PATENT REVIEW OF MINIATURE CAMERA LENSES
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`AND
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`A BRIEF COMPARISON OF TWO RELATIVE DESIGN PATTERNS
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`by
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`Luxin Nie
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`____________________________
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`A Report Submitted to the Faculty of the
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`COLLEGE OF OPTICAL SCIENCES
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`In Partial Fulfillment of the Requirements
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`For the Degree of
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`MASTER OF SCIENCE
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`In the Graduate College
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`THE UNIVERSITY OF ARIZONA
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`2017
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 1 of 33
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`
`
`AND
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`A BRIEF COMPARISON OF TWO RELATIVE DESIGN PATTERNS
`
`by
`
`Luxin Nie
`
`____________________________
`
`A Report Submitted to the Faculty of the
`
`COLLEGE OF OPTICAL SCIENCES
`
`In Partial Fulfillment of the Requirements
`
`For the Degree of
`
`MASTER OF SCIENCE
`
`In the Graduate College
`
`THE UNIVERSITY OF ARIZONA
`
`2017
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 1 of 33
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`
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`STATEMENT BY AUTHOR
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`The master’s report titled Patent Review of Miniature Camera Lenses and a
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`Brief Comparison of two Relative Design Patterns prepared by Luxin Nie has been
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`submitted in partial fulfillment of requirements for a master’s degree at the University
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`of Arizona.
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`Brief quotations from this report are allowable without special permission,
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`provided that an accurate acknowledgement of the source is made. Requests for
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`permission for extended quotation from or reproduction of this manuscript in whole or
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`in part may be granted by the copyright holder.
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` SIGNED: Luxin Nie
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`APPROVAL BY REPORT ADVISOR
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`This report has been approved on the date shown below:
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` _________________________________ Nov 29, 2017
`
` José M. Sasián Date
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` Professor of Optical Sciences
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` Professor of Astronomy
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`ACKNOWLEDGEMENTS
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`
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`I would like to thank my family for their consistent support.
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` I
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` would like to thank Prof. José Sasián for his beneficial advices in writing this
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`report, his enlightening teaching in optics without reservation, and his life-
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`changing influence of living as an ideal lens designer.
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` I
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` would also like to thank my committee, Dr. Jim Schwiegerling and Dr. Dae
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`Wook Kim. Their enthusiasm and devotion in education are very respectable and
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`make me thankful.
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`Thank other professors, staffs and classmates. They together make the experience
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`of studying in OSC enjoyable and unforgettable.
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`TABLE OF CONTENTS
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`Abstract ……………………………………………………………………….7
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`Patents Review ……………………………………………….………………8
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`Representative Patterns ……………………………………………………13
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`A Quick Evaluation ………………………………….…………….………...16
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`Two Relative Designs ………………………………………………….…....19
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`Four Parameters Evaluation ………………………………...………….….20
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`RMS Wave-front Error As Criterion ………………………………………23
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`Tolerancing By Element ………………………………...………………….26
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`Monte Carlo Analysis ………………………………….…….….………….28
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`Conclusions ……………………………………...……………………….….31
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`References ……………………………………………………...……………33
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`LIST OF FIGURES
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`Fig. 1 Numbers of patent publication in different years …………………………9
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`Fig. 2 Element number changing of miniature lenses over years ………………10
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`Fig. 3 Focal length changing of miniature lenses over years ………………….11
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`Fig. 4 F/# changing of miniature lenses over years …………………………….12
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`Fig. 5 FOV changing of miniature lenses over years ………………………….13
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`Fig. 6 (a) Parameters W and S of sixteen lenses in Table 1 ……………………18
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`Fig. 6 (b) Parameters CS and AS of sixteen lenses in Table 1………………….18
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`Fig. 7 (a) Layout of the selected 6-element lens ………………………………19
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`Fig. 7 (b) Layout of the selected 7-element lens ………………………………19
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`Fig. 8 Parameter w of each element of two compared lenses ………………….21
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`Fig. 9 Parameter (cs + as) / 2 of each element of two compared lenses ……….23
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`Fig. 10 RMS wave-front errors over HFOV …………….………………….….24
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`Fig. 11 (a) Histogram of RMS changes at center field …………………………29
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`Fig. 11 (b) Histogram of RMS changes at zonal field …………………………29
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`Fig. 11 (c) Histogram of RMS changes at edge field ………………………….30
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`LIST OF TABLES
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`Table 1 Representative design patterns of different element numbers …………14
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`Table 2 Four parameters of the two compared lenses …………………………20
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`Table 3 Selected field points and the local RMS values ………………………25
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`Table 4 RMS changes of different perturbances at three field points …………27
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`Table 5 Mean and standard deviation of Monte Carlo Analysis ……………...30
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`ABSTRACT
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`The market share of mobile terminals, such as PC, smart phone, and tablet,
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`increases rapidly in recent years. As a consequence, high-quality but low-cost
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`compact camera modules for these platforms are in a great demand as well.
