`
`
`Soom:eso Colameamim(0bcUmmeGi Be
`
`coFilaP51) I Cae Se | » O-€ i SET, oy Bees I cages Sea md Phew §
`
`
`
`
`
`
`
`
`
`
`
`
`
`HANDBOOK OF
`
`S91 dec OHS
`mes IaSULTaNLe caclea
`
`
`
`OOM:
`
`:
`
`ees) Pe) ica
`
`:
`
`IN CHIEF
`MICHAEL BASS, EDITOR.
`ERIC WW. VAN STRYLAND = DAVID R. WILLIAMS © WILLIAM L. WOLFE, ASSOCIATE EDITORS
`
`Exhibit 2008
`IPR2020-00878
`Page 1 of 15
`
`

`

` HANDBOOK OF
` OPTICS
`
` 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 )
` Uni ␷ ersity of Central Florida
` Orlando , Florida
`
` Eric W . Van Stryland Associate Editor
`
` The Center for Research and
` Education in Optics and Lasers ( CREOL )
` Uni ␷ ersity of Central Florida
` Orlando , Florida
`
` David R . Williams Associate Editor
`
` Center for Visual Science
` Uni ␷ ersity of Rochester
` Rochester , New York
`
` William L . Wolfe Associate Editor
`
` Optical Sciences Center
` Uni ␷ ersity 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
`
`Exhibit 2008
`IPR2020-00878
`Page 2 of 15
`
`

`

` Library of Congress Cataloging-in-Publication Data
`
` Handbook of optics / sponsored by the Optical Society of America ;
` Michael Bass , editor in chief . — 2nd ed .
` p .
` cm .
` Includes bibliographical references and index .
` — 2 . Devices , measurement , and properties .
` Contents :
` ISBN 0-07-047974-7
` 2 . Optical instruments—
` 1 . Optics—Handbooks , manuals , etc .
` Handbooks , manuals , etc .
` I .
` Bass , Michael .
` II . 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
` 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 .
`
` 1 2 3 4 5 6 7 8 9 DOC / DOC 9 0 9 8 7 6 5 4
`
` 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 .
`
` 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 .
`
`Exhibit 2008
`IPR2020-00878
`Page 3 of 15
`
`

`

` CHAPTER 7
` MINIATURE AND MICRO-OPTICS
`
` Tom D . Milster
` Optical Sciences Center
` Uni ␷ ersity of Arizona
` Tucson , Arizona
`
` 7 . 1 GLOSSARY
`
` A , B , C , D
` A ( r , z )
` c
` D
` d
` EFL
` f
` g
` h
` i
` k
` k
` LA
` l 0
` M
` NA
` n
` r
` r m a s k
` r m
` t
` u ៮
` W i j k
` X
` x , y
` y
`
` constants
` converging spherical wavefront
` curvature
` dif fusion constant
` dif fusion depth
` ef fective focal length
` focal length
` gradient constant
` radial distance from vertex
` imaginary
` conic constants
` wave number
` longitudinal aberration
` paraxial focal length
` total number of zones
` numerical aperture
` refractive index
` radial distance from optical axis
` mask radius
` radius of the mth zone
` fabrication time
` slope
` wavefront function
` shape factor
` Cartesian coordinates
` height
`
` 7 .1
`
`Exhibit 2008
`IPR2020-00878
`Page 4 of 15
`
`

