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Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications [Kõva köide]

(Universidad Complutense de Madrid, Spain), (Centro de Investigaciones en Óptica AC, Mexico), (Nationale Supérieure des Télécommunications, France; Centro de Investigaciones en Óptica AC, Mexico)
  • Formaat: Hardback, 344 pages, kõrgus x laius x paksus: 251x175x24 mm, kaal: 898 g
  • Ilmumisaeg: 02-Jul-2014
  • Kirjastus: Blackwell Verlag GmbH
  • ISBN-10: 3527411526
  • ISBN-13: 9783527411528
Teised raamatud teemal:
Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and ApplicationsSuurem pilt
  • Formaat: Hardback, 344 pages, kõrgus x laius x paksus: 251x175x24 mm, kaal: 898 g
  • Ilmumisaeg: 02-Jul-2014
  • Kirjastus: Blackwell Verlag GmbH
  • ISBN-10: 3527411526
  • ISBN-13: 9783527411528
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783527411528.html
Märksõnad:
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.

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.

Arvustused

"I recommend this book for several reasons: it provides great insights into the principles and practical applications of classical and advanced interferometry in optical metrology, and it presents the main algorithms for recovering the modulating phase from single or multiple patterns." (Optics & Photonics, 8 October 2014)

Preface xi
List of Symbols and Acronyms
xv
1 Digital Linear Systems
1(56)
1.1 Introduction to Digital Phase Demodulation in Optical Metrology
1(8)
1.1.1 Fringe Pattern Demodulation as an Ill-Posed Inverse Problem
1(2)
1.1.2 Adding a priori Information to the Fringe Pattern: Carriers
3(4)
1.1.3 Classification of Phase Demodulation Methods in Digital Interferometry
7(2)
1.2 Digital Sampling
9(5)
1.2.1 Signal Classification
9(2)
1.2.2 Commonly Used Functions
11(2)
1.2.3 Impulse Sampling
13(1)
1.2.4 Nyquist--Shannon Sampling Theorem
14(1)
1.3 Linear Time-Invariant (LTI) Systems
14(4)
1.3.1 Definition and Properties
15(1)
1.3.2 Impulse Response of LTI Systems
15(2)
1.3.3 Stability Criterion: Bounded-Input Bounded-Output
17(1)
1.4 Z-Transform Analysis of Digital Linear Systems
18(6)
1.4.1 Definition and Properties
18(1)
1.4.2 Region of Convergence (ROC)
19(1)
1.4.3 Poles and Zeros of a Z-Transform
20(1)
1.4.4 Inverse Z-Transform
21(1)
1.4.5 Transfer Function of an LTI System in the Z-Domain
22(1)
1.4.6 Stability Evaluation by Means of the Z-Transform
23(1)
1.5 Fourier Analysis of Digital LTI Systems
24(10)
1.5.1 Definition and Properties of the Fourier Transform
25(1)
1.5.2 Discrete-Time Fourier Transform (DTFT)
25(1)
1.5.3 Relation Between the DTFT and the Z-Transform
26(1)
1.5.4 Spectral Interpretation of the Sampling Theorem
27(2)
1.5.5 Aliasing: Sub-Nyquist Sampling
29(2)
1.5.6 Frequency Transfer Function (FTF) of an LTI System
31(2)
1.5.7 Stability Evaluation in the Fourier Domain
33(1)
1.6 Convolution-Based One-Dimensional (1D) Linear Filters
34(5)
1.6.1 One-Dimensional Finite Impulse Response (FIR) Filters
34(3)
1.6.2 One-Dimensional Infinite Impulse Response (IIR) Filters
37(2)
1.7 Convolution-Based two-dimensional (2D) Linear Filters
39(3)
1.7.1 Two-Dimensional (2D) Fourier and Z-Transforms
39(1)
1.7.2 Stability Analysis of 2D Linear Filters
