USOO7321475 B2
`
`(12) United States Patent
`Wang et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 7,321.475 B2
`*Jan. 22, 2008
`
`(54) IMAGE PICK-UP LENS SYSTEM
`
`(75) Inventors: Zhuo Wang, Beijing (CN); Min-Qiang
`Wang, Beijing (CN); Ying-Bai Yan,
`Beijing (CN); Guo-Fan Jin, Beijing
`(CN); Ji-Yong Zeng, Beijing (CN)
`(73) Assignees: Tsing Hua University, Beijing (CN);
`Hon Hai Precision Industry Co., Ltd.,
`Tu-Cheng, Taipei Hsien (TW)
`
`(*) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 48 days.
`This patent is Subject to a terminal dis
`claimer.
`
`(21) Appl. No.: 10/954,726
`(22) Filed:
`Sep. 30, 2004
`
`(65)
`
`Prior Publication Data
`US 2005/0254147 A1
`Nov. 17, 2005
`Foreign Application Priority Data
`(30)
`May 15, 2004 (CN) ........................ 2004. 1 OO27254
`
`(51) Int. Cl.
`(2006.01)
`GO2B 9/04
`(2006.01)
`GO2B I3/18
`(52) U.S. Cl. ....................... 359/793: 359/717, 359/738
`(58) Field of Classification Search ........ 359/793 795,
`3597738 740
`See application file for complete search history.
`References Cited
`
`(56)
`
`U.S. PATENT DOCUMENTS
`
`8/2000 Tsuchida .................... 359/654
`6,104,545 A
`10/2001 Kaneko et al. ...
`... 359,718
`6,297,915 B1
`9/2002 Dou ........................... 359,793
`6,449, 105 B1
`6,885,508 B2 * 4/2005 Yamaguchi et al. ........ 359/717
`6,970,306 B2 * 1 1/2005 Matsuo ................
`... 359,716
`7,027,234 B2 * 4/2006 Kim et al. ........
`... 359,717
`7,038,861 B2 *
`5/2006 Ninomiya et al. .......... 359/719
`7,075,728 B2 * 7/2006 Yamaguchi et al. ........ 359/676
`7,196.855 B2 * 3/2007 Yamaguchi ..........
`... 359,785
`7,196,856 B2 * 3/2007 Nakamura .................. 359,785
`2003.0117723 A1* 6/2003 Shinohara ................... 359,794
`2003/0197953 A1* 10/2003 Yamaguchi et al. ..
`... 359,717
`2004.0036983 A1
`2/2004 Ninomiya et al. ....
`... 359,719
`2005/0280904 A1* 12/2005 Wang et al. ......
`... 359,717
`
`
`
`FOREIGN PATENT DOCUMENTS
`
`CN
`EP
`EP
`
`12/2003
`1461959
`1, 2003
`1271215 A1
`1357414 A1 10, 2003
`
`* cited by examiner
`Primary Examiner Jordan M. Schwartz
`(74) Attorney, Agent, or Firm Jeffrey T. Knapp
`
`(57)
`
`ABSTRACT
`
`An image pick-up lens system includes an aperture stop
`(10), a biconvex first lens (20), and a meniscus-shaped
`second lens (30) having a concave Surface on a side of an
`object. The aperture stop, the first lens and the second lens
`are aligned in that order from the object side to an image
`side. Each of the lenses has at least one aspheric Surface, and
`the following conditions are satisfied: (1) 0.5-fl/f-0.9, and
`(2) 1<T/f-1.62, wherein fl is a focal length of the first lens,
`f is a focal length of the system, and T is a length from the
`aperture stop to an image pick-up surface of the image side.
`
`5,940,219 A
`
`8/1999 Yamada ...................... 359/642
`
`6 Claims, 16 Drawing Sheets
`
`30
`
`40
`
`20
`
`10
`
`APPL-1024 / Page 1 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 1 of 16
`
`US 7,321.475 B2
`
`20
`
`10
`
`30
`
`40
`
`NY
`
`FIG 1
`
`APPL-1024 / Page 2 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 2 of 16
`
`US 7,321.475 B2
`
`FIG, 2A
`
`FIG, 2B
`
`--------
`--- rar
`
`FIG, 2C
`
`FIG, 2D
`
`
`
`- 2, 22
`
`2, 22
`MILLIMETERS
`
`FIG, 3A
`
`2, 22
`
`s2, 22
`
`2, 22)
`PERCENT
`
`2, 22
`
`FIG, 3B
`
`APPL-1024 / Page 3 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 3 of 16
`
`US 7,321,475 B2
`
`PUP RRDUS : 2, S6 to MILLMETERS
`
`
`
`as 2, 2
`
`2, 22
`MILMETERS
`
`2. 2
`
`FIG, 4.