`

` 7 .2
`
` OPTICAL ELEMENTS
`
` Z
` z
` ⌬
` ␳
` ␭
` ␴ ៮
` ␴ r m s
` ⌽
` ␺
`
` sag
` optical axis
` relative refractive dif ference
` propagation distance
` wavelength
` ␴ r m s / 2 y
` rms wavefront error
` phase
` special function
`
` 7 . 2 INTRODUCTION
`
` Optical components come in many sizes and shapes . A class of optical components that has
` become very useful in many applications is called micro-optics . We define micro-optics
` very broadly as optical components ranging in size from several millimeters to several
` hundred microns . In many cases , micro-optic components are designed to be manufactured
` in volume , thereby reducing cost to the customer . The following paragraphs describe
` micro-optic components that are potentially useful for large-volume applications . The
` discussion includes several uses of micro-optics , design considerations for micro-optic
` components , molded glass and plastic lenses , distributed-index planar lenses , Corning’s
` SMILE T M lenses , microFresnel lenses , and , finally , a few other technologies that could
` become useful in the near future .
`
` 7 . 3 USES OF MICRO - OPTICS
`
` Micro-optics are becoming an important part of many optical systems . This is especially
` true in systems that demand compact design and form factor . Some optical fiber-based
` applications include fiber-to-fiber coupling , laser-diode-to-fiber connections , LED-to-fiber
` coupling , and fiber-to-detector coupling . Microlens arrays are useful for improving
` radiometric ef ficiency in focal-plane arrays , where relatively high numerical aperture (NA)
` microlenslets focus light onto individual detector elements . Microlens arrays can also be
` used for wavefront sensors , where relatively low-NA lenslets are required . Each lenslet is
` designed to sample the input wavefront and provide a deviation on the detector plane that
` is proportional to the slope of the wavefront over the lenslet area . Micro-optics are also
` used for coupling laser diodes to waveguides and collimating arrays of laser diodes . An
` example of a large-volume application of micro-optics is data storage , where the objective
` and collimating lenses are only a few millimeters in diameter . 1
`
` 7 . 4 MICRO - OPTICS DESIGN CONSIDERATIONS
`
` Conventional lenses made with bulk elements can exploit numerous design parameters ,
` such as the number of surfaces , element spacings , and index / dispersion combinations , to
` achieve performance requirements for NA , operating wavelength , and field of view .
` However , fabricators of micro-optic lenses seek to explore molded or planar technologies ,
` and thus the design parameters tend to be more constrained . For example , refractive
`
`Exhibit 2008
`IPR2020-00878
`Page 5 of 15
`
`

`

` MINIATURE AND MICRO-OPTICS
`
` 7 .3
`
` microlenses made by molding , ion exchange , mass transport , or the SMILE T M process
` resemble single-element optics . Performance of these lenses is optimized by manipulating
` one or possibly two radii , the thickness , and the index or index distribution . Index choices
` are limited by the available materials . Distributed-index and graded-index lenses have a
` limited range of index profiles that can be achieved . Additional performance correction is
` possible by aspherizing one or both surfaces of the element . This is most ef ficiently done
` with the molding process , but molded optics are dif ficult to produce when the diameter of
` the lens is less than 1 . 0 mm . In general , one or two aberrations may be corrected with one
` or two aspheres , respectively .
` Due to the single-element nature of microlenses , insight into their performance may be
` gained by studying the well-known third-order aberrations of a thin lens in various
` configurations . Lens bending and stop shift are the two parameters used to control
` aberrations for a lens of a given power and index . Bending refers to distribution of power
` between the two surfaces , i . e ., the shape of the lens , as described in R . Barry Johnson’s
` Chap . 1 , (Vol . II) on ‘‘Lenses . ’’ The shape is described by the shape factor X which is
`
` (1)
`
` X ⫽
`
` C 1 ⫹ C 2
` C 1 ⫺ C 2
` where C 1 and C 2 are the curvatures of the surfaces . The third-order aberrations as a
` function of X are shown in Fig . 1 . These curves are for a lens with a focal length of
` 10 . 0 mm , an entrance pupil diameter of 1 . 0 mm , field angle u ៮ ⫽ 20 ⬚ , an optical index of
` refraction of 1 . 5 , ␭ ⫽ 0 . 6328 ␮ m , and the object at infinity . For any given bending of the
` lens , there is a corresponding stop position that eliminates coma , 2 and this is the stop
` position plotted in the figure . The stop position for which coma is zero is referred to as the
` natural stop shift , and it also produces the least curved tangential field for the given
` bending . Because the coma is zero , these configurations of the thin lens necessarily satisfy
` the Abbe sine condition . When the stop is at the lens (zero stop shift) , the optimum shape
` to eliminate coma is approximately convex-plano ( X ⫽ ⫹ 1) with the convex side toward
` the object . The optimum shape is a function of the index , and the higher the index , the
` more the lens must be bent into a meniscus . Spherical aberration is minimized with the
` stop at the lens , but astigmatism is near its maximum . It is interesting to note that
` biaspheric objectives for data storage tend toward the convex-plano shape .
` Astigmatism can be eliminated for two dif ferent lens-shape / stop-shift combinations , as
`
` FIGURE 1 Third-order aberrations as a function
` of the shape factor , or bending , of a simple thin lens
` with focal length 10 . 0 mm , entrance pupil diameter
` of 1 . 0 mm , field angle 20 ⬚ , n ⫽ 1 . 5 , and object at
` infinity . The stop position shown is the natural stop
` shift , that is , the position that produces zero coma .
`
`Exhibit 2008
`IPR2020-00878
`Page 6 of 15
`
`

