Experimental demonstrations of the digital correction of complex wave errors caused by arbitrary phase-shift errors in phase-shifting interferometry

In previous papers we proposed a digital method of correcting both amplitude and phase distortions caused by arbitrary phase-shift errors in standard four-frame phase-shifting interferometry (PSI), then extended it to the most generalized PSI, and showed the validity of this technique by computer simulations. Here some new simulations and a series of optical experiments with a plane wave, a spherical wave, and a piece of glass as objects are reported. The experimental results have further proved the correctness of our theoretical analysis and confirmed that our method is able to suppress double-frequency fringes in the retrieved amplitude map and the distortions in the phase map that are introduced by phase-shift errors such as to effectively eliminate the wave ripples and wall-like structures that are present in the unwrapped phase map owing to these errors. In addition, our technique can reduce the density of invalid pixels, which are barriers in phase unwrapping. Therefore the accuracy of both amplitude and phase measurements can be considerably improved.