 as on the CGA, each scanline has 90 bytes of pixel data instead of 80.
The 64 KB RAM of the HGC can hold two graphics display pages. Either page can be selected for display by setting a single bit in the Mode Control Register. Another bit, in a configuration register exclusive to the HGC, determines whether the second 32 KB of RAM on the HGC is accessible to the CPU at the base address B8000h. This bit is reset at system reset (e.g. power-on) so that the card does not conflict with a CGA or other color card at address B8000h.
== Use ==
In text mode, the HGC appears exactly like an MDA card. Graphics mode requires new techniques to use. Unlike the MDA and CGA, the PC BIOS provides no intrinsic support for the HGC. Hercules developed extensions, called HBASIC, for IBM Advanced BASIC to add HGC support and Hercules cards came with Graph X, a software library for Hercules graphical-mode support and geometric primitives.
Popular IBM PC programs such as Lotus 1-2-3 spreadsheet, AutoCAD computer-aided drafting, Pagemaker and Xerox Ventura desktop publishing, and Microsoft Flight Simulator 2.0 came with their own drivers to use the Hercules graphics mode.
Though the graphics mode of the Hercules card is not CGA-compatible, it is similar enough to the two CGA graphics modes that with the use of third-party terminate-and-stay-resident programs it can also work with programs written for the CGA card's standard graphics modes. As the Hercules card does not actually have color-generating circuitry, nor can it connect to a color monitor, color appears as simulated grayscale in varying dithering patterns.
Clones of the Hercules appeared, including generic models at very low prices, usually without the printer port. Hercules advertisements implied that use of generic Hercules clones can damage the monitor.
== Reception ==
The Hercules Graphics Card was very successful, especially after Lotus 1-2-3 supported it, with one-half million units sold by 1985. As of June 1986 Hercules Computer Technology had 18% of the graphics card market, second to IBM. Hercules-compatible graphics cards shipped as standard hardware with most PC clones. As a de facto standard, support in software was widespread.
== Card versions ==
The Hercules Graphics Card had several versions.
=== Hercules Graphics Card ===
Several updated versions of the original Hercules Graphics Card exist. The original board from 1982 is referenced as GB100, with updated versions in 1983 (GB101), 1984 (GB102) and 1988 (GB102Z).
=== Hercules Graphics Card Plus ===
The Hercules Graphics Card Plus or HGC+ (GB112) was released in June 1986 at an original retail price of $299. It was an enhancement of the HGC, adding support for redefinable fonts called RAMFONT in MDA-compatible text mode. It was based around a specialty chip designed by Hercules Computer Technology, unlike the original Hercules Graphics Card, which used standard components. Software support included Lotus 1-2-3 v2, Symphony 1.1, Framework II and Microsoft Word 3.
=== Hercules Network Card Plus ===
In 1988 Hercules released the Hercules Network Card Plus, (HNC NB112) a variant of the Graphics Card Plus with an integrated TOPS/FlashTalk-compatible network adapter. Like the HGC+, it supported RAMFONT, but lacked a printer port.
=== Hercules InColor Card ===
The InColor Card (GB222) was introduced in April 1987. It included color capabilities similar to the EGA, with 16 colors from a palette of 64. It retained the same two modes (80 × 25 text with redefinable fonts and 720 × 348 graphics), and was backward-compatible with software written for the earlier monochrome Hercules cards.
=== Hercules Color Card ===
The Hercules Color Card (GB200) was a CGA-compatible video board and should not be confused with the InColor Card. This board could coexist with the HGC and still allow both graphics pages to be used. It would detect when the second graphics page was selected and disable access to its own memory, which would otherwise have been at the same addresses. A version without printer port exists
=== Hercules Text Card ===
The Hercules Text Card was a text-only MDA clone, but offered a parallel printer port.
== Clone boards ==
Other boards offered Hercules compatibility.
