Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation

Abstract

A cascade least-squares scheme for wrapped phase extraction using two or more phase-shifted fringe-patterns with unknown and inhomogeneous surface phase shift is proposed. This algorithm is based on the parameter estimation approach to process fringe-patterns where, except for the interest phase distribution that is a function of the space only, all other parameters are functions of both space and time. Computer simulations and experimental results show that phase computing is possible even when an inhomogeneous phase shift is induced by nonlinearity of the piezoelectric materials or miscalibrated phase shifters. The algorithm's features and its operating conditions will been discussed. Due to the useful properties of this algorithm such as the robustness, computational efficiency, and user-free execution, this proposal could be used in automatic applications.

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

“…• to reduce the error levels induced by the noise [18,19], • to simplify the design of further processing stages [20,21], and…”

“…Namely, Fourier fringe-normalized analysis [36], and the generalized phase-shifting algorithm for inhomogeneous phase shift and spatiotemporal fringe visibility variation [21,37]. Although this last was devised from the viewpoint of phase shifting, it can be classified into the hybrid carrier category.…”

“…For this, a generalized phase-shifting algorithm was proposed [21]. It works with only two phase-shifted frames where the phase shift is unknown nonlinear inhomogeneous, and the visibility of the fringe may be spatiotemporal.…”

Ultrasonic Lamb waves detection using an unstabilized optical interferometer with uncalibrated phase shifts

“…Many different techniques for quantitative phase retrieval from interference patterns have been developed in the last decades [11][12][13][14]. To recover the phase from the interference signal, phase shifts are usually introduced during the measurement, which need to be precisely calibrated.…”

Improving the accuracy performance of phase-shifting profilometry for the measurement of objects in motion

“…We employed such an approach using Matlab on a Dell Vostro 470 computer with 3.4 GHz CPU and 8G memory, and it took 0.41 second to complete one iteration of Step 1 and Step 2 of the proposed algorithm for the fringe pattern of 500 by 500 pixels. It is expected that the time can be further reduced if dedicated hardware such as digital signal processors is employed [9].…”