USOO8508648B2
`
`(12) United States Patent
`Kubota et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 8,508,648 B2
`Aug. 13, 2013
`
`(54) IMAGING LENS
`(75) Inventors: Yoji Kubota, Nagano (JP); Kenichi
`Kubota, Nagano (JP); Hitoshi Hirano,
`Nagano (JP); Ichiro Kurihara, Tochigi
`(JP); Yoshio Ise, Tochigi (JP); Sumio
`Fukuda, Tochigi (JP)
`(73) Assignees: Optical Logic Inc., Nagano (JP);
`Kantatsu Co., Ltd., Tochigi (JP)
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 66 days.
`(21) Appl. No.: 13/206,136
`(22) Filed:
`Aug. 9, 2011
`
`(*) Notice:
`
`(65)
`
`(30)
`
`Prior Publication Data
`US 2012/0044404 A1
`Feb. 23, 2012
`
`Foreign Application Priority Data
`
`Aug. 23, 2010 (JP) ................................. 2010-185703
`
`(2006.01)
`(2006.01)
`(2006.01)
`
`(51) Int. Cl.
`H04N 5/225
`GO2B3/02
`GO2B 9/34
`(52) U.S. Cl.
`USPC ............................ 348/340; 35.9/715; 359/772
`(58) Field of Classification Search
`USPC .................. 348/340; 359/715,772, 773,774
`See application file for complete search history.
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`7,277,238 B2 10/2007 Noda
`8,179,470 B2 * 5/2012 Chen et al. .................... 348/335
`2011 0115962 A1
`5, 2011 Chen et al.
`
`FOREIGN PATENT DOCUMENTS
`JP
`2008-107616 A
`5, 2008
`JP
`2009-02O182
`1, 2009
`* cited by examiner
`Primary Examiner — David N Spector
`(74) Attorney, Agent, or Firm — Kubotera & Associates
`LLC
`
`ABSTRACT
`(57)
`An imaging lens includes an aperture stop ST, a first lens L1
`that is shaped to form a meniscus lens that directs a convex
`Surface to the object side near an optical axis and has positive
`refractive power, a second lens L2 that is shaped to form a
`meniscus lens that directs a convex surface to the object side
`near the optical axis and has negative refractive power, a third
`lens L3 that is shaped to form a meniscus lens that directs a
`concave surface to the object side near the optical axis and has
`positive refractive power, and a fourth lens L4 that is shaped
`to form a meniscus lens that directs a convex surface to the
`object side near the optical axis, arranged in this order from an
`object side to an image side. When the first lens L1 has a focal
`length fl and the second lens L2 has a focal length f2, the
`imaging lens is configured such that a relationship 0.3<fl/
`f2|<0.7 is satisfied.
`
`18 Claims, 18 Drawing Sheets
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`Sheet 1 of 18
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`R11 ~
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`|
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`FIG. 1
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`Sheet 2 of 18
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`
`
`DX
`- (U-39.28
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`- (0-33.20
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`| -- (U-26.14
`
`(U= 18.12
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`(t)=0.00
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 2
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`9. "SDI
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`Sheet 4 of 18
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`R1O
`- R9
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`R8
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`L1
`R.
`STR2 R3
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`R6 Rf
`R.
