LG Electronics, Inc. et al.
`EXHIBIT 1010
`IPR Petition for
`U.S. Patent No. RE43,106
`
`

`
`HANDBOOK
`OPTICS
`
`OF
`
`Volume II
`Devices, Measurements,
`and Properties
`
`Second Edition
`
`Sponsored by the
`OPTICAL SOCIETY OF AMERICA
`
`Michael Bass Editor in Chief
`
`The Center for Research and
`Education in Optics and Lasers (CREOL)
`University of Central Florida
`Orlando, Florida
`
`Eric W. Van Stryland Associate Editor
`The Center for Research and
`Education in Optics and Lasers (CREOL)
`University of Central Florida
`Orlando, Florida
`
`David R. Williams Associate Editor
`Center for Visual Science
`University of Rochester
`Rochester, New York
`
`William L. Wolfe Associate Editor
`Optical Sciences Center
`University of Arizona
`Tucson, Arizona
`
`McGRAW-HILL, INC.
`New York San Francisco Washington, D,C. Auckland Bogota
`Caracas Lisbon London Madrid Mexico City Milan
`Montreal New Delhi San Juan Singapore
`Sydney Tokyo Toronto
`
`

`
`Library of Congress Cataloging-in-Publication Data
`
`Handbook of optics / sponsored by the Optical Society of America ;
`Michael Bass, editor in chief. -- 2nd ed.
`cm.
`Includes bibliographical references and index.
`Contents: -- 2. Devices, measurement, and properties.
`ISBN 0-07-047974-7
`1. Optics--Handbooks, manuals, etc. 2. Optical instruments--
`Handbooks, manuals, etc. I. Bass, Michael. II. Optical Society
`of America.
`QC369.H35 1995
`535--dc20
`
`94-19339
`CIP
`
`Copyright © 1995, 1978 by McGraw-Hill, Inc. All rights reserved. Printed
`in the United States of America. Except as permitted under the United
`States Copyright Act of 1976, no part of this publication may be
`reproduced or distributed in any form or by any means, or stored in a data
`base or retrieval system, without the prior written permission of the
`publisher.
`
`123456789 DOC/DOC 90987654
`
`ISBN 0-07-047974-7
`
`The sponsoring editor for this book was Stephen S. Chapman, the editing
`supervisor was Paul R. Sobel, and the production supervisor was Suzanne
`W. Babeuf. It was set in Times Roman by The Universities Press (Belfast)
`Ltd.
`
`Printed and bound by R.R. Donnelly & Sons Company.
`
`This book is printed on acid-flee paper.
`
`Information contained in this work has been obtained by
`McGraw-Hill, Inc. from sources believed to be reliable. How-
`ever, neither McGraw-Hill nor its authors guarantees the
`accuracy or completeness of any information published herein
`and neither McGraw-Hill nor its authors shall be responsible for
`any errors, omissions, or damages arising out of use of this
`information. This work is published with the understanding that
`McGraw-Hill and its authors are supplying information but are
`not attempting to render engineering or other professional
`services. If such services are required, the assistance of an
`appropriate professional should be sought.
`
`

`
`CONTENTS
`
`Contributors
`
`xvi
`
`Preface xix
`
`Glossary and Fundamental Constants
`
`xxi
`
`Part 1. Optical Elements
`
`Chapter I. Lenses R. Barry Johnson
`
`1.1. Glossary / 1.3
`1.2.
`Introduction / 1.5
`1.3. Basics / 1.5
`1.4. Stops and Pupils / 1.8
`1.5. F-Number and Numerical Aperture / 1.9
`1.6. Magnifier or Eye Loupe / 1.9
`1.7. Compound Microscopes / 1.9
`1.8. Field and Relay Lenses / 1.10
`1.9. Aplanatic Surfaces and Immersion Lenses / 1.10
`1.10. Single ElementLens / 1.11
`1.11. Landscape Lenses and the Influence of Stop Position / 1.17
`1.12. Two-Lens Systems / 1.19
`1.13. Achromatic Doublets / 1.23
`1.14. Triplet Lenses / 1.26
`1.15. Symmetrical Lenses / 1.27
`1.16. Double-Gauss Lenses / 1.28
`1.17. Petzval Lenses / 1.29
`1.18. Telephoto Lenses / 1.29
`1.19. Inverted or Reverse Telephoto Lenses / 1.30
`1.20. Performance of Representative Lenses 1.30
`1.21. Rapid Estimation of Lens Performance / 1.36
`1.22. Bibliography / 1.41
`
`1.1
`
`!.3
`
`Chapter 2, Afocal Systems William B. Wetherell
`
`2.1
`
`2.1. Glossary / 2.1
`2.2.
`Introduction / 2.1
`2.3. Gaussian Analysis of Afocal Lenses / 2.2
`2.4. Keplerian Afocal Lenses / 2. 7
`2.5. Galilean and Inverse Galilean Afocal Lenses / 2.14
`2.6. Relay Trains and Periscopes / 2.16
`2.7. Reflecting and Catadioptric Afocal Lenses / 2.19
`2.8. References / 2.22
`
`