`
`FRY
`
`MRXIMUM FIELO 35, 2222 OEG
`
`RIRY
`
`-S, 22
`
`2, 2
`MICRONS
`
`S, a
`
`FIG, 5
`
`APPL-1024 / Page 4 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 4 of 16
`
`US 7,321,475 B2
`
`
`
`,
`
`E
`
`Ole
`
`sea bec
`
`-2). 22
`
`2, 22
`MLLMETERS
`
`2, 22
`
`r 2, 22
`
`2, 22
`PERCENT
`
`2, 22
`
`FIG, 7A
`
`FIG, 7B
`
`APPL-1024 / Page 5 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 5 of 16
`
`US 7,321,475 B2
`
`PUPIL RRDIUS : 2, S632 MILMETERS
`
`
`
`s (2),
`
`2
`
`2, 22
`MILLIMETERS
`
`FIG, 8
`
`Z, 1 a
`
`MRXMUM FIELO 3S, 2222 OEC
`
`RRY
`
`RRY
`
`oS, 22
`
`a
`2),
`MCRONS
`
`FIG, 9
`
`5, 22
`
`APPL-1024 / Page 6 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 6 of 16
`
`US 7,321,475 B2
`
`Oei ... or - - - - -
`---- a---
`
`FIG, 10B
`
`O8 3.99 E.
`
`FIG 10A
`
`25,
`
`OE
`
`
`
`2, 22
`
`o2, a
`
`al). 22)
`
`2, 22
`MILLIMETERS
`
`FIG, 11A
`
`2, 20
`
`2, 22
`PERCENT
`
`FIG, 11B
`
`APPL-1024 / Page 7 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 7 of 16
`
`US 7,321,475 B2
`
`PUPL RRDIUS : 2, Sea MILLIMETERS
`
`
`
`- 2, 12
`
`2, 22
`MILLIMETERS
`FIG, 12
`
`(2),
`
`2
`
`MRXIMUM FIELO 3S, 222d OEG
`
`RCRY
`
`RRY
`
`- 5, 22)
`
`2, 22
`MICRONS
`FIG, 13
`
`S 22)
`
`APPL-1024 / Page 8 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 8 of 16
`
`US 7,321,475 B2
`
`-------
`FIG, 14B r1
`
`FIG, 14D
`
`FIG, 14C
`
`
`
`re, 22
`
`2, 22
`MLLMETERS
`
`2). 22
`
`- 2, 22
`
`2, 22
`PERCENT
`
`2, 22
`
`FIG, 15A
`
`FIG, 15B
`
`APPL-1024 / Page 9 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 9 of 16
`
`US 7,321.475 B2
`
`FUPL. RROIUS : 2, S8, 8 MLLMETERS
`
`a 2, 1 2)
`
`2, 22
`MILLEMETERS
`
`FIG, 16
`
`2, 1 a
`
`MRXIMUM FIELO 3S, 22.22 OEG
`
`RRY
`
`RRY
`
`- S, 22
`
`2, 22
`MICRONS
`
`FIG, 17
`
`S. 2
`
`APPL-1024 / Page 10 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 10 of 16
`
`US 7,321.475 B2
`
`FIG, 18C
`
`FIG, 18D
`
`
`
`r 2, 22
`2
`
`2, 22
`MILLIME TERS
`
`2, 20
`
`- 2.22
`
`2. 22
`PERCENT
`
`2
`2.2
`
`FIG, 19A
`
`FIG, 19B
`
`APPL-1024 / Page 11 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 11 of 16
`
`US 7,321.475 B2
`
`PUPL RFOUS : 2, S722 MILLIMETERS
`
`
`
`or 7, 1 a
`
`2, 22
`MILMETERS
`FIG, 20
`MAXIMUM FIELD 35, 2222 OEG
`RRY
`AIRY
`
`2, 12
`
`- 12, 22
`
`(2) 22
`MICRONS
`FIG 21
`
`2, 22
`
`APPL-1024 / Page 12 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 12 of 16
`
`US 7,321,475 B2
`
`
`
`
`
`
`
`FIG, 22B re FIG, 22D
`
`s2 22
`
`2, 22
`MILMETERS
`
`0, 22
`
`-222
`
`2, 22
`PERCENT
`
`2, 22
`
`FIG, 23A
`
`FIG, 23B
`
`APPL-1024 / Page 13 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 13 of 16
`
`US 7,321,475 B2
`
`PUPIL RADIUS 2, S492 MILMETERS
`
`V
`
`- 2, 12
`
`2, 22
`MILLIMETERS
`
`FIG, 24
`
`2, 2
`
`MAXIMUM FIELO : 35, 22.22 OEG
`
`FIRY
`
`FRY
`
`-5, 20
`
`2, 22
`MICRONS
`
`FIG, 25
`
`5, 22
`
`APPL-1024 / Page 14 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 14 of 16
`
`US 7,321.475 B2
`
`Oei is,
`
`sc
`
`FIG 26 A
`
`FIG, 26B
`
`---, --
`r FIG 26C
`
`FIG, 26D
`
`
`
`- 22
`
`2, 22
`MILMETERS
`
`2, 22
`
`o2 2.