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`X
`
`R IM
`
`---
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`-----
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`31
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`---
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`R
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`d2
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`d' d3 d4 5
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`di
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`d9
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`11
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`1 O
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`d8
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`FIG. 4
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`Sheet 5 of 18
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`DX
`DY O. 3
`e-es---asses - -, (U-38.23
`
`—-------ee--- - - —- CU–32.22
`
`--------as- - CU-25.30
`
`------
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`- - - (U-17.49
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`(t)=0.00
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 5
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`Sheet 7 of 18
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`CO
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`FIG. 7
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`Sheet 8 of 18
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`DY | O. 3
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`DX
`
`(U=38.84
`
`-
`
`- - (U=32.79
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`(t)=25.79
`
`(U-1785
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`(t)=0.00
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 8
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`Sheet 10 of 18
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`d
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`d8
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`d1 O
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`FIG. 10
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`Sheet 11 of 18
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`DY O. 3
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`DX
`
`(U=38.40
`
`- -
`
`- - ou
`
`(U=32.38
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`- e =-H-F
`
`-
`
`(U-25.43
`
`--------ee-EF- - (U-17.59
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`(U=0.00
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 11
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`Sheet 12 of 18
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`LST (I
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`SVÌ
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`QSO ‘VIS
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`Sheet 13 of 18
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`R11
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`d8
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`d10
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`FIG. 13
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`Sheet 14 of 18
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`DY O. 3
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`DX
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`—- - - -
`
`----F
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`U 38.1 3°
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`- ===---------H--- -- - CU32.12
`
`- - - -Hue- -
`
`| -- CU-25.22
`
`--- -
`
`-ace (UF1 7.43
`
`---------EFF
`
`- --- (U=0.00"
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 14
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`Sheet 16 of 18
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`R1O
`- R9
`L2 -8 R8
`R6
`R4
`R7
`R5
`R3
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`O
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`IM
`R 1
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`-s
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`s1
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`st
`d9 r
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`L1
`R2
`ST
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`r
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`R1
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`d
`
`d2| d4
`d1 d2
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`5
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`d6
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`d
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`d1 O
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`d8
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`FIG. 16
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`Sheet 17 of 18
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`DY O. 3
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`DX
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`-- -
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`(U=39.48
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`-a (U-33.38
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`(t)=26.30
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`- (U-18.24
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`(t)=0.00
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`Tangential direction
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`Sagittal direction
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`Lateral aberration (mm)
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`FIG. 17
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`?, G “ Zç ·ç ·
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`. , ISTOISVÌDSO ’Y??
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`US 8,508,648 B2
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`1.
`IMAGING LENS
`
`BACKGROUND OF THE INVENTION AND
`RELATED ART STATEMENT
`
`10
`
`15
`
`30
`
`35
`
`The present invention relates to an imaging lens for form
`ing an image on an imaging element such as a CCD sensor
`and a CMOS sensor. In particular, the present invention
`relates to an imaging lens suitable for mounting in a relatively
`Small camera such as a cellular phone, a digital still camera, a
`portable information terminal, a security camera, an onboard
`camera, and a network camera.
`In these years, most cellular phone models include an
`onboard camera as standard equipment, and there have been
`attempts to increase added values of cellular phones. Further
`more, there are progresses in integrating a digital still camera
`to a cellular phone every year, and in these days, there have
`been available cellular phones, which have optical perfor
`mances and various functions that are comparable to those of
`digital still cameras.
`An imaging lens to be mounted in Such cellular phone is
`strongly required to have sufficient optical performances Suit
`able for resolution of an imaging element and a small size.
`Conventionally, both sufficient optical performances and
`Small size have been attained by an imaging lens with a
`25
`two-lens configuration or a three-lens configuration. How
`ever, optical performances on demands are higher and higher
`every year as an imaging element has higher resolution, and it
`is impossible to sufficiently correctaberrations by such two
`lens or three-lens configuration, so that it is difficult to fully
`satisfy the demanded optical performances.
`For this reason, there are studies on adding another lens,
`i.e., a lens configuration of four lenses. For example, an
`imaging lens disclosed in Patent Reference includes a first
`lens that is positive and has a convex surface on the both sides;
`a second lens that is negative and has a shape of meniscus lens
`directing a convex surface to the object side; a third lens that
`is positive and has a shape of meniscus lens directing a con
`cave surface to the object side; and a fourth lens that is
`negative and has a concave Surface on the both sides arranged
`in this order from an object side. The configuration attains
`good optical performances while restraining increase of total
`length of the imaging lens by setting preferable range for a
`ratio between a focal length of the fourth lens and a focal
`length of the whole lens system and keeping the ratio within
`the range.
`Patent Reference: Japanese Patent Application Publication
`No. 2009-20182
`According to the imaging lens of Patent Reference, it is
`possible to obtain relatively good aberrations. However, min
`50
`iaturization and functions of cellular phones are advanced
`every year, and cellular phones themselves are increasingly
`required to have a smaller size and higher functions. In the
`lens configuration disclosed in Patent Reference, it is difficult
`to attain both miniaturization and good aberration correction
`to satisfy those demands.