`
`VJ CONTENTS
`
`Chapter 3. Polarizers Jean M, Bennett
`
`3.1
`
`3.1. Glossary / 3.1
`3.2. Prism Polarizers / 3.2
`3.3. Glan-TypePrisms / 3.9
`3.4. Nicol-TypePrism / 3.17
`3.5. Polarizing Beam-Splitter Prisms / 3.19
`3.6. Dichroic and Diffraction-Type Polarizers / 3.26
`3.7. Non-Normal-Incidence Reflection and Transmission Polarizers / 3.36
`3.8. Retardation Plates / 3.46
`3.9. Variable Retardation Plates and Compensators / 3.57
`3.10. Half-Shade Devices / 3.60
`3.11. Minature Polarization Devices / 3.61
`3.12. References / 3.62
`
`Chapter 4. Nondispersive Prisms William L. Wolfe
`
`4.1
`
`4.1. Glossary / 4.1
`4.2.
`Introduction / 4.1
`4.3.
`Inversion, Reversion / 4.2
`4.4. Deviation, Displacement / 4.2
`4.5. Summary of Prism Properties / 4.3
`4.6. Prism Descriptions / 4.3
`4.7. References / 4.29
`
`Chapter 5. Dispersive Prisms and Gratings George J, Zissis
`
`5.1
`
`5.1. Glossary / 5.1
`5.2.
`Introduction / 5.1
`5.3. Prisms / 5.1
`5.4. Gratings / 5.3
`5.5. Prism and Grating Configurations and Instruments / 5.4
`5.6. References / 5.15
`
`Chapter 6. Integrated Optics Thomas L. Koch, F. J. Leonberger, and
`P. G. Suchoski
`
`6.1
`
`6.1. Glossary / 6.1
`Introduction / 6.2
`6.2.
`6.3. Device Physics / 6.3
`Integrated Optics Materials and Fabrication Technology / 6.12
`6.4.
`6.5. Circuit Elements / 6.20
`6.6. Applications of Integrated Optics / 6.28
`6.7. Future Trends / 6.37
`6.8. References / 6.38
`
`Chapter 7. Miniature and Micro-Optics Tom D. Milster
`
`7.1
`
`7.1. Glossary / 7.1
`Introduction / 7.2
`7.2.
`7.3. Uses of Micro-Optics / 7.2
`7.4. Micro-Optics Design Considerations / 7.2
`7.5. Molded Microlenses / 7.4
`
`

`
`CONTENTS vii
`
`7.6. Monolithic Lenslet Modules / 7.12
`7.7. Distributed-Index Planer Microlenses
`7.8. Smile Microlenses / 7.16
`7.9. Micro-FresnelLenses / 7.18
`7.10. Other Technologies / 7.27
`7.11. References / 7.31
`
`/ 7.13
`
`Chapter 8. Binary Optics Michael W. Farn and Wilfrid B. Veldkamp
`
`8.1
`
`8.1. Glossary / 8.1
`8.2.
`Introduction / 8.2
`8.3. Design--Geometrical Optics / 8.2
`8.4. Design--Scalar Diffraction Theory /
`8.5. Design--Vector Diffraction Theory /
`8.6. Fabrication / 8.14
`8.7. References / 8.18
`
`8.10
`8.14
`
`Chapter 9. Gradient Index Optics Duncan T. Moore
`
`9.1
`
`9.1. Glossary / 9.1
`9.2.
`Introduction / 9.1
`9.3. Analytic Solutions / 9.2
`9.4. Mathematical Representation / 9.2
`9.5. Axial Gradient Lenses / 9.2
`9.6. Radial Gradients / 9.5
`9.7. Radial Gradients with Curved Surfaces / 9.7
`9.8. Shallow Radial Gradients [ 9.7
`9.9. Materials / 9.8
`9.10. References / 9.9
`
`Chapter 10. Optical Fibers and Fiber-Optic Communications Tom G. Brown
`
`10.1
`
`10.1.
`10.2.
`10.3.
`10.4.
`10.5.
`10.6.
`10.7.
`10.8.
`10.9.
`10.10.
`10.11.
`
`Glossary / 10.1
`Introduction / 10.3
`Principles of Operation / 10.4
`Fiber Dispersion and Attenuation / 10.8
`Polarization Characteristics of Fibers / 10.11
`Optical and Mechanical Properties of Fibers / 10.12
`Optical Fiber Communications / 10.19
`Nonlinear Optical Properties of Fibers / 10.37
`Optical Fiber Materials: Chemistry and Fabrication / 10.42
`References / 10.46
`Further Reading / 10.49
`
`Chapter 11. X-Ray Optics James E. Harvey
`
`11.1
`
`11.1.
`11.2.
`11.3.
`11.4.
`11.5.
`11.6.
`11.7.
`
`Glossary / 11.1
`Introduction / 11.2
`Historical Background / 11.3
`Optical Performance of X-Ray/EUV Imaging Systems / 11.6
`Diffraction Effects of Grazing Incidence X-Ray Optics / 11.8
`Ghost Images in Grazing Incidence X-Ray Telescopes / 11.14
`Scattering Effects from Optical Fabrication Errors / 11.16
`
`

