Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern

Abstract

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking ͑RPT͒ algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n ϩ 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results.

N-dimensional regularized fringe direction-estimator

“…For our purposes we use as the quality map the magnitude of fringe pattern gradient. Unlike previously reported methods for direction estimation [6,7], from the computational point of view our method has the following advantages: once the region Γ has been defined, the processing time is fixed for every site in the fringe image and it works efficiently because a simple linear system Ap = b have to be solved by means of any direct method, being A of size n × n. This is not the case for methods in references [6,7] that require to solve a non-linear system by means of iterative methods.…”

“…There are two main inconveniences using the methodology of reference [6] to determine the fringe direction: first, several unwrapping processes must be performed, and second, the unwrapping method itself is slow and complicated due to the algorithm to solve a nonlinear system in order to minimize a regularized cost-function. An improvement of the algorithm reported in [6] was proposed in reference [7], the cost function were simplified making some approximations and the time processing reduced, however, the optimization of the proposed cost function still requires to solve a nonlinear system.…”

Spatially Resolved Stress Measurements in Materials With Polarisation-Sensitive Optical Coherence Tomography: Image Acquisition and Processing Aspects

“…We exploit the recently developed technique for single fringe pattern analysis as realized e.g. in (holographic) interferometry or conventional photoelasticity [16,20] and test these algorithms for the analysis of our single PS-OCT retardation image.…”