IN THE UNITED STATES DISTRICT COURT
`FOR THE EASTERN DISTRICT OF TEXAS
`SHERMAN DIVISION
`
`LARGAN PRECISION CO., LTD.,
`Plaintiff,
`
`v.
`ABILITY OPTO-ELECTRONICS
`TECHNOLOGY CO., LTD.; NEWMAX
`TECHNOLOGY CO., LTD.; AND HP
`INC.
`
`§
`§
`§
`§
`§
`§
`§
`§
`§
`§
`
`Defendants.
`
`Civil Action No. 4:19-CV-696-ALM
`Jury Trial Demanded
`
`DECLARATION OF JOSÉ SASIÁN, PH.D., REGARDING CLAIM CONSTRUCTION
`OF UNITED STATES PATENT NOS. 7,274,518, 8,395,691, 8,988,796, AND 9,146,378
`
`EX 2010 Page 1
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`

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`
`I, José Sasián, declare as follows:
`
`I.
`
`INTRODUCTION
`
`1.
`
`My name is José Sasián, Ph.D. I am over the age of twenty-one, competent to
`
`make this declaration, and have personal knowledge of the matters stated herein.
`
`2.
`
`I have been retained to opine on and provide expert testimony regarding United
`
`States Patent Nos. 7,274,518 (the “’518 Patent”), 8,395,691 (the “’691 patent”), 8,988,796 (the
`
`“’796 Patent”), and 9,146,378 (the “’378 Patent”) (collectively, the “Asserted Patents”). My
`
`understanding is that plaintiff Largan Precisions Co., Ltd. (“Largan”) alleges that defendants
`
`Ability Opto-Electronics Technology Co., Ltd. (“Ability”), Newmax Technology Co., Ltd.
`
`(“Newmax”), and HP Inc. (“HP”) (collectively “Defendants”) infringe the Asserted Patents.
`
`3.
`
`For this declaration, I have been asked to opine on the construction of certain
`
`claim terms of the Asserted Patents. To further assist the Court in its claim construction analysis,
`
`I also have been asked to opine on the technology background, subject matter, and teachings of
`
`the Asserted Patents and their field of art.
`
`4.
`
`My understanding is that the Court will hold a claim construction hearing. If I am
`
`called upon to testify at this hearing, or at any other proceeding, I may cite other documents or
`
`information similar to those specifically identified, cited, or discussed in this declaration. I may
`
`also use pictures, demonstrations, graphics, animations, presentations, or other audiovisual aids
`
`to explain and demonstrate my analysis and opinions.
`
`5.
`
`I am currently being compensated at my standard consulting rate of $525 per
`
`hour. I am also being reimbursed for all reasonable expenses that I incur related to this
`
`engagement. My compensation is not dependent on the substance of my testimony or the
`
`outcome of this case and I have no personal interest in the outcome of this case.
`
`
`
`1
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`6.
`
`The materials I have considered to prepare this declaration include: the Asserted
`
`Patents, the prosecution histories of the Asserted Patents, and the proposed claim constructions
`
`of the Plaintiff and of the Defendants. I have also considered and am relying upon my expertise,
`
`knowledge, and experience in the subject matter of the Asserted Patents including in the field,
`
`history, and teachings of optical engineering and instruments, optics, lenses, lens systems,
`
`imaging and sensors, and photographic cameras. I have also considered and relied upon the
`
`knowledge, education and experience of a person of ordinary skill in the art (“POSITA”). I have
`
`also considered and relied upon any of the other materials identified, discussed, or cited in this
`
`declaration.
`
`7.
`
`This declaration, including the materials I have considered, is based on the
`
`information currently available to me. If any additional information becomes available, I reserve
`
`the right to consider those additional materials and to amend and supplement my analysis and
`
`opinions. To date, I have not received or reviewed any claim construction briefing by Largan, or
`
`any expert opinion by Largan’s technical expert. To the extent that any expert witness provides
`
`testimony on behalf of Largan or Largan provides claim construction briefing, I reserve the right
`
`to review and respond to that testimony, evidence, and briefing.