SiS 86C12, 86C22
ATI Small Wonder Graphics Solution, 18700, Graphics Solution Plus
Tamarack Microelectronics TD3088A, TD3088A2, TD3088A3, TD3010, RY-3301, TD3010
Yamaha V6366C-F, V6363-F, V6363
Winbond W86855AF, W86855AF
NEC μPD65042GD
Tseng Labs ET1000-A
DFI MG-150
Hitachi HD6445P4, HD6845SP
RAM MCG2502, MCG2502
Proton PT6121T
Acer M3127
Sigma Designs 53C101+53C280A
CM607P
AST Research AST Preview!
Certain later models of the Tandy 1000 (such as the 1000 TL and SL) and the Epson Equity contained circuitry built into their CPU boards that supported Hercules display modes in addition to their standard CGA modes.
== See also ==
Orchid Graphics Adapter
Plantronics Colorplus
IBM Monochrome Display Adapter
Color Graphics Adapter
Light pen
List of display interfaces
List of defunct graphics chips and card companies
== References ==
== Further reading == | Wikipedia/Hercules_Graphics_Card |
The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as non-randomness or data compression; thus this interpretation also applies to this index. In addition, interpretation of biodiversity as entropy has also been proposed leading to uses of generalized entropy to quantify biodiversity.
== Formula ==
The formula for general entropy for real values of
α
{\displaystyle \alpha }
is:
G
E
(
α
)
=
{
1
N
α
(
α
−
1
)
∑
i
=
1
N
[
(
y
i
y
¯
)
α
−
1
]
,
α
≠
0
,
1
,
1
N
∑
i
=
1
N
y
i
y
¯
ln
y
i
y
¯
,
α
=
1
,
−
1
N
∑
i
=
1
N
ln
y
i
y
¯
,
α
=
0.
{\displaystyle GE(\alpha )={\begin{cases}{\frac {1}{N\alpha (\alpha -1)}}\sum _{i=1}^{N}\left[\left({\frac {y_{i}}{\overline {y}}}\right)^{\alpha }-1\right],&\alpha \neq 0,1,\\{\frac {1}{N}}\sum _{i=1}^{N}{\frac {y_{i}}{\overline {y}}}\ln {\frac {y_{i}}{\overline {y}}},&\alpha =1,\\-{\frac {1}{N}}\sum _{i=1}^{N}\ln {\frac {y_{i}}{\overline {y}}},&\alpha =0.\end{cases}}}
where N is the number of cases (e.g., households or families),
y
i
{\displaystyle y_{i}}
is the income for case i and
α
{\displaystyle \alpha }
is a parameter which regulates the weight given to distances between incomes at different parts of the income distribution. For large
α
{\displaystyle \alpha }
the index is especially sensitive to the existence of large incomes, whereas for small
α
{\displaystyle \alpha }
the index is especially sensitive to the existence of small incomes.
== Properties ==
The GE index satisfies the following properties:
The index is symmetric in its arguments:
G
E
(
α
;
y
1
,
…
,
y
N
)
=
G
E
(
α
;
y
σ
(
1
)
,
…
,
y
σ
(
N
)
)
{\displaystyle GE(\alpha ;y_{1},\ldots ,y_{N})=GE(\alpha ;y_{\sigma (1)},\ldots ,y_{\sigma (N)})}
for any permutation
σ
{\displaystyle \sigma }
.
The index is non-negative, and is equal to zero only if all incomes are the same:
G
E
(
α
;
y
1
,
…
,
y
N
)
=
0
{\displaystyle GE(\alpha ;y_{1},\ldots ,y_{N})=0}
iff
y
i
=
μ
{\displaystyle y_{i}=\mu }
for all
i
{\displaystyle i}
.
The index satisfies the principle of transfers: if a transfer
Δ
>
0
{\displaystyle \Delta >0}
is made from an individual with income
y
i
{\displaystyle y_{i}}
to another one with income
y
j
{\displaystyle y_{j}}
such that
y
i
−
Δ
>
y
j
+
Δ
{\displaystyle y_{i}-\Delta >y_{j}+\Delta }
, then the inequality index cannot increase.
