Statistical study and experimental verification of high-resolution methods in phase-shifting interferometry

J Opt Soc Am A Opt Image Sci Vis. 2007 Mar;24(3):794-813. doi: 10.1364/josaa.24.000794.


The introduction of high-resolution phase-shifting interferometry methods such as annihilation filter, state space, multiple-signal classification, minimum norm, estimation of signal parameter via rotational invariance, and maximum-likelihood estimator have enabled the estimation of phase in an interferogram in the presence of harmonics and noise. These methods are also effective in holographic moiré where incorporating two piezoelectric transducers (PZTs) yields two orthogonal displacement components simultaneously. Typically, when these methods are used, the first step involves estimating the phase steps pixelwise; then the interference phase distribution is computed by designing a Vandermonde system of equations. In this context, we present a statistical study of these methods for the case of single and dual PZTs. The performance of these methods is also compared with other conventional benchmarking algorithms involving the single PZT. The paper also discusses the significant issue of an allowable pair of phase steps in the presence of noise using a robust statistical tool such as the Cramér-Rao bound. Furthermore, experimental validations of these high-resolution methods are presented for the estimation of single phase in holographic interferometry and for the estimation of multiple phases in holographic moiré.