Rotational invariance approach for the evaluation of multiple phases in interferometry in the presence of nonsinusoidal waveforms and noise

Abstract

Incorporation of two phase-shifting devices in a holographic moiré configuration not only renders the interferometer compatible with automated measurements but also allows for simultaneous measurement of multiple phase information in the interferometer. However, simultaneous handling of multiple phase steps and subsequent simultaneous determination of multiple phase distributions requires the introduction of novel tools in phase-shifting interferometry. In this context, the aim of this paper is to propose a subspace invariance approach to address these issues. This approach takes advantage of the rotational invariance of signal subspaces spanned by two temporally displaced data sets formed from the intensity fringes recorded temporally on pixels of the CCD camera. The method first identifies the arbitrary phase steps imparted to the piezoactuator devices. The estimated phase steps are subsequently applied in the linear Vandermonde system of equations to determine the phase distributions. The method also allows for handling nonsinusoidal wavefronts. Since the phase steps are extracted at every point on the interferogram, the method is applicable to configurations that use spherical beams. The robustness of the method is investigated by adding white Gaussian noise during the simulations.