`
`II.
`
`BACKGROUND AND QUALIFICATIONS
`
`8.
`
`My qualifications and professional experience are described in detail in my
`
`Curriculum Vitae, which is attached as Exhibit 1. The following is a brief summary of my
`
`relevant qualifications and professional experience.
`
`9.
`
`I have extensive academic and industry experience with optical engineering.
`
`Specifically, I have over thirty years of academic and industry experience in the field of optical
`
`sciences and optical engineering in general, including optical instrumentation, optical design,
`
`opto-mechanics, and optical fabrication and testing.
`2
`
`
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`10.
`
`I am currently a full-time, tenured Professor of Optical Sciences at the Wyant
`
`College of Optical Sciences at the University of Arizona in Tucson, Arizona, a position I have
`
`held since 2002. As a professor, I teach and perform research in the field of optical design. For
`
`example, I teach my students how to design lenses and mirrors and how to think about light so
`
`that they can design useful optical systems.
`
`11.
`
`As part of my academic and research responsibilities, I am frequently involved
`
`with the design, fabrication, and testing of optical devices. Prior to receiving tenure, I was an
`
`Associate Professor of Optical Sciences at the University of Arizona from 1995 to 2001. Prior to
`
`joining the University of Arizona faculty, I was a member of the technical staff of AT&T Bell
`
`Laboratories from 1990 to 1995. From 1984 to 1987, I was a Research Assistant, and from 1988
`
`to 1990, I was a Research Associate, in the Optical Sciences Center at the University of Arizona.
`
`From 1976 to 1984, I was an optician at the Institute of Astronomy at the University of Mexico.
`
`12.
`
`I received a Bachelor of Science degree in Physics from the University of Mexico
`
`in 1982, a Master of Science degree in Optical Sciences from the University of Arizona in 1987,
`
`and a Ph.D. degree in Optical Sciences from the University of Arizona in 1988. My research
`
`areas include optical design, fabrication, and testing of optical instruments, astronomical optics,
`
`diffractive optics, opto-mechanical design, light in gemstones, and light propagation.
`
`13.
`
`At the University of Arizona, I have taught the courses Lens Design OPTI 517
`
`(1997-present), Introduction to Aberrations OPTI 518 (2005-present), Advanced Lens Design
`
`OPTI 696A (2008, 2012, 2017, 2019), Illumination Optics Seminar (1997-2000), Introduction to
`
`Opto-mechanics OPTI 690 (1998, 2001, 2003, 2004, 2005) and Optical Shop Practices OPTI
`
`597A (1996-present). I teach students how to design lens systems, how to grind, polish, and test
`
`
`
`3
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`aspheric surfaces, how to mount lenses properly so that their physical integrity is preserved, and
`
`how to align lens systems.
`
`14.
`
`I have directed several student reports, theses, and dissertations in the areas of
`
`lens and mirror design. I have lectured regarding my work, and have published, along with
`
`students and colleagues, over one hundred scientific papers in the area of optics. These include
`
`technical papers, student reports and theses done under my direction, related to miniature lenses.
`
`For example:
`
`• Yufeng Yan, Jose Sasian, "Miniature camera lens design with a freeform surface,"
`
`Proc. SPIE 10590, International Optical Design Conference 2017, 1059012 (27
`
`November 2017); doi: 10.1117/12.2292653.
`
`• Dmitry Reshidko, Jose Sasian, “Optical analysis of miniature lenses with curved
`
`imaging surfaces,” Appl. Opt. Oct. 54(28):E216-23, 2015.
`
`• Sukmock Lee, Byongoh Kim, Jiyeon Lee, and Jose Sasian, “Accurate determination
`
`of distortion for smart phone cameras,” Applied Optics, Vol. 53, Issue 29, pp. H1-H6
`
`(2014).
