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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:

enter image description here

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?

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  • $\begingroup$ The second image looks to me like it hasn't had the IFFT applied. It looks just like a shifted version of the first one. $\endgroup$
    – Jason R
    Nov 2, 2015 at 15:33
  • $\begingroup$ Pretty much, although the circular pattern extends out further in the second image (so it has definitly been transformed). $\endgroup$
    – user1991
    Nov 2, 2015 at 16:35

1 Answer 1

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Your Fourier space image is purely real, so the inverse Fourier is going to be radially symmetric about the origin. Because the origin is at (0,0), it takes a shift to put the inverse image in the center of your matrix.

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