Reduction of Phase Estimation Errors in Phase-Shifting Interferometry Using Multifocal Curve Approximation

The objective of the article is to refine the accuracy of phase-shifting algorithms utilized in decoding fringe patterns. To overcome nonlinear errors (specifically gamma distortion) in phase shifting interferometry, a two-step correction approach based on intensity trajectory approximation and correction with multifocal curves fitting is proposed. It is shown that circular intensity trajectory allows to perform accurate fringes decoding. At the same time, conducting precise analysis of interference patterns is a nontrivial task, for example, due to changes in illumination conditions when phase shifts are introduced, nonlinearity of interferogram registration devices. However, various factors introduce errors in the recorded interference patterns, which manifest themselves in the distortion of the trajectory from the elliptical shape. To eliminate the influence of measurement errors, it is necessary to bring the intensity trajectory to an elliptical form with minimizing additional distortions. The article considers an alternative approach to deciphering interference patterns using approximation of the trajectory of interference signals by multifocal (three or more) curves with subsequent correction of the trajectory by reducing it to a single (two) focal curve. This approach allows to reduce the level of errors arising during phase recovery. We illustrate this scenario by simulated set of interferometry frames with gamma distortion. Modelling includes trajectory intensity fitting with three-focal curve and correction step simulation. For correction phase are provided control points traces visualization along with further improvements of developing algorithm.