Fringe Pattern Analysis for Optical Metrology

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 pattern analysis applied to optical metrology. A major novelty of this work is the presentation of a unified theoretical framework based on the Fourier description of phase shifting interferometry using the Frequency Transfer Function (FTF) along with the theory of Stochastic Process for the straightforward analysis and synthesis of phase shifting algorithms with desired properties such as spectral response, detuning and signal-to-noise robustness, harmonic rejection, etc.

Auteur
Manuel Servin received his engineering diploma from the Ecole Nationale Superieure des Telecommunications in France (1982), and his Ph.D. from the Centro de Investigaciones en Optica A. C. (CIO) at Leon Mexico in 1994. He is co-author of the book `Interferogram Analysis for Optical Testing?. Dr. Servin has published more than 100 papers in scientific peer-reviewed journals on Digital Interferometry and Fringe Analysis.

Juan Antonio Quiroga received his Ph.D. in physics in 1994 from the Universidad Complutense de Madrid, Spain. He is now teaching there at the Physics Faculty. His current principal areas of interest are Digital image processing applied to Optical Metrology and applied optics

Moises Padilla is a Ph.D. student in optical sciences at the Centro de Investigaciones en Optica (CIO) at Leon Mexico. He is associated with the optical metrology division of the CIO. His research activities are in digital signal processing and electrical communication engineering applied to processing and analysis of optical interferogram images.

Texte du rabat

This book presents the theoretical principles and practical applications for classical and advanced interferometry in optical-metrology. A major novelty of this work is the use of the Frequency Transfer Function (FTF) and the theory of Stochastic Process in fringe pattern analysis. These mathematical tools better describe the phase demodulation algorithms with desired spectral response, detuning insensitivity, signal-to-noise robustness and harmonic rejection.

From the contents:
• Digital Linear Systems
• Synchronous Temporal Interferometry
• Asynchronous Temporal Interferometry
• Spatial Methods with Carrier
• Spatial Methods without Carrier
• Phase Unwrapping
• List of 40 Phase-Shifting Algorithms

Contenu

Preface XI

List of Symbols and Acronyms XV

1 Digital Linear Systems 1

1.1 Introduction to Digital Phase Demodulation in Optical Metrology 1

1.1.1 Fringe Pattern Demodulation as an I11-Posed Inverse Problem 1

1.1.2 Adding a priori Information to the Fringe Pattern: Carriers 3

1.1.3 Classification of Phase Demodulation Methods in Digital Interferometry 7

1.2 Digital Sampling 9

1.2.1 Signal Classification 9

1.2.2 Commonly Used Functions 11

1.2.3 Impulse Sampling 13

1.2.4 NyquistShannon Sampling Theorem 14

1.3 Linear Time-Invariant (LTI) Systems 14

1.3.1 Definition and Properties 15

1.3.2 Impulse Response of LTI Systems 15

1.3.3 Stability Criterion: Bounded-Input Bounded-Output 17

1.4 Z-Transform Analysis of Digital Linear Systems 18

1.4.1 Definition and Properties 18

1.4.2 Region of Convergence (ROC) 19

1.4.3 Poles and Zeros of a Z-Transform 20

1.4.4 Inverse Z-Transform 21

1.4.5 Transfer Function of an LTI System in the Z-Domain 22

1.4.6 Stability Evaluation by Means of the Z-Transform 23

1.5 Fourier Analysis of Digital LTI Systems 24

1.5.1 Definition and Properties of the Fourier Transform 25

1.5.2 Discrete-Time Fourier Transform (DTFT) 25

1.5.3 Relation Between the DTFT and the Z-Transform 26

1.5.4 Spectral Interpretation of the Sampling Theorem 27

1.5.5 Aliasing: Sub-Nyquist Sampling 29

1.5.6 Frequency Transfer Function (FTF) of an LTI System 31

1.5.7 Stability Evaluation in the Fourier Domain 33

1.6 Convolution-Based One-Dimensional (1D) Linear Filters 34

1.6.1 One-Dimensional Finite Impulse Response (FIR) Filters 34

1.6.2 One-Dimensional Infinite Impulse Response (IIR) Filters 37

1.7 Convolution-Based two-dimensional (2D) Linear Filters 39

1.7.1 Two-Dimensional (2D) Fourier and Z-Transforms 39

1.7.2 Stability Analysis of 2D Linear Filters 40

1.8 Regularized Spatial Linear Filtering Techniques 42

1.8.1 Classical Regularization for Low-Pass Filtering 42

1.8.2 Spectral Response of 2D Regularized Low-Pass Filters 46

1.9 Stochastic Processes 48

1.9.1 Definitions and Basic Concepts 48

1.9.2 Ergodic Stochastic Processes 51

1.9.3 LTI System Response to Stochastic Signals 52

1.9.4 Power Spectral Density (PSD) of a Stochastic Signal 52

1.10 Summary and Conclusions 54

2 Synchronous Temporal Interferometry 57

2.1 Introduction 57

2.1.1 Historical Review of the Theory of Phase-Shifting Algorithms (PSAs) 57

2.2 Temporal Carrier Interferometric Signal 60

2.3 Quadrature Linear Filters for Temporal Phase Estimation 62

2.3.1 Linear PSAs Using Real-Valued Low-Pass Filtering 64

2.4 The Minimum Three-Step PSA 68

2.4.1 Algebraic Derivation of the Minimum Three-Step PSA 68

2.4.2 Spectral FTF Analysis of the Minimum Three-Step PSA 69

2.5 Least-Squares PSAs 71

2.5.1 Temporal-to-Spatial Carrier Conversion: Squeezing Interferometry 73

2.6 Detuning Analysis in Phase-Shifting Interferometry (PSI) 74

2.7 Noise in Temporal PSI 80

2.7.1 Phase Estimation with Additive Random Noise 82

2.7.2 Noise Rejection in N-Step Least-Squares (LS) PSAs 85

2.7.3 Noise Rejection of Linear Tunable PSAs 86

2.8 Harmonics in Temporal Interferometry 87

2.8.1 Interferometric Data with Harmonic Distortion and Aliasing 88

2.8.2 PSA Response to Intensity-Distorted Interferograms 91

2.9 PSA Design Using First-Order Building Blocks 95

2.9.1 Minimum Three-Step PSA Design by First-Order FTF Building Blocks 97

2.9.2 Tunable Four-Step PSAs with Detuning Robustness at 𝜔 = 𝜔0 100

2.9.3 Tunable Four-Step PSAs with Robust Background Illumination Rejection 101

2.9.4 Tunable Four-Step PSA with Fixed Spectral Zero at 𝜔 = 102

2.10 Summary and Conclusions 104 <p...