Skip to main content

Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications

Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications

Manuel Servin, J. Antonio Quiroga, Moises Padilla

ISBN: 978-3-527-68107-5

Jun 2014

344 pages


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.
Chapter 1 Digital Linear Systems
1.1 Introduction
1.2 Digital Sampling
1.3 Linear time-invariant (LTI) systems
1.4 Z-transform analysis of digital linear systems
1.5 Fourier analysis of digital linear systems
1.6 Convolution one-dimensional digital filters
1.7 Convolution two-dimensional linear filters
1.8 Linear regularized filtering techniques
1.9 Stochastic processes
1.10 Linear quadrature filters

Chapter 2 Synchronous Temporal Interferometry
2.1 Introduction
2.2 The temporal carrier interferometric signal
2.3 Quadrature linear filters for phase estimation
2.4 The minimum 3-step PSA
2.5 Least-squares PSAs
2.6 Detuning in temporal interferometry
2.7 Noise in temporal interferometry
2.8 Harmonics in temporal interferometry
2.9 Quadrature filters design by 1st-order building blocks
2.10 Some further topics in linear PSAs theory

Chapter 3 Asynchronous Temporal Interferometry
3.1 Introduction
3.2 Spectral analysis of the Carré algorithm
3.3 Spectral analysis of other self-tunable PSAs
3.4 Self-calibrating PSAs

Chapter 4 Spatial Methods with Carrier
4.1 Introduction
4.2 Linear spatial carrier
4.3 Circular spatial carrier interferogram
4.4 2D Pixelated Spatial Carrier
4.5 Regularized Quadrature Filters
4.6 Relation Between Temporal and Spatial Analysis

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 231
5.5 2D Fringe Direction
5.6 2D Vortex Filter
5.7 The General Quadrature Transform

Chapter 6 Phase Unwrapping
6.1 Introduction
6.2 Phase unwrapping with by 1D line integration
6.3 Phase unwrapping with 1D IIR filters
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 with 2D detection of phase inconsistencies
6.9 Quality Maps and Branch Cut Methods

List of linear phase-shifting algorithms (PSAs)

“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)