`
`2.2
`PERCENT
`
`2, 20
`
`FIG 27 A
`
`FIG, 27B
`
`APPL-1024 / Page 15 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 15 of 16
`
`US 7,321.475 B2
`
`PUPIL RROIUS 2.579 MILLIMETERS
`
`
`
`- 2, 2
`
`2, 2
`M.ILL.METERS
`
`2),
`
`2
`
`FIG, 28
`
`MRXIMUM FIELO : 39, 2022 OEG
`RIRY
`RRY
`
`- 2, 22
`
`2, 22
`MICRONS
`
`FIG, 29
`
`2, 22
`
`APPL-1024 / Page 16 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`U.S. Patent
`
`Jan. 22, 2008
`
`Sheet 16 of 16
`
`US 7,321,475 B2
`
`
`
`FIG, 30
`CPRIOR ART)
`
`APPL-1024 / Page 17 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`1.
`IMAGE PICK-UP LENS SYSTEM
`
`US 7,321,475 B2
`
`TECHNICAL FIELD
`
`The present invention relates to an image pick-up lens
`system which projects an image of an object onto an image
`pick-up surface, the image pick-up lens system being Suit
`able for use in products such as camera modules.
`BACKGROUND
`
`10
`
`2
`However, the ratio of a total length of the lens system to a
`total focal length of the three lenses (L/f) is about 2. It is
`difficult to make the lens system compact. In addition, the
`plurality of lenses increases costs.
`In order to satisfy all the requirements of compactness,
`low cost and excellent optical performance, it is commonly
`believed that a two-lens system is desirable.
`A well-known two-lens system is the retro-focus type lens
`system. A typical Such lens system can be found in U.S. Pat.
`No. 6,449,105B1. The lens system comprises, from an
`object side to an image side, a first meniscus lens having
`negative refracting power and a convex surface on the object
`side, a stop, and a second meniscus lens having positive
`refracting power and a convex surface on the image side.
`The lens system helps correct wide angle aberrations. How
`ever, a shutter is positioned between the second lens and the
`image side, which adds to the distance between the second
`lens and the image side. Thus, the compactness of the lens
`system is limited.
`U.S. Patent Publication No. 2004/0036983 discloses an
`image pick-up lens which overcomes the above described
`problems. As represented in FIG. 30 hereof, the image
`pick-up lens comprises, from an object side to an image side:
`an aperture stop 1; a biconvex positive lens 2; and a
`meniscus lens 3 having a concave surface on the object side.
`When each of the lenses 2, 3 has at least one aspheric
`Surface, the image pick-up lens satisfies the following con
`ditions: 0.3<fl/f-0.9 and T/f-2.4. In these expressions, “f
`is an overall focal length of the lens system, “fl' is a focal
`length of the positive lens 2, and “T” is a length from the
`aperture stop 1 to an image pick-up Surface 5.
`However, the ratio of the total length of the lens system
`to the total focal length of the lenses 2, 3 (L/f) is generally
`about 2. The smallest ratio obtainable is 1.7, which still
`constitutes a limitation on the compactness of the lens
`system. In addition, it is difficult to correct lateral chromatic
`aberration effectively, and thus the optical performance of
`the lens system is limited.
`Therefore, a low-cost image pick-up lens system which
`can properly correct aberrations and has a compact configu
`ration is desired.
`
`15
`
`30
`
`35
`
`40
`
`45
`
`In recent years, camera modules for taking photos have
`begun to be incorporated in mobile terminals such as mobile
`phones and lap-top computers. Downsizing the camera
`modules is a prerequisite for enhancing the portability of
`these apparatuses. The camera module operates with an
`image pickup device Such as a CCD (Charged Coupled
`Device) or a CMOS (Complementary Metal Oxide Semi
`conductor). Recently, a pixel having the size of approxi
`mately a few micrometers has become commercially fea
`sible, and an image pickup device with high resolution and
`a compact size can now be commercialized. This is accel
`erating the demand for downsizing of image pick-up lens
`systems so that they are able to be suitably used with
`miniaturized image pick-up devices. It is also increasing
`25
`expectations of cost reductions in image pick-up lens sys
`tems, commensurate with the lower costs enjoyed by mod
`ern image pickup devices. All in all, an image pick-up lens
`system needs to satisfy the oft-conflicting requirements of
`compactness, low cost, and excellent optical performance.
