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Ass i s tan t E d i t o r

Dr. W e r n e r Skolaut Springer-Verlag Heidelberg Topics in Applied Physics Tiergartenstr. 17 69121 Heidelberg Germany Emall: skolaut@springer.de

Dr. Hans J. K61sch Springer-Verlag Heidelberg Topics in Applied Physics Tiergartenstr. 17 69121 Heidelberg Germany Email: koelsch@springer.de

Pramod K. Rastogi (Ed.)

Photomechanics

With 314 Figures

¢ Springer

Dr. P r a m o d K. R a s t o g i (Ed. )

Stress Analysis Laboratory IMAC-DGC Swiss Federal Institute of Technology lO15 Lausanne Switzerland Email: rastogi@irnac.epfl.ch

Library of Congress Cataloging-in-Publication Data

Photomechanics / Pramod K. Rastogi (ed.). p. cm. -- (Topics in applied physics, ISSN 03034216 ; v. 77)

Includes bibliographical references and index. ISBN 3540659900 (hardcover : alk. paper) 1. Non-destructive testing. 2. Photonics. 3. Holographic interferometry. 4. Moir~

method. 5. Optoelectronic devices. I. Rastogi, P. K. (Pramod K.) II. Series.

ta417.2 .P483 1999 620.1'127--dc21

Physics a n d A s t r o n o m y Class i f ica t ion Scheme (PACS): 06.3o.-k; 06.20.-f; 42.62.Eh

99-052204

ISSN p r i n t edi t ion: 0303-4216 ISSN e lec t ronic edi t ion: 1437-0859 ISBN 3-540-65990-0 Spr inger -Ver lag Berl in He ide lbe rg N e w York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.

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The important thing in science is not so much to obtainnew facts as to discover new ways to thinking about them.

Sir William Lawrence Bragg.

in Beyond Reductionism, A. Koestler and J. R. Smithies

(London: Hutchinson) p. 115.

Preface

The word “photomechanics” describes the synergy between the fields of pho-tonics and mechanics. Photonics is the technology of generating and detectingradiant energy whose basic unit is the photon. Mechanics, on the other hand,is the science that deals with objects (solids or fluids) at rest or in motion andunder the action of external loads. Photomechanics thus refers to the tech-nology that uses photonics for measurements in mechanics. In other words,photomechanics forms the basis of a whole range of photonics-related tech-niques used in the measurement of variations in certain important physicalquantities such as displacements, strains, densities, etc. in solid mechanicsand flow problems. While photonics by definition is supposed to encompassthe entire spectral width, the scope of the present book has been intention-ally limited to cover a broad selection of topics in the visible range of thespectrum in order to keep the length of the book within reasonable limits.

The application of photomechanics has experienced constant expansionover the last several years to just about every field of engineering sciences.This has been driven, first, by the extreme flexibility and the unique featuresassociated to optical measurement methods; second, by an improved under-standing of the physics behind these methods, permitting their performanceto be optimized; third, by advances in the rapid acquisition and analysis ofdata through the availability of refined information-technology tools; and lastbut not the least, by a growing awareness among the engineers and scientistsof the real utility of these methods in diverse areas of science and engineering.There is every reason to believe that this strong growth will continue in thefuture.

The book is broadly targeted to meet the requirements of beginners and ofall those scientists and engineers who want to use, or are involved in, opticalnondestructive measurements. The first two Chapters are of an introductorycharacter. The first Chapter, by D. Malacara-Hernandez, provides a brief in-sight into relevant optical principles for engineers, while the introduction toengineering mechanics by A. Asundi in the next chapter is addressed specif-ically to physicists involved in the development of photomechanics methods.The contribution, by Y. Surrel, treats fringe analysis using digital imageprocessing. The next chapter , by R. K. Rastogi, introduces the principlesof holographic interferometry and speckle metrology and describes the ex-perimental methods needed to perform in situ measurements. In the fifth

