Suppressing ripple distortions and spurious pistons in phase-shifting interferometry

In this work, we deduce explicit conditions to design phase shifting algorithms (PSAs) in order to suppress errors in phase measurement, the double-frequency ripple distortion and the spurious piston. These errors arise when non-uniform phase-shifting interferograms are processed with conventional PSAs which assume uniform phase shifts. By modeling the non-uniform phase shifts as a polynomial of the unperturbed phase shift value !0, we show that the conditions for eliminating those errors are associated to the m-th derivative of the PSA's frequency transfer function (FTF). Thus, we propose an approach to design robust algorithms based on the FTF formalism, and we present a ready-to-apply eight-frame PSA. Finally, our conclusions are supported by computer simulations.