The index satisfies population replication axiom: if a new population is formed by replicating the existing population an arbitrary number of times, the inequality remains the same:
G
E
(
α
;
{
y
1
,
…
,
y
N
}
,
…
,
{
y
1
,
…
,
y
N
}
)
=
G
E
(
α
;
y
1
,
…
,
y
N
)
{\displaystyle GE(\alpha ;\{y_{1},\ldots ,y_{N}\},\ldots ,\{y_{1},\ldots ,y_{N}\})=GE(\alpha ;y_{1},\ldots ,y_{N})}
The index satisfies mean independence, or income homogeneity, axiom: if all incomes are multiplied by a positive constant, the inequality remains the same:
G
E
(
α
;
y
1
,
…
,
y
N
)
=
G
E
(
α
;
k
y
1
,
…
,
k
y
N
)
{\displaystyle GE(\alpha ;y_{1},\ldots ,y_{N})=GE(\alpha ;ky_{1},\ldots ,ky_{N})}
for any
k
>
0
{\displaystyle k>0}
.
The GE indices are the only additively decomposable inequality indices. This means that overall inequality in the population can be computed as the sum of the corresponding GE indices within each group, and the GE index of the group mean incomes:
G
E
(
α
;
y
g
i
:
g
=
1
,
…
,
G
,
i
=
1
,
…
,
N
g
)
=
∑
g
=
1
G
w
g
G
E
(
α
;
y
g
1
,
…
,
y
g
N
g
)
+
G
E
(
α
;
μ
1
,
…
,
μ
G
)
{\displaystyle GE(\alpha ;y_{gi}:g=1,\ldots ,G,i=1,\ldots ,N_{g})=\sum _{g=1}^{G}w_{g}GE(\alpha ;y_{g1},\ldots ,y_{gN_{g}})+GE(\alpha ;\mu _{1},\ldots ,\mu _{G})}
where
g
{\displaystyle g}
indexes groups,
i
{\displaystyle i}
, individuals within groups,
μ
g
{\displaystyle \mu _{g}}
is the mean income in group
g
{\displaystyle g}
, and the weights
w
g
{\displaystyle w_{g}}
depend on
μ
g
,
μ
,
N
{\displaystyle \mu _{g},\mu ,N}
and
N
g
{\displaystyle N_{g}}
. The class of the additively-decomposable inequality indices is very restrictive. Many popular indices, including Gini index, do not satisfy this property.
== Relationship to other indices ==
An Atkinson index for any inequality aversion parameter can be derived from a generalized entropy index under the restriction that
ϵ
=
1
−
α
{\displaystyle \epsilon =1-\alpha }
- i.e. an Atkinson index with high inequality aversion is derived from a GE index with small
α
{\displaystyle \alpha }
.
The formula for deriving an Atkinson index with inequality aversion parameter
ϵ
{\displaystyle \epsilon }
under the restriction
ϵ
=
1
−
α
{\displaystyle \epsilon =1-\alpha }
is given by:
A
=
1
−
[
ϵ
(
ϵ
−
1
)
G
E
(
α
)
+
1
]
(
1
/
(
1
−
ϵ
)
)
ϵ
≠
1
{\displaystyle A=1-[\epsilon (\epsilon -1)GE(\alpha )+1]^{(1/(1-\epsilon ))}\qquad \epsilon \neq 1}
A
=
1
−
e
−
G
E
(
α
)
ϵ
=
1
{\displaystyle A=1-e^{-GE(\alpha )}\qquad \epsilon =1}
Note that the generalized entropy index has several income inequality metrics as special cases. For example, GE(0) is the mean log deviation a.k.a. Theil L index, GE(1) is the Theil T index, and GE(2) is half the squared coefficient of variation.