`
`viii CONTENTS
`
`Image Quality Predictions for Various Applications / 11.25
`11.8.
`11.9. Summary and Conclusion / 11.29
`11.10. References / 11.30
`
`Chapter 12. Acousto-Optic Devices and Applications I.C. Chang
`
`12.1
`
`12.1. Glossary / 12.1
`12.2.
`Introduction / 12.2
`12.3. Theory of Acousto-Optic Interaction / 12.3
`12.4. Acoustic-OpticMaterials / 12.14
`12.5. Basic Acousto-Optic Devices / 12.16
`12.6. Applications / 12.34
`12.7. References / 12.49
`
`Chapter 13. Electro-Optic Modulators Theresa A. Maldonado
`
`13.1
`
`13.1. Glossary / 13.1
`13.2.
`Introduction / 13.3
`13.3. Crystal Optics and the Index Ellipsoid / 13.4
`13.4. The Electro-Optic Effect / 13.6
`13.5. Modulator Devices / 13.15
`13.6. Appendix: Euler Angles / 13.33
`13.7. References / 13.33
`
`Chapter 14. Liquid Crystals Shin-Tson Wu
`
`14.1
`
`14.1. Glossary / 14.1
`14.2.
`Introduction / 14.2
`14.3. Physical Properties of Thermotropic Liquid Crystals / 14.2
`14.4. Physical Mechanisms for Modulating Light / 14.10
`14.5. Electro-Optics of Nematic Liquid Crystals / 14.12
`14.6. Electro-Optics of Polymer-Dispersed Liquid Crystals / 14.17
`14.7. Electro-Optics of Ferroelectric Liquid Crystals / 14.19
`14.8. Conclusion / 14.23
`14.9. References / 14.24
`
`15.1
`
`15.3
`
`Part 2. Optical Instruments
`
`Chapter 15. Cameras Norman Goldberg
`
`Introduction / 15.3
`15.1.
`15.2. Background / 15.3
`15.3. Properties of the Final Image / 15.4
`15.4. Film Choice / 15.5
`15.5. Resolving Fine Detail / 15.5
`15.6. Film Sizes / 15.6
`15.7. Display / 15.6
`15.8. Distributing the Image / 15.7
`15.9. Video Cameras / 15.7
`15.10. Instant Pictures / 15.8
`15.11. Critical Features / 15.8
`15.12. Time Lag / 15.9
`15.13. Automation / 15.10
`
`

`
`CONTENTS ix
`
`15.14. Flash / 15.16
`15.15. Flexibility through Features and Accessories
`15.16. Advantage of Various Formats / 15.18
`15.17. Large Format: A Different World / 15.19
`15.18. Special Cameras / 15.21
`15.19. Further Reading / 15.28
`
`/ 15.17
`
`Chapter 16. Camera Lenses Ellis Betensky, M. Kreitzer, and J. Moskovich
`
`16.1
`
`16.1.
`Introduction / 16.1
`Imposed Design Limitations / 16.1
`16.2.
`16.3. Modern Lens Types / 16.2
`16.4. Classification System ] 16.20
`16.5. Lens Performance Data [ 16.25
`16.6. Acknowledgments / 16.26
`16.7. References / 16.26
`
`Chapter 17. Microscopes Shinya Inou~ and Rudoff Oldenboug
`
`17.1
`
`17.1. Glossary / 17.1
`17.2.
`Introduction ] 17.1
`17.3. General Optical Considerations / 17.4
`17.4. Microscope Lenses, Aberrations / 17.12
`17.5. Contrast Generation / 17.22
`Illumination and Imaging Modes / 17.37
`17.6.
`17.7. Optical Manipulation of Specimen with the Light Microscope
`17.8. Mechanical Standards / 17.48
`17.9. Acknowledgments / 17.49
`17.10. References / 17.49
`
`/ 17.47
`
`Chapter 18. Reflective and Catadioptric Objectives Lloyd Jones
`
`18.1
`
`18.1. Glossary / 18.1
`18.2.
`Introduction / 18.1
`18.3. Glass Varieties / 18.2
`Introduction to Catadioptric and Reflective Objectives
`18.4.
`18.5. Field-of-ViewPlots / 18.38
`18.6. Definitions / 18.40
`18.7. References / 18.42
`
`/ 18.2
`
`Chapter 19. Scanners Leo Beiser and R. Barry Johnson
`
`19.1
`
`19.1. Glossary / 19.1
`19.2.
`Introduction / 19.2
`19.3. Scanned Resolution / 19.7
`19.4. Scanners for Remote Sensing / 19.15
`19.5. Scanning for Input/Output Imaging / 19.26
`19.6. Scanner Devices and Techniques / 19.34
`19.7. Scan-Error Reduction / 19.51
`19.8. References / 19.54
`19.9. Further Reading / 19.56
`
`