`

` 7 .4
`
` OPTICAL ELEMENTS
`
` FIGURE 2 Contours of normalized rms wavefront deviation , ␴ ៮ ⫽ 1000 ␭ ␴ r m s / 2 y , versus field angle and
` NA , where 2 y is the diameter of the stop . The stop is located at the lens . The focus is adjusted to give
` minimum rms deviation of the wavefront , so ef fects of Petzval curvature are not included . A : X ⫽ 1 ,
` n ⫽ 1 . 5 ; B : X ⫽ ⫺ 1 , n ⫽ 1 . 5 ; C : X ⫽ 1 , n ⫽ 3 . 0 ; D : X ⫽ ⫺ 1 , n ⫽ 3 . 0 .
`
` shown in Fig . 1 . The penalty is an increase in spherical aberration . Note that there is no
` lens shape for which spherical , coma , and astigmatism are simultaneously zero in Fig . 1 ,
` that is , there is no aplanatic solution when the object is at infinity . The aplanatic condition
` for a thin lens is only satisfied at finite conjugates .
` The plano-convex shape ( X ⫽ ⫺ 1) that eliminates astigmatism is particularly interesting
` because the stop location is in front of the lens at the optical center of curvature of the
` second surface . All chief rays are normally incident at the second surface . Thus , the design
` is monocentric . 3 (Obviously , the first surface is not monocentric with respect to the center
` of the stop , but it has zero power and only contributes distortion . )
` Two very common configurations of micro-optic lenses are X ⫽ ⫹ 1 and X ⫽ ⫺ 1 with
` the stop at the lens . Typically , the object is at infinity . In Fig . 2 , we display contours of
` normalized rms wavefront deviation , ␴ ៮ ⫽ ␴ ␭ r m s / 2 y , versus u ៮ and NA , where 2 y ⫽ diameter
` of the stop . Aberration components in ␴ r m s include third-order spherical , astigmatism , and
` coma . The focus is adjusted to give minimum rms deviation of the wavefront , so ef fects of
` Petzval curvature are not included . Tilt is also subtracted . As NA or field angle is
` increased , rms wavefront aberration increases substantially . The usable field of view of the
` optical system is commonly defined in terms of Mare ´ chal’s criterion 4 as field angles less
` than those that produce 2 y ␴ ៮ / 1000 ␭ ⱕ 0 . 07 wave . For example , if the optical system
` operates at 2 y ⫽ 1 . 0 mm , ␭ ⫽ 0 . 6328 ␮ m , NA ⫽ 0 . 1 , X ⫽ ⫹ 1 , n ⫽ 1 . 5 , and u ៮ ⫽ 2 ⬚ , the
` wavefront aberration due to third-order contributions is
` ␴ r m s ⫽ 2 y ␴ ៮
` (1 . 0 ⫻ 10 ⫺ 3 m)(0 . 015)
` ⬇
` (10 3 )(0 . 6328 ⫻ 10 ⫺ 6 m / wave)
` 1000 ␭
`
` ⫽ 0 . 024 wave
`
` (2)
`
`Exhibit 2008
`IPR2020-00878
`Page 7 of 15
`
`