== See also ==
Atkinson index
Gini coefficient
Hoover index (a.k.a. Robin Hood index)
Income inequality metrics
Lorenz curve
Rényi entropy
Suits index
Theil index
== References == | Wikipedia/Generalized_entropy_index |
In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function
f
:
R
d
→
R
{\displaystyle f:\mathbb {R} ^{d}\rightarrow \mathbb {R} }
that for all
x
,
y
∈
R
d
{\displaystyle x,y\in \mathbb {R} ^{d}}
such that
x
{\displaystyle x}
is majorized by
y
{\displaystyle y}
, one has that
f
(
x
)
≤
f
(
y
)
{\displaystyle f(x)\leq f(y)}
. Named after Issai Schur, Schur-convex functions are used in the study of majorization.
A function f is 'Schur-concave' if its negative, −f, is Schur-convex.
== Properties ==
Every function that is convex and symmetric (under permutations of the arguments) is also Schur-convex.
Every Schur-convex function is symmetric, but not necessarily convex.
If
f
{\displaystyle f}
is (strictly) Schur-convex and
g
{\displaystyle g}
is (strictly) monotonically increasing, then
g
∘
f
{\displaystyle g\circ f}
is (strictly) Schur-convex.
If
g
{\displaystyle g}
is a convex function defined on a real interval, then
∑
i
=
1
n
g
(
x
i
)
{\displaystyle \sum _{i=1}^{n}g(x_{i})}
is Schur-convex.
=== Schur–Ostrowski criterion ===
If f is symmetric and all first partial derivatives exist, then
f is Schur-convex if and only if
(
x
i
−
x
j
)
(
∂
f
∂
x
i
−
∂
f
∂
x
j
)
≥
0
{\displaystyle (x_{i}-x_{j})\left({\frac {\partial f}{\partial x_{i}}}-{\frac {\partial f}{\partial x_{j}}}\right)\geq 0}
for all
x
∈
R
d
{\displaystyle x\in \mathbb {R} ^{d}}
holds for all
1
≤
i
,
j
≤
d
{\displaystyle 1\leq i,j\leq d}
.
== Examples ==
f
(
x
)
=
min
(
x
)
{\displaystyle f(x)=\min(x)}
is Schur-concave while
f
(
x
)
=
max
(
x
)
{\displaystyle f(x)=\max(x)}
is Schur-convex. This can be seen directly from the definition.
The Shannon entropy function
∑
i
=
1
d
P
i
⋅
log
2
1
P
i
{\displaystyle \sum _{i=1}^{d}{P_{i}\cdot \log _{2}{\frac {1}{P_{i}}}}}
is Schur-concave.
The Rényi entropy function is also Schur-concave.
x
↦
∑
i
=
1
d
x
i
k
,
k
≥
1
{\displaystyle x\mapsto \sum _{i=1}^{d}{x_{i}^{k}},k\geq 1}
is Schur-convex if
k
≥
1
{\displaystyle k\geq 1}
, and Schur-concave if
k
∈
(
0
,
1
)
{\displaystyle k\in (0,1)}
.
The function
f
(
x
)
=
∏
i
=
1
d
x
i
{\displaystyle f(x)=\prod _{i=1}^{d}x_{i}}
is Schur-concave, when we assume all
x
i
>
0
{\displaystyle x_{i}>0}
. In the same way, all the elementary symmetric functions are Schur-concave, when
x
i
>
0
{\displaystyle x_{i}>0}
.
A natural interpretation of majorization is that if
x
≻
y
{\displaystyle x\succ y}
then
x
{\displaystyle x}
is less spread out than
y
{\displaystyle y}
. So it is natural to ask if statistical measures of variability are Schur-convex. The variance and standard deviation are Schur-convex functions, while the median absolute deviation is not.