`Compactness means in particular that a length from a lens
`edge of the lens system to an image pick-up surface should
`be as short as possible.
`Low cost means in particular that the lens system should
`include as few lenses as possible; and that the lenses should
`be able to be formed from a resin or a plastic and be easily
`assembled.
`Excellent optical performance can be classified into the
`following four main requirements:
`First, a high brightness requirement, which means that the
`lens system should have a small F number (FNo.) Generally,
`the FNo. should be 2.8 or less.
`Second, a wide angle requirement, which means that half
`of the field of view of the lens system should be 30° or more.
`Third, a uniform illumination on the image surface
`requirement, which means that the lens system has few
`eclipses and/or narrows down an angle of incidence onto an
`image pick-up device.
`Fourth, a high resolution requirement, which means that
`the lens system should appropriately correct fundamental
`aberrations such as spherical aberration, coma aberration,
`curvature of field, astigmatism, distortion, and chromatic
`aberration.
`In a lens system which satisfies the low cost requirement,
`a single lens made from a resin or a plastic is desired. Typical
`such lens systems can be found in U.S. Pat. No. 6.297,915B1
`and EP Pat. No. 1271215A2. However, even if the lens has
`two aspheric surfaces, it is difficult to achieve excellent
`optical performance, especially if a wide angle Such as 70°
`is desired. Thus, the single lens system can generally only be
`used in a low-resolution image pick-up device Such as a
`CMOS. In addition, a thick lens is generally used for
`correcting aberrations. Thus, a ratio of a total length of the
`lens system to a focal length of the lens (L/f) is about 2. In
`other words, it is difficult to make the lens system compact.
`In a lens system which satisfies the excellent optical
`performance requirement, three lenses are desired. A typical
`such lens system can be found in U.S. Pat. No. 5,940.219.
`
`SUMMARY OF THE INVENTION
`
`Accordingly, an object of the present invention is to
`provide an image pick-up lens system which has a relatively
`short total length.
`Another object of the present invention is to provide an
`image pick-up lens system which can optimally correct
`fundamental aberrations.
`To achieve the above-described objects, an image pick-up
`lens system in accordance with the present invention com
`prises an aperture stop, a biconvex first lens, and a meniscus
`shaped second lens having a concave Surface on a side of an
`object. The aperture stop, the first lens and the second lens
`are aligned in that order from the object side to an image
`side. Each of the lenses has at least one aspheric Surface.
`According to a first aspect, the following conditions are
`satisfied:
`
`0.53fl/f-0.9, and
`
`(1)
`
`50
`
`55
`
`60
`
`65
`
`APPL-1024 / Page 18 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`US 7,321,475 B2
`
`3
`wherein, fl is a focal length of the first lens, f is a focal
`length of the system, and T is a length from the aperture stop
`to an image pick-up surface of the image side.
`According to a second aspect, preferably, both a first
`Surface on the object side and a second Surface on the image
`side of the first lens are aspheric, and the following condi
`tions are satisfied:
`
`0.2<R2/R1 <1, and
`
`1.2<d/R2<2.1,
`
`(3)
`
`(4)
`
`10
`
`wherein, R1 is an absolute value of a radius of curvature of
`the first surface, R2 is an absolute value of a radius of
`curvature of a second Surface, and d is a thickness of the first
`lens.
`Further, to correct field curvature, each of the first and
`second lenses is aspheric on both surfaces thereof, and the
`following condition is satisfied:
`0.5<(1/R3)/(1/R1+1/R2+1/R4)<1,
`
`(5)
`
`15
`
`wherein, R3 is an absolute value of a radius of curvature of
`a third surface of the second lens on the object side, and R4
`is an absolute value of a radius of curvature of a fourth
`Surface of the second lens on the image side.