`

` MINIATURE AND MICRO-OPTICS
`
` 7 .5
`
` FIGURE 3 Ef fect of a window on wavefront
` distortion at ␭ ⫽ 830 nm .
`
` which is acceptable for most situations . Note that the configuration for X ⫽ ⫺ 1 yields
` ␴ r m s ⬇ 0 . 079 wave , which is beyond the acceptable limit . When large values of ␴ r m s are
` derived from Fig . 2 , care must be taken in interpretation of the result because higher-order
` aberrations are not included in the calculation . Also , if field curvature is included in the
` calculation , the usable field of view is significantly reduced .
` Coma and astigmatism are only significant if the image field contains of f-axis locations .
` In many laser applications , like laser diode collimators , the micro-optic lens is designed to
` operate on axis with only a very small field of view . In this case , spherical aberration is
` very significant . A common technique that is used to minimize spherical aberration is to
` aspherize a surface of the lens . Third- , fifth- , and higher orders of spherical aberration may
` be corrected by choosing the proper surface shape . In some lens design codes , the shape is
` specified by
`
` Z ⫽
`
` ch 2
` 1 ⫹ 4 1 ⫺ (1 ⫹ k ) c 2 h 2
`
` ⫹ Ah 4 ⫹ Bh 6 ⫹ Ch 8 ⫹ Dh 1 0
`
` (3)
`
` where Z is the sag of the surface , c is the base curvature of the surface , k is the conic
` constant ( k ⫽ 0 is a sphere , k ⫽ ⫺ 1 is a paraboloid , etc . ) , and h ⫽ 4 x 2 ⫹ y 2 is the radial
` distance from the vertex . The A , B , C , and D coef ficients specify the amount of aspheric
` departure in terms of a polynomial expansion in h .
` When a plane-parallel plate is inserted in a diverging or converging beam , such as the
` window glass of a laser diode or an optical disk , spherical aberration is introduced . The
` amount of aberration depends on the thickness of the plate , the NA of the beam , and to a
` lesser extent the refractive index of the plate , 5 as shown in Fig . 3 . The magnitude of all
` orders of spherical aberration is linearly proportional to the thickness of the plate . The
` sign is opposite that of the spherical aberration introduced by an X ⫽ ⫹ 1 singlet that could
` be used to focus the beam through the plate . Therefore , the aspheric correction on the
` singlet compensates for the dif ference of the spherical aberration of the singlet and the
` plate . This observation follows the fact that minimum spherical aberration without
` aspheric correction is achieved with the smallest possible air gap between the lens and the
` plate . For high-NA singlet objectives , one or two aspheric surfaces are added to correct the
` residual spherical aberration .
`
` 7 . 5 MOLDED MICROLENSES
`
` Molded micro-optic components have found applications in several commercial products ,
` which include compact disk players , bar-code scanners , and diode-to-fiber couplers .
` Molded lenses become especially attractive when one is designing an application that
`
`Exhibit 2008
`IPR2020-00878
`Page 8 of 15
`
`

`

` 7 .6
`
` OPTICAL ELEMENTS
`
` requires aspheric surfaces . Conventional techniques for polishing and grinding lenses tend
` to be time-expensive and do not yield good piece-to-piece uniformity . Direct molding , on
` the other hand , eliminates the need for any grinding or polishing . Another advantage of
` direct molding is that useful reference surfaces can be designed directly into the mold . The
` reference surfaces can take the form of flats . 6 The reference flats are used to aid in aligning
` the lens element during assembly into the optical device . Therefore , in volume applications
` that require aspheric surfaces , molding becomes a cost-ef fective and practical solution . The
` molding process utilizes a master mold , which is commonly made by single-point diamond
` turning and post polishing to remove tooling marks and thus minimize scatter from the
` surface . The master can be tested with conventional null techniques , computer-generated
` null holograms , 7 or null Ronchi screens . 8 Two types of molding technology are described in
` the following paragraphs . The first is molded glass technology . The second is molded
` plastic technology .
`
` Molded Glass
`
` One of the reasons glass is specified as the material of choice is thermal stability . Other
` factors include low birefringence , high transmission over a broad wavelength band , and
` resistance to harsh environments .
` Several considerations must be made when molding glass optics . Special attention must
` be made to the glass softening point and refractive index . 9 The softening point of the glass
` used in molded optics is lower than that of conventional components . This enables the
` lenses to be formed at lower temperatures , thereby increasing options for cost-ef fective
` tooling and molding . The refractive index of the glass material can influence the design of
` the surface . For example , a higher refractive index will reduce the surface curvature .
` Smaller curvatures are generally easier to fabricate and are thus desirable .
` An illustration is Corning’s glass molding process . 9 The molds that are used for aspheric
` glass surfaces are constructed with a single-point diamond turning machine under strict
` temperature and humidity control . The finished molds are assembled into a precision-
` bored alignment sleeve to control centration and tilt of the molds . A ring member forms
` the outside diameter of the lens , as shown in Fig . 4 . The glass material , which is called a
` preform , is inserted between the molds . Two keys to accurate replication of the aspheric
` surfaces are forming the material at high glass viscosity and maintaining an isothermal
` environment . After the mold and preform are heated to the molding temperature , a load is
` applied to one of the molds to press the preform into shape . After molding , the assembly
`
` FIGURE 4 Mold for glass optics .
`
`Exhibit 2008
`IPR2020-00878
`Page 9 of 15
`
`