40(2)
1.8 Regularized Spatial Linear Filtering Techniques
42(6)
1.8.1 Classical Regularization for Low-Pass Filtering
42(4)
1.8.2 Spectral Response of 2D Regularized Low-Pass Filters
46(2)
1.9 Stochastic Processes
48(6)
1.9.1 Definitions and Basic Concepts
48(3)
1.9.2 Ergodic Stochastic Processes
51(1)
1.9.3 LTI System Response to Stochastic Signals
52(1)
1.9.4 Power Spectral Density (PSD) of a Stochastic Signal
52(2)
1.10 Summary and Conclusions
54(3)
2 Synchronous Temporal Interferometry
57(50)
2.1 Introduction
57(3)
2.1.1 Historical Review of the Theory of Phase-Shifting Algorithms (PSAs)
57(3)
2.2 Temporal Carrier Interferometric Signal
60(2)
2.3 Quadrature Linear Filters for Temporal Phase Estimation
62(6)
2.3.1 Linear PSAs Using Real-Valued Low-Pass Filtering
64(4)
2.4 The Minimum Three-Step PSA
68(3)
2.4.1 Algebraic Derivation of the Minimum Three-Step PSA
68(1)
2.4.2 Spectral FTF Analysis of the Minimum Three-Step PSA
69(2)
2.5 Least-Squares PSAs
71(3)
2.5.1 Temporal-to-Spatial Carrier Conversion: Squeezing Interferometry
73(1)
2.6 Detuning Analysis in Phase-Shifting Interferometry (PSI)
74(6)
2.7 Noise in Temporal PSI
80(7)
2.7.1 Phase Estimation with Additive Random Noise
82(3)
2.7.2 Noise Rejection in N-Step Least-Squares (LS) PSAs
85(1)
2.7.3 Noise Rejection of Linear Tunable PSAs
86(1)
2.8 Harmonics in Temporal Interferometry
87(8)
2.8.1 Interferometric Data with Harmonic Distortion and Aliasing
88(3)
2.8.2 PSA Response to Intensity-Distorted Interferograms
91(4)
2.9 PSA Design Using First-Order Building Blocks
95(9)
2.9.1 Minimum Three-Step PSA Design by First-Order FTF Building Blocks
97(3)
2.9.2 Tunable Four-Step PSAs with Detuning Robustness at ω = ω0
100(1)
2.9.3 Tunable Four-Step PSAs with Robust Background Illumination Rejection
101(1)
2.9.4 Tunable Four-Step PSA with Fixed Spectral Zero at ω = π
102(2)
2.10 Summary and Conclusions
104(3)
3 Asynchronous Temporal Interferometry
107(42)
3.1 Introduction
107(1)
3.2 Classification of Temporal PSAs
108(2)
3.2.1 Fixed-Coefficients (Linear) PSAs
108(1)
3.2.2 Tunable (Linear) PSAs
108(1)
3.2.3 Self-Tunable/(Nonlinear) PSAs
109(1)
3.3 Spectral Analysis of the Carre PSA
110(12)
3.3.1 Frequency Transfer Function of the Carre PSA
112(1)
3.3.2 Meta-Frequency Response of the Carre PSA
113(1)
3.3.3 Harmonic-Rejection Capabilities of the Carre PSA
114(2)
3.3.4 Phase-Step Estimation in the Carre PSA
116(2)
3.3.5 Improvement of the Phase-Step Estimation in Self-Tunable PSAs
118(2)
3.3.6 Computer Simulations with the Carre PSA with Noisy Interferograms
120(2)
3.4 Spectral Analysis of Other Self-Tunable PSAs
122(14)
3.4.1 Self-Tunable Four-Step PSA with Detuning-Error Robustness
123(3)
3.4.2 Self-Tunable Five-Step PSA by Stoilov and Dragostinov
126(2)
3.4.3 Self-Tunable Five-Step PSA with Detuning-Error Robustness
128(2)
3.4.4 Self-Tunable Five-Step PSA with Double Zeroes at the Origin and the Tuning Frequency
130(1)
3.4.5 Self-Tunable Five-Step PSA with Three Tunable Single Zeros
131(2)
3.4.6 Self-Tunable Five-Step PSA with Second-Harmonic Rejection
133(3)
3.5 Self-Calibrating PSAs
136(9)
3.5.1 Iterative Least-Squares, the Advanced Iterative Algorithm
137(3)
3.5.2 Principal Component Analysis
140(5)