`Furthermore, cameras mounted in cellular phones are used
`in various ways, and for example, those cameras are widely
`used to take picture of himself/herself with his/her friend(s)
`while holding his/her cellular phone with his/her hand, take
`picture of himself/herself with landscape as the background,
`etc. Since a person who takes a picture himself/herself is an
`object to take a photo in those uses, imaging lenses of cameras
`mounted in cellular phones are required to have enlarged
`imaging angle of view, i.e. wide angle of view.
`Here, attaining both miniaturization and good aberration
`correction and wider angle is not specific issues to imaging
`
`40
`
`45
`
`55
`
`60
`
`65
`
`2
`lenses mounted in the cellular phones and is a common issue
`even in imaging lenses mounted in relatively small cameras
`Such as digital still cameras, portable information terminals,
`security cameras, onboard cameras, and network cameras.
`In view of the problems of the conventional techniques
`described above, an object of the present invention is to pro
`vide an imaging lens that has a small size, is capable of
`properly correcting aberration and has relatively wide imag
`ing angle of view.
`
`SUMMARY OF THE INVENTION
`
`In order to attain the object described above, according to
`the present invention, an imaging lens includes a first lens
`having positive refractive power, a second lens having nega
`tive refractive power; a third lens having positive refractive
`power; and a fourth lens arranged in an order from an object
`side to an image side. The first lens is formed in a shape so that
`both a curvature radius of a surface thereof on the object side
`and a curvature radius of a surface thereof on the image side
`are positive. The second lens is formed in a shape so that both
`a curvature radius of a surface thereof on the object side and
`a curvature radius of a Surface thereof on the image side are
`positive. The third lens is formed in a shape so that both a
`curvature radius of a surface thereof on the object side and a
`curvature radius of a surface thereof on the image side are
`negative. The fourth lens is formed in a shape so that both a
`curvature radius of a surface thereof on the object side and a
`curvature radius of a surface thereof on the image side are
`positive. In addition, the first lens has stronger refractive
`power than the second lens, the third lens, and the fourth lens,
`and the fourth lens has weaker refractive power than the first
`lens, the second lens, and the third lens. Furthermore, when
`the first lens has a focal length fl and the second lens has a
`focal length f2, the imaging lens is configured to satisfy the
`following conditional expression (1):
`
`According to the invention, since the first lens has stronger
`refractive power than the second lens, the third lens, and the
`fourth lens, it is possible to suitably attain miniaturization of
`the imaging lens. Furthermore, when the imaging lens with
`the configuration described above satisfies the conditional
`expression (1), it is possible to restrain the chromatic aberra
`tion, spherical aberration, and coma aberration respectively
`within Suitable range while attaining miniaturization and
`wide angle of view of the imaging lens. In the conditional
`expression (1), when the value exceeds the upper limit"0.7'.
`the first lens has refractive power relatively stronger than that
`of the second lens and the off-axis chromatic aberration of
`magnification is excessively corrected (that of a short wave
`length increases in a plus direction in relative to that of a
`reference wavelength). In addition, the coma aberration
`increases for an off-axis light beam. Therefore, it is difficult to
`obtain Satisfactory imaging performance. Moreover, for cor
`recting those aberrations, the total length of the lens system is
`long and thereby it is difficult to reduce the size of the imaging
`lens. On the other hand, when the value is below the lower
`limit “0.3, since the second lens has refractive power rela
`tively weaker than that of the first lens, the axial chromatic
`aberration and the off-axis chromatic aberration of magnifi
`cation are insufficiently corrected (that of a short wavelength
`increases in a minus direction in relative to that of a reference
`wavelength) although it is advantageous for reducing the size
`of the imaging lens. Therefore, it is also difficult in this case
`to obtain satisfactory image forming performance.
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`10
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`15
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`25
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`30
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`35
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`3
`When the whole lens system has a focal length f and a
`composite focal length of the first lens and the second lens is
`f12, in the imaging lens with the above configuration, it is
`preferred to satisfy the following conditional expression (2):
`1.5<f12 f-2.5
`(2)
`When the above conditional expression (2) is satisfied, it is
`possible to restrain the axial chromatic aberration within sat
`isfactory range while reducing the size of the imaging lens.
`When the value exceeds the upper limit “2.5', composite
`refractive power of the first lens and the second lens is rela
`tively weaker than that of the whole lens system, and it is
`difficult to reduce the size of the imaging lens. On the other
`hand, when the value is below the lower limit “1.5', the
`composite refractive power of the first lens and the second
`lens is stronger than that of the whole lens system, so that the
`axial chromatic aberration is insufficiently corrected and it is
`difficult to obtain satisfactory imaging performance, although
`it is advantageous for reducing the size of the imaging lens.