`

` MINIATURE AND MICRO-OPTICS
`
` 7 .7
`
` is cooled to below the glass transformation point before the lens is removed . Optical
` performance characteristics of the finished lens are determined by the quality of the mold
` surfaces , the glass material , and the preform volume , which also determines the thickness
` of the lens when pressed .
` An alternative process is used at Kodak , Inc ., where molded optics are injection molded
` and mounted into precision lens cells . 1 0 In this process , a tuned production mold can
` reproduce intricate mounting datum features and extremely well-aligned optics . It can also
` form a stop , baf fle , or a film-plane reference in the system . Table 1 lists preferred and
` possible tolerances for molded glass components . The Kodak process has been tested with
` over 50 optical glasses , which include both crowns and flints . This provides a wide
` index-of-refraction range , 1 . 51 ⬍ n ⬍ 1 . 85 , to choose from .
` Most of the molded glass microlenses manufactured to date have been designed to
` operate with infrared laser diodes at ␭ ⫽ 780 – 830 nm . The glass used to make the lenses is
` transparent over a much broader range , so the operating wavelength is not a significant
` factor if designing in the visible or near infrared . Figure 5 displays a chart of the external
` transmission of several optical materials versus wavelength . LaK09 (curve B) is represen-
` tative of the type of glass used in molded optics . The external transmission from 300 nm to
` over 2200 nm is limited primarily by Fresnel losses due to the relatively high index of
` refraction ( n ⫽ 1 . 73) . The transmission can be improved dramatically with antireflection
` coatings . Figure 6 displays the on-axis operating characteristics of a Corning 350110 lens ,
` which is used for collimating laser diodes . The rms wavefront variation and ef fective focal
` length (EFL) are shown versus wavelength . The highest aberration is observed at shorter
` wavelengths . As the wavelength increases , the EFL increases , which decreases the NA
` slightly . Table 2 lists several optical properties of molded optical materials . The trend in
` molded glass lenses is to make smaller , lighter , and higher NA components . 1 1 Reduction in
` mass and size allows for shorter access times in optical data storage devices , and higher
` NA improves storage density in such devices .
`
` Molded Plastic
`
` Molded plastic lenses are an inexpensive alternative to molded glass . In addition , plastic
` components are lighter than glass components . However , plastic lenses are more sensitive
` to temperatures and environmental factors . The most common use of molded plastic lenses
` is in compact disk (CD) players .
` Precision plastic microlenses are commonly manufactured with injection molding
` equipment in high-volume applications . However , the classical injection molding process
` typically leaves some inhomogeneities in the material due to shear and cooling stresses . 1 2
` Improved molding techniques can significantly reduce variations , as can compression
` molding and casting . The current state of the art in optical molding permits master surfaces
` to be replicated to an accuracy of roughly one fringe per 25 mm diameter , or perhaps a bit
` better . 1 3 Detail as small as 5 nm may be transferred if the material properties and
` processing are optimum and the shapes are modest . Table 3 lists tolerances of
` injection-molded lenses . 1 4 The tooling costs associated with molded plastics are typically
` less than those associated with molded glass because of the lower transition temperature of
` the plastics . Also , the material cost is lower for polymers than for glass . Consequently , the
` costs associated with manufacture of molded plastic microlenses are much less than those
` for molded glass microlenses . The index of refraction for the plastics is less than that for
` the glass lenses , so the curvature of the surfaces must be greater , and therefore harder to
` manufacture , for comparable NA .
` The glass map for molded plastic materials is shown in Fig . 7 . The few polymers that
` have been characterized lie mainly outside the region containing the optical glasses and
` particularly far from the flint materials . 1 5 Data on index of refraction and Abbe number
` are particularly dif ficult to obtain for molded plastic . The material is supplied in pelletized
`
`Exhibit 2008
`IPR2020-00878
`Page 10 of 15
`
`