`
`X CONTENTS
`
`Chapter 20. Optical Spectrometers Brian Henderson
`
`20.1
`
`20.1. Glossary / 20.1
`20.2.
`Introduction / 20.2
`20.3. Optical Absorption Spectrometers / 20.2
`20.4. Luminescence Spectrometers / 20.5
`20.5. Photoluminescence Decay Time ] 20.12
`20.6. Polarization Spectrometers / 20.15
`20.7. High-Resolution Techniques ] 20.23
`20.8. Light Scattering / 20.30
`20.9. References / 20.32
`
`Chapter 21. Interferometers P. Hariharan
`
`21.1
`
`21.1. Glossary / 21.1
`Introduction / 21.1
`21.2.
`21.3. Basic Types of Interferometers / 21.2
`21.4. Three-Beam and Double-Passed Two-Beam Interferometers / 21.7
`21.5. Fringe-Counting Interferometers / 21.10
`21.6. Two-Wavelength interferometry / 21.11
`21.7. Frequency-Modulation Interferometers / 21.11
`21.8. Heterodyne Interferometers / 21.12
`21.9. Phase-Shifting Interferometers / 21.13
`21.10. Phase-Locked Interferometers / 21.14
`21.11. Laser-Dopplerlnterferometers / 21.15
`21.12. Laser-Feedback Interferometers / 21.16
`21.13. Fiber Interferometers / 21.17
`21.14. InterferometricWave Meters / 21.19
`21.15. Second-Harmonic and Phase-Conjugate Interferometers / 21.21
`21.16. Stellar Interferometers / 21.22
`21.17. Michelson’s Stellar Interferometers / 21.22
`21.18. Gravitational-Wave Interferometers / 21.23
`21.19. References / 21.25
`
`Chapter 22. Polarimetry Russell A. Chipman
`
`22.1
`
`22.1. Glossary / 22.1
`22.2. Objectives / 22.3
`22.3. Polarimeters / 22.3
`22.4. Light-Measuring and Sampling-Measuring Polarimeters / 22.3
`22.5. Sample-Measuring Polarimeters / 22.4
`22.6. Complete and Incomplete Polarimeters / 22.4
`22.7. Polarization Generators and Analyzers / 22.4
`22.8. Classes of Light-Measuring Polarimeters / 22.5
`22.9. Time-Sequential Measurements / 22.5
`22.10. Polarization Modulation / 22.5
`22.11. Division of Aperture / 22.5
`22.12. Division of Amplitude / 22.6
`22.13. Definitions / 22.6
`22.14. Stokes Vectors and Mueller Matrices / 22.8
`22.15. Phenomenological Definition of the Stokes Vector / 22.8
`22.16. Polarization Properties of Light Beams / 22.9
`22.17. MuellerMatrices / 22.10
`22.18. Coordinate System for the Mueller Matrix / 22.12
`22.19. Elliptical and Circular Polarizers and Analyzers / 22.13
`22.20. Light-MeasuringPolarimeters / 22.14
`
`

`
`CONTENTS xJ
`
`22.21.
`22.22.
`22.23.
`22.24.
`22.25.
`22.26.
`22.27.
`22.28.
`22.29.
`22.30.
`22.31.
`22.32.
`22.33.
`22.34.
`22.35.
`22.36.
`22.37.
`22.38.
`
`Sample-Measuring Polarimeters for Measuring Mueller Matrix Elements / 22.16
`Polarimetric Measurement Equation and Polarimetric Data Reducation Equation / 22.17
`Dual Rotating Retarder Polarimeter / 22.19
`Incomplete Sample-Measuring Polarimeter / 22.20
`Dual Rotating Polarizer Polarimeter / 22.20
`Nonideal Polarization Elements / 22.22
`Polarization Properties of Polarization Elements / 22.23
`Common Defects of Polarization Elements / 22.23
`The Muller Matrix for Polarization Component Characterization / 22.25
`Application of Polarimetry / 22.26
`Interpretation of Mueller Matrices / 22.28
`Diattenuation and Polarization Sensitivity / 22.28
`Polarizance / 22.29
`Physically Realizable Mueller Matrices / 22.30
`Depolarization / 22.30
`Nondepolarizing Mueller Matrices and Jones Matrices / 22.31
`Homogeneous and Inhomogeneous Polarization Elements / 22.32
`References / 22.33
`
`Chapter 23. Holography and Holographic Instruments Lloyd Huff
`
`23.1
`
`23.1. Glossary / 23.1
`Introduction / 23.2
`23.2.
`23.3. Background and Basic Principles / 23.2
`23.4. Holographic Interferometry / 23.5
`23.5. Holographic Optical Elements / 23.12
`23.6. Holographic Inspection / 23.17
`23.7. Holographic Lithography / 23.16
`23.8. Holographic Memory / 23.25
`23.9. Conclusion / 23.26
`23.10. References / 23.26
`
`Part 3. Optical Measurements
`
`Chapter 24. Radiometry and Photometry Edward F. Zalewski
`
`24.1
`
`24.3
`
`24.1. Glossary / 24.3
`Introduction / 24.6
`24.2.
`24.3. Radiometric Definitions and Basic Concepts / 24.8
`24.4. Radiant Transfer Approximations / 24.15
`24.5. Absolute Measurements / 24.12
`24.6. Photometry / 24.40
`24.7. References / 24.48
`
`Chapter 25. The Measurement of Transmission, Absorption, Emission, and
`Reflection James M. Palmer
`
`25.1
`
`25.1. Glossary / 25.1
`Introduction and Terminology
`25.2.
`25.3. Transmittance / 25.3
`25.4. Absorption / 25.4
`25.5. Reflectance / 25.4
`25.6. Emittance / 25.7
`
`/ 25.2
`
`