A probability example: If
X
1
,
…
,
X
n
{\displaystyle X_{1},\dots ,X_{n}}
are exchangeable random variables, then the function
E
∏
j
=
1
n
X
j
a
j
{\displaystyle {\text{E}}\prod _{j=1}^{n}X_{j}^{a_{j}}}
is Schur-convex as a function of
a
=
(
a
1
,
…
,
a
n
)
{\displaystyle a=(a_{1},\dots ,a_{n})}
, assuming that the expectations exist.
The Gini coefficient is strictly Schur convex.
== References ==
== See also ==
Quasiconvex function | Wikipedia/Schur-concave_function |
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group.
== Factor of automorphy ==
In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group
G
{\displaystyle G}
acts on a complex-analytic manifold
X
{\displaystyle X}
. Then,
G
{\displaystyle G}
also acts on the space of holomorphic functions from
X
{\displaystyle X}
to the complex numbers. A function
f
{\displaystyle f}
is termed an automorphic form if the following holds:
f
(
g
.
x
)
=
j
g
(
x
)
f
(
x
)
{\displaystyle f(g.x)=j_{g}(x)f(x)}
where
j
g
(
x
)
{\displaystyle j_{g}(x)}
is an everywhere nonzero holomorphic function. Equivalently, an automorphic form is a function whose divisor is invariant under the action of
G
{\displaystyle G}
.
The factor of automorphy for the automorphic form
f
{\displaystyle f}
is the function
j
{\displaystyle j}
. An automorphic function is an automorphic form for which
j
{\displaystyle j}
is the identity.
Some facts about factors of automorphy:
Every factor of automorphy is a cocycle for the action of
G
{\displaystyle G}
on the multiplicative group of everywhere nonzero holomorphic functions.
The factor of automorphy is a coboundary if and only if it arises from an everywhere nonzero automorphic form.
For a given factor of automorphy, the space of automorphic forms is a vector space.
The pointwise product of two automorphic forms is an automorphic form corresponding to the product of the corresponding factors of automorphy.
Relation between factors of automorphy and other notions:
Let
Γ
{\displaystyle \Gamma }
be a lattice in a Lie group
G
{\displaystyle G}
. Then, a factor of automorphy for
Γ
{\displaystyle \Gamma }
corresponds to a line bundle on the quotient group
G
/
Γ
{\displaystyle G/\Gamma }
. Further, the automorphic forms for a given factor of automorphy correspond to sections of the corresponding line bundle.
The specific case of
Γ
{\displaystyle \Gamma }
a subgroup of SL(2, R), acting on the upper half-plane, is treated in the article on automorphic factors.
== Examples ==
Kleinian group – Discrete group of Möbius transformations
Elliptic modular function – Modular function in mathematicsPages displaying short descriptions of redirect targets
Modular function – Analytic function on the upper half-plane with a certain behavior under the modular groupPages displaying short descriptions of redirect targets
Complex torus
== References ==
A.N. Parshin (2001) [1994], "Automorphic Form", Encyclopedia of Mathematics, EMS Press
Andrianov, A.N.; Parshin, A.N. (2001) [1994], "Automorphic Function", Encyclopedia of Mathematics, EMS Press
Ford, Lester R. (1929), Automorphic functions, New York: McGraw-Hill, JFM 55.0810.04
Fricke, Robert; Klein, Felix (1897), Vorlesungen über die Theorie der automorphen Functionen (in German), vol. I. Die gruppentheoretischen Grundlagen., Leipzig: B. G. Teubner, JFM 28.0334.01
Fricke, Robert; Klein, Felix (1912), Vorlesungen über die Theorie der automorphen Functionen. Zweiter Band: Die funktionentheoretischen Ausführungen und die Anwendungen. 1. Lieferung: Engere Theorie der automorphen Funktionen. (in German), Leipzig: B. G. Teubner., JFM 32.0430.01 | Wikipedia/Automorphic_function |
In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function
f
:
R
d
→
R
{\displaystyle f:\mathbb {R} ^{d}\rightarrow \mathbb {R} }
that for all
x
,
y
∈
R
d
{\displaystyle x,y\in \mathbb {R} ^{d}}
such that
x
{\displaystyle x}
is majorized by
y
{\displaystyle y}
, one has that
f
(
x
)
≤
f
(
y
)
{\displaystyle f(x)\leq f(y)}
. Named after Issai Schur, Schur-convex functions are used in the study of majorization.