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`Therefore, a large number of miniature camera lenses are designed and their
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`patents are published. In this report, about 750 U.S. patents of miniature camera
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`lenses are reviewed and the trend of their evolution is revealed. Then, sixteen
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`representative designs are tabulated, and a quick evaluation on them is made to
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`tell the optimums. Finally, two relative designs are selected and the tolerancing
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`sensitivity on particular elements is studied.
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`Patents Review
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`Time span of the reviewed U.S. patents is from 2000 to 2017. Nearly all of them
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`are assigned to five leading companies, namely Largan Precision Co., Kantatsu
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`Co., Genius Electronic Optical Co., Fujifilm Co., and Samsung Electro-
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`Mechanics Co., in the field of designing, manufacturing, and producing compact
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`camera modules for mobile devices.
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`In each patent document, besides the Date of Patent, there is also a Prior
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`Publication Data, where its prior publication date can be found. This date can be
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`regarded as the first time an invention or design being publicized in the U.S. For
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`example, the patent (Patent No.: US 9,733,454 B2. Date of Patent: Aug. 15,
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`2017.) has a Prior Publication Data: US 2016/0170184 A1 Jun. 16, 2016. Then,
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`June 16th in 2016 was the first time this patent application being publicized in
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`U.S., though it didn’t formally become a patent until Aug. 15, 2017. In this report,
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`each time related study uses this date as the time factor.
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`Fig. 1 is the numbers of patent publication in each year over the past two decades.
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`We can see that the trend starts to speed up in 2012. About 160 patents were
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`published in 2015, which makes it the bumper harvest year. The second summit
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`came in 2014, which has about 130 patent publications. The patents in 2014 and
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`2015 share about 38.6% of the total. The year 2012, 2013, and 2016 together
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`make about 31.3% of the total amount. However, the numbers in 2016 and 2017
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`are incomplete, since many designs initially published in these two years will not
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`formally become U.S. patents until some years later and thus are not counted. In
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`a short word, before 2016, the patent publication in the field of miniature camera
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`lenses started to boom in 2012 and came to its summit in 2015.
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`Fig. 1 Numbers of patent publication in different years
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`Camera lenses commonly have more than one element to make good imaging
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`performance, like balancing aberrations, and so do miniature camera lenses. More
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`elements usually mean more degrees of freedom to make a better design. Due to
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`the advances in technique of polymer materials and injection modeling, adoption
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`of non-traditional materials and aspherical elements becomes common, and even
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`strengthens this advantage. In Fig. 2, the number of elements adopted in each
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`9
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`200
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`180
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`160
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`140
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`120
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`100
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`80
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`60
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`40
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`20
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`Numbers of Patent Publication
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`0
`2000
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`2002
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`2004
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`2006
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`2008
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`2010
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`2012
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`2014
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`2016
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`2018
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`design is plotted. Powerless elements like IR filter are not counted.
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`Fig. 2 Element number changing of miniature lenses over years
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`Three- and four-element patterns seem to be classical. They appeared almost at
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`the early stage of miniature camera lens design and have thrived up till now. Both
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`of the two patterns balance the requirements of good performance, robustness,
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`and easy manufacture well, which makes them long-lasting over the past twenty
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`years, and probably in the future.
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`
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`Five-element pattern largely emerged in 2011, followed by six-element pattern
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`arising in 2013, and seven-element pattern boomed one year later, in 2014. This
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`trend reflects that due to largely reduced cost and highly improved assembling
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`
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`10
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` Largan
` Kantatsu
` Genius
` Fuji
` Samsung
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`9
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`8
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`7
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`6
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`5
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`4
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`3
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`2
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`#
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`1
`2000
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`2002
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`2004
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`2006
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`2008
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`2010
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`2012
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`2014
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`2016
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`2018
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`Prior Publication Date
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`technique, the pursuing of versatile performance starts to dominate.