`When the whole lens system has a focal length fand the
`composite focallength of the second lens and the third lens is
`f23, in the imaging lens with the above-described configura
`tion, it is preferred to satisfy the following conditional expres
`sion (3):
`(3)
`1.5<f23ff-9.0
`When the above expression (3) is satisfied, it is possible to
`restrain the field curvature within satisfactory range while
`reducing the size of the imaging lens. When the value exceeds
`the upper limit “9.0', the off-axis best image surface signifi
`cantly tilts in a minus direction (on the object side) in relative
`to the axial best image surface and it is difficult to obtain a flat
`image surface and it is difficult to reduce the size of the
`imaging lens. On the other hand, when the value is below the
`lower limit “1.5”, since the composite refractive power of the
`second lens and the third lens is relatively stronger than that of
`the whole lens system, although it is advantageous for reduc
`ing the size of the imaging lens, the off-axis best image
`Surface significantly tilts in a plus direction (on the image
`side) in relative to the axial best image Surface, it is also
`difficult in this case to obtain a flat image surface. Therefore,
`in either case, it is difficult to obtain satisfactory imaging
`performance.
`In addition, in the imaging lens with the configuration
`described above, it is preferred to further satisfy the following
`conditional expression (3A):
`(3A)
`1.5<f23ff-6.5
`When the above expression (3A) is satisfied, it is possible
`to restrain the field curvature within more preferred range
`while Suitably reducing the size of the imaging lens.
`In the imaging lens with configuration described above, when
`the composite focal length of the first lens and the second lens
`is fl2 and the composite focal length of the second lens and
`the third lens is f23, it is preferred to satisfy the following
`conditional expression (4):
`
`4
`below the lower limit “0.2, since the image surface signifi
`cantly tilts in the minus direction (on the object side), it is also
`difficult in this case to obtain satisfactory imaging perfor
`aCC.
`In the imaging lens with configuration described above,
`when the surface of the first lens on the object side has
`curvature radius R1f and the surface of the first lens on the
`image side has curvature radius R1r, it is preferred to satisfy
`the following conditional expression (5):
`
`When the conditional expression (5) is satisfied, it is pos
`sible to restrain the off-axis aberration within satisfactory
`range while reducing the size of the imaging lens. When the
`value exceeds the upper limit “0.25', although it is advanta
`geous for reducing the size of the imaging lens, an inward
`coma aberration is generated for an off-axis light beam and it
`is difficult to obtain satisfactory imaging performance. On the
`other hand, when the value is below the lower limit"0.05', an
`outward coma aberration is generated for an off-axis light
`beam and astigmatic difference increases, and it is difficult
`also in this case to obtain satisfactory imaging performance.
`In the imaging lens with configuration described above, when
`the Surface of the first lens on the image side has curvature
`radius R1 rand the surface of the second lens on the object side
`has curvature radius R2f, it is preferred to satisfy the follow
`ing conditional expression (6):
`
`When the conditional expression (6) is satisfied, it is pos
`sible to restrain the off-axis aberration within satisfactory
`range. When the value exceeds the upper limit “0.7”, an
`inward coma aberration is generated for an off-axis light
`beam and Sagittal image surface of the astigmatisms signifi
`cantly tilts in a minus direction. Therefore, the astigmatic
`difference increases and it is difficult to obtain satisfactory
`imaging performance. On the other hand, when the value is
`below the lower limit “0.1, an outward coma aberration is
`generated for an off-axis light beam and the Sagittal image
`Surface of the astigmatisms significantly tilts in a plus direc
`tion. Therefore, the astigmatic difference also increases in
`this case and it is difficult to obtain satisfactory imaging
`performance.
`In the invention, when an aperture stop is arranged on the
`object side of the first lens and the aperture stop has an
`aperture diameter D, it is preferred to satisfy the following
`conditional expression (7):
`
`As described above, imaging elements have higher and
`higher resolution in these years and the imaging lenses are
`required to have even higher optical performances than those
`in conventional ones. Among them, imaging lenses are sig
`nificantly required to have brightness, i.e., a small F number.