`
`xJi CONTENTS
`
`25.7. Kirchhoff’s Law / 25.8
`25.8. Relationship Between Transmittance, Reflectance, and Absorption / 25.8
`25.9. Measurement of Transmittance ] 25.8
`25.10. Measurement of Absorption / 25.11
`25.11. Measurement of Reflectance ] 25.11
`25.12. Measurement of Emittance / 25.16
`25.13. References [ 25.18
`25.14. Further Reading / 25.25
`
`Chapter 26. Scatterometers John C. Stover
`
`26.1
`
`26.1. Glossary / 26.1
`Introduction / 26.1
`26.2.
`26.3. Definitions and Specifications [ 26.2
`Instrument Configurations and Component Descriptions / 26.5
`26.4.
`Instrumentation Issues [ 26.9
`26.5.
`26.6. Measurement Issues / 26.11
`Incident Power Measurement, System Calibration, and Error Analysis [ 26.13
`26.7.
`26.8. Summary ] 26.14
`26.9. References / 26.15
`
`Chapter 27. Ellipsometry Rasheed M. A. Azzam
`
`27.1
`
`27.1. Glossary / 27.1
`Introduction / 27.2
`27.2.
`27.3. Conventions / 27.3
`27.4. Modeling and Inversion ] 27.4
`27.5. Transmission Ellipsometry ] 27.10
`27.6.
`Instrumentation / 27.10
`Jones-Matrix Generalized Ellipsometry / 27.19
`27.7.
`27.8. Mueller-Matrix Generalized Ellipsometry / 27.20
`27.9. Applications / 27.22
`27.10. References / 27.22
`
`Chapter 28. Spectroscopic Measurements Brian Henderson
`
`25.1
`
`28.1. Glossary / 28.i
`Introductory Comments / 28.2
`28.2.
`28.3. Optical Absorption Measurements of Energy Levels / 28.2
`28.4. The Homogeneous Lineshape of Spectra / 28.14
`28.5. Absorption, Photoluminescence, and Radiactive Decay Measurements / 28.20
`28.6. References / 28.26
`
`Chapter 29. Optical Metrology Daniel Malacara and Zacarias Malacara
`
`29.1
`
`29.1.
`29.2.
`29.3.
`29.4.
`29.5.
`29.6.
`29.7.
`
`Glossary / 29.1
`Introduction and Definitions / 29.1
`Lengths and Straightness Measurements / 29.3
`Angle Measurements / 29.12
`Curvature and Focal Length Measurements / 29.20
`Velocity Measurements / 29.27
`References / 29.29
`
`

`
`Chapter 30. Optical Testing Daniel Malacara
`
`30.1
`
`CONTENTS xiii
`
`30.1. Glossary / 30.1
`Introduction / 30.1
`30.2.
`30.3. Classical Noninterferometric Tests / 30.1
`InterferometricTests / 30.6
`30.4.
`Increasing and Sensitivity of Interferometers / 30.8
`30.5.
`Interferogram Evaluation / 30.12
`30.6.
`30.7. Phase-Shifting Interferometry / 30.16
`30.8. Measuring Aspherical Wavefronts / 30.22
`30.9. References / 30.25
`
`Chapter 31. Use of Computer-Generated Holograms in Optical
`Testing Katherine Creath and James C. Wyant
`
`31.1
`
`31.1. Glossary / 31.1
`31.2.
`Introduction / 31.2
`31.3. Types of CGHs / 31.2
`31.4. Plotting CGHs / 31.3
`interferometers Using Computer-Generated Holograms / 31.6
`31.5.
`31.6. AcuracyLimitations / 31.7
`31.7. Experimental Results / 31.8
`31.8. References / 31.10
`
`Chapter 32. Transfer Function Techniques Glenn D. Boreman
`
`32.1
`
`32.1. Glossary / 32.1
`32.2.
`Introduction / 32.1
`32.3. Definitions / 32.2
`32.4. MTF Calculations / 32.4
`32.5. MTFMeasurements / 32.7
`32.6. References / 32.9
`
`Part 4. Optical and Physical Properties of Materials
`
`Chapter 33. Properties of Crystals and Glasses William J. Tropf,
`Michael E. Thomas, and Terry J. Harris
`
`33.1
`
`33.3
`
`33.1. Glossary / 33.3
`33.2.
`Introduction / 33.5
`33.3. Optical Materials / 33.6
`33.4. Properties of Materials / 33.7
`33.5. Properties Tables / 33.38
`33.6. References / 33.84
`
`Chapter 34. Polymeric Optics John D. Lytle
`
`34.1
`
`34.1. Glossary / 34.1
`Introduction / 34.1
`34.2.
`34.3. Forms / 34.2
`34.4. Physical Properties / 34.2
`
`

