Fourier Transform in cylindrical coordinate system

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I'm trying to compute the Fourier transform of an image in cylindrical coordinate system. The image input is of (x,y,z) format. In Matlab, I use the cart2pol command to convert to (rho, theta, z) format. But the challenge is to compute FT of Zs of respective rhos along all thetas. I'd like to be able to have thetas from 0 to 355 degrees, but that is not the case I observe. What's a good way to go about this? If interpolation is any solution, can anyone here recommend a good strategy?

Thanks.