`As well known, with advancement of imaging elements with
`higher resolution, pitches of pixels that compose an imaging
`element tend to be narrower. For example, while a pixel pitch
`is 1.4 um in case of a /4 inch imaging element having 5 mega
`pixels, a pixel pitch is as narrow as 1.1 um in case of an
`imaging element that has the same /4 size and has 8 mega
`pixels. Generally speaking, when a pixel pitch is narrower, a
`light-receiving area of each pixel decreases, so that a resultant
`image obtained through the imaging element is darker than
`that obtained through a conventional one. For this reason, as
`one of methods to solve those problems, there are attempts to
`decrease an F number of an imaging lens.
`
`40
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`45
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`50
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`55
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`When the conditional expression (4) is satisfied, it is pos
`sible to restrain the off-axis coma aberration, chromatic aber
`ration, and field curvature respectively within satisfactory
`range. When the value exceeds the upper limit “1.0, the
`image surface significantly tilts in a plus direction (on the
`image side) and the chromatic aberration of magnification is
`insufficiently corrected. In addition, the off-axis coma aber
`ration also increases, so that it is difficult to obtain satisfactory
`imaging performance. On the other hand, when the value is
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`60
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`65
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`5
`When the conditional expression (7) is satisfied, it is pos
`sible to decrease the F number while reducing the size of the
`imaging lens. When the value exceeds the upper limit “2.8'.
`since the aperture diameter is small for the focal length of the
`whole lens system, although it is advantageous for reducing
`the size of the imaging lens, brightness is insufficient for a
`high-resolution imaging element. On the other hand, when
`the value is below the lower limit “1.5”, since the aperture
`diameter is large for the focal length of the whole lens system,
`it is possible to further decrease the F number of the imaging
`lens and configure an imaging lens with brightness Suitable
`for a high-resolution imaging element, but it is difficult to
`reduce the size of the imaging lens.
`In the imaging lens with configuration described above, it
`is further preferred to satisfy the following conditional
`expression (7A):
`
`In addition, in the imaging lens of the invention, so as to
`restrain the axis chromatic aberration and the off-axis chro
`matic aberration within satisfactory range, when the first lens
`has Abbe’s number vd1 for a d line, the second lens has
`Abbe’s number vd2 for a d line, the third lens has Abbe’s
`number vd3 for a d line, and the fourth lens has Abbe’s
`number vd4 for a d line, it is preferred to satisfy each of the
`following conditional expressions:
`v1-SO
`
`US 8,508,648 B2
`
`6
`FIG. 8 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG. 7:
`FIG. 9 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG.7;
`FIG. 10 is a schematic sectional view showing a configu
`ration of an imaging lens in Numerical Data Example 4
`according to the embodiment;
`FIG. 11 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG. 10;
`FIG. 12 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG. 10;
`FIG. 13 is a schematic sectional view showing a configu
`ration of an imaging lens in Numerical Data Example 5
`according to the embodiment;
`FIG. 14 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG. 13;
`FIG. 15 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG. 13;
`FIG. 16 is a schematic sectional view showing a configu
`ration of an imaging lens in Numerical Data Example 6
`according to a second embodiment;
`FIG. 17 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG.16; and
`FIG. 18 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG. 16.
`
`10
`
`15
`
`25
`
`30
`
`35
`
`Here, in the imaging lens with the configuration described
`above, when the same lens material is used for those of the
`first lens, the third lens, and the fourth lens, only two types of
`lens materials are used to configure the imaging lens, so that
`it is possible to reduce the manufacturing cost of the imaging
`lens.
`According to the imaging lens of the invention, it is pos
`sible to both reduce the size of the imaging lens and correct
`the aberrations properly, thereby making it possible to pro
`vide the imaging lens with relatively wide imaging angle of
`45
`V1eW.
