Local frequency estimation from intensity gradients in spatial carrier fringe pattern analysis

Abstract

Spatial carrier fringe pattern analysis is an effective tool in optical measurement, e.g. in interferometry and fringe projection technique. With it, the very large phase deformations in a spatial carrier fringe pattern may increases the bandwidth of fringe component thus leading to difficulties in retrieving its phase map. In order to overcome this problem, many local-adaptive methods have been developed for processing the spatial carrier fringe pattern with large phase variations, and in fact, the local spatial frequency estimation is central to these methods. This paper introduces a simple algorithm for estimating the local frequencies of a fringe pattern with spatial carrier. First, the intensity gradients of the fringe pattern are calculated, and then the standard deviations (SDs) of the intensity gradients at each pixel are estimated from its neighborhood. Finally the local frequencies are estimated from the SDs just calculated simply using an arccosine function. This algorithm is potential in developing effective techniques for retrieving phases from a spatial carrier fringe pattern with large phase variations. For example, we can recover the phase map by directly integrating the local frequencies or by use of an adaptive spatial carrier phase shifting algorithm (SCPS) with the local frequencies being the local phase shifts. It can also be used in Fourier transform method for exactly determining the carrier frequencies, or for extrapolating aperture in order to reduce the boundary effect. Combined with time-frequency techniques such as windowed Fourier transform and wavelet transform methods, it is helpful for alleviating the computational burdens.