Phase determination algorithms compensating for spatially nonuniform phase modulation in phase-shifting interferometry

In phase shifting interferometers, spatial non-uniformity of the phase modulation often happens and affects high- precision phase measurement. Many phase measuring algorithms have been reported which compensate for nonlinear sensitivities of the phase shifter. This nonlinearity of the phase shifter usually gives only a constant bias to the measured phase in these algorithms. However, when the phase shift is spatially nonuniform, the measured phase is shown to suffer significant errors from these bias phase. We have shown that if we add a new symmetry to an algorithm we can remove the errors caused by the spatial nonuniformity of the phase shift. The algorithm needs at least one more image frame to acquire the symmetry. The lowest-order algorithm that compensates for a quadratic and spatially nonuniform phase shift consists of six frames. We have compared the performance of the new algorithm on several types of phase nonuniformity to the conventional error-compensating algorithms.