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Library of Congress Cataloging-in-Publication Data Goodwin, Eric P. Field guide to interferometric optical testing / Eric P. Goodwin & James C. Wyant. p. cm. -- (The field guide series; 10) Includes bibliographical references and index. ISBN 0-8194-6510-0 1. Optical instruments--Testing. 2. Interferometry. I. Wyant, James C. II. Title. TS514.G66 2004 535′.470287--dc22 2006024169 Published by SPIE—The International Society for Optical Engineering P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email: spie@spie.org Web: http://spie.org The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America.
Introduction to the SeriesWelcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org. John E. Greivenkamp, Series Editor Optical Sciences Center The University of Arizona The Field Guide SeriesKeep information at your fingertips with all of the titles in the Field Guide Series: Field Guide to Geometrical Optics, John E. Greivenkamp (FG01) Field Guide to Atmospheric Optics, Larry C. Andrews (FG02) Field Guide to Adaptive Optics, Robert K. Tyson and Benjamin W. Frazier (FG03) Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04) Field Guide to Polarization, Edward Collett (FG05) Field Guide to Optical Lithography, Chris A. Mack (FG06) Field Guide to Optical Thin Films, Ronald R. Willey (FG07) Field Guide to Spectroscopy, David W. Ball (FG08) Field Guide to Infrared Systems, Arnold Daniels (FG09) Field Guide to Interferometric Optical Testing, Eric P. Goodwin and James C. Wyant (FG10) Field Guide to Interferometric Optical TestingThe material covered in the Field Guide to Interferometric Optical Testing is derived from a course taught by Dr. Wyant at the College of Optical Sciences at the University of Arizona. The material has evolved over the years as the underlying technologies and techniques have changed. This text is meant as a reference of interferometric principles and methods for the practicing engineer. Eric Goodwin dedicates this Field Guide to his wife, Sam, and their daughter, Ryan. James Wyant dedicates this Field Guide to the memory of Louise. Eric P. Goodwin and James C. Wyant College of Optical Sciences University of Arizona Table of ContentsGlossary x Fundamentals of Interferometry 1 Two-Beam Interference Equation 1 Basic Concepts and Definitions 2 Conditions for Obtaining Fringes 3 Visibility 4 Spatial Coherence 5 Polarization 6 Beamsplitters 7 Plate and Pellicle Beamsplitters 8 Interferometers 9 The Interferometer 9 Classic Fizeau Interferograms 10 Newton’s Rings 11 Twyman-Green Interferometer 12 Compensating Plate 13 PBS-based Twyman-Green Interferometer 14 Laser-based Fizeau 15 Mach-Zehnder Interferometer 17 Beam Testing 18 Lateral Shear Interferometry 19 Rotating Grating LSI 20 Radial Shear Interferometer 21 Interferograms 22 Interferograms 22 Wavefront Aberration Coefficients 23 Zernike Polynomials 24 RMS Wavefront Error 26 Spherical Aberration Interferograms 27 Astigmatism Interferograms 28 Interferograms—Other Aberrations 29 Moiré 30 Moiré and Interferograms 31 Phase-Shifting Interferometry 32 Direct Phase Measurement 32 Methods for Phase Shifting 33 Continuous Phase Shifting 34 Liquid Crystal Retarder 35 Phase Shifting Algorithms 36 Basic Phase Unwrapping 37 Phase-Stepping vs. Phase-Ramping 38 Errors in PSI 39 Quantization Errors 40 Incorrect Phase Shift 41 Avoiding Vibrations 42 Spatial Synchronous and Fourier Methods 43 Spatial Carrier Interferometry 44 Ground Glass 45 Surface Microstructure 46 Surface Microstructure 46 Nomarski Interference Microscope 47 Fringes of Equal Chromatic Order (FECO) 48 Phase-Shifting Interference Microscope 49 Multiple-Wavelength Interferometer 50 Vertical Scanning Techniques 51 Flat Surface Testing 52 Flat Surface