`
`• Ying Ting Liu, “Review and Design of a Mobile Phone Camera Lens for 21.4 Mega-
`
`Pixels Image Sensor,” M. Sc. Report, University of Arizona, 2017.
`
`• Luxin Nie, “Patent Review of Miniature Camera Lenses,” M. Sc. Report, University
`
`of Arizona, 2017.
`
`• Cheng Kuei-Yeh, “Cell phone zoom lens design and patent research,” M. Sc. Report,
`
`University of Arizona, 2010.
`
`• Rob Bates, “Design for Fabrication: Miniature Camera Lens Case Study,” M. Sc.
`
`Report, University of Arizona, 2008.
`
`
`
`4
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`15.
`
`Since 1995, I have been a consultant and have provided to industry solutions to a
`
`variety of projects that include lenses for cell-phones, lenses for microscopes, and lenses for fast
`
`speed photography. I also have consulted in the area of plastic optics. I hold patents and patent
`
`applications related to lens systems.
`
`16.
`
`I have been a topical editor and reviewer for the peer-reviewed journals Applied
`
`Optics and Optical Engineering. I am a fellow of the International Society for Optics and
`
`Photonics (SPIE), a fellow of the Optical Society of America (OSA), and a lifetime member of
`
`the Optical Society of India.
`
`17.
`
`I have served as a co-chair for the conferences “Novel Optical Systems: Design
`
`and Optimization” (1997-2006), “Optical systems alignment, tolerancing, and verification”
`
`(2007-2020), and “International Optical Design Conference,” (2002). I have taught in Japan
`
`(2014, 2016, and 2017) the course: Advanced Lens Design: Art and Science.
`
`18.
`
`I have been a co-editor of approximately 21 published conference proceedings
`
`from SPIE. I am the author of the book, “Introduction to Aberrations in Optical Imaging
`
`Systems,” by Cambridge University Press, 2013, and of the book “Introduction to Lens Design,”
`
`by Cambridge University Press 2019. I am named as an inventor on approximately 13 U.S.
`
`patents.
`
`III. LEGAL STANDARDS
`Although I am not a lawyer, I understand that claim construction is governed by
`19.
`
`certain legal principles. I have discussed those legal principles with counsel and have used them
`
`in forming my opinions. However, my understanding is that it is ultimately for the Court to
`
`determine the legal principles that apply to this case, including those that relate to claim
`
`construction. Also, my understanding is that claim construction is, in the end, a legal issue the
`
`Court will decide.
`
`
`
`5
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`20. My understanding is that the meaning of a patent claim should be determined
`
`based on what the patent claim would mean to POSITA.
`
`21. My understanding is that when determining the meaning of a patent claim to a
`
`POSITA, one should first look to the intrinsic evidence. My understanding is that the intrinsic
`
`evidence includes the patent, both its claim language and its specification. My understanding is
`
`that generally, limitations and embodiments from the specification should not be read into the
`
`claims. However, I also understand that a patentee may have ascribed or defined a particular
`
`meaning to a term in the specification, in which case the patentee’s particular meaning may
`
`determine the meaning of a claim term.
`
`22. My understanding is that the intrinsic evidence also includes the patent’s
`
`prosecution history. The prosecution history is the record of the examination of a patent
`
`application before the U.S. Patent and Trademark Office (PTO). The prosecution history may
`
`provide evidence of how the inventor and the patent examiner understood the patent application
`
`and the claims. It is my understanding that arguments, amendments, or disclaimers made during
`
`prosecution and about the prior art may determine the meaning of the patent claims.
`
`23. My understanding is that a POSITA is deemed to read a claim term not only in the
`
`context of the particular claim in which it appears, but also in the context of the entire patent,
`
`including its specification and prosecution history. My understanding is that this context in
`
`which a claim is read also includes the claim term’s meaning in the art, and the education,
`
`knowledge, and experience of the POSITA.