`
`40
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a schematic sectional view showing a configura
`tion of an imaging lens in Numerical Data Example 1 accord
`ing to a first embodiment of the invention;
`FIG. 2 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG. 1;
`FIG. 3 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG. 1:
`FIG. 4 is a schematic sectional view showing a configura
`tion of an imaging lens in Numerical Data Example 2 accord
`ing to the embodiment;
`FIG. 5 is an aberration diagram showing a lateral aberra
`tion of the imaging lens of FIG. 4;
`FIG. 6 is an aberration diagram showing a spherical aber
`ration, an astigmatism, and a distortion of the imaging lens of
`FIG. 4;
`FIG. 7 is a schematic sectional view showing a configura
`tion of an imaging lens in Numerical Data Example 3 accord
`ing to the embodiment;
`
`50
`
`55
`
`60
`
`65
`
`DETAILED DESCRIPTION OF PREFERRED
`EMBODIMENTS
`
`(First Embodiment)
`Hereunder, referring to the accompanying drawings, a first
`embodiment of the present invention will be fully described.
`FIGS. 1,4,7,10, and 13 are sectional views of image lenses
`in Numerical Data Examples 1 to 5 according to the embodi
`ment, respectively. Since a basic lens configuration is the
`same among the Numerical Data Examples 1 to 5, the lens
`configuration of the embodiment will be described with ref
`erence to the lens sectional view of Numerical Data Example
`1.
`As shown in FIG. 1, the imaging lens of the embodiment
`has an aperture stop ST, a first lens L1 having positive refrac
`tive power, a second lens L2 having negative refractive
`power; a third lens L3 having positive refractive power; and a
`fourth lens L4 having negative refractive power arranged in
`this order from an object side to an image side of the imaging
`lens. In other words, the imaging lens of this embodiment is
`configured as the one having an aperture stop on the front
`side, i.e. having an aperture stop ST on the object side of the
`first lens L1. Here, a filter 10 is provided between the fourth
`lens L4 and an image plane IM. It is noted that the filter 10
`may be optionally omitted.
`In the imaging lens with the configuration described above,
`the first lens L1 has a shape, in which both a curvature radius
`R2 thereof on the object side and a curvature radius R3
`thereof on the image side are positive, i.e. a shape of a menis
`cus lens that directs the convex surface to the object side near
`an optical axis X. The second lens L2 has a shape, in which
`both a curvature radius R4 thereof on the object side and a
`curvature radius R5 thereof on the image side are positive, i.e.
`a shape of a meniscus lens that directs the convex surface to
`the object side near the optical axis X.
`The third lens L3 has a shape, in which both a curvature
`radius R6 thereof on the object side and a curvature radius R7
`
`APPL-1025 / Page 22 of 31
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`7
`thereof on the image side are negative, i.e. a shape of a
`meniscus lens that directs the concave surface to the object
`side near the optical axis X. The fourth lens L4 has a shape, in
`which both a curvature radius R8 thereof on the object side
`and a curvature radius R9 thereof on the image side are
`positive, i.e. a shape of a meniscus lens that directs the convex
`surface to the object side near the optical axis X.
`The imaging lens of this embodiment satisfies the follow
`ing conditional expressions (1) to (6). Therefore, according to
`the imaging lens of the embodiment, it is possible to attain
`both miniaturization and satisfactory aberration correction.
`
`US 8,508,648 B2
`
`8
`Surfaces of the lens Surfaces may be expressed as follows
`(which will be the same in a second embodiment described
`below):
`
`H2
`
`H2
`1 + 1 - (k+1)
`
`10
`
`Formula 1
`
`Next, Numerical Data Examples of the embodiment will be
`described. In each of the Numerical Data Examples, frepre
`sents a focal length of a whole lens system, Fno represents an
`F number, and () represents a half angle of view, respectively.
`In addition, i represents a Surface number counted from the
`object side, R represents a curvature radius, d represents a
`distance between lens Surfaces (surface spacing) on the opti
`cal axis, Nd represents a refractive index for ad line, and val
`represents Abbe's number for the d line, respectively. Here,
`aspheric surfaces are indicated with surface numbers iaffixed
`with * (asterisk).
`
`NUMERICAL DATA EXAMPLE 1.
`
`Basic lens data are shown below.