`Further still, the two lenses are made from a resin or a
`plastic. To correct chromatic aberration, the Abbe constant
`v1 of the first lens and the Abbe constant v2 of the second
`lens preferably satisfy the following condition:
`
`25
`
`30
`
`4
`cal aberration, and lateral chromatic aberration curves for an
`image pick-up lens system in accordance with a first exem
`plary embodiment of the present invention;
`FIGS. 6-9 are graphs respectively showing transverse ray
`fan plots, field curvature and distortion, longitudinal spheri
`cal aberration, and lateral chromatic aberration curves for an
`image pick-up lens system in accordance with a second
`exemplary embodiment of the present invention;
`FIGS. 10-13 are graphs respectively showing transverse
`ray fan plots, field curvature and distortion, longitudinal
`spherical aberration, and lateral chromatic aberration curves
`for an image pick-up lens system in accordance with a third
`exemplary embodiment of the present invention;
`FIGS. 14-17 are graphs respectively showing transverse
`ray fan plots, field curvature and distortion, longitudinal
`spherical aberration, and lateral chromatic aberration curves
`for an image pick-up lens system in accordance with a fourth
`exemplary embodiment of the present invention;
`FIGS. 18-21 are graphs respectively showing transverse
`ray fan plots, field curvature and distortion, longitudinal
`spherical aberration, and lateral chromatic aberration curves
`for an image pick-up lens system in accordance with a fifth
`exemplary embodiment of the present invention;
`FIGS. 22-25 are graphs respectively showing transverse
`ray fan plots, field curvature and distortion, longitudinal
`spherical aberration, and lateral chromatic aberration curves
`for an image pick-up lens system in accordance with a sixth
`exemplary embodiment of the present invention;
`FIGS. 26-29 are graphs respectively showing transverse
`ray fan plots, field curvature and distortion, longitudinal
`spherical aberration, and lateral chromatic aberration curves
`for an image pick-up lens system in accordance with a
`seventh exemplary embodiment of the present invention;
`and
`FIG. 30 is a schematic representation of an image pick-up
`lens in accordance with a prior publication.
`
`35
`
`40
`
`45
`
`Because the first lens is positioned adjacent the aperture
`stop and has at least one aspheric Surface, the image pick-up
`lens system can appropriately correct spherical and coma
`aberrations. In addition, because the second lens is posi
`tioned away from the aperture stop and has at least one
`aspheric surface, different chief rays of different field angle
`can have very different corresponding projection heights at
`the second lens. Therefore the system can appropriately
`correct astigmatism, field curvature and distortion, all of
`which are related to the field angle. Furthermore, the fourth
`Surface of the second lens has a gradually varying refraction
`from a central portion thereof near an optical axis of the
`system to a peripheral edge portion thereof. Thus, a central
`portion of the second lens diverges light rays and a periph
`eral edge portion of the second lens converges light rays, so
`that the meridional/sagittal sections easily coincide. For all
`the above reasons, the optical image performance in wide
`angles of the system is enhanced. Moreover, because the first
`and second lenses can be made from a resin or a plastic, the
`system is relatively easy and inexpensive to mass manufac
`ture.
`Other objects, advantages and novel features of the
`present invention will become more apparent from the
`following detailed description when taken in conjunction
`with the accompanying drawings, in which:
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a schematic view of an image pick-up lens
`system in accordance with the present invention;
`FIGS. 2-5 are graphs respectively showing transverse ray
`fan plots, field curvature and distortion, longitudinal spheri
`
`DETAILED DESCRIPTION OF EMBODIMENTS
`OF THE INVENTION
`
`FIG. 1 shows a schematic configuration of an image
`pick-up lens system in accordance with the present inven
`tion. The system comprises an aperture stop 10, a biconvex
`first lens 20, and a meniscus-shaped second lens 30 having
`a concave surface on a side of an object. The aperture stop
`10, the first lens 20 and the second lens 30 are aligned in that
`order from the object side to an image side. The first and the
`second lenses 20, 30 each have at least one aspheric surface.
`The first and second lenses 20, 30 can be made from a resin
`or a plastic, which makes their manufacture relatively easy
`and inexpensive.
`The aperture stop 10 is arranged closest to the object in
`order to narrow down an incident angle of chief rays onto an
`image pick-up surface 40 located at the image side. In
`addition, this arrangement of the aperture stop 10 helps
`shorten a total length of the system. For further cost reduc
`tion, the aperture stop 10 is preferably formed directly on a
`first surface (not labeled) of the first lens 20 on the object
`side. In practice, a portion of the first surface of the first lens
`20 through which light rays are not transmitted is coated
`with a black material, which functions as the aperture stop
`10.
`
`50
`
`55
`
`60
`
`65
`
`APPL-1024 / Page 19 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`5
`In order to provide compactness and excellent optical
`performance, the first and second lenses 20, 30 satisfy the
`following conditions:
`1<T/f& 1.62, and
`
`(1)
`
`(2)0.5<fl/f-0.9,
`
`(2)
`
`wherein, f1 is a focal length of the first lens 20, f is a focal
`length of the system, and T is a length from the aperture stop
`10 to the image pick-up surface 40. The first condition (1) is
`for limiting the total length of the system. The second
`condition (2) is for correcting monochromatic aberrations,
`and providing both compactness and a desirable distribution
`of refracting power. In one aspect, when the ratio f1/f is
`above the lower limit of 0.5, the system provides satisfactory
`total refracting power and keeps high-order spherical aber
`ration, high-order coma and lateral chromatic aberration of
`the system in a controlled range. In another aspect, when the
`ratio f1/f is below the upper limit of 0.9, the system is
`compact and provides satisfactory total refracting power.
