Computational optical measurement

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Links between fringe pattern analysis and digital image correlation : windowed, optimal, and tracking (WOT)

A windowed, optimal and tracking (WOT) strategy for measurement data analysis is described, explained and discussed. Many fringe pattern analysis and digital image correlation algorithms adopted this strategy, and thus their similarities and links are revealed. Although this strategy is not new, highlighting it is believed to be helpful for future algorithm development.Published versio

Windowed fringe pattern analyis

This book provides solutions to the challenges involved in fringe pattern analysis, covering techniques for full-field, noncontact, and high-sensitivity measurement. The primary goal of fringe pattern analysis is to extract the hidden phase distributions that generally relate to the physical quantities being measured. Both theoretical analysis and algorithm development are covered to facilitate the work of researchers and engineers. The information presented is also appropriate as a specialized subject for students of optical and computer engineering

Digital wavefront recording, reconstruction and 3D display

In this report, we summarize the work we have done under the support of SUG 15/06: Digital wavefront recording, reconstruction, and 3D display. The importance of the project is from the fact that phase of optical wavefronts are more important in precision metrology, though we sense the amplitude of optical wavefronts every day. Thus the objective of the project is measure, analyze and display the phase. Throughout the investigation, we have the following achievements: 1. For phase measurement, a novel phase measurement method, frequency-shifting method was proposed. It only needs two fringe patterns, comparing with traditional phase-shifting technique which needs at least three fringe patterns. 2. For phase analysis, a spatially adaptive strategy for windowed Fourier transform was proposed and compared with the spatially fixed strategy and their respective advantages and disadvantages were revealed, which was useful for reliable phase analysis. 3. For phase display, we focused more on the phase unwrapping technique, which converts a discontinuous phase map to a continuous phase map and consequently the shape of wavefronts can be readily displayed. Before phase unwrapping, phase denoising is usually necessary. We for the first time compared many effective filters and surprisingly revealed that they were all equivalent. We also pointed out that a popular filter, sine/cosine average filter, is not reliable. We further worked on the windowed Fourier based phase unwrapping technique and found that it would not be affected by threshold, which greatly improves the robustness of the method. 4. Finally we pushed the work by one level higher: we unified windowed Fourier based fringe pattern analysis and digital image correlation from an optimization point of view. These two fields were isolated previously but we built a bridge between them and thus the researchers in two areas can communicate more effectively. The successful completion of the project and findings we achieved inspire us to a bolder ambition to ultimately solve the phase analysis problem: an accurate, robust and real-time fringe analysis tool.SUG 15/0

A comparison study of denoising techniques in fringe pattern analysis

Optical interferometry is a popular technique for high precision measurement. It produces fringe patterns for analysis. The output fringe patterns usually have noises, and thus a filtering process for fringe patterns is necessary. A few filtering algorithms, such as windowed Fourier filtering (WFF), have been proposed specially for fringe pattern denoising. Meanwhile, filtering techniques have been intensively studied for a long time in the general image processing area. It is curious that how the filtering techniques in general image processing area perform on fringe pattern denoising. In this paper, a state-of-the-art filtering algorithm, block-matching 3D filtering (BM3D), is selected and compared with the WFF.Published versio

WFF-BM3D : a hybrid denoising scheme for fringe patterns

Fringe patterns are widely used in the optical interferometry. The captured fringe patterns usually have noises, and thus a filtering process for fringe patterns is necessary. The windowed Fourier filtering (WFF) algorithm is proposed specially for fringe pattern denoising. The WFF performs well in continuous areas, but has problems in discontinuous areas. In this paper, we proposed a hybrid denoising scheme which combines the advantages of the local WFF algorithm and non-local block-matching 3D filtering (BM3D) algorithm. This new scheme can recover fringe pattern information from the WFF residuals, and improve the denoising results effectively.NRF (Natl Research Foundation, S’pore)Published versio

Windowed Fourier ridges as a spatial carrier phase-shifting algorithm

The windowed Fourier ridges (WFR) algorithm is shown to be a phase-shifting algorithm for phase extraction from a carrier fringe pattern. However, the former only provides a phase estimation with a controllable phase error, whereas the latter pursues exact phase extraction. This link not only is interesting but also enhances the understanding of different phase extraction techniques. Advantages and disadvantages of the WFRs algorithm are discussed.NRF (Natl Research Foundation, S’pore)Published versio

General iterative algorithm for phase-extraction from fringe patterns with random phase-shifts, intensity harmonics and non-uniform phase-shift distribution

Advanced iterative algorithm (AIA) is a flexible and effective phase-shifting algorithm (PSA) which can extract phase from fringe patterns with random unknown phase-shifts, making it attractive in the scenarios where phase-shifts are unknown or not accurate. However, accuracy of AIA degrades when intensity harmonics and/or phase-shift non-uniformity are presented. To solve this problem, multiple PSAs have been proposed, but they restrict their fringe model in one way or another, and thus sacrifice the immunity to certain error source(s). In this paper, a general iterative algorithm (GIA) which adopts a most general fringe model is proposed. In GIA, the many unknowns in the fringe pattern model are divided into three groups including: (i) the fringe amplitudes, (ii) the phase and (iii) the phase-shifts related parameters, and alternatively optimized through univariate search technique group by group to improve accuracy and convergence. The Levenberg-Marquart method is used for the optimization of each group of unknowns due to its excellent accuracy and robustness. GIA is shown to have better accuracies than all of its relevant competitors through both a large number of simulations as well as real experiments with a Fizeau interferometer.Published versio

A comparison of n-ary simple code and n-ary gray code phase unwrapping in high-speed fringe projection profilometry

Binary defocusing technique has been widely used in fringe projection profilometry for high-speed measurement. This technique projects designed binary patterns with a defocused projector to generate fringes for wrapped phase calculation, and n-ary simple codes (nSC) or n-ary gray codes (nGC) for phase unwrapping. The unwrapped phase reflecting the object surface profile is calculated by a phase-shifting algorithm with nSC/nGC phase unwrapping. However, it remains unclear which phase unwrapping method, nSC or nGC, is more appropriate for high-accuracy and high-speed measurement. This paper comprehensively compares nSC and nGC with the consideration of various factors, including the strategies for error removal, the base n, the step heights and invalid regions on the measured objects, defocusing level and noise level of the system. From simulations and experiments, we conclude that, (i) in general, nSC with a proposed identification and binary classification (IBC) method has a similar result as nGC; (ii) when accuracy is critical, binary simple code (nSC with n = 2) and binary gray code (nGC with n = 2) methods are recommended; (iii) when speed is critical, quaternary simple code (nSC with n = 4) method with continuity/geometry constraints is recommended