I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I take the FFT of this image and get a 3D volume in the frequency domain. I then take a 2d slice from this 3D volume at an arbitrary angle making sure that the centre of the slice and the centre of the 3D FFT image volume pass through the same point. I then inverse FFT this 2d extracted plane to get a projection of my 3d volume.
I have noticed that I get an overlapping of artifacts but they are shifted by bit, also their intensity is reduced. If I sample at a higher rate the shift becomes greater to a point where it doesn't overlap anymore. Why does sampling at a higher rate increase the shift of the overlapped image? What can I do to stop the artifacts from being produced?