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`Focal length is one of the most important parameters of lenses. It determines
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`many imaging properties of lenses and is always first given. As plotted in Fig. 3,
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`the distribution of focal length over publication year doesn’t show any obvious
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`preference. The value distribution of focal length is around 4 millimeters. This
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`promises an appealing small thickness in modern slim electronic devices.
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`Fig. 3 Focal length changing of miniature lenses over years
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`Unlike focal length, the distribution of F-number (F/#) over publication year in
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`Fig. 4 demonstrates an obvious decreasing trend. F/# is related to the “speed” of
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`a lens. Current miniature camera lenses have smaller F/#, and thus are “faster”
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`11
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` Largan
` Kantatsu
` Genius
` Fuji
` Samsung
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`14
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`13
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`12
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`11
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`10
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`0123456789
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`f (mm)
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`2000
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`2002
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`2004
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`2006
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`2008
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`2010
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`2012
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`2014
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`2016
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`2018
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`Prior Publication Date
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`than they used to be. “Fast” camera lenses usually have better performance in
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`imaging moving object. Given that the application scenes of modern mobile
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`devices are often in sport and video recording, this trend of F/# changing is
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`reasonable.
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`Fig. 4 F/# changing of miniature lenses over years
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`Another important lens parameter is field of view (FOV, HFOV for half FOV).
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`Fig. 5 demonstrates the trend of FOV changing. The average of FOV over past
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`twenty years increases slightly from about 60 to 70 degrees. However, the value
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`range of FOV diverges with respect to years. Newly designed miniature camera
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`lenses have various FOVs. This is probably a response to more diverse usage
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`requirements in nowadays consumer electronics market, like a wide-angle lens in
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`12
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` Largan
` Kantatsu
` Genius
` Fuji
` Samsung
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`5.0
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`4.5
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`4.0
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`3.5
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`3.0
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`2.5
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`2.0
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`1.5
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`F/#
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`1.0
`2000
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`2002
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`2004
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`2006
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`2008
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`2010
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`2012
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`2014
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`2016
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`2018
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`Prior Publication Date
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`a dual-lens module.
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`Fig. 5 FOV changing of miniature lenses over years
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`Representative Patterns
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`After some statistics, the evolution of design patterns is also interested. Some
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`representative patterns with three, four, five, six, seven or even eight elements are
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`shown in Table 1. Many other designs are varieties of them or got by shifting the
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`stop.
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`Whatever the type of design, it is obvious that aspherical surfaces are widely used
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`in miniature camera lenses. In fact, every surface in Table 1 except IR filters is
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`aspheric, and notably, last two or three elements are usually highly aspherical.
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`
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`13
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` Largan
` Kantatsu
` Genius
` Fuji
` Samsung
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`120
`
`100
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`80
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`60
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`40
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`20
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`FOV (degree)
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`0
`2000
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`2002
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`2004
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`2006
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`2008
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`2010
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`2012
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`2014
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`2016
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`2018
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`Prior Publication Date
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`Table 1 Representative design patterns of different element numbers.
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`3-element
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`4-element
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`(f: focal length, in mm; HFOV: half field of view, in degrees)
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`A: US20140049840A1
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`B: US20120013998A1
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`C: US20140198397A1
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`D: US20150146308A1
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`f = 1.53, F/2.75, HFOV = 33.0
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`f = 3.34, F/2.81, HFOV = 34.0
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`f = 2.22, F/2.20, HFOV = 33.7
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`f = 2.89, F/2.24, HFOV = 37.7
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`E: US20130258501A1
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`F: US20150022707A1
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`G: US20150316752A1
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`H: US20150077866A1
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`5-element
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`f = 5.44, F/2.90, HFOV = 33.0
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`f = 3.97, F/2.20, HFOV = 37.68
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`f = 4.138, F/2.18, HFOV = 34.89
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`f = 4.109, F/2.20, HFOV = 35.6
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`Table 1 -continued.