Testing 52 Mirrors—Continued 53 Windows—Continued 54 Prisms 55 Corner Cubes 56 Curved Surface Testing 57 Testing Curved Surfaces—Test Plate 57 Curved Surfaces—Twyman-Green 58 Curved Surfaces—Laser-based Fizeau 59 Testing Lenses or Lens Systems 60 Shack Cube Interferometer 61 Scatterplate Interferometer 62 Phase-Shifting Scatterplate Interferometer 63 Long-Wavelength Interferometry 64 Smartt Point Diffraction Interferometer 65 Phase Shifting a PDI 66 Sommargren Diffraction Interferometer 67 Curved Surfaces, VSWLI 68 Absolute Measurements 69 Absolute Measurements: Flats 69 Absolute Measurements: Spheres 70 Asphere Testing 71 Aspheric Surfaces 71 Aspheric Testing 72 Hyperboloid Null Tests 73 Offner Null 74 Holographic Null Optics 75 CGH Basics 76 CGH Design Guidelines 77 Non-Null Tests 78 Reverse Raytracing 79 Sub-Nyquist Interferometry 80 Long-Wavelength Interferometry 81 Appendices 82 Non-Interferometric Testing 82 Foucault (Knife-Edge) Test 83 Ronchi Test 85 Equation Summary 86 Bibliography 93 Index 97 GlossaryFrequently used variables and symbols: a Average phase shift between frames A Amplitude An Aspheric surface coefficients b Number of bits for quantization error B Obscuration ratio c Speed of light C Moiré fringe spacing C Curvature d Distance, displacement D Diameter DHS Diameter of Hindle Sphere f Focal length f Spatial frequency f/# F-number F Focal point F Coefficient of finesse g[θ′] Zernike angular component G G-factor h Height H Normalized field height i Step number, frame number I Irradiance Lc Coherence length m Diffraction order or fringe order m Fresnel zone plate zone number m Transverse or lateral magnification n Index of refraction ne Extraordinary index, uniaxial crystal no Ordinary index, uniaxial crystal N Number of algorithm steps N Integer number of 2p NA Numerical aperture OPD Optical path difference OPL Optical path length p p-polarization state r Non-normalized radial coordinate rm Radius of mth bright fringe rp Pupil radius R Radius of curvature R/T Reflection/transmission ratio Rs Radial shear coefficient s s-polarization state s(r) Sag as function of part radius S Fringe spacing SNR Signal to noise ratio t Thickness tc Coherence time T Lateral translation υ Speed of light in medium or velocity V Visibility Vsc Visibility factor due to spatial coherence Wijk Wavefront aberration coefficients W(x, y) Wavefront as function of spatial position x Spatial coordinate xp Pupil coordinate xs Pixel spacing xw Pixel width y Spatial coordinate yp Pupil coordinate z Object distance, axial position z′ Image distance (lens) Z Zernike polynomial coefficients α Angle between two polarization states α Moiré angle, wedge angle β Tilt δ β Tilt difference Γ Fringe contrast δ(x, y) Grating errors, function of position Δ Fringe displacement Δ Integrated phase change ε Linear phase shift error ε Angle error for 90-degree prism εz Axial distance from paraxial focus η Diffraction efficiency θ Angle, shear angle, tilt orientation θ′ Angle, Zernike polynomial set θd Diffraction angle θi Incident angle κ Conic constant λ Wavelength λc Center wavelength λeq Equivalent wavelength Λ Diffraction grating or moiré grating period υ Frequency Δυ Frequency difference ξc Cutoff frequency ξc,sa Cutoff frequency for a sparse array detector ξNy Nyquist frequency ρ Reflectance (ratio of reflected irradiance) ρ Normalized pupil radius (0 < ρ < 1) σ RMS wavefront error σ2 Wavefront variance σϕ,i Standard deviation, irradiance fluctuations σϕ,q Standard deviation, quantization phase error ϕ Phase ϕ (t) Phase shift as a function of time Ω Rotation rate Ω Solid angle |
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Interferometry
Interferometers
Geometrical optics
Optical testing
Adaptive optics
Atmospheric optics
Phase shifting
