Fringe pattern analysis for optical metrology : theory, algorithms, and applications
Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications The main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of modern fringe patte...
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| Main Authors: | , , |
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| Format: | eBook Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2014
Wiley John Wiley & Sons, Incorporated |
| Edition: | 1 |
| Subjects: | |
| ISBN: | 9783527411528, 3527411526, 9783527681105, 3527681108 |
| Online Access: | Get full text |
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Table of Contents:
- 4.6 Relation Between Temporal and Spatial Analysis -- 4.7 Summary and Conclusions -- Chapter 5 Spatial Methods Without Carrier -- 5.1 Introduction -- 5.2 Phase Demodulation of Closed-Fringe Interferograms -- 5.3 The Regularized Phase Tracker (RPT) -- 5.4 Local Robust Quadrature Filters -- 5.5 2D Fringe Direction -- 5.5.1 Fringe Orientation in Interferogram Processing -- 5.5.2 Fringe Orientation and Fringe Direction -- 5.5.3 Orientation Estimation -- 5.5.4 Fringe Direction Computation -- 5.6 2D Vortex Filter -- 5.6.1 The Hilbert Transform in Phase Demodulation -- 5.6.2 The Vortex Transform -- 5.6.3 Two Applications of the Vortex Transform -- 5.7 The General Quadrature Transform -- 5.8 Summary and Conclusions -- Chapter 6 Phase Unwrapping -- 6.1 Introduction -- 6.1.1 The Phase Unwrapping Problem -- 6.2 Phase Unwrapping by 1D Line Integration -- 6.2.1 Line Integration Unwrapping Formula -- 6.2.2 Noise Tolerance of the Line Integration Unwrapping Formula -- 6.3 Phase Unwrapping with 1D Recursive Dynamic System -- 6.4 1D Phase Unwrapping with Linear Prediction -- 6.5 2D Phase Unwrapping with Linear Prediction -- 6.6 Least-Squares Method for Phase Unwrapping -- 6.7 Phase Unwrapping Through Demodulation Using a Phase Tracker -- 6.8 Smooth Unwrapping by Masking out 2D Phase Inconsistencies -- 6.9 Summary and Conclusions -- Chapter Appendix A List of Linear Phase-Shifting Algorithms (PSAs) -- A.1 Brief Review of the PSAs Theory -- A.2 Two-Step Linear PSAs -- A.2.1 Two-Step PSA with a First-Order Zero at -ω0 (ω0=π/2) -- A.3 Three-Step Linear PSAs -- A.3.1 Three-Step Least-Squares PSA (ω0=2π/3) -- A.3.2 Three-Step PSA with First-Order Zeros at ω ={0,-ω0} (ω0=π/2) -- A.4 Four-Step Linear PSAs -- A.4.1 Four-Step Least-Squares PSA (ω0=2π/4) -- A.4.2 Four-Step PSA with a First-Order Zero at ω =0 and a Second-Order Zero at -ω0 (ω0=2π/3)
- A.8.1 Eight-Step Least-Squares PSA (ω0=2π/8)
- Intro -- Fringe Pattern Analysis for Optical Metrology -- Contents -- Preface -- List of Symbols and Acronyms -- Chapter 1 Digital Linear Systems -- 1.1 Introduction to Digital Phase Demodulation in Optical Metrology -- 1.1.1 Fringe Pattern Demodulation as an Ill-Posed Inverse Problem -- 1.1.2 Adding a priori Information to the Fringe Pattern: Carriers -- 1.1.3 Classification of Phase Demodulation Methods in Digital Interferometry -- 1.2 Digital Sampling -- 1.2.1 Signal Classification -- 1.2.2 Commonly Used Functions -- 1.2.3 Impulse Sampling -- 1.2.4 Nyquist-Shannon Sampling Theorem -- 1.3 Linear Time-Invariant (LTI) Systems -- 1.3.1 Definition and Properties -- 1.3.2 Impulse Response of LTI Systems -- 1.3.3 Stability Criterion: Bounded-Input