`
`24. My understanding is that when determining the meaning of a patent claim to a
`
`POSITA, extrinsic evidence may also be considered. My understanding is that extrinsic
`
`evidence may include dictionaries, textbooks, learned treatises, and other relevant technical
`
`
`
`6
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`publications. My understanding is that the extrinsic evidence may also include expert testimony.
`
`However, my understanding is that extrinsic evidence cannot take precedence over the meaning
`
`of the claim language based on the intrinsic evidence.
`
`25. My understanding is that a claim must inform a POSITA about the scope of the
`
`claims with reasonable certainty. My understanding is that if a claim fails to do so, then the
`
`claim is invalid as indefinite. My understanding is that one way that a claim term may be
`
`indefinite is if there are different, equally reasonable interpretations of the claim to a POSITA,
`
`but that it is unclear from the intrinsic and extrinsic evidence which interpretation is correct.
`
`IV.
`
`THE LEVEL OF SKILL IN THE ART
`
`26.
`
`I understand that patent claims are interpreted from the perspective of a POSITA
`
`at the time of the invention. The Asserted Patents have the following filing priority dates:
`
`• U.S. Patent No. 7,274,518 (“’518 Patent”): October 6, 2006
`
`• U.S. Patent No. 8,395,691 (“’691 Patent”): October 26, 2010
`
`• U.S. Patent No. 8,988,796 (“’796 Patent”): December 13, 2013
`
`• U.S. Patent No. 9,146,378 (“’378 Patent”): December 2, 2013
`
`For purposes of this declaration, I consider the time of the inventions to be the filing dates of the
`
`patents identified above.
`
`27.
`
`The relevant field of the Asserted Patents is comprised of people having an
`
`engineering degree or its equivalent. In particular, a POSITA typically would have a Bachelor’s
`
`Degree in Electrical Engineering, Physics, Optical Engineering, or an equivalent undergraduate
`
`degree. A POSITA also typically would have at least three years of experience in the design of
`
`photographic lenses, especially for mobile devices. A POSITA also may have taken a lens
`
`design course and have experience with specification, adjustment, optimizing lenses for cell
`
`
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`phones or other mobile devices. Further, a POSITA would also be familiar with software for
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`lens designs such as Code V, Zemax, or similar software tools and have some familiarity with
`
`photography optics and mechanical devices. Because a POSITA is a hypothetical person having
`
`a general set of qualifications and experience, this description and these qualifications,
`
`knowledge, and experience of a POSITA are approximate and generalized. For any particular
`
`person or expert who might qualify as a POSITA, a higher level of education or skill may make
`
`up for less experience, and vice-versa, e.g., an associate’s degree in the above fields with 4–6
`
`years of experience in the industry.
`
`V.
`
`TECHNOLOGY BACKGROUND
`
`28.
`
`In this section, I provide a brief overview of optical lens technology. This
`
`overview includes discussions of key lens features, the history of lenses, and the job of a lens
`
`designer.
`
`A.
`
`Lens focal length f, field of view FOV, F-number F/#, aperture stop, total
`length TL, and optical power
`
`29.
`
`An optical lens element mainly consists of a transparent material like glass or
`
`plastic having two optical surfaces.
`
`30.
`
`A main characteristic of a lens is its focal length, which for a thin lens in air, is the
`
`distance from the lens to its focal point where parallel rays after refraction by the lens are
`
`focused as illustrated in Figure 1. The lens surfaces can be spherical in shape, or non-spherical
`
`(aspheric). The lenses of the Asserted Patents are symmetric about a line that is known as the
`
`optical axis.
`
`
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`
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`Figure 1. Optical layout of a singlet lens and light rays in blue color.
`
`31.
`
`The focal length of a lens can be determined with the aid of the lens maker
`
`equation (Equation 1) where r1 and r2 are the surface radii of curvature at the optical axis, t is the
`
`axial lens thickness, and n is the index of refraction. The index of refraction n changes with the
`
`color of light (light wavelength). The inverse of the focal length is known in the art as the lens
`
`optical power or refractive power (φ). Positive powered lenses can concentrate light in a focus,
`
`
`
`and negative powered lenses can make light diverge.
