Phase gradients from intensity gradients: a method of spatial carrier fringe pattern analysis

Abstract

In optical measurement, spatial carrier fringe pattern analysis is suitable for measuring dynamic events in real-time. This paper presents a novel technique for analyzing a spatial carrier fringe pattern. It estimates the local phase gradients at a pixel from its neighborhood, by use of statistics of the intensity gradients. Using the estimated phase gradients, the phase map of the fringe pattern is recovered by solving numerical partial derivative equations or using an adaptive spatial carrier phase shifting (SCPS) algorithm. Simulation and experimental results demonstrate this algorithm to be valid.

Principal-vector-directed fringe-tracking technique

“…Then we track each fringe using Eqs. (14) and (15), and get the results as shown in Fig. 24, with the curves being the skeletons of the bright and dark fringes.…”

“…Among them, the phasemeasuring techniques, e.g., temporal phase shifting [1][2][3][4][5][6][7][8][9][10], Fourier transform [11][12][13][14], spatial carrier phase shifting [14,15], time-frequency analysis [16][17][18][19], regularized phase tracking [20][21][22][23], and empirical mode decomposition [24][25][26] techniques are superior in achieving high resolutions. Even so, the fringe-tracking method [27], as one of the most straightforward techniques for processing a single fringe pattern, is still popularly used, especially when the pattern contains closed fringes or its profile of fringes is not sinusoidal.…”

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

“…In [33], we presented a method for estimating the local frequency from the intensity gradients, which was deduced by emulating the temporal phase shift estimation method proposed in [34]. For a pixel (x, y), we can calculate its intensity gradient along the horizontal direction using the forward difference formula h ( ) ( …”

“…In [33], we proposed an algorithm recovering the phase map by numerically integrating the estimated phase gradients. Its procedure is very much similar to that of least-squares phase unwrapping technique proposed by Ghiglia and Romero [40].…”

“…In [33] we have presented a simple algorithm for estimating the local frequencies from a spatial carrier fringe pattern. It calculates the standard deviations (SDs) of the intensity gradients at each pixel from its neighborhood, and then estimates the local frequencies simply using an arccosine function.…”