zern_generator.py

import math

import matplotlib.pyplot as plt
import numpy as np
from zernike import RZern
import utils

SAMPLE_SIZE = 256
span = (-1, 1)



class Zernike:
    def __init__(self):
        self.set_image_params()
        self.term = [
            "PISTON",
            "V-TILT",
            "H-TILT",
            "O-PR-ASTIGMATISM",
            "DEFOCUS",
            "V-PR-ASTIGMATISM",
            "V-TREFOIL",
            "V-PR-COMA",
            "H-PR-COMA",
            "O-TREFOIL",
            "O-QUADRAFOIL",
            "O-SC-ASTIGMATISM",
            "P-SPHERICAL",
            "V-SC-ASTIGMATISM",
            "V-QUADRAFOIL",
            
            # "V-SC-COMA",
            # "H-SC-COMA",
            # "V-SC-TREFOIL",
            # "O-SC-TREFOIL",
            # "O-PENTAFOIL",
            # "V-PENTAFOIL"
            ]
        
    def set_image_params(self, span = (-(10 ** -2), 10 ** -2), npix = 2**8):
        self.span = span
        self.npix = npix
        ddx = np.linspace(*self.span, self.npix)
        ddy = np.linspace(*self.span, self.npix)
        self.xv, self.yv = np.meshgrid(ddx, ddy) 
    
    def generate_zern_screen(self, zerns, norm_radius = 1):
        zerns = self._osa_to_noll_list(zerns)
        num_zerns = len(zerns)
        mask = utils.circle_mask(self.xv, self.yv, norm_radius)
        
        
        degree = math.ceil((-3 + math.sqrt(8 * num_zerns + 1)) / 2)
        zerns = list(zerns) + [0] * int((((degree + 1) * (degree + 2) / 2) - len(zerns)))
        cart = RZern(degree)
        cart.make_cart_grid(self.xv/norm_radius, self.yv/norm_radius)
        screen =  np.array(cart.eval_grid(np.array(zerns), matrix=True))
        screen[mask == 0] = 0
        screen[np.isnan(screen)] = 0
        return screen

    def generate_zern_wavefront_fig(self, *zerns):
        Phi = self.generate_zern_screen(zerns)
        # Phi[np.isnan(Phi)] = 0
        fig_2d, ax_2d = plt.subplots()
        fig_3d, ax_3d = plt.subplots(subplot_kw={"projection": "3d"})
        a = ax_2d.imshow(Phi, extent=(*span, *span), cmap='gray')
        ax_3d.plot_surface(self.xv, self.yv, Phi)
        fig_2d.colorbar(a)
        plt.show()
        return fig_2d, fig_3d
    
    def add_defocus(self, defocus_value, zernikes):
        zernikes = list(zernikes)
        if len(zernikes) < 5:
            zernikes += [0] * (5-len(zernikes))
        zernikes[4] += defocus_value
        return zernikes


    def generate_batch(self, resolution):
        #term = ["PISTON","V-TILT","H-TILT","DEFOCUS","O-PR-ASTIGMATISM","V-PR-ASTIGMATISM","V-PR-COMA","H-PR-COMA","V-TREFOIL","O-TREFOIL","P-SPHERICAL","O-SC-ASTIGMATISM","V-SC-ASTIGMATISM","V-QUADRAFOIL","O-QUADRAFOIL","V-SC-COMA","H-SC-COMA","V-SC-TREFOIL","O-SC-TREFOIL","O-PENTAFOIL","V-PENTAFOIL"]
        fig = plt.figure()
        fig.set_figwidth(30)
        fig.set_figheight(20)
        zern_index = 1
        for i in range(5):
            for j in range(6):
                if j > i:
                    continue

                zern = [0] * (zern_index - 1) + [1]
                ax = plt.subplot2grid((5, 6), (i, j))
                Phi = self.generate_zern_screen(zern, norm_radius=self.span[1]/2)
                ax.set_title(f" \n Zernike {zern_index-1} — {self.term[zern_index-1]} ")
                ax.imshow(Phi, extent=(*span, *span), cmap='gray')

                zern_index += 1
        plt.show()
        return fig


    def _osa_to_mn(self, idx):
        n = math.ceil((-3 + math.sqrt((9 + 8 * idx))) / 2)
        m = 2 * idx - n * (n + 2)
        return m, n

    def _mn_to_noll(self, m, n):
        first = (n * (n + 1)) // 2
        second = abs(m)
        third = 0
        # I wanted to simplify the logic but it seems to work like a colander
        if m > 0 and n % 4 in [0, 1]:
            third = 0
        elif m < 0 and n % 4 in [2, 3]:
            third = 0
        elif m >= 0 and n % 4 in [2, 3]:
            third = 1
        elif m <= 0 and n % 4 in [0, 1]:
            third = 1
        j = first + second + third
        return j


    def _osa_to_noll(self, idx):
        return self._mn_to_noll(*self._osa_to_mn(idx))

    def _osa_to_noll_list(self, zernikes):
        indexed_zerns = sorted(map(lambda x: (self._osa_to_noll(x[0]), x[1]), enumerate(zernikes)), key=lambda x: x[0])
        used_indeces = [x for x, _ in indexed_zerns]
        mn, mx = min(used_indeces), max(used_indeces)
        missing_indeces = set(range(mn, mx+1)) - set(used_indeces)
        return [x[1] for x in list(sorted(indexed_zerns + [(x, 0) for x in missing_indeces]))]

term = ["PISTON","V-TILT","H-TILT","DEFOCUS","O-PR-ASTIGMATISM","V-PR-ASTIGMATISM","V-PR-COMA","H-PR-COMA","V-TREFOIL","O-TREFOIL","P-SPHERICAL","O-SC-ASTIGMATISM","V-SC-ASTIGMATISM","V-QUADRAFOIL","O-QUADRAFOIL","V-SC-COMA","H-SC-COMA","V-SC-TREFOIL","O-SC-TREFOIL","O-PENTAFOIL","V-PENTAFOIL"]
print(Zernike()._osa_to_noll_list(list(range(0,15))))