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`6-element
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`I: US20140049843A1
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`J: US20150054994A1
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`K: US20160252711A1
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`L: US20160011405A1
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`f = 3.66, F/2.20, HFOV = 38.0
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`f = 5.00, F/2.03, HFOV = 37.5
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`f = 3.02, F/2.40, HFOV = 37.1
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`f = 3.054, F/2.41, HFOV = 40.9
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`M: US20160341937A1
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`N: US20160033742A1
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`O: US20140376105A1
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`P: US9523841B1
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`7-element
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`8-element
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`f = 4.01, F/2.00, HFOV = 44.3
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`f = 3.89, F/1.60, HFOV = 35.8
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`f = 6.76, F/2.4, HFOV = 41.2
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`f = 5.38, F/1.90, HFOV = 39.0
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`A Quick Evaluation
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`To figure out the potential optimum designs in Table 1, four parameters W, S, CS,
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`and AS are used as criteria12. W and S are related to design patterns and often
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`mentioned together. CS and AS describe tolerancing sensitivity and are grouped
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`together.
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` W
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` is the square root of the averaged and squared weighted powers of each surface
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`in a lens. It describes the power distribution among optical surfaces. Small W
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`means the lens efficiently uses the power of its surfaces and large W indicates
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`surfaces contribute powers inefficiently. For aspherical surface, the optical power
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`is calculated based on the axial curvature and regardless of the conic constant or
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`high order aspherical coefficients.
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` is constructed in a similar way as W. It describes the lens symmetry. Because
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` S
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`lens symmetry can help cancel or avoid some aberrations, it is also an important
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`consideration in lens evaluation. Due to the requirement of incident ray angles on
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`sensor, in miniature camera lenses, the stop is usually set as the first or front part,
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`which is more or less against the element arrangement of sysmetry3.
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`CS and AS represent coma and astigmatism sensitivity respectively. They describe
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`the tolerancing sensitivity of a lens. All of the four parameters are independent of
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`lens scaling, aperture size, field angle, or conjugation, which makes them a
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`universal tool aiding in lens design and evaluation.
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`The calculations of W, S, CS, and AS are realized by macro files in lens design
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`software and are applied to the sixteen designs in Table 1. The results are plotted
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`separately in Fig. 6. In such a quick evaluation of multiple designs, CS and AS
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`are also calculated based on the paraxial rays, which consist with W and S.
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`
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`Though the main mechanism of sharp imaging is aberration cancellation, the four
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`parameters still provide an inspection on the lens properties and prediction of lens
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`performance. From Fig. 6, the potential optimum designs of each element number
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`can be told, which are G for 5-, J for 6-, N for 7-, and P for 8-element, since all
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`of their four parameters are less than 0.8. In contrast, O may not be a good design,
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`because it has extraordinary high values of the four parameters.
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`(a)
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`(b)
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`Fig. 6 Parameters (a) W, S, (b) CS, and AS of sixteen lenses in Table 1
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`18
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` W
` S
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`2.2
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`2.0
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`1.8
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`1.6
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`1.4
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`1.2
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`1.0
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`0.8
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`0.6
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`0.4
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`0.2
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`0.0
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`A
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`B C D E
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`F G H
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`I
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`J
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`K
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`L M N O P
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`Design
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` CS
` AS
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`10
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`9
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`8
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`2.0
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`1.5
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`1.0
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`0.5
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`0.0
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`A
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`B C D E
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`F G H
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`I
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`J
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`K
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`L M N O P
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`Design
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`Two Relative Designs
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`Now that introducing more elements in lens design becomes a trend, to find out
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`the possible differences made by doing so, two relative designs are compared.
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`The selected two designs are from the hand of same two inventers, Tsung-Han
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`Tsai and Hsin-Hsuan Huang from Largan Co. Fig. 7 are their layouts.
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`(a) (b)
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`Fig. 7 Layouts of the selected (a) 6-element lens4 and (b) 7-element lens5
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`The lens design (a) in Fig. 7 is published on February 26th in 2015 and (b) is
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`published later on November 24th in 2016. One can see that these two designs are
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`almost the same, except the third element of (a) is split into two parts in (b) (in
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`red boxes of Fig. 7). For conventional lens design, element splitting is a common
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`method in controlling spherical aberration and other concerns. However, for the
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`lens design adopting so many aspherical surfaces, which makes the nonlinearity
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`in imaging process go further, is the element splitting same useful in improving
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`lens performance? Next, some primary analyses are made to answer.
