I have an circularly symmetric image in Fourier space:
where the 0-frequency is in the center. Now, I want to take the FFT of this image. Having numpy's FFT conventions in mind (i.e. 0 frequency at (0,0)), I first apply the the inverse-fftshift, and then apply the inverse-fourier transform. As follows:
image = np.fft.ifft2(np.fft.ifftshift(FT_image))
This results in the following real space image:
But I can't really wrap my head around this result. It looks as if another fftshift would be in order, but in real space this shouldn't be necessary. I would expect a radially symmetric transform, centered in the center of the image.
Is this expectation wrong, or is my computation wrong? And either way: can you explain why?