A two-step method for retrieving the longitudinal profile of an electron bunch from its coherent radiation

The coherent radiation emitted by an electron bunch provides a diagnostic signal that can be used to estimate its longitudinal distribution. Commonly only the amplitude of the intensity spectrum can be measured and the associated phase must be calculated to obtain the bunch profile. Very recently an iterative method was proposed to retrieve this phase. However ambiguities associated with non-uniqueness of the solution are always present in the phase retrieval procedure. Here we present a method to overcome the ambiguity problem by first performing multiple independent runs of the phase retrieval procedure and then second, sorting the good solutions by means of cross-correlation analysis. Results obtained with simulated bunches of various shapes and experimental measured spectra are presented, discussed and compared with the established Kramers-Kronig method. It is shown that even when the effect of the ambiguities is strong, as is the case for a double peak in the profile, the cross-correlation post-processing is able to filter out unwanted solutions. We show that, unlike the Kramers-Kronig method, the combined approach presented is able to faithfully reconstruct complicated bunch profiles.