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Phase Estimation in Optical Interferometry





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ISBN 9781466598317
Published November 21, 2014 by CRC Press
366 Pages 17 Color & 305 B/W Illustrations

 
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Book Description

Phase Estimation in Optical Interferometry covers the essentials of phase-stepping algorithms used in interferometry and pseudointerferometric techniques. It presents the basic concepts and mathematics needed for understanding the phase estimation methods in use today.

The first four chapters focus on phase retrieval from image transforms using a single frame. The next several chapters examine the local environment of a fringe pattern, give a broad picture of the phase estimation approach based on local polynomial phase modeling, cover temporal high-resolution phase evaluation methods, and present methods of phase unwrapping. The final chapter discusses experimental imperfections that are liable to adversely influence the accuracy of phase measurements.

Responding to the push for the deployment of novel technologies and fast-evolving techniques, this book provides a framework for understanding various modern phase estimation methods. It also helps readers get a comparative view of the performance and limitations of the approaches.

Table of Contents

Fourier Fringe Demodulation Mitsuo Takeda
INTRODUCTION
PRINCIPLE OF THE GENERIC FTM FOR FRINGE DEMODULATION
GENERAL FEATURES OF THE FTM
APPLICATIONS OF FOURIER FRINGE DEMODULATION
CONCLUSION
REFERENCES

Windowed Fourier Transforms Jingang Zhong and Jiawen Weng
INTRODUCTION
PHASE DEMODULATION BASED ON FOURIER TRANSFORM
PHASE DEMODULATION BASED ON WINDOWED FOURIER TRANSFORM
PHASE DEMODULATION BASED ON ADAPTIVE WINDOWED FOURIER TRANSFORM
NUMERICAL ANALYSIS
EXPERIMENTAL ANALYSIS EXAMPLE
CONCLUSION
REFERENCES

Continuous Wavelet Transforms Lionel R. Watkins
INTRODUCTION
THE ONE-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM
WAVELET CENTERS AND BANDWIDTHS
SCALOGRAMS
RIDGE OF THE CONTINUOUS WAVELET TRANSFORM
THE GRADIENT METHOD
THE PHASE METHOD
FOURIER APPROACH TO CWT
EFFECT OF DISCONTINUITIES AT THE SIGNAL EDGE
ONE-DIMENSIONAL WAVELET FUNCTIONS
TWO-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM
CONCLUSIONS
APPENDIX A
RIDGE OF THE TWO-DIMENSIONAL CWT
REFERENCES

The Spiral Phase Transform Kieran G. Larkin
INTRODUCTION
THEORY
IMPLEMENTATION
WHEN TO USE THE SPIRAL PHASE TRANSFORM
PRACTICAL DEMODULATION EXAMPLE
SUMMARY
REFERENCES

Regularized Phase Estimation Methods in Interferometry Moises Padilla and Manuel Servin
INTRODUCTION
REGULARIZED LOW-PASS LINEAR FILTERING
CONVOLUTION-BASED TEMPORAL PHASE-SHIFTING INTERFEROMETRY
SPATIALLY REGULARIZED TEMPORAL LINEAR CARRIER INTERFEROMETRY
CONVOLUTION-BASED SPATIAL-CARRIER INTERFEROMETRY
REGULARIZATION IN GENERAL SPATIAL CARRIER INTERFEROMETRY
TEMPORAL REGULARIZATION IN PHASE-SHIFTING INTERFEROMETRY
REGULARIZED PHASE ESTIMATION OF SINGLE-IMAGE CLOSED-FRINGES INTERFEROGRAMS
REGULARIZED SPATIAL INTERPOLATION-EXTRAPOLATION IN INTERFEROMETRY
REGULARIZATION IN LATERAL SHEARING INTERFEROMETRY
CONCLUSIONS
REFERENCES

Local Polynomial Phase Modeling and Estimation Gannavarpu Rajshekhar, Sai Siva Gorthi, and Pramod Rastogi
INTRODUCTION
DIGITAL HOLOGRAPHIC INTERFEROMETRY
PRINCIPLE
MAXIMUM LIKELIHOOD ESTIMATION
CUBIC PHASE FUNCTION
HIGH-ORDER AMBIGUITY FUNCTION
PHASE-DIFFERENCING OPERATOR
CONCLUSIONS
REFERENCES

Signal-Processing Methods in Phase-Shifting Interferometry Abhijit Patil, Rajesh Langoju, and Pramod Rastogi
INTRODUCTION
TEMPORAL TECHNIQUES
LINEAR PHASE STEP ESTIMATION METHODS
EVALUATION OF PHASE DISTRIBUTION
DUAL PZT IN HOLOGRAPHIC MOIRÉ
EVALUATION OF PHASE DISTRIBUTION IN HOLOGRAPHIC MOIRÉ
NONLINEAR PHASE STEP ESTIMATION METHOD
SUMMARY OF SIGNAL-PROCESSING METHODS
REFERENCES

Phase Unwrapping David R. Burton
INTRODUCTION
THE BASIC OPERATION OF PHASE UNWRAPPING
PHASE UNWRAPPING: THE PRACTICAL ISSUES AND CHALLENGES
PHASE UNWRAPPING AND DEFENSIVE PROGRAMMING
PHASE-UNWRAPPING ALGORITHMS
ONLINE SOURCES OF UNWRAPPING CODES
CONCLUSION
REFERENCES

Uncertainty in Phase Measurements Erwin Hack
INTRODUCTION
INFLUENCE QUANTITIES
QUANTIFICATION OF UNCERTAINTY CONTRIBUTIONS
UNCERTAINTY CONTRIBUTIONS FOR IMAGING
UNCERTAINTY CONTRIBUTIONS FOR LINEAR PHASE-STEPPING ALGORITHMS
PHASE MEASUREMENT UNCERTAINTY FOR CARRÉ-TYPE ALGORITHMS
PHASE MEASUREMENT UNCERTAINTY FOR SINGLE-FRAME ALGORITHMS
SUMMARY
REFERENCES

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Editor(s)

Biography

Professor Pramod Rastogi is the author or coauthor of over 150 scientific papers in peer-reviewed archival journals, the author of encyclopedia articles, and editor of several books in the field of optical metrology. Professor Rastogi is also the co-editor-in-chief of the International Journal of Optics and Lasers in Engineering. A recipient of the 2014 SPIE Dennis Gabor Award, he is a member of the Swiss Academy of Engineering Sciences and a fellow of the Society of the Photo-Optical Instrumentation Engineers and the Optical Society of America. He received a PhD from the University of Franche Comté.

Dr. Erwin Hack is a senior scientist at EMPA, lecturer at ETH Zurich, associate editor of Optics and Lasers in Engineering, vice chair of CEN WS71 on validation of computational solid mechanics models using strain fields from calibrated measurement (VANESSA), vice president of the Swiss Society for Non-Destructive Testing, and a member of EOS and OSA. Dr. Hack has authored or coauthored more than 80 papers in peer-reviewed journals and conferences and coedited the book Optical Methods in Solid Mechanics. He received a PhD in physical chemistry from the University of Zurich. His research interests include THz imaging, digital speckle pattern interferometry, and thermography.