1st Edition

Phase Estimation in Optical Interferometry

Edited By Pramod Rastogi, Erwin Hack Copyright 2015
    366 Pages 17 Color & 305 B/W Illustrations
    by CRC Press

    366 Pages 17 Color & 305 B/W Illustrations
    by CRC Press

    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.

    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

    Index

    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.