`
`f = 3.650 mm, Fno = 2.226, () = 39.28°
`Unit: mm
`
`Surface Data
`
`R
`
`d
`
`Nd
`
`wd
`
`1.5<fl2f-2.5
`
`1.5<f23ff-9.0
`
`(2)
`
`15
`
`(3)
`
`In the above conditional expressions,
`f: Focal length of the whole lens system
`fl: Focal length of the first lens L1
`f2: Focal length of the second lens L2
`fl2: Composite focal length of the first lens L1 and the
`second lens L2
`f23: Composite focal length of the second lens L2 and the
`third lens L3
`Rlf: Curvature radius of a surface of the first lens L1 on the
`object side
`R1r: Curvature radius of a surface of the first lens L1 on the
`image side
`R2f; Curvature radius of a surface of the second lens L2 on
`the object side
`The imaging lens of the embodiment satisfies the following
`conditional expression (3A) to attain miniaturization of the
`imaging lens while further satisfactorily correcting the field
`Curvature:
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`(3A)
`1.5<f23ff-6.5
`Here, it is not necessary to satisfy all of the conditional
`expressions (1) to (6) (including the conditional expression
`(3A), which is hereinafter the same). When any single one of
`the conditional expressions (1) to (6) is individually satisfied,
`it is possible to obtain an effect corresponding to the respec
`tive conditional expression.
`In the imaging lens of this embodiment, the second lens L2
`the Abbe’s number that is lower than those of the first lens L1,
`the third lens L3, and the fourth lens L4 and that is within the
`following range so as to restrain an axial chromatic aberration
`and off-axis chromatic aberration within satisfactory range.
`Abbe’s number of the first lens L1 for ad line vol.1: vod1>50
`Abbe’s number of the second lens L2 for a d line va2:
`vd2<35
`Abbe’s number of the third lens L3 for ad line vol3:vd3-50
`Abbe’s number of the fourth lens L4 for a d line va4:
`vd450
`In the embodiment, each lens has a lens Surface that is
`formed to be an aspheric surface as necessary. When the
`aspheric Surfaces applied to the lens Surfaces have an axis Zin
`the optical axis direction, a height H in a direction perpen
`dicular to the optical axis, a conical coefficient k, and aspheric
`coefficients A4, A6. As Alo, A12, A14, and A16, the aspheric
`
`Surface
`Number i
`
`(Object)
`1 (Stop)
`2:
`
`3:
`
`4:
`
`5*
`6*
`
`7:
`8:8
`
`9*
`10
`11
`(Image plane)
`
`56.2
`(=vd1)
`
`26.0
`(=vd2)
`
`56.0
`(=vd3)
`
`56.2
`(=vd4)
`
`ce
`ce
`1999
`(=R1f)
`27.793
`(=R1r)
`9.264
`(=R2f)
`3.154
`-1.281
`
`-1.OSS
`1.091
`
`O.893
`ce
`ce
`ce
`
`ce
`O.OOOO
`O.6600
`
`O.2OOO
`
`1.52470
`
`O.3OOO
`
`1.6142O
`
`1.54340
`
`1.52470
`
`O.S600
`O4200
`
`O.2600
`0.5250
`
`O.SOOO
`O.3OOO
`1.0701
`
`fl = 4.069 mm
`f2 = -7.934 mm
`f12 = 6.706 mm
`f23 = 19.718 mm
`Aspheric Surface Data
`
`1.S1633
`
`64.1
`
`Second Surface
`
`60
`
`65
`
`k = -4.294.173E-01, A = 2.684306E-02, A = -1.530709E-01,
`As = 2.60243OE-01, Ao = -2.448736E-01
`Third Surface
`
`k = 0.000000, A = -6.08.0442E-02, A = -4.573234E-01, As =
`5.368732E-01, A = -2.824423E-01
`Fourth Surface
`
`k = 0.000000, A = -9.71 1859E-02, A = -8.900873E-01, As =
`9.32595OE-01, A = -2.514303E-01
`
`APPL-1025 / Page 23 of 31
`APPLE INC. v. COREPHOTONICS LTD.
`
`

`

`-continued
`
`f = 3.650 mm, Fno = 2.226, () = 39.28
`Unit: mm
`
`Fifth Surface
`
`k = 7.044876, A = 8.517387E-03, A = -6.211149E-01, As =
`8.568767E-01, Ao = -6.14247OE-01, A2 = 1.694307E-01, A =
`-4.588471E-O3
`Sixth Surface
`
`k = -2.468875, A = 9.20935OE-02, A = -9.063033E-02, As =
`–4.852762E-02, A = 5.447794E-02, A = 2.64694OE-01, A =
`–4.069938E-01, A = 1.595 617E-01
`Seventh Surface
`
`US 8,508,648 B2
`
`10
`Furthermore, when an aperture diameter of the aperture