Tomographic reconstruction of the full 4D transverse phase space

We present a method to measure and reconstruct the full 4D transverse phase space of a particle beam. The method assumes that it is possible to freely and independently rotate the separate 2D transverse phase spaces in the horizontal and vertical directions. Using images of the beam that would be captured on a screen, we develop a mathematical procedure that will reconstruct the full 4D particle distribution. We simulate this procedure for a hypothetical distribution and show that the reconstruction agrees with the actual distribution. Finally, we demonstrate for the practical case of a two-quadrupole setup that it is indeed possible to adjust the quadrupole strengths so that the separate 2D transverse phase spaces can be rotated independently. However, in this setup, the rotation angles are restricted to smaller ranges. Even so, the reconstructed results reproduce the actual distribution clearly.