VIII Preface

contribution D. Post, B. Han and P. G. Ifju present several Moire approacheswith emphasis on applications. The contribution, by T. Y. Chen, offers anintroduction to digital photoelasticity and the following contribution, by J.S. Sirkis and D. Inaudi, respectively, consider concepts involved in fiber-opticsensing, with special emphasis on their use in an engineering environment.The contribution, by S. Krishnaswamy, describes the use of shearing inter-ferometer and caustics for experimental stress analysis. The contribution, byM. A. Sutton, S. R. McNeill, J. D. Helm and Y. J. Chao, details the use oftwo- and three-dimensional computer-vision methods for the measurement ofsurface shapes and surface deformations in simple and complex objects. Thecontribution, by J. M. Coupland which follows, describes the underlying prin-ciples of laser-Doppler and pulsed-laser velocimetries for the characterizationof fluid flow. The last contribution, by D. J. Whitehouse, gives a representa-tive view of the techniques useful for surface characterization and roughnessmeasurement in engineering.

Thus, the book brings within the scope of graduate students as well aspracticing scientists and engineers engaged in diverse fields, a compilation ofthe underlying principles, methods, and a variety of application possibilitiesof a broad range of topics in photomechanics, otherwise not readily availablein a single textbook. A list of selected references at the end of each chapterwill help readers interested in particular topics to pursue their interests inmore detail.

My very special thanks are due to Professor Leopold Pflug. Without hisencouragement the final goal would not have been achieved. His generosityis most appreciated. I wish to thank Jean-Louis Guignard for modifying anddrawing many of the figures that are reproduced in this volume. I am thankfulto Dr. Werner Skolaut for his cooperation and prompt handling of the book. Iwish to thank Dr. Claus Ascheron for his motivation and support throughoutthe development of the book.

Lausanne, Pramod K. RastogiOctober 1999

Contents

Optics for EngineersDaniel Malacara-Hernandez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Geometrical Optics Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.1. Fermat’s Principle and the Law of Refraction . . . . . . . . . . . . . . . . . . . . . 12.2. First-Order Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32.3. Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3. Wave-Optics Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1. Young’s Double Slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2. Michelson Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3. Coherence and Light Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4. Main Interferometers Used in Optical Engineering . . . . . . . . . . . . . . . . . . . . 154.1. Fizeau Interferometer and Newtons Rings . . . . . . . . . . . . . . . . . . . . . . . .164.2. Twyman-Green Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194.3. Ronchi and Lateral-Shear Interferometers . . . . . . . . . . . . . . . . . . . . . . . . 224.4. Talbot Interferometer and Moire Deflectometry . . . . . . . . . . . . . . . . . . 264.5. Foucault Test and Schlieren Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 274.6. Two-Wavelength Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.7. Holographic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Introduction to Engineering MechanicsAnand Asundi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.1. Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.2. Stress Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3. Stress Transformation Using Mohr’s Circle . . . . . . . . . . . . . . . . . . . . . . .362.4. Displacement and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .372.5. Strain Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.6. Stress-Strain Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.7. Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3. Theory of Elasticity Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.1. Plane Stress Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2. Plane Strain Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

X Contents

4. Strength of Materials Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1. Axial Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2. Bending of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3. Combined Bending and Axial Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Fringe AnalysisYves Surrel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552. Phase Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.1. Local and Global Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.2. Local Phase detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3. Global Phase Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .772.4. Residual Phase Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.5. Effect of Additive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3. Phase Unwrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.1. Spatial Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.2. Temporal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Principles of Holographic Interferometryand Speckle MetrologyPramod K. Rastogi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103

1. Holographic Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1031.1. Types of Holographic Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . 1041.2. Thermoplastic Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1071.3. Mapping of the Resolved Part of Displacement . . . . . . . . . . . . . . . 1091.4. Determination of the Wavefront Phase

Using Phase-shifting Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . 1101.5. Out-of-plane Displacement Measurement . . . . . . . . . . . . . . . . . . . . . 1111.6. In-plane Displacement Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 1121.7. Holographic Shearing Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . 1151.8. Comparative Holographic Interferometry . . . . . . . . . . . . . . . . . . . . . 1171.9. Vibration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

2. Speckle Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1242.1. Focused Speckle Photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1252.2. Defocused Speckle Photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1282.3. Speckle Shearing Photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1292.4. Speckle Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312.5. Speckle Shearing Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Contents XI

