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Spie Press Book

Windowed Fringe Pattern Analysis
Author(s): Qian Kemao
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Book Description

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.

Book Details

Date Published: 2 August 2013
Pages: 300
ISBN: 9780819496416
Volume: PM239

Table of Contents
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1. Introduction
1.1 Formation of Fringe Patterns
1.2 Fringe Model
1.3 Phase-shifting Technique
      1.3.1 Basic principle
      1.3.2 Special and known phase shifts
      1.3.3 Regular and unknown phase shifts
      1.3.4 Arbitrary and known phase shifts
      1.3.5 Arbitrary and unknown phase shifts
      1.3.6 Extensions
1.4 Fourier Transform Technique
1.5 Phase Unwrapping
1.6 Fringe Pattern Classification
      1.6.1 Exponential phase fields
      1.6.2 Wrapped phase maps
      1.6.3 Carrier fringe patterns
      1.6.4 Single closed fringe patterns
1.7 Fringe Pattern Simulation
1.8 Windowed Fringe Pattern Analysis
1.9 Book Organization
References

2. Windowed Fourier Ridges for Exponential Phase Fields
2.1 Problem Statement in 1D EPF Analysis
      2.1.1 Signal model
      2.1.2 Noise model
      2.1.3 Noise problem
      2.1.4 Parameter estimation and Cramer–Rao bounds
      2.1.5 Maximum-likelihood estimators
      2.1.6 Suboptimal estimators
2.2 1D Windowed Fourier Ridges (WFR) Concept and Feasibility
      2.2.1 WFR concept
      2.2.2 WFR feasibility
2.3 WFR Error Analysis
      2.3.1 Windowed Fourier spectrum of the noise and its probabilistic properties
      2.3.2 Windowed Fourier spectrum of a noisy EPF and its probabilistic properties
      2.3.3 Local frequency error
      2.3.4 Phase error
      2.3.5 Window size and shape
2.4 WFR Implementation and Performance
      2.4.1 Implementation
      2.4.2 Default parameter setting
      2.4.3 Speed
      2.4.4 Accuracy verification
2.5 Problem Statement in 2D EPF Analysis
2.6 2D Windowed Fourier Ridges Algorithm (WFR2)
2.7 WFR2 Error Analysis
      2.7.1 Local frequency errors
      2.7.2 Phase error
      2.7.3 Window size and shape
2.8 WFR2 Implementation and Performance
      2.8.1 Implementation
      2.8.2 Default parameter setting
      2.8.3 Speed
      2.8.4 Accuracy verification
2.9 Two Real Examples
      2.9.1 EPF with light noise
      2.9.2 EPF with heavy noise
2.10 n-Dimensional Windowed Fourier Ridges (WFRn)
Appendix 2A Perturbation Analysis of a 1D Estimator
Appendix 2B Perturbation Analysis of a 2D Estimator
References

3. Windowed Fourier Filtering for Exponential Phase Fields
3.1 1D Windowed Fourier Filtering (WFF)
      3.1.1 1D windowed Fourier transform pair
      3.1.2 WFF concept
3.2 WFF Error Analysis
      3.2.1 Thresholded coefficients for reconstruction
      3.2.2 Intrinsic signal after filtering
      3.2.3 Noise after filtering
      3.2.4 Noisy signal after filtering
      3.2.5 Phase error
      3.2.6 Frequency error
3.3 WFF Implementation and Performance
      3.3.1 Implementation
      3.3.2 Default parameter setting
      3.3.3 Speed
      3.3.4 Accuracy verification
3.4 WFF for Higher-Order Polynomial Phase
3.5 2D Windowed Fourier Filtering (WFF2)
3.6 WFF2 Error Analysis
      3.6.1 Thresholded coefficients for reconstruction
      3.6.2 Intrinsic signal after filtering
      3.6.3 Noise after filtering
      3.6.4 Noisy signal after filtering
      3.6.5 Phase error
      3.6.6 Frequency error
3.7 WFF2 Implementation and Performance
      3.7.1 Implementation
      3.7.2 Default parameter setting
      3.7.3 Speed
      3.7.4 Accuracy verification
3.8 WFF2 for a Higher-Order Polynomial Phase
3.9 Two Real Examples
      3.9.1 EPF with light noise
      3.9.2 EPF with heavy noise
3.10 n-D Windowed Fourier Filtering (WFFn)
References

4. Quality-guided Phase Unwrapping and Refinement
4.1 Exponential Phase Fields versus Wrapped Phase Maps
4.2 WFR2/WFF2-Assisted and Quality-guided Phase Unwrapping (WFR2/WFF2-QG)
      4.2.1 WFR2/WFF2 denoising in phase unwrapping
      4.2.2 WFR2/WFF2 for invalid region identification in phase unwrapping
      4.2.3 WFR2/WFF2 assisted quality-guided phase unwrapping
      4.2.4 Dealing with true phase discontinuities
      4.2.5 Gabor meets Gabor
4.3 Implementation of the WFR2/WFF2-QG
      4.3.1 Direct implementation
      4.3.2 Implementation with interlaced indexed linked list (I2L2)
4.4 Phase Refinements
      4.4.1 Phase congruence
      4.4.2 Denoising the congruent phase by least squares fitting
References

5. Carrier Fringe Pattern Demodulation
5.1 WFR2/WFF2 for Carrier Fringe Pattern Demodulation
      5.1.1 Carrier fringe pattern model
      5.1.2 Demodulation using only Fourier transform (FT)
      5.1.3 FT-WFR2/WFF2 for sequential demodulation and denoising
      5.1.4 WFR2/WFF2 for simultaneous demodulation and denoising
      5.1.5 FT-WFR2/WFF2 versus WFR2/WFF2
5.2 WFR2/WFF2 for Fringe Projection Profilometry
References

