2d fourier analysis of shapes

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I'm studying for a re-examn in a physical measuring techniques course that includes some fourier analysis. On old exams there are always a question about a graphical 2d fourier transform. It can be an ellipse containing a grid of circels, or something like that. In the solutions he takes the transform of the surrounding shape, the grid and the shape of the grid.
I can't find any information about this approach the course litterature (The Fourier Transform & Its Applications) nor on the internet. Does this approach have a name, and does anyone know of information about this?

Thanks
 

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