Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry

Abstract

We have investigated the effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry (GPSI) systematically. A general formula of the mean square wave reconstruction error for different phase shift selection and different phase shift errors is derived, and its specific expressions for the equal, linear, and random phase shift errors are deduced. The results reveal that there is a wide range for phase shift selection in GPSI, and the equal phase step algorithm is superior to the one of unequal step where the three kinds of phase shift errors are concerned. Specifically, the phase step leads to the minimum wave reconstruction error in the cases of equal and linear phase shift errors, while the phase step 1.91 rad yields the smallest wave reconstruction error for random phase shift errors. These results have been verified by a large number of computer simulations with over 100,000 samples.