`
`xJv CONTENTS
`
`34.5. Optical Properties / 34.6
`34.6. Optical Design / 34.8
`34.7. Processing / 34.12
`34.8. Coatings / 34.19
`34.9. References / 34.20
`
`Chapter 35. Properties of Metals Roger A. Paquin
`
`35.1
`
`35.1. Glossary / 35.1
`Introduction / 35.3
`35.2.
`35.3. Summary Data / 35.12
`35.4. References / 35.74
`
`Chapter 36. Optical Properties of Semiconductors PaulM. Amirtharaj and
`David G. Seiler
`
`36.1
`
`36.1. Glossary / 36.1
`36.2.
`Introduction / 36.3
`36.3. Optical Properties / 36.8
`36.4. Measurement Techniques / 36.59
`36.5. Acknowledgments / 36.82
`36.6. Summary and Conclusions / 36.82
`36.7. References / 36.92
`
`Chapter 37, Black Surfaces for Optical Systems Stephen M. Pompea and
`Robert P. Breault
`
`37.1
`
`Introduction / 37.1
`37.1.
`37.2. Selection Process for Black Baffle Surfaces in Optical Systems / 37.12
`37.3. The Creation of Black Surfaces for Specific Applications / 37.15
`37.4. Environmental Degradation of Black Surfaces / 37.18
`37.5. Optical Characterization of Black Surfaces / 37.21
`37.6. Surfaces for Ultraviolet and Far-Infrared Applications / 37.23
`37.7. Survey of Surfaces with Optical Data / 37.29
`37.8. Paints / 37.30
`37.9. Conclusions / 37.63
`37.10. Acknowledgments / 37.63
`37.11. References / 37.63
`
`Part 5. Nonlinear and Photorefractive Optics
`
`Chapter 38. Nonlinear Optics Chung L. Tang
`
`38.1
`
`38.3
`
`38.1. Glossary / 38.3
`Introduction / 38.4
`38.2.
`38.3. Basic Concepts / 38.6
`38.4. Material Considerations / 38.20
`38.5. Appendix / 38.23
`38.6. References / 38.25
`
`

`
`Chapter 39. Photorefractive Materials and Devices Mark Cronin-Golomb and
`Marvin Klein
`
`39.1
`
`CONTENTS xv
`
`Introduction / 39.1
`39.1.
`39.2. Materials / 39.11
`39.3. Devices / 39.25
`39.4. References / 39.35
`39.5. Further Reading / 39.42
`
`Index follows Chapter 39 1.1
`
`

`
`CHAPTER 8
`BINARY OPTICS
`
`Michael W. Farn and Wilfrid B. Veldkamp
`MIT / Lincoln Laboratory
`Lexington, Massachusetts
`
`8.1 GLOSSARY
`
`A
`
`C
`
`aspheric
`
`describes spherical aberration
`
`Fourier coefficients
`
`c
`
`curvature
`
`c(x, y)
`
`complex transmittance
`
`D
`f
`k, 1
`l,
`
`local period
`
`focal length
`
`running indices
`
`paraxial image position
`
`L,M
`
`direction cosines
`
`m
`
`P
`
`s
`
`t
`v,
`
`diffraction order
`
`partial dispersion
`
`spheric
`
`thickness
`
`Abbe number
`
`x, y, z
`
`Cartesian coordinates
`
`A
`
`wavelength
`
`diffraction efficiency
`
`paraxial image height
`
`qb(x, y)
`
`phase
`
`O,i
`
`!
`
`iterative points
`
`diffracted
`
`8.1
`
`