`
`=
`φ
`
`1
`f
`
`32.
`
`
`1
`1
`
`r
`r
`
`2
`1
`Equation 1
`
`Because there are two refracting surfaces in a lens, one can change the lens
`
`=
`
`(
`
`n
`
`−
`
`)
`1
`
`−
`
`+
`
`−
`1
`t n
`
`n r r
`
`1 2
`
`
`
`surfaces while maintaining the same focal length; this creates different lens shapes that have the
`
`same optical power as shown in Figure 2 below. This lens shape change process is known in the
`
`art as lens bending. Positive lenses with spherical surfaces in the top row of Figure 2 are thicker
`
`in the center and thinner at the edge. Negative lenses in the bottom row of Figure 2 are thicker at
`
`the edge and thinner at the center. Lenses with one convex and one concave surface are named
`
`
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`meniscus lenses. Lenses with a planar surface are named plano-convex or plano-concave.
`
`Lenses with two convex surfaces or two concave surfaces are named biconvex or biconcave.
`
`
`Figure 2. Lens bending. Top row: Positive powered lenses of the same focal length;
`Bottom row: Negative powered lenses of the same focal length.
`
`A main function of a lens is to produce an optical image that is located at the
`
`33.
`
`focus of the lens from an illuminated object. A sensor, like photographic film or a charged
`
`coupled device (CCD), is located at the focus of the lens and can capture an image of the object.
`
`In 1839, the invention of photography was made public in a meeting of the French academy of
`
`sciences and arts. At that time, it took approximately 30 minutes to expose the photographic film
`
`to record an image with a simple lens. It was then recognized that to reduce the time of exposure
`
`a lens that produced a bright image was needed. The brightness depended on the relative
`
`aperture of the lens, which is the ratio of the focal length f of the lens and its diameter D
`
`(entrance pupil diameter), commonly known as the lens f-number or F/#=f/D. Typical F-
`
`numbers are 8, 4, 2.8, and 2. Smaller F-number lenses cast brighter images.
`
`34.
`
`The lens field of view (FOV) is the angular subtend of the object to be imaged by
`
`the lens. For example, the FOV of a 35 mm photographic lens with a 50 mm focal length is +/-
`
`23°. Many lenses for mobile phones have fields of view ranging from about +/- 33° to 38°.
`
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`
`
`Figure 3. A meniscus lens and three beams of parallel rays that are focused by the lens to
`form an image.
`
`Figure 3 above shows a meniscus lens accepting parallel light rays at field angles
`
`35.
`
`of 33°, 0°, and -33° with respect to the optical axis. The three beams of parallel rays originate
`
`from an object on the left of the lens are focused and contribute to form the image at right of the
`
`lens. The black arrows represent the aperture stop of the lens that determines the diameter D
`
`used to calculate the F-number of the lens. The aperture stop limits the amount of light that can
`
`enter the lens. In a lens, there are other apertures known as glare stops that help suppress
`
`unwanted light that can diminish the image contrast. However, the aperture stop position in a
`
`lens helps to control lens image defect known as aberrations. In some lenses the aperture stop is
`
`set in the front of the lens as shown in Figure 3 so that the angle of incidence of light at the
`
`image plane where the electronic sensor is located, is smaller than a given specification.
`
`36.
`
`The object to be imaged is customarily assumed to be to the left of the lens and
`
`the image to the right of the lens, the two surfaces in a lens element are referred in the patent
`
`literature as object side surface or as image side surface.
`
`37.
`
`One lens feature in mobile phone lenses is the lens total length TL, which is the
`
`length measured from the first surface of the lens to the image plane where the lens sensor is
`
`
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`located along the optical axis. If the sensor is not located at the image plane, then the image will
`
`appear blurred. This defect is known as defocus.
`
`38.
`
`In the art a lens system comprising one or more lens elements is also known as a
`
`lens assembly.
`
`B.
`39.