3.6 Summary and Conclusions
145(4)
4 Spatial Methods with Carrier
149(52)
4.1 Introduction
149(1)
4.2 Linear Spatial Carrier
149(24)
4.2.1 The Linear Carrier Interferogram
149(3)
4.2.2 Instantaneous Spatial Frequency
152(3)
4.2.3 Synchronous Detection with a Linear Carrier
155(4)
4.2.4 Linear and Nonlinear Spatial PSAs
159(5)
4.2.5 Fourier Transform Analysis
164(6)
4.2.6 Space--Frequency Analysis
170(3)
4.3 Circular Spatial Carrier
173(4)
4.3.1 The Circular Carrier Interferogram
173(1)
4.3.2 Synchronous Detection with a Circular Carrier
174(3)
4.4 2D Pixelated Spatial Carrier
177(9)
4.4.1 The Pixelated Carrier Interferogram
177(3)
4.4.2 Synchronous Detection with a Pixelated Carrier
180(6)
4.5 Regularized Quadrature Filters
186(12)
4.6 Relation Between Temporal and Spatial Analysis
198(1)
4.7 Summary and Conclusions
198(3)
5 Spatial Methods Without Carrier
201(40)
5.1 Introduction
201(1)
5.2 Phase Demodulation of Closed-Fringe Interferograms
201(3)
5.3 The Regularized Phase Tracker (RPT)
204(11)
5.4 Local Robust Quadrature Filters
215(1)
5.5 2D Fringe Direction
216(13)
5.5.1 Fringe Orientation in Interferogram Processing
216(3)
5.5.2 Fringe Orientation and Fringe Direction
219(3)
5.5.3 Orientation Estimation
222(3)
5.5.4 Fringe Direction Computation
225(4)
5.6 2D Vortex Filter
229(6)
5.6.1 The Hilbert Transform in Phase Demodulation
229(1)
5.6.2 The Vortex Transform
230(3)
5.6.3 Two Applications of the Vortex Transform
233(2)
5.7 The General Quadrature Transform
235(4)
5.8 Summary and Conclusions
239(2)
6 Phase Unwrapping
241(30)
6.1 Introduction
241(3)
6.1.1 The Phase Unwrapping Problem
241(3)
6.2 Phase Unwrapping by 1D Line Integration
244(6)
6.2.1 Line Integration Unwrapping Formula
244(2)
6.2.2 Noise Tolerance of the Line Integration Unwrapping Formula
246(4)
6.3 Phase Unwrapping with 1D Recursive Dynamic System
250(1)
6.4 1D Phase Unwrapping with Linear Prediction
251(4)
6.5 2D Phase Unwrapping with Linear Prediction
255(2)
6.6 Least-Squares Method for Phase Unwrapping
257(1)
6.7 Phase Unwrapping Through Demodulation Using a Phase Tracker
258(4)
6.8 Smooth Unwrapping by Masking out 2D Phase Inconsistencies
262(4)
6.9 Summary and Conclusions
266(5)
Appendix A List of Linear Phase-Shifting Algorithms (PSAs)
271(44)
A.1 Brief Review of the PSAs Theory
271(3)
A.2 Two-Step Linear PSAs
274(1)
A.2.1 Two-Step PSA with a First-Order Zero at --ω0 (ω0 = π/2)
274(1)
A.3 Three-Step Linear PSAs
275(2)
A.3.1 Three-Step Least-Squares PSA (ω0 = 2π/3)
275(1)
A.3.2 Three-Step PSA with First-Order Zeros at ω = {0, --ω0} (ω0 = π/2)
276(1)
A.4 Four-Step Linear PSAs
277(5)
A.4.1 Four-Step Least-Squares PSA (ω0 = 2π/4)
277(1)
A.4.2 Four-Step PSA with a First-Order Zero at ω = 0 and a Second-Order Zero at --ω0 (ω0 = π/2)
278(1)
A.4.3 Four-Step PSA with First-Order Zeros at ω = {0, -ω0/2, --ω0} (ω = π/2)
279(1)
A.4.4 Four-Step PSA with a First-Order Zero at -ω0 and a Second-Order Zero at ω = 0 (ω0 = π/2)
280(1)
A.4.5 Four-Step PSA with a First-Order Zero at ω = 0 and a Second-Order Zero at --ω0 (ω0 = 2π/3)
281(1)
A.5 Five-Step Linear PSAs
282(6)
A.5.1 Five-Step Least-Squares PSA (ω0 = 2π/5)
282(1)
A.5.2 Five-Step PSA with First-Order Zeros at ω = {0, ±2ω0} and a Second-Order Zero at --ω0 (ω0 = π/2)
