PHASE-SHIFTING ALGORITHMS FOR NONLINEAR AND SPATIALLY NONUNIFORM PHASE-SHIFTS

In phase-shifting interferometry spatial nonuniformity of the phase sh ift gives a significant error in the evaluated phase when the phase sh ift is nonlinear. However, current error-compensating algorithms can c ounteract the spatial nonuniformity only in linear miscalibrations of the phase shift. We describe an error-expansion method to construct ph ase-shifting algorithms that can compensate for nonlinear and spatiall y nonuniform phase shifts. The condition for eliminating the effect of nonlinear and spatially nonuniform phase shifts is given as a set of linear equations of the sampling amplitudes. As examples, three new al gorithms (six-sample, eight-sample, and nine-sample algorithms) are gi ven to show the method of compensation for a quadratic and spatially n onuniform phase shift. (C) 1997 Optical Society of America.