`

` 7 .8
`
` OPTICAL ELEMENTS
`
` TABLE 1 Preferred and Possible Tolerances for
` Molded Glass Components 1 0
`
` Preferred
`
` Possible
`
` Center thickness (mm)
`
` Diameter (mm)
`
` Diameter of lens
` beyond clear
` aperture (mm)
` Surface quality
` Axis alignment
`
` Radius (mm)—
` best fit sphere
` Slope ( ␭ / mm)
` Wavelengths ( ␭ )
` departure from BFS
`
` 10 . 00 max
` 0 . 40 min
` Ú 0 . 030 tol
` 25 . 00 max
` 4 . 00 min
` Ú 0 . 10 tol
` 2 . 00
`
` 80 – 50
` 3 ⫻ 10 ⫺ 3
` radians
` 5 to ⬁
`
` 50 max
` ⱕ 250
`
` 25 . 00
` 0 . 35
` Ú 0 . 015
` 50 . 00
` 2 . 00
` Ú 0 . 01
` 0 . 50
`
` 40 – 20
` 2 ⫻ 10 ⫺ 3
` radians
` 2 to ⬁
`
` 100 max
` ⱕ 500
`
` FIGURE 5 External transmission of several optical materials versus wavelength . ( a ) Polystyrene
` 1 . 0 mm thick , which is used for molded plastic lenses , 1 2 ( b ) LaK09 10 . 0 mm thick , which is used
` for molded glass lenses ; 6 5 ( c ) Polycarbonate 3 . 175 mm thick , which is used for molded plastic
` lenses , 1 2 ( d ) Fotoform glass 1 . 0 mm thick , which is used in the production of SMILE T M lenses . 3 8
`
`Exhibit 2008
`IPR2020-00878
`Page 11 of 15
`
`

`

` MINIATURE AND MICRO-OPTICS
`
` 7 .9
`
` FIGURE 6 On-axis operating characteristics versus wavelength of a Corning 350110 lens , which
` is a molded glass aspheric used for collimating laser diodes . 6 6
`
` TABLE 2 Properties of Materials Used for Molding Micro-optics
`
` Property
`
` PMMA
` (acrylic)
`
` PMMA
` (imide)
`
` SSMA
`
` Poly-
` carbonate
`
` Poly-
` styrene
`
` Index ( n d )
` Abbe 4 ( V d )
` Density (g / mm 3 )
` Max service
` temp ( ⬚ C)
` Thermal
` expansion
` coef ficient
` (1E-
` 6 mm / mm ⬚ C)
` Thermal index
` coef ficient
` (1E-6 / ⬚ C)
` Young’s
` modulus
` (10E4 kg / cm 2 )
` Impact strength
` Abrasion resistance
` Cost / lb
` Birefringence
`
` 1 . 491
` 57 . 4
` 1 . 19
` 72
`
` 67 . 9
`
` ⫺ 105
`
` 3 . 02
`
` 2
` 4
` 3
` 2
`
` (1 ⫽ lowest / 5 ⫽ highest) .
`
` 1 . 528
` 48
` 1 . 21
` 142
`
` —
`
` 1 . 564
` 35
` 1 . 09
` 87
`
` 56 . 0
`
` 1 . 586
` 30
` 1 . 20
` 121
`
` 65 . 5
`
` 1 . 589
` 31
` 1 . 06
` 75
`
` 50 . 0
`
` LaK09
`
` 1 . 734
` 51 . 5
` 4 . 04
` 500
`
` 5 . 5
`
` BK7
`
` 1 . 517
` 64 . 2
` 2 . 51
` 500
`
` 7 . 1
`
` —
`
` —
`
` —
` —
` —
` —
`
` —
`
` ⫺ 107
`
` —
`
` 6 . 5
`
` 3
`
` 3 . 30
`
` 2 . 43
`
` 3 . 16
`
` 11 . 37
`
` 83 . 1
`
` 3
` 3
` 2
` 4
`
` 5
` 1
` 4
` 3
`
` 4
` 2
` 2
` 5
`
` —
` —
` —
` —
`
` 1
` 5
` 5
` 1
`
`Exhibit 2008
`IPR2020-00878
`Page 12 of 15
`
`