A function f is 'Schur-concave' if its negative, −f, is Schur-convex.
== Properties ==
Every function that is convex and symmetric (under permutations of the arguments) is also Schur-convex.
Every Schur-convex function is symmetric, but not necessarily convex.
If
f
{\displaystyle f}
is (strictly) Schur-convex and
g
{\displaystyle g}
is (strictly) monotonically increasing, then
g
∘
f
{\displaystyle g\circ f}
is (strictly) Schur-convex.
If
g
{\displaystyle g}
is a convex function defined on a real interval, then
∑
i
=
1
n
g
(
x
i
)
{\displaystyle \sum _{i=1}^{n}g(x_{i})}
is Schur-convex.
=== Schur–Ostrowski criterion ===
If f is symmetric and all first partial derivatives exist, then
f is Schur-convex if and only if
(
x
i
−
x
j
)
(
∂
f
∂
x
i
−
∂
f
∂
x
j
)
≥
0
{\displaystyle (x_{i}-x_{j})\left({\frac {\partial f}{\partial x_{i}}}-{\frac {\partial f}{\partial x_{j}}}\right)\geq 0}
for all
x
∈
R
d
{\displaystyle x\in \mathbb {R} ^{d}}
holds for all
1
≤
i
,
j
≤
d
{\displaystyle 1\leq i,j\leq d}
.
== Examples ==
f
(
x
)
=
min
(
x
)
{\displaystyle f(x)=\min(x)}
is Schur-concave while
f
(
x
)
=
max
(
x
)
{\displaystyle f(x)=\max(x)}
is Schur-convex. This can be seen directly from the definition.
The Shannon entropy function
∑
i
=
1
d
P
i
⋅
log
2
1
P
i
{\displaystyle \sum _{i=1}^{d}{P_{i}\cdot \log _{2}{\frac {1}{P_{i}}}}}
is Schur-concave.
The Rényi entropy function is also Schur-concave.
x
↦
∑
i
=
1
d
x
i
k
,
k
≥
1
{\displaystyle x\mapsto \sum _{i=1}^{d}{x_{i}^{k}},k\geq 1}
is Schur-convex if
k
≥
1
{\displaystyle k\geq 1}
, and Schur-concave if
k
∈
(
0
,
1
)
{\displaystyle k\in (0,1)}
.
The function
f
(
x
)
=
∏
i
=
1
d
x
i
{\displaystyle f(x)=\prod _{i=1}^{d}x_{i}}
is Schur-concave, when we assume all
x
i
>
0
{\displaystyle x_{i}>0}
. In the same way, all the elementary symmetric functions are Schur-concave, when
x
i
>
0
{\displaystyle x_{i}>0}
.
A natural interpretation of majorization is that if
x
≻
y
{\displaystyle x\succ y}
then
x
{\displaystyle x}
is less spread out than
y
{\displaystyle y}
. So it is natural to ask if statistical measures of variability are Schur-convex. The variance and standard deviation are Schur-convex functions, while the median absolute deviation is not.
A probability example: If
X
1
,
…
,
X
n
{\displaystyle X_{1},\dots ,X_{n}}
are exchangeable random variables, then the function
E
∏
j
=
1
n
X
j
a
j
{\displaystyle {\text{E}}\prod _{j=1}^{n}X_{j}^{a_{j}}}
is Schur-convex as a function of
a
=
(
a
1
,
…
,
a
n
)
{\displaystyle a=(a_{1},\dots ,a_{n})}
, assuming that the expectations exist.
The Gini coefficient is strictly Schur convex.
== References ==
== See also ==
Quasiconvex function | Wikipedia/Schur-convex_function |
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