In digital holography, errors of the reference field degrade the quality of the reconstructed object field. In this paper, we propose an effective method in phase-shifting digital holography in which the reference field does not need to be known and perfect. The unknown complex amplitudes of both reference and object fields are derived simultaneously. The method employs only five digital holograms and a single execution of a phase retrieval algorithm. So, the required measurements and algorithm executions in this method are fewer than those in other methods; it suggests a simpler and faster method. The effectiveness of the suggested method is indicated by simulation, under
noise-free and noisy conditions. Moreover, the capability of the method to extract full information about the phase
singularities in both fields is demonstrated.
An advanced phase retrieval algorithm in N-step phase-shifting interferometry with unknown phase shifts