We experimentally demonstrate a method for reconstructing the transverse 4D phase space of an electron beam at the time of emission from downstream diagnostics of the 4D phase space. This method does not rely on detailed knowledge of the beamline transport, besides assuming that linearity and symplecticity are satisfied. We apply this method to measure the transverse position and momentum phase space of electrons emitted from a spatially-structured alkali-antimonide cathode. This method can uncover local correlations between emission location and momentum spread. We formulate this method analytically and investigate resolution limits.
Zhang et al. (Mon,) studied this question.