`

` 7 .10
`
` OPTICAL ELEMENTS
`
` TABLE 3 Injection Molding Tolerances for Plastic Lenses
`
` Focal length
` Radius of curvature
` Spherical power
` Surface quality
` Vertex thickness (in)
` Diameter (in . per in . DIA . )
` Repeatability lens-to-lens
`
` Ú 0 . 5%
` Ú 0 . 5%
` 2 to 5 f*
` 60 / 40 (40 / 20 possible)
` Ú 0 . 0005
` Ú 0 . 002 to 0 . 0005
` 0 . 1% to 0 . 3%
`
` * Tolerances given in optical fringes abbreviated by ‘‘f’’ .
` Vertex-to-edge thickness ratio
` 4 : 1
` Dif ficult to mold
` 3 : 1
` Moderately easy to mold
` 2 : 1
` Easy to mold
`
` form , so it must first be molded into a form suitable for measurement . The molding
` process subjects the material to a heating and annealing cycle that potentially af fects the
` optical properties . Typically , the ef fect of the additional thermal history is to shift the
` dispersion curve upward or downward , leaving the shape unchanged . A more complete
` listing of optical plastics and their properties is given in Ref . 12 . Additional information
` 1 6 the Plastics Technology ,
` can be obtained from the Modern Plastics Encyclopedia ,
` ’ s Guide , 1 7 and in John D . Lytle’s Chap . 34 , (Vol . II)
` Manufacturing Handbook and Buyer
` on ‘‘Polymeric Optics . ’’
` Changes in dimension or refractive index due to thermal variations occur in both
` molded glass and molded plastic lenses . However , the ef fect is more pronounced in
` polymer optical systems because the thermal coef ficients of refractive index and expansion
` are ten times greater than for optical glasses , as shown in Table 2 . When these changes are
` modeled in a computer , a majority of the optical systems exhibit a simple defocus and a
` change of ef fective focal length and corresponding first-order parameters . An experimental
` study 1 8 was made on an acrylic lens designed for a focal length of 6 . 171 mm at ␭ ⫽ 780 nm
` and 20 ⬚ C . At 16 ⬚ C , the focal length changed to 6 . 133 mm . At 60 ⬚ C , the focal length
` changed to 6 . 221 mm . Thermal gradients , which can introduce complex aberrations , are a
` more serious problem . Therefore , more care must be exercised in the design of
` athermalized mounts for polymer optical systems .
` The transmission of two common optical plastics , polystyrene and polycarbonate , are
`
` FIGURE 7 Glass map for molded plastic materials ,
` which are shown as triangles in the figure . The few
` polymers that have been characterized lie mainly outside
` the region containing the optical glasses and particularly
` far from the flint materials . 1 3
`
`Exhibit 2008
`IPR2020-00878
`Page 13 of 15
`
`