`
`Lens aberrations, aspheric surfaces, optical glass, and plastic
`
`Lenses do not produce perfect images due to image defects known as optical
`
`aberrations. The focal length of a lens changes due to variations of the index of refraction with
`
`color (wavelength of light). The left of Figure 4 below shows the chromatic aberration of a
`
`positive plano-convex lens.
`
`
`Figure 4. Left: chromatic aberration in a singlet lens; Right achromatic doublet lens.
`
`The rays traced in Figure 4 have wavelengths of 487 nm (blue), 587 nm (green),
`
`40.
`
`and 656 nm (red); these rays are also known as the F, d, and C lines respectively. The variation
`
`of focusing the wavelengths is known as chromatic aberration. A lens maker can correct or
`
`mitigate chromatic aberration by adding a second negative lens of opposite optical power and of
`
`a different material as shown in Figure 4 at right.
`
`41.
`
`Optical materials are characterized by their index of refraction n and their Abbe
`
`number V. The Abbe number is defined by Equation 2, shown below, where nF, nC and nd are
`
`the indices of refraction for the F, d, and C wavelengths. The lens at right in Figure 4 used
`
`
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`
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`glasses with different Abbe numbers and it is known as an achromatic doublet that is corrected
`
`for chromatic aberration.
`
`v
`
`=
`
`1d
`n
`−
`n
`n
`−
`C
`F
`Equation 2.
`
`Optical materials can be made out of glass, plastic (polymers), or crystals. Figure
`
`
`
`42.
`
`5 at left shows a map of optical glasses where the index of refraction varies from about 1.5 to 2.0
`
`and the Abbe number V from 20 to 90. Figure 5 at right shows a similar map of polymer optical
`
`materials.
`
`
`
`Figure 5. Maps for glass and polymer materials.
`
`There are five other image defects that impact lenses and lens systems: spherical
`
`43.
`
`aberration, coma aberration, astigmatism aberration, field curvature aberration, and distortion
`
`aberration. A lens maker can correct or mitigate these aberrations by modifying the lens
`
`curvatures, glass index of refraction, lens element air spacings, and by using aspherical surfaces
`
`
`
`(non-spherical).
`
`
`
`13
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`
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`Figure 6. Profile of an aspheric surface with an inflection point.
`
`44. Many lens specifications use aspheric surfaces as the superposition of a conic
`
`surface (parabola, ellipse, hyperbola) and a polynomial; such aspheric surfaces are defined by
`
`Equation 3 where Sag is the depth of the surface at the radial distance S from the optical axis as
`
`shown in Figure 6. The conic constant is K, A1 ,A2 , A3, A4 … are aspheric coefficients, and r
`
`is the surface radius of curvature at the optical axis. In particular, the surface profile in Figure 6
`
`changes curvature, from positive to negative, and the point where the curvature is zero is known
`
`as an inflection point (at about where the red broken lines meet the surface profile).
`
`Mathematically, an inflection point is located where the second derivative of the lens surface is
`
`zero. Lenses for mobile phones use aspheric surfaces to control aberration. Aspheric surfaces in
`
`polymer materials that are mass produced by injection molding are less expensive than the
`
`equivalent surfaces in glass materials. Spherical surfaces are the easiest to manufacture.
`
`+
`
`A S A S
`+
`1
`2
`
`2
`
`+
`
`3
`
`A S
`3
`
`+
`
`4
`
`A S
`4
`
`+
`
`...
`
`
`
`2 2
`
`S
`r
`
`K
`
`)
`
`(
`Sag S
`
`)
`
`=
`
`2
`
`S
`(
`1
`− +
`
`r
`
`
`
`
`
`
`1
`
`+
`
`1
`
`
`
`
`
`
`Equation 3.
`
`
`The Job of a Lens Designer
`
`C.
`45.