3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

Moire Methods for Engineering and Science –Moire Interferometry and Shadow MoireDaniel Post, Bongtae Han, and Peter G. Ifju . . . . . . . . . . . . . . . . . . . . . . . . . . .151

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512. Moire Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

2.1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1522.2. Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1562.3. Specimen Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1572.4. Bithermal Loading (Isothermal Loading) . . . . . . . . . . . . . . . . . . . . . 1582.5. Fringe Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1582.6. Strain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602.7. Carrier Fringes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602.8. Out-of-Plane Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

3. Advanced Techniques in Moire Interferometry . . . . . . . . . . . . . . . . . . . . 1643.1. Microscopic Moire Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1643.2. Curved Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1663.3. Replication of Deformed Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

4. Diverse Applications of Moire Interferometry . . . . . . . . . . . . . . . . . . . . . 1714.1. Thermal Deformations of Microelectronics Devices . . . . . . . . . . . 1714.2. Textile Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1734.3. Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1764.4. Micromechanics: Grain Deformations . . . . . . . . . . . . . . . . . . . . . . . . 177

5. Shadow Moire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1805.1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1805.2. Additional Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

6. Increased Sensitivity, Shadow Moire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1846.1. Phase Stepping (or Quasi-heterodyne) Method . . . . . . . . . . . . . . . 1846.2. Optical/Digital Fringe Multiplication (O/DFM) . . . . . . . . . . . . . 185

7. Applications of Shadow Moire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1857.1. Post-buckling Behavior of a Composite Column . . . . . . . . . . . . . . 1857.2. Pre-buckling Behavior of an Aluminum Channel . . . . . . . . . . . . . 1897.3. Warpage of Electronic Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194

Digital PhotoelasticityTerry Y. Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .197

1. Basic Principles of Photoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1971.1. Light and Complex Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1971.2. Polarization of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1981.3. Retardation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2001.4. Optical Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2001.5. The Stress-Optic Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

XII Contents

1.6. Plane Polariscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2041.7. Circular Polariscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

2. Computer Evaluation of Photoelastic Fringe Patterns . . . . . . . . . . . . . 2102.1. Digital Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2112.2. Extraction of Fringe Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2132.3. Fringe Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2132.4. Determination of the Isochromatic Fringe Order . . . . . . . . . . . . . 2152.5. Determination of Principal Stress Direction . . . . . . . . . . . . . . . . . . 222

3. Applications of Evaluated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2263.1. Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2263.2. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

4. System and Error Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2275. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .230

Optical Fiber Strain Sensing in Engineering MechanicsJames S. Sirkis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

1. Intrinsic Fabry-Perot Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2341.1. Optical Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2341.2. Response to Strain and Temperature . . . . . . . . . . . . . . . . . . . . . . . . 2361.3. Sensor Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

2. Extrinsic Fabry-Perot Strain Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2392.1. Optical Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2412.2. Response to Strain and Temperature . . . . . . . . . . . . . . . . . . . . . . . . 2422.3. Self-temperature Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2432.4. EFP Sensor Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2442.5. Sensor Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

3. Bragg Grating Strain Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2463.1. Bragg Grating Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2473.2. Strain and Temperature Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 2503.3. Effects of Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2503.4. Bragg Grating Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513.5. Sensor Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

4. Fiber-Optic Coatings and Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2535. Commercial Packaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2566. Sensor Bonding Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2577. Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

7.1. Serrodyne Fringe Counting (IFP Sensors) . . . . . . . . . . . . . . . . . . . . 2597.2. White Light Cross-Correlator (EFP Sensors) . . . . . . . . . . . . . . . . . 2607.3. Scanning Fabry-Perot Filter (Bragg Grating Sensors) . . . . . . . . 2627.4. Spectral Interrogation (EFP Sensors) . . . . . . . . . . . . . . . . . . . . . . . . 2637.5. Other Demodulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

8. Sensor Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .269

Contents XIII

Long-Gage Fiber-Optic Sensors for Structural MonitoringDaniele Inaudi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

1. Introduction: Monitoring versus Measuring Structures . . . . . . . . . . . . 2732. Long-Gage versus Short-Gage Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2743. Interferometric Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