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`Four Parameters Evaluation
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`Both of the lenses are reoptimized. The focal length after re-optimization of the
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`6-element lens (abbreviated as 6EL) is 5.077 mm and of the 7-element lens
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`(abbreviated as 7EL) is 3.651 mm. To make the two lenses more comparable, the
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`dimensions of 6-element lens is rescaled (abbreviated as R6EL) by factor 0.72 to
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`have a focal length of 3.655 mm.
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`
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`Firstly, we use the method of calculating four parameters introduced in last
`
`section to obtain a general evaluation of the two lenses. In such a case, CS and
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`AS are calculated based on real ray tracing to makes the analysis closer to the real
`
`imaging process. Four parameters of the two lenses are tabulated in Table 2.
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`Table 2 Four parameters of the two compared lenses.
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`
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`W
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`S
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`CS
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`AS
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`R6EL
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`7EL
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`0.57
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`0.73
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`0.56
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`0.65
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`0.0242
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`0.0122
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`1.1240
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`0.0238
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`(CS + AS) / 2
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`0.5741
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`0.0180
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`20
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`Exhibit 2022 Page 20 of 33
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`From Table 2, we can see that their W are quite the same, which indicates that the
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`efficiency of the two lenses using their elements are almost the same. The
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`difference between their S is also not big. The absolute values of their CS are
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`small, but that of R6EL is twice as large as 7EL. AS of 7EL is also small but that
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`of R6EL is extraordinary large.
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`Fig. 8 Parameter w of each element of two compared lenses
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`To further illustrate the power distribution in the two lenses, w of each element
`
`of the two lenses are plotted in Fig. 8. To make a clear representation, the bars of
`
`4th to 6th element of R6EL are lay back one spacing, so that each of them is next
`
`to the bars of 5th to 7th element of 7EL respectively, since each pair have similar
`
`shapes and are thus comparable.
`
`
`
`21
`
` Re. 6-element
` 7-element
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`Element #.
`
`1.4
`
`1.2
`
`1.0
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0.0
`
`-0.2
`
`-0.4
`
`-0.6
`
`w
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 21 of 33
`
`
`
`From Fig. 8, it can be seen that the power distribution of two lenses are quite
`
`similar, which implies that these two designs have intrinsic similarity. This is
`
`consistent with our first observation. For the 1st, 2nd, 5th, 6th, and 7th element pairs,
`
`w of 7EL are all smaller than that of R6EL, except w of 4th element of 7EL is
`
`bigger than that of the 3rd element of R6EL. Given that the summation of w for
`
`any lens is unity as it’s constructed this way, the existence of the 4th element in
`
`7EL helps reduce the w values of the other elements, which is an obvious benefit
`
`of having more elements in lens design.
`
`
`
`To make an element-by-element inspection on the tolerancing sensitivity, the
`
`average of cs and as of each element, providing an integral evaluation of
`
`sensitivity rather than solely focusing on coma or astigmatism sensitivity, are
`
`computed and plotted in Fig. 9.
`
`
`
`From Fig. 9, we can see that the first element of each of the lenses has the
`
`dominating tolerancing sensitivity than the any element else does. This is
`
`corresponding to the fact that both of their first element has the most optical
`
`power distribution among others, which has been shown in Fig. 8.
`
`
`
`22
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 22 of 33
`
`
`
`Fig. 9 Parameter (cs + as) / 2 of each element of two compared lenses
`
`
`
`
`
`RMS Wave-front Error As Criterion
`
`For lenses working near the diffraction limit, RMS wave-front errors are preferred
`
`as the criteria for evaluating imaging quality. RMS wave-front error reflects the
`
`uniformity of wave-front at exit pupil, and will not be remarkably influenced by
`
`local extremum. Smaller the RMS, smoother is the wave-front at exit pupil.
`
`Changes in RMS wave-front errors reflect the degradation in lens performance
`
`caused by perturbation.
`
`
`
`As it has been mentioned, both of the lenses are reoptimized to have their RMS
`
`wave-front errors as close to zero as possible over the full field of view. In Fig.
`
`
`
`23
`
` Re. 6-element
` 7-element
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`Element #.