`
`One job of a lens designer is to mitigate optical aberrations in lenses to produce
`
`an image that is detailed with good contrast. A lens designer uses lens design software such as
`
`
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`14
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`EX 2010 Page 15
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`

`

`
`
`CODEV or OpticStudio to analyze, adjust, modify, optimize, or invent a lens. Often a lens
`
`design starts from an existing lens, say from the patent literature or performance specification,
`
`and the designer may adjust such a lens to the desired focal length by simply scaling the original
`
`lens; the adjustment is also made for the field of view and F-number. The lens performance
`
`specifications consist primarily of the focal length, field of view, f-number, total lens length, and
`
`image quality. The lens design software uses an error function to quantify image quality and the
`
`lens designer adjusts the lens and optimizes for image quality in many steps until the lens meets
`
`the performance specifications. Lens design software uses the following variables while
`
`performing automatic optimization: the lens curvatures and number of lenses, lens materials, lens
`
`air spacings, and aspheric coefficients. The lens designer guides the software to converge to a
`
`lens that meets the specifications. Adjusting a lens for a variety of reasons such as
`
`manufacturing is a routine task for a lens designer. A main product of the lens designer’s work
`
`is the lens prescription table that defines the lens(es) and contains, surface by surface, the surface
`
`radius of curvature, the spacing to the next surface, the lens material, and aspheric coefficients.
`
`For example, Figure 7 shows the prescription table for embodiment 1 of U.S. Patent No.
`
`6,804,067.
`
`Figure 7. United States Patent No. 6,804,067, Embodiment #1 Prescription table and lens
`cross section (Annotated).
`
`
`
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`A lens prescription table provides information about the optical constructional
`
`46.
`
`parameters of a lens, but it does not address how the lens elements will be mounted in a lens
`
`barrel. An opto-mechanical engineer may determine actual lens diameters, lens edge features
`
`such as bevels, and any lens flange for the lens elements to be mounted in a lens barrel.
`
`47.
`
`The total length of the lens TL, also known as the total track length TTL, is
`
`calculated by summing all lens spacing in the prescription table, including the spacing from the
`
`last lens surface to the image plane known as the back focal distance.
`
`48.
`
`Typically a lens designer adjusts, modifies, or designs a lens for a given electronic
`
`sensor that captures the image formed by the lens. The image circle of a lens is the diameter at
`
`the image plane of the lens where the lens has been corrected for aberration. The image circle
`
`can be specified slightly bigger than the sensor diagonal to allow for small misalignments
`
`between the sensor and the lens, and still illuminate all the sensor pixels. The sensor is located at
`
`the image plane of the lens otherwise defocus aberration will blur the image. Sensors are
`
`manufactured with different formats. For example, a 1/3” sensor format measures 4.8 mm wide
`
`by 3.6 mm in height, and 6 mm in diagonal.
`
`
`Figure 8. Barrel and pincushion distortion aberration.
`
`Figure 8 illustrates the distortion aberration, barrel and pincushion, which a lens
`
`49.
`
`system may have. When there is no distortion the relationship between the image circle diameter
`
`d, the lens focal length f, and half the field of view angle w is
`
`d
`
`=
`
`2
`
`f
`
`×
`
`tan
`
`(
`)
`ω
`
`. Thus for a 1/3”
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`
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`sensor and a field of view of
`(
`)
`/ 2 tan 37.5
`≅
`
`
`
`37.5
`ω= ±
` , the lens must have a focal length of
`
`
`
`3.91mm
`
`. The lens designer then would target the image height in the
`
`f
`
`=
`
`6
`
`mm
`
`optimization error function to be 3 mm and the focal length to 3.91 mm when half the field of
`
`view is set to 37.5°. Control over image sharpness, distortion aberration, and total lens length
`
`TL, would be also added to the error function. Given a set of lens variables that the lens designer
`
`deems to be appropriate, the automatic optimization routine in the lens design program
`
`minimizes the error function with the goal of producing a lens that meets the lens performance
`
`goals set by the lens application. This process is repeated with input from the lens designer until
`
`an acceptable lens is obtained.
`
`50.
