Add optional target physical-range mapping: README.md

README.md

@@ -175,6 +175,53 @@ Important encoding note:
 - Mueller matrix tensors are stored as measured/processed values, not forcibly
   clipped to `[-1, 1]`.
 
+### Optional Mapping From Grayscale Targets to Physical Ranges
+
+For rows whose `target_encoding` is
+`png_uint8_normalized_to_float32_0_1`, the stored target tensor is a normalized
+grayscale representation in `[0, 1]`. To map these values back to the nominal
+physical parameter ranges used in the paper, apply:
+
+```python
+import numpy as np
+
+TARGET_CHANNELS = ["D", "Delta", "eta", "theta", "psi", "R"]
+
+
+def normalized_modalities_to_physical(target, channel_axis=0, clip=False):
+    """Map normalized grayscale modalities to nominal physical ranges.
+
+    Use this only for targets encoded as
+    ``png_uint8_normalized_to_float32_0_1``. If a split already stores physical
+    Lu-Chipman values, do not apply this conversion again.
+    """
+    target = np.asarray(target, dtype=np.float32)
+    values = np.moveaxis(target, channel_axis, 0)
+    if values.shape[0] != 6:
+        raise ValueError(f"Expected 6 target channels, got shape {target.shape}")
+
+    g = np.clip(values, 0.0, 1.0) if clip else values
+    physical = np.empty_like(g, dtype=np.float32)
+    physical[0] = g[0]                      # D: [0, 1]
+    physical[1] = g[1]                      # Delta: [0, 1]
+    physical[2] = np.pi * g[2]              # eta: [0, pi)
+    physical[3] = np.pi * (g[3] - 0.5)      # theta: [-pi/2, pi/2)
+    physical[4] = np.pi * (g[4] - 0.5)      # psi: [-pi/2, pi/2)
+    physical[5] = np.pi * g[5]              # R: [0, pi)
+    return np.moveaxis(physical, 0, channel_axis)
+```
+
+The inverse mapping is:
+
+```text
+D_gray = D
+Delta_gray = Delta
+eta_gray = eta / pi
+theta_gray = theta / pi + 0.5
+psi_gray = psi / pi + 0.5
+R_gray = R / pi
+```
+
 ## Reference Label Generation
 
 The target modalities are generated using Lu-Chipman decomposition from measured