`
`0.06
`
`0.05
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0.00
`
`-0.01
`
`-0.02
`
`-0.5
`
`-1.0
`
`-1.5
`
`( cs+as ) / 2
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 23 of 33
`
`
`
`10, RMS of 6EL, R6EL, and 7EL over +Y field are plotted due to the symmetry
`
`about X-Z plane. The reference wavelength is 587.6 nm.
`
`Fig. 10 RMS wave-front errors over HFOV
`
`
`
`
`
`In Fig. 10, the blue line is totally beneath the light red line, which means 7EL has
`
`a better overall optimizing result than 6EL. However, the curvature changing of
`
`three lines are quite the same; that is their local maximum or minimum appears
`
`at same pace. This reflects the element arrangement of these two lenses has
`
`intrinsic similarity, and is another evidence of their relativeness. The RMS of
`
`R6EL is closer to that of 7EL. The comparison will be made between them as
`
`before.
`
`
`
`
`
`24
`
` 6-element
` Re. 6-element
` 7-element
`
`10
`
`20
`
`30
`
`40
`
`Field +Y (Degrees)
`
`0.06
`
`0.05
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0.00
`
`0
`
`RMS (waves)
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 24 of 33
`
`
`
`To further quantitively compare the tolerancing sensitivity on the third element
`
`as a unity with that on two split elements, a couple of field points where the RMS
`
`changes will be observed are chosen. The first principle for choosing such kind
`
`of field points is that both of them should be where the local extremum shows up.
`
`This guarantees that these two field points have same imaging properties. The
`
`second is that their corresponding RMS should be close to each other, which
`
`makes the calculation results more comparable. In Table 3, three pairs of such
`
`kind of field points and their corresponding RMS are tabulated.
`
`
`
`
`
`Table 3 Selected field points and the local RMS values.
`
`(Field: in degrees; RMS: in waves)
`
`Re. 6-element
`
`7-element
`
`Field
`
`RMS
`
`Field
`
`RMS
`
`0
`
`0.0271
`
`0
`
`0.0332
`
`19.5
`
`0.0160
`
`18.75
`
`0.0126
`
`32.625 0.0317
`
`31.875 0.0284
`
`Point (0, 0.0271) and (0, 0.0332) in Table 3 are center field points and should be
`
`compared. (19.5, 0.0160) and (18.75, 0.0126) are both local minimum and close
`
`to each other. They could be treated as zonal field points. (32.625, 0.0317) and
`
`(31.875, 0.0284) are both local maximum and close to each other as well. They
`
`could be viewed as the edge field points.
`
`
`
`25
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 25 of 33
`
`
`
`Tolerancing By Element
`
`For the two lenses, the third element of R6EL and third and fourth elements of
`
`7EL will be perturbed in the same manner, and the RMS changes at three selected
`
`field points will be observed. The third, fourth elements and the air gap in between
`
`of 7EL are perturbed as a unity like a sandwich. The perturbation manners include
`
`element decentering along X and Y axis and tilting about X and Y axis in opposite
`
`directions.
`
`
`
`The amplitude for element decentering is 0.003 mm and for tilting is 0.172
`
`degrees, so that the amplitude of edge moving is also 0.003 mm according to the
`
`lens dimension6. The RMS changes with respect to different perturbances are
`
`tabulated in Table 4.
`
`
`
`In Table 4, both of the absolute and relative RMS changes are listed. For each of
`
`the perturbation at different fields, the smaller relative RMS changes, that is also
`
`the better tolerancing performance, is marked bold and red for R6EL, blue for
`
`7EL.
`
`
`
`According to Table 4, for the tolerancing sensitivity at center field, 7EL is quite
`
`looser than R6EL. No matter what the perturbation is, the RMS of 7EL at center
`
`field stays almost unchanged. However, for the zonal or edge field, neither R6EL
`
`nor 7EL shows a prominent imaging stability in tolerancing. One lens may show
`
`
`
`26
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 26 of 33
`
`
`
`a loose tolerancing for some kinds of perturbation while the other may have more
`
`stable performance under other kinds of perturbation.
`
`
`
`Table 4 RMS changes of different perturbances at three field points.
