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Iterative phase retrieval algorithm for reconstruction of two arbitrary interfering fields

We present a simple and robust method to simultaneously reconstruct two unknown interfering fields. First, the interference field (IF) is recovered from diffraction interference intensity recordings. The recovered IF along with a set of interference intensities generated by the phase shifting technique is used in an iterative phase retrieval algorithm to derive both the phase and amplitude information of the interfering fields. Numerical simulations are presented to validate the proposed method. In the simulation, we consider two arbitrary interfering fields with unrelated amplitudes and phases, creating a difficult problem where two complicated fields must be retrieved simultaneously. In addition, the phase of the second interfering field contains a vortex with a topological charge of 5. Under noise-free conditions, the relative errors of phases, defined as the root-mean-square (RMS) value of the residual phase divided by the RMS value of the original phase, for the first and second interfering fields are of the order of 10−5 and 10−6, respectively, where the relative error of amplitudes is of the order of 10−7. For 5% and 10% noise, the obtained relative error of phase is of the order of 10−2 for the first interfering field and 10−3 for the second interfering field, where the relative error of amplitudes is of the order of 10−2. These results show the success of the proposed method even under noisy conditions and in the presence of phase vortices.