Bounded-Output -- 1.4 Z-Transform Analysis of Digital Linear Systems -- 1.4.1 Definition and Properties -- 1.4.2 Region of Convergence (ROC) -- 1.4.3 Poles and Zeros of a Z-Transform -- 1.4.4 Inverse Z-Transform -- 1.4.5 Transfer Function of an LTI System in the Z-Domain -- 1.4.6 Stability Evaluation by Means of the Z-Transform -- 1.5 Fourier Analysis of Digital LTI Systems -- 1.5.1 Definition and Properties of the Fourier Transform -- 1.5.2 Discrete-Time Fourier Transform (DTFT) -- 1.5.3 Relation Between the DTFT and the Z-Transform -- 1.5.4 Spectral Interpretation of the Sampling Theorem -- 1.5.5 Aliasing: Sub-Nyquist Sampling -- 1.5.6 Frequency Transfer Function (FTF) of an LTI System -- 1.5.7 Stability Evaluation in the Fourier Domain -- 1.6 Convolution-Based One-Dimensional (1D) Linear Filters -- 1.6.1 One-Dimensional Finite Impulse Response (FIR) Filters -- 1.6.2 One-Dimensional Infinite Impulse Response (IIR) Filters -- 1.7 Convolution-Based two-dimensional (2D) Linear Filters -- 1.7.1 Two-Dimensional (2D) Fourier and Z-Transforms -- 1.7.2 Stability Analysis of 2D Linear Filters
- 1.8 Regularized Spatial Linear Filtering Techniques -- 1.8.1 Classical Regularization for Low-Pass Filtering -- 1.8.2 Spectral Response of 2D Regularized Low-Pass Filters -- 1.9 Stochastic Processes -- 1.9.1 Definitions and Basic Concepts -- 1.9.2 Ergodic Stochastic Processes -- 1.9.3 LTI System Response to Stochastic Signals -- 1.9.4 Power Spectral Density (PSD) of a Stochastic Signal -- 1.10 Summary and Conclusions -- Chapter 2 Synchronous Temporal Interferometry -- 2.1 Introduction -- 2.1.1 Historical Review of the Theory of Phase-Shifting Algorithms (PSAs) -- 2.2 Temporal Carrier Interferometric Signal -- 2.3 Quadrature Linear Filters for Temporal Phase Estimation -- 2.3.1 Linear PSAs Using Real-Valued Low-Pass Filtering -- 2.4 The Minimum Three-Step PSA -- 2.4.1 Algebraic Derivation of the Minimum Three-Step PSA -- 2.4.2 Spectral FTF Analysis of the Minimum Three-Step PSA -- 2.5 Least-Squares PSAs -- 2.5.1 Temporal-to-Spatial Carrier Conversion: Squeezing Interferometry -- 2.6 Detuning Analysis in Phase-Shifting Interferometry (PSI) -- 2.7 Noise in Temporal PSI -- 2.7.1 Phase Estimation with Additive Random Noise -- 2.7.2 Noise Rejection in N-Step Least-Squares (LS) PSAs -- 2.7.3 Noise Rejection of Linear Tunable PSAs -- 2.8 Harmonics in Temporal Interferometry -- 2.8.1 Interferometric Data with Harmonic Distortion and Aliasing -- 2.8.2 PSA Response to Intensity-Distorted Interferograms -- 2.9 PSA Design Using First-Order Building Blocks -- 2.9.1 Minimum Three-Step PSA Design by First-Order FTF Building Blocks -- 2.9.2 Tunable Four-Step PSAs with Detuning Robustness at ω =-ω0 -- 2.9.3 Tunable Four-Step PSAs with Robust Background Illumination Rejection -- 2.9.4 Tunable Four-Step PSA with Fixed Spectral Zero at ω =π -- 2.10 Summary and Conclusions -- Chapter 3 Asynchronous Temporal Interferometry -- 3.1 Introduction