`
`Lens Type
`
`Re. 6-element
`
`7-element
`
`Element
`
`3rd
`
`3rd & 4th
`
`Fields
`
`RMS Changes
`
`Δ
`
`%
`
`Δ
`
`%
`
`Decenter +X
`
`0.0161
`
`59.41 0.0001
`
`0.30
`
`Decenter -X
`
`-
`
`-
`
`-
`
`-
`
`Decenter +Y
`
`0.0161
`
`59.41 0.0001
`
`0.30
`
`Decenter -Y
`
`-
`
`-
`
`-
`
`-
`
`Tilt +X
`
`Tilt -X
`
`Tilt +Y
`
`Tilt -Y
`
`Center
`
`0.0145
`
`53.51 0.0000
`
`0.03
`
`-
`
`-
`
`-
`
`-
`
`0.0145
`
`53.51 0.0000
`
`0.03
`
`-
`
`-
`
`-
`
`-
`
`Decenter +X
`
`0.0177
`
`110.63 0.0140
`
`111.11
`
`Decenter -X
`
`-
`
`-
`
`-
`
`-
`
`315.08
`
`Decenter +Y
`
`0.0157
`
`98.13 0.0397
`
`Decenter -Y
`
`0.0221
`
`138.13 0.0467
`
`370.63
`
`Tilt +X
`
`Tilt -X
`
`Tilt +Y
`
`Tilt -Y
`
`Zonal
`
`0.0428
`
`267.50 0.0515
`
`408.73
`
`0.0438
`
`273.75 0.0456
`
`361.90
`
`0.0314
`
`196.25 0.0215
`
`170.63
`
`-
`
`-
`
`-
`
`-
`
`Decenter +X
`
`0.0107
`
`33.75 0.0053
`
`18.66
`
`Decenter -X
`
`-
`
`-
`
`-
`
`-
`
`Decenter +Y
`
`0.0722
`
`227.76 0.0051
`
`17.96
`
`Decenter -Y
`
`0.0295
`
`93.06 0.0357
`
`125.70
`
`Tilt +X
`
`Tilt -X
`
`Tilt +Y
`
`Tilt -Y
`
`Edge
`
`0.0382
`
`120.50 0.1053
`
`370.77
`
`0.0815
`
`257.10 0.0549
`
`193.31
`
`0.0184
`
`58.04 0.0109
`
`38.38
`
`-
`
`-
`
`-
`
`-
`
`
`
`
`
`27
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 27 of 33
`
`
`
`Monte Carlo Analysis
`
`In real scenarios of application, the third and fourth elements of 7EL may not and
`
`should not move as a unity. On the contrary, they may be moved by different
`
`kinds of perturbation in different amplitudes. To simulate this more actual
`
`circumstance, Monte Carlo analysis is needed.
`
`
`
`Monte Carlo analysis will generate as many lenses as defined. For each lens, all
`
`of the tolerancing operands are randomly set using the defined value range and a
`
`statistical model of the distribution over the specified range7.
`
`
`
`For our study, 200 perturbed lenses are generated for R6EL and 7EL respectively.
`
`The kinds of perturbation are same as those listed in Table 4. The statistic model
`
`of tolerancing parameters is set as normal distribution. The histograms of changes
`
`of RMS wave-front errors by the initial values at center, zonal, and edge fields
`
`are plotted in Fig. 11. Mean and standard deviation for each figure are tabulated
`
`in Table 5.
`
`
`
`28
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 28 of 33
`
`
`
`(a) Center field
`
`
`
`
`
`(b) Zonal field
`
`
`
`29
`
` Re. 6-element
` 7-element
`
`150
`
`100
`
`50
`
`0
`
`80
`
`100
`
`120
`
`140
`
`160
`
`180
`
`200
`
`220
`
`240
`
`260
`
`Change by (%)
`
` Re. 6-element
` 7-element
`
`100
`
`75
`
`50
`
`25
`
`0
`
`0
`
`100 200 300 400 500 600 700 800 900 1000 1100 1200
`
`Change by (%)
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 29 of 33
`
`
`
`(c) Edge field
`
`
`
`Fig. 11 Histograms of RMS changes at (a) center, (b) zonal, and (c) edge fields
`
`
`
`
`
`Table 5 Mean and standard deviation of Monte Carlo Analysis.