`The surfaces of the first and second lenses 20, 30 are
`appropriately aspheric, which enables this Small number of
`lenses to satisfy many if not all of the above-described
`requirements of compactness, low cost, and excellent optical
`performance.
`In addition, preferably, both the first surface and a second
`surface (not labeled) of the first lens 20 on the image side are
`aspheric, and the following conditions are satisfied:
`
`10
`
`15
`
`25
`
`30
`
`wherein, R1 is an absolute value of a radius of curvature of
`the first surface, R2 is an absolute value of a radius of
`curvature of the second Surface, and d is a thickness of the
`first lens 20. The third condition (3) governs a distribution of
`refracting power for the first lens 20, in order to correct
`monochromatic aberrations. The fourth condition (4) is for
`lessening an incident angle of the second Surface of the first
`lens 20, to further correct high-order aberrations.
`The concave surface of the second lens 30 is defined as a
`third surface (not labeled). The first lens 20 and the second
`lens 30 satisfy the following condition:
`0.5<(1/R3)/(1/R1+1/R2+1/R4)<1,
`
`35
`
`40
`
`(5)
`
`45
`wherein, R3 is an absolute value of a radius of curvature of
`the third surface of the second lens 30, and R4 is an absolute
`value of a radius of curvature of a fourth surface (not
`labeled) of the second lens 30 on the image side.
`The fifth condition (5) is for correcting field curvature and
`obtaining a flat field. In one aspect, when the ratio (1/R3)/
`(1/R1+1/R2+1/R4) is above the lower limit of 0.5, the
`negative Petzval’s Sum produced by the third surface of the
`second lens 30 can compensate the total positive Petzvals
`Sum produced by the first and second surfaces of the first
`lens 20 and the fourth surface of the second lens 30. Thus,
`it is relatively easy to correct field curvature of the system.
`In another aspect, when the ratio (1/R3)/(1/R1+1/R2+1/R4)
`is below the upper limit of 1, the negative refracting power
`produced by the third surface of the second lens 30 can
`effectively compensate the positive coma and lateral chro
`matic aberration produced by the first lens 20. Meanwhile,
`the radius of curvature R3 of the third surface of the second
`lens 30 is not so small that increases the high-order aberra
`tions of the system, and the negative refractive power
`provide by R3 can correct the lateral chromatic aberration of
`Lens 20. Furthermore, the radius of curvature R3 of the third
`surface of the second lens 30 has the smallest absolute value
`
`50
`
`55
`
`60
`
`65
`
`US 7,321,475 B2
`
`6
`among the four absolute values of radiuses of curvature R1,
`R2, R3, R4 of the first and second lenses 20, 30. Thus in
`order to correct field curvature without producing high-order
`aberrations, the third surface of the second lens 30 is
`concave to the aperture stop 10.
`Also, in order to appropriately correct the chromatic
`aberration of the system, the Abbe constant v1 of the first
`lens 20 and the Abbe constant v2 of the second lens 30
`preferably satisfy the following condition:
`
`Further, the fourth surface of the second lens 30 prefer
`ably has a gradually varying refraction from a central
`portion thereof near an optical axis of the system to a
`peripheral edge portion thereof. Thus, a central portion of
`the second lens 30 diverges light rays and a peripheral edge
`portion of the second lens 30 converges light rays, so that
`meridional/sagittal sections easily coincide. This feature
`further enhances the optical image performance in wide
`angles of the system.
`The above explanations outline fundamental constituent
`features of the system of the present invention. Examples of
`the system will be described below with reference to FIGS.
`2-29. It is to be understood that the invention is not limited
`to these examples. The following are symbols used in each
`exemplary embodiment.
`T. length from the aperture stop to the image pick-up surface
`f total length of the system
`FNo: F number
`(): half field angle
`2(1): field angle
`R: radius of curvature
`d: distance between surfaces on the optical axis of the
`system
`Nd: refractive index of lens
`v: Abbe constant
`In each example, the first and second surfaces of the first
`lens 20 and the third and fourth surfaces of the second lens
`30 are aspheric. The shape of each aspheric surface is
`provided by expression 1 below. Expression 1 is based on a
`Cartesian coordinate system, with the vertex of the surface
`being the origin, and the optical axis extending from the
`vertex being the X-axis.
`Expression 1:
`
`h2
`is +XAh
`X
`1 + v 1 - (k + 1)ch?
`wherein, h is a height from the optical axis to the Surface, c
`is a vertex curvature, k is a conic constant, and A, are i-th
`order correction coefficients of the aspheric surfaces.
`
`EXAMPLE 1.
`
`Tables 1 and 2 show lens data of Example 1.
`
`TABLE 1.
