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`HANDBOOK OF
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`yale aUaNSe7Dea
`3 ¢ SECOND. EDITION *.
`rele:
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`3.
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`MICHAEL BASS, EDITOR IN CHIEF
`ERIC W. VAN STRYLAND ¢ DAVID R. WILLIAMS #© WILLIAM L. WOLFE, ASSOCIATE EDITORS
`
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`IMMERVISION Ex. 2013
`LG v. ImmerVision
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`HANDBOOK OF
`OPTICS
`
`Volume Il
`Devices, Measurements,
`and Properties
`
`Second Edition
`
`Sponsored by the
`OPTICAL SOCIETY OF AMERICA
`
`Michael Bass|Editorin 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
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`Library of Congress Cataloging-in-Publication Data
`
`Handbookof optics / sponsored by the Optical Society of America ;
`Michael Bass, editor in chief. — 2nd ed.
`p.
`cm.
`Includes bibliographical references and index.
`Contents: — 2. Devices, measurement, and properties.
`ISBN 0-07-047974-7
`
`2. Optical instruments—
`1. Optics—Handbooks, manuals, etc.
`Handbooks, manuals, etc.
`I. Bass, Michael.
`I. Optical Society
`of America.
`QC369.H35
`535—dc20
`
`1995
`
`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
`reproducedor distributed in any form or by any means,or stored in a data
`base orretrieval system, without the prior written permission of the
`publisher.
`
`23456789 DOC/DOC 9098765
`
`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-free paper.
`
`appropriate professional should be sought.
`
`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
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`

`

`34.6
`
`OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS
`
`the total market for a given resin formulation, and since these materials are sold at
`prices ranging from less than two dollars to a
`few dollars per pound,
`the market
`opportunity represented by optical applications seems minuscule to most polymer vendors.
`
`34,5 OPTICAL PROPERTIES
`
`Variations
`
`It is only a fortuitous accident that some of the polymers exhibit useful optical behavior,
`since most all of these materials were originally developed for other end uses. The
`possible exceptions are the materials used for eyeglass applications (poly-diallylglycol), and
`the materials for optical information storage (specially formulated polycarbonate). Citation
`of optical properties for any polymeric material must be done with some caution and
`qualification, as different melt flow grades (having different molecular weight distribution)
`may exhibit slightly different refractive index properties. Additives to regulate lubricity,
`color, and so on can also produce subtle alterations in the spectral transmission properties.
`
`Spectral Transmission
`
`In general, the carbon-based optical polymers are visible-wavelength materials, absorbing
`fairly strongly in the ultraviolet and throughout
`the infrared.’*'*' This is not readily
`apparent from the absorption spectra published in numerous references,
`though. Such
`data are normally generated by spectroscopists for the purpose of identifying chemical
`structure, and are representative of very thin samples. One can easily develop the
`impression from this information that
`the polymers transmit well over a wide spectral
`range. Parenthetically, most of these polymers, while they have been characterized in the
`laboratory, are not commercially available. What is needed for optical design purposes is
`transmission data (for available palymers) taken from samples having sufficient thickness
`to be useful for imaging purposes.
`Some specially formulated variants of poly-methylmethacrylate have useful transmis-
`sion down to 300nm.'* Most optical polymers, however, begin to absorb in the blue
`portion of the visible spectrum, and have additional absorption regions at about 900 nm,
`1150nm, 1350 nm,
`finally becoming totally opaque at about 2100nm. The chemical
`structure which results in these absorption regions is common to almost all carbon-based
`polymers, thus the internal transmittance characteristics of these materials are remarkably
`similar, with the possible exception of the blue and near-UV regions. A scant few polymers
`do exhibit some spotty narrowband transmission leakage in the far-infrared portion of the
`spectrum, but in thicknesses suitable only for use in filter applications.
`
`Refractive Index
`
`The chemistry of carbon-based polymers is markedly different from that ofsilicate glasses
`and inorganic crystals in common use as optical matcrials. Consequently, the refractive
`properties differ significantly. In general,
`the refractive indices are lower, extending to
`about 1.73 on the high end, and down to a lower limit of about 1.3. In practice, those
`materials which are readily available for purchase exhibit a more limited index range—
`from about 1.42 to 1.65. The Abbe values for these materials vary considerably, though,
`from about 100 to something less than 20. Refractive index data for a few of these
`polymers, compiled from a number ofsources, is displayed in Table 2.
`In the chart,
`
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`polyvinyl naphthalene.