`
`Re. 6-element
`
`7-element
`
`Field
`
`Mean
`
`S. Dev
`
`Mean
`
`S. Dev
`
`Center
`
`140.81%
`
`31.73% 116.20%
`
`14.76%
`
`Zonal
`
`242.25%
`
`77.81% 375.63% 184.13%
`
`Edge
`
`182.84%
`
`87.92% 297.85% 149.08%
`
`From Fig. 11 and Table 5, we can find that for center field, both of mean and
`
`standard deviation of 7EL are less than those of R6EL. However, for zonal and
`
`
`
`30
`
` Re. 6-element
` 7-element
`
`120
`
`90
`
`60
`
`30
`
`0
`
`0
`
`100
`
`200
`
`300
`
`400
`
`500
`
`600
`
`700
`
`800
`
`900
`
`Change by (%)
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 30 of 33
`
`
`
`edge field, both of mean and standard deviation of R6EL are smaller. This
`
`verifies the conclusion obtained in last section that 7EL has a much more stable
`
`performance at center field than R6EL does. But for the zonal and edge field,
`
`Monte Carlo Analysis shows that R6EL performs better than 7EL, which is not
`
`concluded in last section.
`
`
`
`Conclusions
`
`First of all, the trend of miniature camera lenses evolution is depicted by
`
`reviewing a large number of patents. In the past twenty years, the element number
`
`keeps increasing and the f-number keeps decreasing steady, which indicates the
`
`lenses become more sophisticated and faster. Other aspects of miniature camera
`
`lenses keep going various as the market demands is becoming diverse.
`
`
`
`The representative design patterns having different numbers of elements are
`
`shown, of which the basic lens properties like focal length, F/#, and FOV are
`
`listed as well. Besides intuitive observation, a quick evaluation by calculating
`
`four parameters is also applied to the designs. The possible optimum designs of
`
`each element number are thus figured out.
`
`
`
`Second, two relative designs published chronologically by the same inventors are
`
`picked out from a crowd of patents. The most significant difference of the two
`
`lenses is that the third element of the 6-element lens is split into two parts in the
`
`
`
`31
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 31 of 33
`
`
`
`7-element lens, which makes the third and fourth elements of the latter, leaving
`
`almost all of the other characters of the two lenses similar.
`
`
`
`Next, we perturb the third element of 6-element lens and the third and fourth
`
`elements of 7-element lens in the same manners to observe the changes of RMS
`
`wave-front errors of each lens over the half field. In this part of study, the third
`
`and fourth elements of 7-element lens are perturbed as a unity. By this manual
`
`tolerancing analysis, it can be found that the 7-element lens has a much more
`
`stable performance at the center field than the 6-element lens. However, for the
`
`zonal and edge field, neither lenses show an obviously better tolerance than each
`
`other.
`
`
`
`Finally, to analyze the tolerancing sensitivity on the third and fourth elements of
`
`7-element lens separately, and to compare with that of the third element of 6-
`
`element lens, Monte Carlo analysis is applied to both lenses. The number of
`
`cycles of running Monte Carlo simulation is 200 and the statistic model of the
`
`amplitude of perturbation is normal distribution. As the result, the 7-element lens
`
`has a much more stable performance at the center field, which is coincide with
`
`the conclusion obtained in manual tolerancing analysis. However, for the zonal
`
`and edge field, 6-element lens has a better tolerance to the perturbances, which is
`
`not concluded in the manual analysis.
`
`
`
`
`
`32
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 32 of 33
`
`
`
`References
`
`1. J. M. Sasián, M. R. Descour. “Power distribution and symmetry in lens
`
`systems.” Optical Engineering, 37(3), 1001-1004 (1998).
`
`2. L. Wang, J. M. Sasián. “Merit Figures for Fast Estimating Tolerancing
`
`Sensitivity.” International Optical Design Conference 2010. Proc. SPIE-OSA
`
`7652, 76521P (2010).
`
`3. T. V. Galstian. Smart Mini-Cameras. CRC Press, 2013.
`
`4. U.S. Patent No.: 2015/0054994 A1.
`
`5. U.S. Patent No.: 2016/0341937 A1.
`
`6. R. Bates. “Performance and Tolerance Sensitivity Optimization of Highly
`
`Aspheric Miniature Camera Lenses.” Optical System Alignment, Tolerancing,
`
`and Verification IV. Proc. SPIE 7793, 779302 (2010).
`
`7. OpticStudio® 16.5 SP3 Help Files.
`
`
`
`33
`
`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2022 Page 33 of 33
`
`
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