`
`f = 3.21 mm T = 4.00 mm FNO = 2.83 () = 35°
`
`Surface No.
`
`R (mm)
`
`D (mm)
`
`Nd
`
`w
`
`k
`
`Stop 10
`1 surface
`2" surface
`3' surface
`4 surface
`
`-0.08
`infinite
`1949767
`1908685
`0.8410808
`-1.386019
`-0.6313817 0.92.96156 1.585
`-1.14047S
`0.2679967
`
`1492
`
`57.4
`
`29.9
`
`O
`O.3969374
`O4322471
`-0.6737203
`-O.9677394
`
`APPL-1024 / Page 20 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`APPL-1024 / Page 21 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`US 7,321,475 B2
`
`10
`EXAMPLE 4
`
`9
`FIGS. 6-9 are graphs of aberrations (transverse ray fan
`plots, field curvature/distortion, longitudinal spherical aber
`ration, and lateral chromatic aberration) of the system of
`Example 2. FIGS. 6A-6D respectively show aberrations
`curves of meridional/sagittal sections in 0°, 15, 25° and 35°
`field angles. FIGS. 7A and 7B respectively show field
`curvature and distortion curves. The first lens 20 is made
`from polymethyl methacrylate (PMMA), and the second
`lens 30 is made from a polycarbonate.
`
`Lens data of Example 4 are shown in tables 7 and 8. In the
`lens data shown below, E shows powers of 10.
`
`10
`
`TABLE 7
`
`EXAMPLE 3
`
`f = 3.26 mm T = 4.22 mm FNO = 2.80 () = 35°
`
`Lens data of Example 3 are shown in tables 5 and 6. In the
`lens data shown below, E shows powers of 10; that is, for
`example, 2.5E-0.3 means 2.5x10.
`
`TABLE 5
`
`f = 3.21 mm T = 4.05 mm FNo = 2.83 () = 35°
`
`Surface No.
`
`R (mm)
`
`D (mm)
`
`Nd
`
`w
`
`k
`
`Surface N
`
`80t
`
`O.
`
`R (mm)
`
`l
`
`D (mm)
`
`l
`
`Nd
`
`w
`
`k
`
`15
`
`Stop 10
`1 surface
`2" surface
`3 surface
`'' 4th surface
`
`infinite
`2.124272
`-1.327932
`-0.68.07691
`-1.337.036
`
`1492
`
`-0.067878
`1991 OOS
`0.7080908
`0.65685.42 1.58S
`0.861976
`
`O
`S74 - 12.41067
`-O.1739S28
`-0.994.0377
`-3.86OO14
`
`29.9
`
`Stop 10
`1 surface
`2" surface
`3 surface
`4" surface
`
`-0.0798
`infinite
`1951123.
`1.937576
`0.842203
`-1.395695
`-0.6367427 O.9198.73S 1.58S
`-1.111585
`031196.58
`
`1492
`
`O
`S74 -1026366
`O.3649843
`-0.6782141
`–4.560295
`
`29.9
`
`2.5
`
`FIGS. 14-17 are graphs of aberrations (transverse ray fan
`plots, field curvature/distortion, longitudinal spherical aber
`
`TABLE 6
`
`Surface No.
`
`1 Surface
`
`2" surface
`
`3 surface
`
`4 surface
`
`Aspherical A2 = 0
`coefficient A4 = -0.0090154464
`A6 = -0.027257396
`A8 = -O31450985
`A10 = 0.6O707428
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = 0.047546265
`A6 = -0.0674287O3
`A8 = 0.0886.13357
`A10 = -0.04786747
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = 0
`A4 = -OO67457258
`A6 = 0.0487O2325
`A8 = -OOO16956663
`A10 = -84.14046E-005
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = -0.17525752
`A6 = 0.053841628
`A8 = 0.0007158852
`A10 = -OOO1238689
`A12 = 0
`A14 = 0
`A16 = O
`
`FIGS. 10-13 are graphs of aberrations (transverse ray fan
`plots, field curvature/distortion, longitudinal spherical aber
`ration, and lateral chromatic aberration) of the system of 45
`Example 3. FIGS. 10A-10D respectively show aberrations
`curves of meridional/sagittal sections in 0°, 15, 25° and 35°
`field angles. FIGS. 11A and 11B respectively show field
`curvature and distortion curves. The first lens 20 is made
`from polymethyl methacrylate (PMMA), and the second
`lens 30 is made from a polycarbonate.
`
`TABLE 8
`
`Surface No.
