A new method for phase retrieval on non-monotonous fringes

Abstract

A novel method based on continuous wavelet transform (CWT) and guidance of inflexion points of unwrapped phase is developed to measure the phase of non-monotonous fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT. To increase the resolution of measurement and reduce the noise, the scale incremental step is determined by a proper criterion and the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. Based on the homograph relationship between an inflexion point and an ambiguous point, the real phase values can be retrieved by directly identifying any inflexion point from an unwrapped phase map without the use of a carrier. The proposed method is analyzed theoretically in great details. Furthermore, the algorithm developed is validated by computer simulation, which includes one-dimensional and two-dimensional cases both with and without noise, and an experiment based on micro interferometry. Simulations and experimental results for both static and dynamic shapes and deformations of a micro structure demonstrate that the proposed method is effective for the analysis of a closed fringe pattern and subsequent deformation measurement, which has the capability of high accuracy and good noise reduction with a maximum error less than 4%.