3.1. Optical Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2763.2. Strain and Temperature Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 2763.3. Demodulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2773.4. Sensor Packaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2803.5. Application Example: Monitoring the Versoix Bridge . . . . . . . . . 283

4. Intensity-Based Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2845. Brillouin-Scattering Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

5.1. Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2865.2. Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2875.3. Sensor Packaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2895.4. Application Example: Temperature Monitoring

of the Luzzone Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2906. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .292

Techniques for Non-Birefringent Objects:Coherent Shearing Interferometry and CausticsSridhar Krishnaswamy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2952. Elasto-Optic Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

2.1. Optical Phase Shift due to Transmission through anOptically Isotropic Linear Elastic Medium . . . . . . . . . . . . . . . . . . . 297

2.2. Optical Phase-Shift due to Reflection from a Polished Surface 2983. Shearing Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

3.1. A Dual-Grating Shearing Interferometer –The Coherent Gradient Sensor (CGS) . . . . . . . . . . . . . . . . . . . . . . . 300

3.2. A Polarization-Based Shearing Interferometer:Compact Polariscope / Shearing Interferometer (PSI) . . . . . . . . 304

4. Optical Caustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3095. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

5.1. Compressive Line Load on the Edge of a Plate . . . . . . . . . . . . . . . 3125.2. Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319

XIV Contents

Advances in Two-Dimensionaland Three-Dimensional Computer VisionMichael A. Sutton, Stephen R. McNeill, Jeffrey D. Helm,and Yuh J. Chao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3232. Theory and Numerical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

2.1. Two-Dimensional Video Image Correlation . . . . . . . . . . . . . . . . . . . 3262.2. Three-Dimensional Video Image Correlation . . . . . . . . . . . . . . . . . 334

3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3433.1. Two-Dimensional Video Image Correlation . . . . . . . . . . . . . . . . . . . 3433.2. Three-Dimensional Video Image Correlation . . . . . . . . . . . . . . . . . 354

4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3665. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .368

Laser Doppler and Pulsed Laser Velocimetryin Fluid MechanicsJeremy M. Coupland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3731.1. The Scattering and Dynamic Properties of Seeding Particles . 375

2. Laser Doppler Velocimetry (LDV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3762.1. Fundamentals of LDV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3762.2. Fourier Optics Model of LDV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3812.3. The Doppler Signal and Signal Processing . . . . . . . . . . . . . . . . . . . 3862.4. LDV Measurements in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

3. Planar Doppler Velocimetry (PDV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3914. Pulsed Laser Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

4.1. Particle Image Velocimetry (PIV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3954.2. Removal of Directional Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3994.3. PIV Measurements in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4004.4. Three-Dimensional PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4024.5. Holographic Particle Image Velocimetry (HPIV) . . . . . . . . . . . . . 402

5. Conclusions, Discussion and Future Development . . . . . . . . . . . . . . . . . 408References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .410

Surface Characterization and Roughness Measurementin EngineeringDavid J. Whitehouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4131.1. Historical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4131.2. Nature and Importance of Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 4141.3. Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

2. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4192.1. General Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Contents XV

2.2. The Stylus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4222.3. Basic Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4252.4. The Stylus Method (Mechanical) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4272.5. The Optical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4282.6. Other Conventional Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4332.7. Non-conventional Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

3. Pre-Processing and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4333.1. Levelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4333.2. Curve Fitting for Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4333.3. Filtering for Waviness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

4. Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4394.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4394.2. Height Parameters (see [36] for example) . . . . . . . . . . . . . . . . . . . . . 4404.3. Peak Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4414.4. Spacing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4424.5. Peak Parameters (Statistical) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4434.6. Hybrid Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4454.7. Effects of Filtering on Parameter Values . . . . . . . . . . . . . . . . . . . . . 445

5. Random Process Analysis in Surface Metrology . . . . . . . . . . . . . . . . . . . 4465.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4465.2. Height Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4465.3. Spacing Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

6. Areal (or Three-Dimensional) Parameters . . . . . . . . . . . . . . . . . . . . . . . . 4536.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4536.2. Comments on Areal Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .459

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .463