Non-iterative blind phase-shifting algorithm for two-step phase-shifting interferometry based on an analytical formula

An algorithm for retrieval of the complex amplitude of the recorded object in blind two-step phase-shifting interferometry is proposed, in which the complex amplitude of the object wave can be found out directly from the recorded intensity patterns without the process of extracting the phase-shifting value in advance. A simple analytical formula for calculating the complex amplitude (including both the amplitude and the phase) of the object wave based on the recorded intensities is derived. Both the theoretical analysis and experimental results demonstrated the feasibility of this kind of blind phase-shifting algorithm in small phase shift situations.