- 3.2 Classification of Temporal PSAs -- 3.2.1 Fixed-Coefficients (Linear) PSAs -- 3.2.2 Tunable (Linear) PSAs -- 3.2.3 Self-Tunable (Nonlinear) PSAs -- 3.3 Spectral Analysis of the Carré PSA -- 3.3.1 Frequency Transfer Function of the Carré PSA -- 3.3.2 Meta-Frequency Response of the Carré PSA -- 3.3.3 Harmonic-Rejection Capabilities of the Carré PSA -- 3.3.4 Phase-Step Estimation in the Carré PSA -- 3.3.5 Improvement of the Phase-Step Estimation in Self-Tunable PSAs -- 3.3.6 Computer Simulations with the Carré PSA with Noisy Interferograms -- 3.4 Spectral Analysis of Other Self-Tunable PSAs -- 3.4.1 Self-Tunable Four-Step PSA with Detuning-Error Robustness -- 3.4.2 Self-Tunable Five-Step PSA by Stoilov and Dragostinov -- 3.4.3 Self-Tunable Five-Step PSA with Detuning-Error Robustness -- 3.4.4 Self-Tunable Five-Step PSA with Double Zeroes at the Origin and the Tuning Frequency -- 3.4.5 Self-Tunable Five-Step PSA with Three Tunable Single Zeros -- 3.4.6 Self-Tunable Five-Step PSA with Second-Harmonic Rejection -- 3.5 Self-Calibrating PSAs -- 3.5.1 Iterative Least-Squares, the Advanced Iterative Algorithm -- 3.5.2 Principal Component Analysis -- 3.6 Summary and Conclusions -- Chapter 4 Spatial Methods with Carrier -- 4.1 Introduction -- 4.2 Linear Spatial Carrier -- 4.2.1 The Linear Carrier Interferogram -- 4.2.2 Instantaneous Spatial Frequency -- 4.2.3 Synchronous Detection with a Linear Carrier -- 4.2.4 Linear and Nonlinear Spatial PSAs -- 4.2.5 Fourier Transform Analysis -- 4.2.6 Space-Frequency Analysis -- 4.3 Circular Spatial Carrier -- 4.3.1 The Circular Carrier Interferogram -- 4.3.2 Synchronous Detection with a Circular Carrier -- 4.4 2D Pixelated Spatial Carrier -- 4.4.1 The Pixelated Carrier Interferogram -- 4.4.2 Synchronous Detection with a Pixelated Carrier -- 4.5 Regularized Quadrature Filters
- A.4.3 Four-Step PSA with First-Order Zeros at ω ={0,-ω0/2,-ω0} (ω0=2π/3) -- A.4.4 Four-Step PSA with a First-Order Zero at -ω0 and a Second-Order Zero at ω =0 (ω0=π/2) -- A.4.5 Four-Step PSA with a First-Order Zero at ω =0 and a Second-Order Zero at -ω0 (ω0=2π/3) -- A.5 Five-Step Linear PSAs -- A.5.1 Five-Step Least-Squares PSA (ω0=2π/5) -- A.5.2 Five-Step PSA with First-Order Zeros at ω ={0,± 2ω0} and a Second-Order Zero at -ω0 (ω0=π/2) -- A.5.3 Five-Step PSA with Second-Order Zeros at ω ={0,-ω0} (ω0=2π/3) -- A.5.4 Five-Step PSA with Second-Order Zeros at ω ={0,-ω0} (ω0=π/2) -- A.5.5 Five-Step PSA with a First-Order Zero at ω =0 and a Third-Order Zero at -ω0 (ω0=π/2) -- A.5.6 Five-Step PSA with a First-Order Zero at ω =0 and a Third-Order Zero at -ω0 (ω0=2π/3) -- A.6 Six-Step Linear PSAs -- A.6.1 Six-Step Least-Squares PSA (ω0=2π/6) -- A.6.2 Six-Step PSA with First-Order Zeros at {0, ±2ω0} and a Third-Order Zero at -ω0 (ω0=π/2) -- A.6.3 Six-Step PSA with a First-Order Zero at ω =0 and a Fourth-Order Zero at -ω0 (ω0=π/2) -- A.6.4 Six-Step PSA with a First-Order Zero at ω =0 and Second-Order Zeros at {-ω0,± 2ω0} (ω0=π/2) -- A.6.5 Six-Step (5LS + 1) PSA with a Second-Order Zero at -ω0 (ω0=2π/5) -- A.7 Seven-Step Linear PSAs -- A.7.1 Seven-Step Least-Squares PSA (ω0=2π/7) -- A.7.2 Seven-Step PSA with First-Order Zeros at {0,-ω0,2ω0, ±3ω0} and a Second-Order Zero at -2ω0 (ω0=2π/6) -- A.7.3 Seven-Step PSA with First-Order Zeros at {0,-ω0,2ω0} and a Second-Order Zero at ± 3ω0 (ω0=2π/6) -- A.7.4 Seven-Step PSA with First-Order Zeros at {0, ± 2ω0} and a Fourth-Order Zero at -ω0 (ω0=π/2) -- A.7.5 Seven-Step PSA with Second-Order Zeros at {0,-ω0, ±2ω0} (ω0=π/2) -- A.7.6 Seven-Step PSA with a First-Order Zero at ω =0 and a Fifth-Order Zero at -ω0 (ω0=π/2) -- A.7.7 Seven-Step (6LS + 1) PSA with a Second-Order Zero at -ω0 (ω0=2π/6) -- A.8 Eight-Step Linear PSAs