`

` MINIATURE AND MICRO-OPTICS
`
` 7 .11
`
` shown in Fig . 5 . The useful transmittance range is from 380 to 1000 nm . The transmission
` curve is severely degraded above 1000 nm due to C-H vibrational overtone and
` recombination bands , except for windows around 1300 nm and 1500 nm . Sometimes , a blue
` dye is added to the resins to make the manufactured part appear ‘‘water clear , ’’ instead of
` slightly yellowish in color . It is recommended that resins be specified with no blue toner for
` the best and most predictable optical results . 1 2
` The shape of the lens element influences how easily it can be manufactured .
` Reasonable edge thickness is preferred in order to allow easier filling . Weak surfaces are
` to be avoided because surface-tension forces on weak surfaces will tend to be very
` indeterminate . Consequently , more strongly curved surfaces tend to have better shape
` retention due to surface-tension forces . However , strongly curved surfaces are a problem
` because it is dif ficult to produce the mold . Avoid clear apertures that are too large of a
` percentage of the physical surface diameter . Avoid sharp angles on flange surfaces . Use a
` center / edge thickness ratio less than 3 for positive lenses (or 1 / 3 for negative lenses) .
` Avoid cemented interfaces . Figure 8 displays a few lens forms . The examples that mold
` well are C , E , F , and H . Form A should be avoided due to a small edge thickness . Forms
` A and B should be avoided due to weak rear surfaces . Form D will mold poorly due to bad
` edge / center thickness ratio . Form G uses a cemented interface , which could develop
` considerable stress due to the fact that thermal dif ferences may deform the pair , or
` possibly even destroy the bond .
` Since polymers are generally softer than glass , there is concern about damage from
` ordinary cleaning procedures . Surface treatments , such as diamond films , 1 9 can be applied
` that greatly reduce the damage susceptibility of polymer optical surfaces .
` A final consideration is the centration tolerance associated with aspheric surfaces . With
` spherical optics , the lens manufacturer is usually free to trade of f tilt and decentration
` tolerances . With aspheric surfaces , this tradeof f is no longer possible . The centration
`
` FIGURE 8 Example lens forms for molded plastic lenses . Forms C , E ,
` F , and H mold well . Form A should be avoided due to small edge
` thickness . Forms A and B should be avoided due to weak rear surfaces .
` Form D will mold poorly due to bad edge / center ratio . Form G uses a
` cemented interface , which could develop stress . 1 5
`
`Exhibit 2008
`IPR2020-00878
`Page 14 of 15
`
`

`

` 7 .12
`
` OPTICAL ELEMENTS
`
` tolerance for molded aspherics is determined by the alignment of the mold halves . A
` common specification is 4 to 6 ␮ m , although 3 to 4 ␮ m is possible .
`
` 7 . 6 MONOLITHIC LENSLET MODULES
`
` Monolithic lenslet modules (MLMs) are micro-optic lenslets configured into close-packed
` arrays . Lenslets can be circular , square , rectangular , or hexagonal . Aperture sizes range
` from as small as 25 ␮ m to 1 . 0 mm . Overall array sizes can be fabricated up to 68 ⫻ 68 mm .
` These elements , like those described in the previous section , are fabricated from molds .
` Unlike molded glass and plastic lenses , MLMs are typically fabricated on only one surface
` of a substrate , as shown in the wavefront sensing arrangement of Fig . 9 . An advantage of
` MLMs over other microlens array techniques is that the fill factor , which is the fraction of
` usable area in the array , can be as high as 95 to 99 percent . Applications for MLMs include
` Hartman testing , 2 0 spatial light modulators , optical computing , video projection systems ,
` detector fill-factor improvement , 2 2 and image processing .
` There are three processes that have been made used to construct MLMs . 2 2 All three
` techniques depend on using a master made of high-purity annealed and polished material .
` After the master is formed , a small amount of release agent is applied to the surface . In
` the most common fabrication process , a small amount of epoxy is placed on the surface of
` the master . A thin glass substrate is placed on top . The lenslet material is a single-part
` polymer epoxy . A slow-curing epoxy can be used if alignment is necessary during the
` curing process . 2 3 The second process is injection molding of plastics for high-volume
` applications . The third process for fabrication of MLMs is to grow infrared materials , like
` zinc selenide , on the master by chemical va