`
`In practice, the design of a lens system involves trade-offs such as increasing the
`
`field of view at the expense of reducing the optical speed (i.e. increasing the f-number) for a
`
`given image quality. Another example of these tradeoffs is sacrificing image quality to minimize
`
`lens length TL. Lens systems are not perfect in their imaging.
`
`51.
`
`A large variety of lenses have been around since the invention of photography in
`
`1839. The Petzval portrait lens of 1840 made photography a practical reality since its optical
`
`speed of F/3.7 reduced the exposure time from about half an hour to about 30 seconds. The
`
`Cooke triplet invented in about 1895 was the first lens that could correct all primary aberrations
`
`mentioned above. Both of these lenses are illustrated in cross section in Figure 9.
`
`
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`17
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`
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`Figure 9. Left Petzval portrait objective of 1840; Right Cooke triplet lens of 1895
`
`The Petzval portrait objective was innovative because of its superior image
`
`52.
`
`quality and fast optical speed. It is said that the commercial success of the Petzval portrait lens
`
`was immediate and extraordinary, and that it spread with unexpected rapidity.
`
`D. Miniature Lenses
`A multitude of miniature lenses have been developed since about the year 2000
`53.
`
`for portable electronic devices such as personal digital assistants PDAs, laptop computers, and
`
`mobile phones. Lens assemblies consisting of two, three, and four lens elements were developed
`
`first. These miniature lenses have the benefits of scale in which most aberrations also scale
`
`down with the size of the lens. In addition, with plastic injection molding, complex aspheric
`
`surfaces could be specified. The improvement of polymer materials also helped the development
`
`of miniature lenses for portable electronics. In parallel, electronic sensors, such as charge
`
`coupled devices CCDs and complementary oxide metal semiconductor devices CMOS, with
`
`large number of pixels were developed to capture fine details in the images produced by such
`
`miniature lenses.
`
`54.
`
`The technical literature and patents of miniature lenses has hundreds, if not
`
`thousands, of lens examples. Earlier photographic lens design forms were scaled down and
`
`optimized to obtain miniature lens designs. Virtually by about 2006 all two, three, and four
`
`element lens assemblies of practical forms had been disclosed in the patent literature. For
`
`example, the ’691 Patent discloses a 4-lens system of the following general type: the first lens
`
`has a positive refractive power; the second lens has a negative refractive power; the third lens has
`
`a positive refractive power; and the fourth lens has a negative refractive power. This type of lens
`
`structure and lens types were disclosed as early as the 1970s. See U.S. Patent No. 3,961,844.
`
`These general structures were well known in the art in the early 2000s. For example, Figures 10
`18
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`

`
`
`and 11 illustrate some three and four element miniature lenses out of many in the patent literature
`
`of the 2000s.
`
`
`Figure 10. Lens assemblies with three lens elements of the optical power sequence positive,
`positive, negative.
`
`
`
`
`Figure 11. Lens assemblies with four lens elements of various forms.
`
`19
`
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`
`
`55.
`
`In regard to the Cooke triplet, Rudolf Kingslake has written in his History of the
`
`Photographic Lens (Academic Press 1989), page 106, “[s]ince that time every manufacturer has
`
`made Triplet lenses under a wide variety of trade names and, surprisingly, there have been over
`
`eighty patents issued covering lenses of the three element Cooke type. These patented designs
`
`differ from one another in the type of glass used and how the unavoidable aberration residuals
`
`are adjusted, but it is hard to regard these as ‘inventions.’ They appear to be routine designs that,
`
`in principle, could be generated automatically by a sufficiently complex computer program.”
`
`56.
`
`Dennis Taylor, the inventor of the Cooke triplet clarified that his lens was not the
`
`first triplet lens, but explained that the lens novelty of his triplet was that it substantially
`
`corrected for field curvature, something that had not been done before in a triplet lens, and that
`
`resulted in a new photographic lens with improved image quality.
`
`57.
`
`Routine lens optimization is performed in lenses f