6. Denoising a Single Closed Fringe Pattern
6.1 Adaptive Windowed Fourier Filtering
      6.1.1 Closed-fringe-pattern model
      6.1.2 WFF2 for denoising a closed fringe pattern
      6.1.3 Adaptive WFF2 (AWFF2) for denoising a closed fringe pattern
      6.1.4 Simulation results
6.2 Fringe Orientation Estimation
      6.2.1 Definitions of fringe orientation and direction
      6.2.2 Gradient-based fringe orientation estimation
      6.2.3 WFR2-based fringe orientation estimation
6.3 Oriented Filters: Oriented PDEs, ACED, and Spin Filters
      6.3.1 Isotropic diffusion
      6.3.2 Anisotropic diffusion through oriented PDEs
      6.3.3 Anisotropic diffusion through ACED
      6.3.4 Spin filters
      6.3.5 Error analysis
      6.3.6 Simulation results
6.4 AWFF2 versus ACED
References

7. Demodulating a Single Closed Fringe Pattern
7.1 Fundamental Problems in Demodulating a Single Closed Fringe Pattern
7.2 Fringe Background Removal and Amplitude Normalization
      7.2.1 Background removal
      7.2.2 Amplitude normalization
      7.2.3 Simultaneous background removal and amplitude normalization
      7.2.4 Discussion of ill-posedness
7.3 The WFR2 and the Quadrature Transform: Transform-based Demodulation
      7.3.1 WFR2 algorithm
      7.3.2 Quadrature transform
      7.3.3 Summary and similar works
7.4 Frequency-guided Sequential Demodulation (FSD): Decoupled Demodulation
      7.4.1 FSD algorithm
      7.4.2 Fast FSD algorithm
      7.4.3 Summary and similar works
7.5 Regularized Phase Tracking Technique: Integrated demodulation
      7.5.1 RPT algorithm
      7.5.2 Quadratic phase matching and frequency-guided RPT (QFGRPT) algorithm
      7.5.3 QFGRPT incorporating the fringe amplitude b (x, y) (bQFGRPT)
      7.5.4 Generalized RPT (GRPT)
      7.5.5 Summary and similar works
7.6 Two Real Examples
7.7 Dealing with Discontinuity
Appendix 7A Frequency-guided Orientation Unwrapping for Direction Estimation
Appendix 7B Derivation of ∇fv (x, y)=|∇φ (x, y)|
Appendix 7C Levenberg–Marquardt (LM) Optimization Method
Appendix 7D From the GRPT to the tML
References

8. Extracting Dynamic Phase from a Sequence of Fringe Patterns
8.1 Introduction
      8.1.1 Fringe pattern sequence model
      8.1.2 Temporal phase-shifting methods
      8.1.3 Spatial phase-shifting methods
      8.1.4 Spatial Fourier transform method and other transform-based methods
      8.1.5 Temporal Fourier transform method and other transform-based methods
8.2 Spatiotemporal Least-Squares Approaches to Some Unknowns (LSxU)
      8.2.1 Spatiotemporal coherence
      8.2.2 LS3U
      8.2.3 LS2U
      8.2.4 LS1U
      8.2.5 Important considerations
      8.2.5 Related works
8.3 LSxU Error Analysis
8.4 LSxU Implementation and Performance
      8.4.1 Implementation
      8.4.2 Fringe projection profilometry example
      8.4.3 Speckle shearography example
References

9. Algorithm Acceleration using Parallel Computing
9.1 Introduction
      9.1.1 Parallel computing
      9.1.2 Parallel computing hardware
      9.1.3 Rationale of parallel fringe pattern analysis
      9.1.4 Existing works on parallel fringe pattern analysis
9.2 Accelerating the WFF2 by Parallel Computing
      9.2.1 Task parallelism through a multicore computer
      9.2.2 Data parallelism through a GP
References

Index

Preface

Fringe patterns can be formed coherently using various interferometers and incoherently using the moiré technique. They can also be designed in fringe projection profilometry. All of these techniques are useful 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. This book addresses the challenges and solutions involved in this process. Both theoretical analysis and algorithm development will be covered to facilitate the work of both researchers and engineers. The information herein may also serve as a specialized subject for students of optical and/or computer engineering. Readers are encouraged to provide the author with feedback for improvement.

I would like to thank all of my collaborators, Prof. Anand Asundi, Dr. Yu Fu, Dr. Wenjing Gao, Dr. Lei Huang, Ms. Nguyen Thi Thanh Huyen, Prof. Li Kai, Prof. Feng Lin, Dr. Qi Liu, Dr. Ho Sy Loi, Prof. Hong Miao, Mr. Le Tran Hoai Nam, Prof. Bing Pan, Prof. Hock Soon Seah, Dr. Fangjun Shu, Prof. Xianyu Su, Dr. Haixia Wang, Prof. Xiaoping Wu, Prof. Huimin Xie, Prof. Boqin Xu, Prof. Qican Zhang, and Mr. Ming Zhao. Because of you, I have been enjoying the beauty of fringe patterns. Special thanks go to Dr. Lei Huang, Dr. Haixia Wang, and Dr. Wenjing Gao for proofreading my manuscript, and to the peer reviewers who provided encouragement and constructive comments. Thanks also go to Mr. Timothy Lamkins for quickly turning a proposal into a project, to editor Kerry Eastwood for her professional and terrific hard work on the manuscript, to the SPIE staff who have helped facilitate the production of this book, and to SPIE Press for publishing the book. Finally, I owe much thanks to my parents, my parents in-law, my wife Xiaocong, and my son Zihan for their love and support.

Qian Kemao
Nanyang Technological University
August 2013



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