Principal-vector-directed fringe-tracking technique

Abstract

Fringe tracking is one of the most straightforward techniques for analyzing a single fringe pattern. This work presents a principal-vector-directed fringe-tracking technique. It uses Gaussian derivatives for estimating fringe gradients and uses hysteresis thresholding for segmenting singular points, thus improving the principal component analysis method. Using it allows us to estimate the principal vectors of fringes from a pattern with high noise. The fringe-tracking procedure is directed by these principal vectors, so that erroneous results induced by noise and other error-inducing factors are avoided. At the same time, the singular point regions of the fringe pattern are identified automatically. Using them allows us to determine paths through which the "seed" point for each fringe skeleton is easy to find, thus alleviating the computational burden in processing the fringe pattern. The results of a numerical simulation and experiment demonstrate this method to be valid.

Phase retrieval from single interferogram without carrier using Lissajous ellipse fitting technology

“…It is important to clarify three points in advance. First, the iterative correction process around the critical points of Garbusi’s method is not included in this comparison; Second, the fringe direction map estimation in SPT is performed by the principal component analysis (PCA) based method proposed by Zhang and Guo in 16 , 17 ; Third, the phase sign change map for APLEF and Garbusi’s method is estimated by directly performing the phase difference calculation along the fringe orientation. Here, the fringe orientation at pixel (i, j) is simply defined as the maximum intensity difference along 1,2,3,4 in Fig.…”