`
`8.2
`
`OPTICAL ELEMENTS
`
`8.2 INTRODUCTION
`
`Binary optics is a surface-relief optics technology based on VLSI fabrication techniques
`(primarily photolithography and etching), with the "binary" in the name referring to the
`binary coding scheme used in creating the photolithographic masks. The technology allows
`the creation of new, unconventional optical elements and provides greater design freedom
`and new materials choices for conventional elements. This capability allows designers to
`create innovative components that can solve problems in optical sensors, optical
`communications, and optical processors. Over the past decade, the technology has
`advanced sufficiently to allow the production of diffractive elements, hybrid refractive-
`diffractive elements, and refractive micro-optics which are satisfactory for use in cameras,
`military systems, medical applications, and other demanding areas.
`The boundaries of the binary optics field are not clearly defined, so in this section, the
`concentration will be on the core of the technology: passive optical elements which are
`fabricated using VLSI technology. As so defined, binary optics technology can be broadly
`divided into the areas of optical design and VLSI-based fabrication. Optical design can be
`further categorized according to the optical theory used to model the element: geometrical
`optics, scalar diffraction theory, or vector diffraction theory; while fabrication is composed
`of two parts: translation of the optical design into the mask layout and the actua!
`micromachining of the element. The following sections discuss each of these topics in
`some detail, with the emphasis on optical design. For a more general overview, the reader
`is referred to Refs. 1 for many of the original papers, 2 and 3 for a sampling of
`applications and research, and 4-6 for a lay overview.
`Directly related areas which are discussed in other sections but not in this section
`include micro-optics and diffractive optics fabricated by other means (e.g., diamond
`turning, conventional manufacturing, or optical production), display holography (especially
`computer-generated holography), mass replication technologies (e.g., embossing, injection
`molding, or epoxy casting), integrated optics, and other micromachining technologies.
`
`8.3 DESIGN GEOMETRICAL OPTICS
`
`In many applications, binary optics elements are designed by ray tracing and "classical"
`lens design principles. These designs can be divided into two classes: broadband and
`monochromatic. In broadband applications, the binary optics structure has little optical
`power in order to reduce the chromatic aberrations and its primary purpose is aberration
`correction. The device can be viewed as an aspheric aberration, corrector, similar to a
`Schmidt corrector, when used to correct the monochromatic aberrations and it can be
`viewed as a material with dispersion an order of magnitude greater than and opposite in
`sign to conventional materials when used to correct chromatic aberrations. In mono-
`chromatic applications, binary optics components can have significant optical power and
`can be viewed as replacements for refractive optics.
`In both classes of designs, binary optics typically offers the following key advantages:
`
`¯ Reduction in system size, weight, and/or number of elements
`
`¯ Elimination of exotic materials
`¯ Increased design freedom in correcting aberrations, resulting in better system
`performance
`
`¯ The generation of arbitrary lens shapes (including micro-optics) and phase profiles
`
`

`
`Analytical Models
`
`BINARY OPTICS 8.3
`
`Representation of a Binary Optics Element. As with any diffractive element, a binary
`optics structure is defined by its phase profile ¢(x, y) (z is taken as the optical axis), design
`wavelength A0, and the surface on which the element lies. For simplicity, this surface is
`assumed to be planar for the remainder of this section, although this is commonly not the
`case. For example, in many refractive/diffractive systems, the binary optics structurc is
`placed on a refractive lens which may be curved. The phase function is commonly
`represented by either explicit analytical expression or decomposition into polynomials in x
`and y (e.g., the HOE option in CODE V).
`Explicit analytic expressions are used in simple designs, the two most common being
`lenses and gratings. A lens used to image point (Xo, Yo, Zo) to point (xi, yi, zi) at wavelength
`h0 has a phase profile
`
`¢(x, y) = ~ [Zo(V(x - Xo)2/z2 + (y - yo)2/z2 + 1 - 1)
`
`Zi(~/(X.. .. -- Xi)2/Z2, . . + (y -.,- ., - .vi)2/z2 ~- 1 - 1)]
`
`where Zo and zi are both taken as positive to the right of the lens. The focal length is given
`by the Gaussian lens formula:
`
`l/f0= 1/zi- 1/Zo
`
`(2)
`
`with the subscript indicating that f0 is the focal length at A0. A grating which deflects a
`normally incident ray of wavelength )to to the direction with direction cosines (L, M) is
`described by
`
`qb(x, y) = V- (xL + yM)
`ao
`
`Axicons are circular gratings and are described by
`
`¢(x, y) = ~-(V~x2 + y2L)
`Ao
`
`(3)
`
`(4)
`
`where L now describes the radial deflection.
`For historical reasons, the polynomial decomposition of the phase profile of the element
`commonly consists of a spheric term and an aspheric term:
`
`¢(x, y) = Cs(X, y) + CA(X, y)
`
`(5)
`
`where
`
`2JrE
`Y) = ~Ok ~ ak,xkY’
`
`CA(X,
`
`and the spheric term Cs(X, y) takes the form of Eq. (1). Since the phase profiles produced
`by binary optics technology are not constrained to be spheric, Cs(X, y) is often set to zero
`by using the same object and image locations and the aspheric term alone is used to
`describe the profile. The binary optics element is then optimized by optimizing the
`
`

