Gerchberg–Saxton算法

伪代码：

Let:
 FT – forward Fourier transform
 IFT – inverse Fourier transform
 i – the imaginary unit, √−1 (square root of −1)
 exp – exponential function (exp(x)=ex)
 Target and Source be the Target and Source Amplitude planes respectively
 A, B, C & D be complex planes with the same dimension as Target and Source
 Amplitude – Amplitude-extracting function:
   e.g. for complex z = x + iy, amplitude(z) = sqrt(x·x + y·y)
       for real x, amplitude(x) = |x|
 Phase – Phase extracting function:
   e.g. Phase(z) = arctan(y/x)
end Let

Gerchberg–Saxton Algorithm(Source, Target, Retrieved_Phase)
 A = IFT(Target)
 while error criterion is not satisfied
   B = Amplitude(Source) * exp(i*Phase(A))
   C = FT(B)
   D = Amplitude(Target) * exp(i*Phase(C))
   A = IFT(D)
 end while
 Retrieved_Phase = Phase(A)
end Gerchberg–Saxton Algorithm

python代码

import math
import numpy as np


def Ger_Sax_algo(img, max_iter):
    h, w = img.shape
    pm_s = np.random.rand(h, w)
    pm_f = np.ones((h, w))
    am_s = np.sqrt(img)
    am_f = np.ones((h, w))

    signal_s = am_s*np.exp(pm_s * 1j)

    for iter in range(max_iter):
        signal_f = np.fft.fft2(signal_s)
        pm_f = np.angle(signal_f)
        signal_f = am_f*np.exp(pm_f * 1j)
        signal_s = np.fft.ifft2(signal_f)
        pm_s = np.angle(signal_s)
        signal_s = am_s*np.exp(pm_s * 1j)

    pm =pm_f
    return pm