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I want to generate Fourier transforms of a picture. the transform can represent the diffraction pattern of the picture.

Basically, if I have a picture. Then, the result should look like this:

enter image description here enter image description here

For a more complicated case, for the image on the left, The results should look like:

enter image description here enter image description here

I was hoping Mathematica will have some built-in function to full fill the result. I saw a demonstration project with similar function. But the shapes are built in also. I need to process some of my own image. And retrieve the original image from the spectrum image.

Thanks for any suggestion

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marked as duplicate by Kuba, Jason B., MarcoB, user9660, Daniel Lichtblau Jan 28 '16 at 16:09

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