The coherent radiation emitted by an electron bunch provides a diagnosticsignal that can be used to estimate its longitudinal distribution. Commonlyonly the amplitude of the intensity spectrum can be measured and the associatedphase must be calculated to obtain the bunch profile. Very recently aniterative method was proposed to retrieve this phase. However ambiguitiesassociated with non-uniqueness of the solution are always present in the phaseretrieval procedure. Here we present a method to overcome the ambiguity problemby first performing multiple independent runs of the phase retrieval procedureand then second, sorting the good solutions by mean of cross-correlationanalysis. Results obtained with simulated bunches of various shapes andexperimental measured spectra are presented, discussed and compared with theestablished Kramers-Kronig method. It is shown that even when the effect of theambiguities is strong, as is the case for a double peak in the profile, thecross-correlation post-processing is able to filter out unwanted solutions. Weshow that, unlike the Kramers-Kronig method, the combined approach presented isable to faithfully reconstruct complicated bunch profiles.
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