My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in Fourier space:
As you can see, there is a radially symmetric part of concentric circles, superimposed with a cross-pattern. Now, I do not understand this last part, but I highly suspect this to be an artifact that is not supposed to be there...
It would not surprise me if this is a problem that more people have run into this problem, but I have not been able to find an answer yet.
So, bottom line: Why is there a cross-pattern in my image?