Strange grid pattern in 2D Fourier transform

Question

Morgan Facchin 2021-1-14

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https://ww2.mathworks.cn/matlabcentral/answers/716948-strange-grid-pattern-in-2d-fourier-transform

回答： Hrishikesh Borate 2021-2-4

采纳的回答： Hrishikesh Borate

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Hi everyone,

I want to plot the phase of the 2D Fourier transform of a random phase mask with the following code:

size_mask=10; mag=5;
mask=exp(1i*2*pi*rand(size_mask));
mask_pad=padarray(mask,[mag*size_mask mag*size_mask],0,'both');
phase=angle(fft2(mask_pad)); 
imagesc(phase)

Which gives this:

It has the expected global pattern, but there is an additional grid pattern on top of it.

Can anyone help me understand the origin of this and how to eliminate it?

Many thanks

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Answer 1

Hrishikesh Borate 2021-2-4

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https://ww2.mathworks.cn/matlabcentral/answers/716948-strange-grid-pattern-in-2d-fourier-transform#answer_614402

在 MATLAB Online 中打开

Hi,

I understand that you are displaying phase spectrum of FFT of a mask. In the output image there is global grid pattern formed, which you are trying to remove.

One reason for this grid pattern is that mask_pad is not centered about zero, which results in a phase shift of the FFT output. The phase shift is essentially negating every other element (odd samples) of the output of the FFT which causes the high frequency oscillation you're observing (as explained here).

This can be corrected as follows :-

phase = angle(fftshift(fftshift((fft2(fftshift((mask_pad)))))));

For more information, refer to fftshift, fft2.