Modified G-S Algorithm - does not converge to target

hi everyone,

i am trying to implement modified G-S algorithm to create Coded Phase Mask

the modification is that the mask should be pure phase so the constraint on the amplitude is to be 1 in mask plane, and sparse matrix on detector plane.

the issue is that i cannot converge to uniform amplitude in mask plane and also it converges to the sparse matrix imidiately and stays the same for all iterations.

i would appretiate any help!

;

clear all; close all;

num_of_Pixels=256; dot_N=100;

N=num_of_Pixels; dotN=dot_N; sigX=round(N/100); sigY=round(N/10);

Det_Plane = zeros(N); dp_amplitude1=zeros(N-2*sigX,N-2*sigY); dp_amplitude1(1:dotN,1)=255;

dp_amplitude1=reshape(dp_amplitude1(randperm((N-2*sigX)*(N-2*sigY))),N-2*sigX,N-2*sigY);

Det_Plane(sigX:(size(Det_Plane,1)-sigX-1),sigY:(size(Det_Plane,2)-sigY-1))= dp_amplitude1;

phase = (2*rand(N,N)-1)*pi;

CPM_Plane =255*exp(1i*phase);

error = []; error2 = [];

iteration_num = 200;

Norm_Det_Plane=(Det_Plane-min(min(Det_Plane)))./(max(max(Det_Plane))-min(min(Det_Plane))); %Normalized Det_Plane for error calculation

A=fftshift(fft2(fftshift(CPM_Plane)));%first fft of ones with rand phase

for j=1:iteration_num

B = Det_Plane.* exp(1i*angle(A)); %Det plane with set amp and calculated phase

C = fftshift(ifft2(fftshift(B))); % cpm plane

D = exp(1i*angle(C)); % cpm plane with ones and calculated phase

A = fftshift(fft2(fftshift(D))); % next fft of cpm plane: actual detector plane

Norm_Mask_on_Det=(abs(A)-min(min(abs(A))))./(max(max(abs(A)))-min(min(abs(A)))); %Normalized mask values for error calculation

error = [error; immse(Norm_Det_Plane,Norm_Mask_on_Det)];

error2 = [error2; immse(C,D)];

end

figure

subplot(2,2,1);

imagesc(Det_Plane);colormap('Gray'); colorbar;

title('Desired Mask on Detector')

subplot(2,2,2);

imagesc(abs(A)); colormap('Gray'); colorbar; %last pattern

title('Actual Mask on Detector');

subplot(2,2,3);

imagesc(abs(C)); colormap('Gray'); colorbar; %last pattern

title('Amp of Mask on CPM Plane');

subplot(2,2,4);

imagesc((angle(C))); colormap('Gray'); %colorbar; %last pattern

title('Phase of Mask on CPM Plane');

figure

j = 1:1:j;

subplot (1,2,1)

plot(j,(error));

title('Error of detector plane');

subplot (1,2,2)

plot(j,(error2)); %last pattern

title('error of cpm plane');