`
`19
`
`_ o
`
`REFRACTIVE
`
`40
`
`30
`
`20
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`5/6
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`70
`
`POLYMERIC OPTICS
`
`34.7
`
`
`
`
`
`TABLE 2 Refractive Index of Some Optical Polymers
`Line ID PCHMA Wavi.,nm PMMA P-styr P-carb SAN PEI
`
`
`
`
`1014.0
`1.4831
`1.5726
`1.5672
`1.5519
`852.1
`1.4850
`1.5762
`1.5710
`1.5551
`s
`706.5
`1.4878
`1.5820
`1.5768
`1.5601
`r
`656.3
`1.4892
`1.5849
`1.5799
`1.5627
`Cc
`643.9
`1.4896
`1.5858
`1.5807
`1.5634
`Cc’
`589.3
`1.4917
`1.5903
`1.5853
`1.5673
`D
`587.6
`1.4918
`1.5905
`1.5855
`1.5674
`d
`546.1
`1.4938
`1.5950
`1.5901
`1.5713
`e
`486.1
`1.4978
`1.6041
`1.5994
`1.5790
`F
`480.0
`1.4983
`1.6052
`1.6007
`1.5800
`F’
`435.8
`1.5026
`1.6154
`1.6115
`1.5886
`2
`404.7
`1.5066
`1.6253
`1.6224
`1.5971
`h
`365.0
`1.5136
`1.6431
`1.6432
`1.6125
`i
`56.1
`18,3
`57.4
`30.9
`29,9
`34.8
`Abbe number
`
`dn/dT X1O4PC -11 —1.05 —14 —1.07
`
`
`
`
`1.502
`
`1.505
`
`1.511
`
`1.651
`
`1.660
`1.668
`
`1.687
`
`PMMAsignifies polymethylmethacrylate; P =styr, polystyrene; p=care, polycarbonate;
`san, styrene acrylonitrile; PEI, polyetherimide; PCHMA,polycyclohexylmethacrylate. The
`thermo-optic coefficients at room temperature (change in refractive index with tempera-
`ture) are also listed. Note that
`these materials, unlike most glasses, experience a
`reduction in refractive index with increasing temperature. Figure 1, a simplified rendition
`
`INDEXn 80
`
`50
`60
`ABBE’ VALUE Vy
`FIGURE 1 Optical glasses and polymers: (a) polymethylmethacrylate: (b) polystyrene; (c)
`NAS; (d) styrene acrylonitrile; (e) polycarbonate; (f) polymethyl pentene; (g) acrylonitrile-
`butadicne styrene (ABS); (1) polysulfone;(7) polystyrene co-maleic anhydride; (j) polycyclo-
`hexylmethacrylate (PCHMA); (&) polyallyl diglycol carbonte; (/) polyetherimide (PEI); (1)
`
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`F
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`;
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`34.8
`
`OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS
`
`of the familiar glass map (n vs. v), shows the locations of some of the more familiar
`polymers. Note that these materials all occupy the lower and right-hand regions of the
`map. In the Schott classification system, the polymers populate mostly the FK, TikK, anc
`TiF regions of the map.”®
`
`Homogeneity
`
`It must be kept constantly in mind that polymeric optics are molded and not mechanical!»
`shaped. The exact optical properties of a piece cannot, therefore, be quantified prior tc
`manufacture of the element. In fact, the precise optical properties of the bulk material in
`an optical element are virtually certain to be a function of both the matcrialitself, and ot
`the process which produced the part. Some materials, notably styrene and butyrate resins.
`are crystalline to some degree, and therefore inherently birefringent. Birefringence may
`develop in amorphous materials, though, if the injection mold and process parameters are
`not optimized to prevent
`this occurrence. Likewise,
`the bulk scalter properties of
`=
`
`molded optical clement are a function of the inherent properties of the material, but a
`also strongly related to the cleanliness of the processing and the heat history of the finishec
`part.
`
`34.6 OPTICAL DESIGN
`
`Design Strategy
`
`Virtually all optical design techniques which have evolved for use with glass materials work
`well with polymer
`optics. Ray-tracing formulary,
`optimization
`approaches,
`and
`fundamental optical construction principals are equally suitable for glass or plastic, The
`generalized approach to optical design with polymeric materials should be strongly
`
`medium-oriented, though. That is, every effort must be made to capitalize upon the design
`flexibility which the materials and manufacturing processes afford. Integration of form and
`function should be relentlessly pursued, since mechanical features may be molded integral
`with the optics to reduce the metal part count and assembly labor content in many systems.
`
`Aberration Control
`
`The basic optical design task normally entails the simultaneous satisfaction of several
`first-order constraints, the correction of the monochromatic aberrations, and the control of
`the chromatic variation of both first-order quantities and higher-order aberrations. It is
`well known that management of the Petzval sum, while maintaining control of the
`chromatic defects, may be the most difficult aspect of this cffort.’”"* It
`is also widely
`recognized that
`the choice of optical materials is key to success. While the available
`polymer choices cover a wide range of Abbe values, insuring that achromatization ma}
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