283(1)
A.5.3 Five-Step PSA with Second-Order Zeros at ω = {0, -ω0} (ω0 = 2π/3)
284(1)
A.5.4 Five-Step PSA with Second-Order Zeros at ω = {0, --ω0} (ω0 = π/2)
285(1)
A.5.5 Five-Step PSA with a First-Order Zero at ω = 0 and a Third-Order Zero at -ω0 (ω0 = π/2)
286(1)
A.5.6 Five-Step PSA with a First-Order Zero at ω = 0 and a Third-Order Zero at -ω0 (ω0 = 2π/3)
287(1)
A.6 Six-Step Linear PSAs
288(5)
A.6.1 Six-Step Least-Squares PSA (ω0 = 2π/6)
288(1)
A.6.2 Six-Step PSA with First-Order Zeros at {0, ±2ω0} and a Third-Order Zero at --ω0 (ω0 = π/2)
289(1)
A.6.3 Six-Step PSA with a First-Order Zero at ω = 0 and a Fourth-Order Zero at --ω0 (ω0 = π/2)
290(1)
A.6.4 Six-Step PSA with a First-Order Zero at ω = 0 and Second-Order Zeros at {--ω, ±2ω0} (ω0 = π/2)
291(1)
A.6.5 Six-Step (5LS + 1) PSA with a Second-Order Zero at --ω0 (ω0 = 2π/5)
292(1)
A.7 Seven-Step Linear PSAs
293(7)
A.7.1 Seven-Step Least-Squares PSA (ω0 = 2π/7)
293(1)
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)
294(1)
A.7.3 Seven-Step PSA with First-Order Zeros at {0, --ω0, 2ω0} and a Second-Order Zero at ±3ω0 (ω0 = 2π/6)
295(1)
A.7.4 Seven-Step PSA with First-Order Zeros at {0,±2ω0} and a Fourth-Order Zero at --ω0 (ω0 = π/2)
296(1)
A.7.5 Seven-Step PSA with Second-Order Zeros at {0, --ω0, ±2ω0} (ω0 = π/2)
297(1)
A.7.6 Seven-Step PSA with a First-Order Zero at ω = 0 and a Fifth-Order Zero at --ω0 (ω0 = π/2)
298(1)
A.7.7 Seven-Step (6LS + 1) PSA with a Second-Order Zero at --ω0 (ω0 = 2π/6)
299(1)
A.8 Eight-Step Linear PSAs
300(6)
A.8.1 Eight-Step Least-Squares PSA (ω0 = 2π/8)
300(1)
A.8.2 Eight-Step Frequency-Shifted LS-PSA (ω0 = 2 X 2π/8)
301(1)
A.8.3 Eight-Step PSA with First-Order Zeros at {0, --ω0, ±2ω0, π/10, --3π/10, --7π/10, 9π/10}
302(1)
A.8.4 Eight-Step PSA with Second-Order Zeros at {0, ±2ω0} and a Third-Order Zero at --ω0 (ω0 = π/2)
303(1)
A.8.5 Eight-Step PSA with First-Order Zeros at {0, --π/6, --5π/6, ±2ω0} and a Fourth-Order Zero at --ω0 (ω0 = π/2)
304(1)
A.8.6 Eight-Step PSA with First-Order Zeros at {0, ±2ω0} and a Fifth-Order Zero at --ω0 (ω0 = π/2)
305(1)
A.9 Nine-Step Linear PSAs
306(3)
A.9.1 Nine-Step Least-Squares PSA (ω0 = 2π/9)
306(1)
A.9.2 Nine-Step PSA with First-Order Zeros at {0, ±2ω0} and Second-Order Zeros at {--ω0, --π/4, --3π/4} (ω0 = π/2)
307(1)
A.9.3 Nine-Step (8LS + 1) PSA (ω0 = 2π/8)
308(1)
A.10 Ten-Step Linear PSAs
309(2)
A.10.1 Ten-Step Least-Squares PSA (ω0 = 2π/10)
309(1)
A.10.2 Ten-Step PSA with a First-Order Zero at ω = 0 and Second-Order Zeros at {--ω0,±2ω0,±3ω0} (ω0 = π/3)
310(1)
A.11 Eleven-Step Linear PSAs
311(3)
A.11.1 Eleven-Step Least-Squares PSA (ω0 = 2π/11)
311(1)
A.11.2 Eleven-Step PSA with Second-Order Zeros at {0, --ω0,±2ω0,±3ω0} (ω0 = π/3)
312(1)
A.11.3 Eleven-Step Frequency-Shifted LS-PSA (ω0 = 3 X 2π/11)
313(1)
A.12 Twelve-step linear PSAs
314(1)
A.12.1 Twelve-step frequency-shifted LS-PSA (ω0 = 5 X 2π/12)
314(1)
References 315(10)
Index 325
Manuel Servin received his engineering diploma from the École Nationale Supérieure des Télécommunications in France (1982), and his Ph.D. from the Centro de Investigaciones en Óptica 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 Óptica (CIO) at León 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.