Seah Hock Soon

Sequential demodulation of a single fringe pattern guided by local frequencies

A simple but effective approach for the demodulation of a single fringe pattern is proposed. The phase with an undetermined sign is directly obtained by taking the arccosine value of a preprocessed fringe pattern. The local frequencies, also with an undetermined sign, are then estimated by local matching. The sign ambiguity is then removed simply by forcing the continuity of the local frequencies. The priority of sign determination is guided by the value of total local frequency (fringe density) so that the critical points are processed last. The proposed approach is verified by successful demodulation of a simulated fringe pattern and two experimental fringe patterns.

Comparative analysis on some filters for wrapped phase maps.

Some effective filtering methods for wrapped phase maps, a regularized phase-tracking method (RPT) without the regularization term, a multiple-parameter least-square method (MPLS), a windowed Fourier ridges method (WFR), an autocorrelation function method (ACF), and a sine/cosine average filter (SCAF), are analyzed in order to establish their transversal relationship. The analysis shows that principles of the RPT, MPLS, WFR, and ACF are equivalent and the SCAF also leads to the WFR by some extension, which elegantly unifies all these methods for filtering unwrapped phase maps.

Instantaneous frequency and its application to strain extraction in moire interferometry

Moire interferometry is an effective experimental technique for measurement of in-plane deformation. However, it is information on the derivatives of the deformation, i.e., strains, that is usually desired in experimental mechanics. It is shown that the desired strains are the instantaneous frequencies of the fringe pattern and that either an energy operator or wavelet ridges can be used to extract the instantaneous frequencies from a single fringe pattern. The energy operator is a pixelwise processor; thus the strain extraction can be done on the fly, but it is sensitive to noise. The wavelet ridges extract the local features in the fringe pattern. The strain extraction is thus insensitive to noise, and good results are obtainable at the cost of longer computation time. The two methods can thus be chosen for different needs in strain analysis. The properties of the two methods as well as their applications to a real fringe pattern are given. The effectiveness of the proposed methods is illustrated by their comparison with traditional methods.

Phase-shifting windowed Fourier ridges for determination of phase derivatives

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.

Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis

The two-dimensional continuous windowed Fourier transform has been shown to be effective for fringe pattern analysis in our previous work. In this paper, we first estimate the sampling intervals, using frame theory, to discretize the transform. Suitable sampling intervals are esti- mated as 1/x and 1/y, which is verified by simulations. Noise reduc- tion using windowed Fourier frames is then investigated and compared with that using the orthogonal wavelet transform. Due to the coherence of its kernels and fringe patterns and its redundancy, windowed Fourier frames are able to reduce noise more effectively, which is verified by processing both simulated and experimental fringe patterns. The relative errors are reduced by half, in various simulations, from those with or- thogonal wavelet filtering.

Valid point detection in fringe projection profilometry

Fringe projection profilometry has become one of the most popular 3D information acquisition techniques being developed over the past three decades. However, the general and practical issues on valid point detection, including object segmentation, error correction and noisy point removal, have not been studied thoroughly. Furthermore, existing valid point detection techniques require multiple case-dependent thresholds which increase processing inconvenience. In this paper, we proposed a new valid point detection framework, which includes the k-means clustering for automatic background segmentation, unwrapping error correction based on theoretical analysis, and noisy point detection in both temporal and spatial directions with automatic threshold setting. Experimental results are given to validate the proposed framework.

Smoothing filters in phase-shifting interferometry

Abstract The images used in phase-shifting interferometry are usually noisy and smoothing filters are frequently used. Filtering can be done on the fringe patterns before phase retrieving or on the phase map after phase retrieving. Filtering fringe patterns—a form of preprocessing, requires the same processing to be done on at least three patterns. Filtering phase map, on the other hand, needs processing of only one pattern. Preprocessing prevents noise from being carried through while post-processing might clip parts of the signal. Thus there is a need to evaluate which one is better. A theoretical analysis was carried out for this basic problem, followed by computer simulations and a real experiment for verification. The comparison was also extended to phase difference measurement which uses similar but slightly different phase retrieval algorithms.

A Simple Phase Unwrapping Approach Based on Filtering by Windowed Fourier Transform (II)

Phase unwrapping is an important and challenging process in optical interferometry. Difficulties in phase unwrapping are usually caused by either noise (“bad” pixels) or invalid areas (“bad” regions). If the “bad” pixels can be removed, the problems due to the noise are solved. Further, if the “bad” regions can be identified, they can be avoided in phase unwrapping. In our previous work the noise can be successfully removed using a windowed Fourier transform [Optics and Lasers Technology, 37:458-462 (2005)]. In this paper we will show that the invalid areas can be identified by the same windowed Fourier transform. Thus a single windowed Fourier transform is able to process both “bad” pixels and “bad” regions simultaneously, which makes the phase unwrapping simple and effective.

Fault detection from temporal unusualness in fringe patterns

In this paper temporal unusualness of faults are emphasized and three approaches, Fourier transform, normalized cross correlation and windowed Fourier transform are analyzed and compared. The result shows all the approaches can detect the faults in the example, while the WFT is the most promising approach.

Metrological Fringe inpainting

In optical metrology, important information is often carried by fringe patterns, which can be expressed as ) , ( cos ) , ( ) , ( y x y x b y x f (1) where ) , ( y x f , ) , ( y x b and ) , ( y x are the recorded intensity, fringe amplitude and phase distribution, respectively. We have assumed that the background intensity could be removed by, say, low-pass filtering, and hence is not shown in Eq. (1). Sometimes the fringe patterns have some undesired invalid areas due to the irregularity of the tested specimen, illumination shadows, or imperfection of the optical elements and detector. These invalid areas may introduce difficulties for further processing [1-3]. It is hence often required to “repair” the fringe patterns. This is very similar to the digital inpainting of artistic pieces [4,5]. Fringe extrapolation and interpolation usually carry the same meaning. Assume the intensity of the fringe pattern (usually noisy), f, is available at the entire image plane , except for some areas D. The goal of inpainting is to reconstruct the intensity at D (usually without noise), f0, as faithfully as possible. This task can be model by the Maximum A Posteriori (MAP) optimization, i.e., determining f0( ) that maximizes the posterior probability ) ( ) ( 0 D f f p .