`
`1 surface
`
`2" surface
`
`3 surface
`
`4 surface
`
`Aspherical A2 = 0
`coefficient A4 = 0.10925473
`A6 = -0.13095248
`A8 = O
`A10 = 0
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = O.O11162728
`A6 = -0.066705593
`A8 = 0.0684924.17
`A10 = -0.04357828
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = -0.22040448
`A6 = O.O1920O829
`A8 = -0.0231.14479
`A10 = -9.0582917E-005
`A12 = 0
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = -0.14881856
`A6 = O.OS1775666
`A8 = 0.00118.71839
`A10 = -OOO1327.1067
`A12 = 0
`A14 = 0
`A16 = O
`
`APPL-1024 / Page 22 of 25
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`US 7,321,475 B2
`
`12
`EXAMPLE 6
`
`11
`ration, and lateral chromatic aberration) of the system of
`Example 4. FIGS. 14A-14D respectively show aberrations
`curves of meridional/sagittal sections in 0°, 15, 25° and 35°
`field angles. FIGS. 15A and 15B respectively show field
`curvature and distortion curves. The first lens 20 is made
`from polymethyl methacrylate (PMMA), and the second
`lens 30 is made from a polycarbonate.
`
`Lens data of Example 6 are shown in tables 11 and 12.
`
`EXAMPLE 5
`Lens data of Example 5 are shown in tables 9 and 10.
`
`10
`
`TABLE 11
`
`f = 3.19 mm T = 4.32 mm FNo = 2.8 () = 35°
`
`TABLE 9
`
`f = 3.22 mm T = 4.99 mm FNo = 2.80 () = 35°
`
`Surface No.
`
`R (mm)
`
`D (mm)
`
`Nd
`
`w
`
`k
`
`Surface No.
`
`R (mm)
`
`D (mm)
`
`Nd
`
`w
`
`k
`
`-0.03
`infinite
`Stop 10
`2.042576.
`3.567241
`1 surface
`O.82S6124
`-1.204826
`2. Surface
`3. Lic E. O.8.186415 1.58S
`
`1492
`
`O
`S74 -0.9115067
`-O.1979544
`2.
`
`29.9
`
`15
`
`Stop 10
`1 surface
`ind
`2"Surface
`3" surface
`20 4" surface
`
`M
`infinite
`2.704951
`
`-0.05
`1.9340O8
`
`1.531
`
`S6.0
`
`-1.264784
`-0.60228
`-1.056885
`
`O.8348153
`O.91.18O4S 1.585
`O.64O254
`
`29.9
`
`O
`-19.70274
`
`-O.306O2O2
`-09132682
`-2.01608
`
`TABLE 10
`
`Surface No.
`
`1 surface
`
`2" surface
`
`3" surface
`
`4" surface
`
`Aspherical A2 = 0
`coefficient A4 = -0.038187626
`A6 = O.O2S227628
`A8 = 0.05774S58
`A10 = -0.4454O332
`A12 = 0.1964647
`A14 = 0
`A16 = O
`
`A2 = 0
`A4 = 0.046356766
`A6 = -OOO32353324
`A8 = -OOO2.8835816
`A10 = O.OO191852O1
`A12 = O.OOO24573464
`A14 = 0
`A16 = O
`
`A2 = 0
`A4 = 0.04O616649
`A6 = O.O85273579
`A8 = -O.O796.57862
`A10 = 0.0508348.21
`A12 = -O.O16829857
`A14 = 0
`A16 = O
`
`A2 = 0
`A4 = 0.0185752
`A6 = O.OO3OO64393
`A8 = 0.002911957
`A10 = O.OOO6524O269
`A12 = -OOOO3396.5939
`A14 = 0
`A16 = O
`
`FIGS. 18-21 are graphs of aberrations (transverse ray fan a
`plots, field curvature/distortion, longitudinal spherical aber
`ration, and lateral chromatic aberration) of the system of
`Example 5. FIGS. 18A-18D respectively show aberrations
`curves of meridional/sagittal sections in 0°, 15, 25° and 35°
`field angles. FIGS. 19A and 19B respectively show field
`curvature and distortion curves. The first lens 20 is made
`from polymethyl methacrylate (PMMA), and the second
`lens 30 is made from a polycarbonate.
`
`45
`
`TABLE 12
`
`Surface No.
`
`1 Surface
`
`2" surface
`
`3 surface
`
`4 surface
`
`Aspherical A2 = 0
`coefficient A4 = 0.078640248
`A6 = -O.198.6909
`A8 = 0.273S3815
`A10 = -0.482.15993
`A12 = 0.21645868
`A14 = 0
`A16 = O
`
`A2 = 0
`A4 = 0.043790817
`A6 = -O.O92545745
`A8 = 0.12998.134
`A10 = -0.11896713
`A12 = 0.038733469
`A14 = 0
`A16 = O
`
`A2 = O
`A4 = 0.086709045
`A6 = O.049096719
`A8 = -0.101.31265
`A10 =