Effects of measurement errors on both the amplitude and the phase reconstruction in phase-shifting interferometry: a systematic analysis

摘要

In many applications of phase-shifting interferometry (PSI) the actually recorded object wave is the diffraction field of an object surface. In this case not only the phase error but also the amplitude error in the retrieval process have effects on the object wave reconstruction in its original plane. In this paper, for the first time that we know, the amplitude errors in wave reconstruction in PSI are discussed systematically. Some general relations between the amplitude errors and the phase errors for three commonly encountered error sources, namely the phase shift error. the light source intensity fluctuation and the detector nonlinearity. are revealed. The analyticai expressions of the amplitude and phase errors for six frequently used algorithms in PSI are derived. The statistical variances of the two kinds of error are introduced to describe the overall performance of these algorithms and are quantitatively calculated. A series of computer simulations are also given as a verification of our analyses. These results can be used for evaluating the complete wave errors in PSI and developing new methods for their correction.