Beam tomography in transverse normalised phase space

We demonstrate that the normalised phase space can be used to improve the quality of the reconstructed image in phase space tomography. This study uses the Filtered Back Projection (FBP) for reconstruction. We simulate the tomographic projections of a Gaussian phase space distribution in real phase space and in normalised phase space. The reconstruction can be carried out in real phase space directly. It can also be done first in normalised phase space, and then the co-ordinates can be transformed to real phase space. Using FBP, we show that the latter procedure produces images that agree well with the original distribution even when there are only three angles. It also gives better resolution for a more complex distribution, which we simulate with a random collection of Gaussian spots.