In my quest to understand Math during the Christmas holidays I'm working on Fourier transforms today. I understand that a single point in Fourier space corresponds to line in normal 2D image space. However I was wondering what happens if you square it. My logic would dictate that given that the real part of the transform is determined by the amplitude of the wave and the amplitude of the wave is squared when we square the individual intensities of each pixel, so I would expect the real part of each pixel to also get squared.So for example if we have the following sequence in image space
$$0.5,0,0.5,0 $$
then we have a amplitude of $0.5$ and a period of $2$ pixels. If we square the input then we get
$$0.25,0,0.25,0$$
amplitude of $0.25$ and period of $2$ pixels. However when I apply this to a real image in matlab (lena) then end up with nothing but a set of straight lines. So that is obviously wrong but why? What is screwing up this seemingly simple solution?