`
`8./[
`
`OPTICAL ELEMENTS
`
`polynomial coefficients a~t. If necessary, the aspheric term can be forced to be radially
`symmetric by constraining the appropriate polynomial coefficients.
`It is possible to describe the phase profile of a binary optics element in other ways. For
`example, 49(x, y) could be described by Zernicke polynomials or could be interpolated
`from a two-dimensional look-up table. However, these methods are not widely used since
`lens design software currently does not support these alternatives.
`
`Ray Tracing by the Grating Equation. A binary optics element with phase oh(x, y) can
`be ray traced using the grating equation by modeling the element as a grating, the period
`of which varies with position. This yields
`
`mA 04)
`L’ = L + ---
`2Jr Ox
`
`mA O~b
`M’ = M + 2re Oy
`
`(6)
`
`(7)
`
`where m is the diffracted order, L, M are the direction cosines of the incident ray, and
`L’, M’ are the direction cosines of the diffracted ray.7 In geometrical designs, the element
`is usually blazed for the first order (m = 1). Note that it is the phase gradient Vqb(x, y) (a
`vector quantity proportional to the local spatial frequency) and not the phase 4)(x, y)
`which appears in the grating equation. The magnitude of the local period is inversely
`proportional to the local spatial frequency and given by
`
`D(x, y) = 2It/IV4,1
`
`(8)
`
`where 11 denotes the vector magnitude. The minimum local period determines the
`minimum feature size of the binary optics structure, a concern in device fabrication (see
`"Fabrication" later in this chapter).
`
`Ray Tracing by the $weatt Model. The Sweatt model,8 which is an approximation to the
`grating equation, is another method for ray tracing. The Sweatt approach models a binary
`optics element as an equivalent refractive element and is important since it allows results
`derived for refractive optics to be applied to binary optics. In the Sweatt model, a binary
`optics element with phase qS(x, y) at wavelength A0 is replaced by a refractive equivalent
`with thickness and refractive index given by
`
`t(x, y) -
`
`A~ 49(x, y) + to
`no - 1 2to
`
`A
`- 1 = (n0 - 1)
`
`(9)
`
`(10)
`
`Here, to is a constant chosen to make t(x, y) always positive and no is the index of the
`material at wavelength Ao. The index no is chosen by the designer and as no---~ ~, the
`Sweatt model approaches the grating equation. In practice, values of no = 10,000 are
`sufficiently high for accurate results.9
`In the special case of a binary optics lens described by Eq. (1), the more accurate
`Sweatt lens1° can be used. In this case, the element is modeled by two surfaces of curvature
`
`Co = 1/[(1 - no)Zo]
`
`c, = 11[(1 - no)Zi]
`
`(11)
`
`(12)
`
`

`
`BINARY OPTICS 8.5
`
`Y
`
`..... X ...................
`
`~GE
`
`/
`]
`OBJECT
`(0,,, ,I ,) (0,, o,I o)
`
`~z
`
`LENS
`
`FIGURE 1 Primary aberrations of a binary optics
`lens]
`
`and conic constant -n2, with the axis of each surface passing through the respective point
`source. The refractive index is still modeled by Eq. (10).
`
`Aberration Correction
`
`Aberrations of a Binary Optics Singlet. As a simple example of a monochromatic
`imaging system, consider a binary optics singlet which is designed to image the point
`(0, O, Zo) to the point (0, 0, zi) at wavelength h0. The phase profile of this lens can be
`derived from Eq. (1) and the focal length f0 from Eq. (2). Now consider an object point of
`wavelength h located at (0, ~o, lo). The lens will form an image at (0, ~i, li) (see Fig. 1),
`with the paraxial image position l~ and height ~i given by7
`
`1 h 1
`+
`li f0h0 l0
`
`~,/l, = ~o/lo
`
`(13)
`
`(14)
`
`Note that the first equation is just the Gaussian lens law but using a wavelength-dependent
`focal length of
`
`f(*) =fo~
`
`(15)
`
`The focal length being inversely proportional to the wavelength is a fundamental property
`of diffractive lenses. In addition, due to the wavelength shift and position change of the
`object point, the lens will form a wavefront with a primary aberration of7
`
`1
`1
`h 1
`W(x, y)=~ [(~-~o)- Aoo (Q-zl~o)](x2+
`
`y2)2
`
`1 1 1
`2
`y2)
`-- ~o)~iy(x ÷
`
`2l~ (~
`3 1
`+ ~2/2 (~ - ~o)~:i2Y2+! 1
`
`2
`
`(16)
`
`where the ray strikes the lens at (x, y). The first term is spherical aberration, the second is
`coma, and the last two are tangential and sagittal field curvature. As noted by Welford, all
`the off-axis aberrations can be eliminated if and only if l~ = lo, a useless configuration. In
`most systems of interest, the limiting aberration is coma.
`The performance of the binary optics singlet can be improved by introducing more
`degrees of freedom: varying the stop position, allowing the binary optics lens to be placed
`
`

`
`8.6
`
`OPTICAL ELEMENTS
`
`on a curved surface, using additional elements, etc. For a more detailed discussion, see
`Refs. 1, 7, and 11.
`
`Chromatic Aberration Correction. Binary optics lenses inherently suffer from large
`chromatic aberrations, the wavelength-dependent focal length [Eq. (15)] being a prime
`example. By themselves, they are unsuitable for broadband imaging and it has been shown
`that an achromatic system consisting only of diffractive lenses cannot produce a real
`image,l~
`However, these lenses can be combined successfully with refractive lenses to achieve
`chromatic correction (for a more detailed discussion than what follows, see Refs. 4, 13, and
`14). The chromatic behavior can be understood by using the Sweatt model, which states
`that a binary optics lens behaves like an ultrahigh index refractive lens with an index which
`varies linearly with wavelength [let no---> o~ in Eq. (10)]. Accordingly, they can be used to
`correct the primary chromatic aberration of conventional refractive lenses but cannot