# Patent

## Title
Imaging lens

## Abstract

A five element lens system for use with an imaging sensor includes first, second, third, fourth, and fifth lens elements and an optical filter that are arranged sequentially in order from an object side to an imaging side. The lens elements are coated with an anti-reflective film. The lens system further includes an optical filter that is disposed at a distance from the imaging sensor. The lens elements are relatively positioned to each other to satisfy specific conditions. The lens elements further include thickness to diameters ratios that satisfy specific conditions. The lens system is capable of focusing images of objects located from a range of 10 cm to infinity from the lens system.

## Background
BACKGROUND
The present disclosure relates to an imaging lens and an imaging lens system having the same, more particularly to an imaging lens with five lens elements and to an imaging lens system having the same.
In recent years, various electronic devices have been designed to include imaging lenses and imaging sensors for image-capturing and video-recording capabilities. To improve portability and imaging performance while reducing dimensions and weights of the electronic devices, different combinations of lenses are installed in electronic devices that have embedded charge coupled device (CCD) sensors or complementary metal oxide semiconductor (CMOS) imaging sensors. There is thus a need for compact imaging lenses and imaging lens systems that provide improved image quality. Compactness in a lens system is determined by the size of the clear aperture diameters of the lens elements in the lens system. In the description below, the diameter of a lens element is referred to its clear aperture diameter for the sake of brevity.
U.S. Pat. No. 8,072,695 discloses imaging lenses with five lens elements. Each of the imaging lenses has a unique combination and arrangement of lens elements with different surface shapes to thereby achieve a specific combination of optical characteristics. However, in achieving the specific combination of optical characteristics, certain aspects of optical performance are compromised. Therefore, the need to develop other imaging lenses with better combinations of optical characteristics still exists in the market.
SUMMARY
Embodiments of the present invention provide imaging lenses and systems with a desired combination of optical characteristics.
According to an embodiment of the present invention, an imaging lens includes first, second, third, fourth, and fifth lens elements arranged sequentially in order from an object side to an imaging side, each of the first, second, third, fourth, and fifth lens elements having an object-side surface facing toward the object side, and an imaging-side surface facing toward the imaging side. The imaging lens satisfies the conditions of 20<vd1−vd2, 0≦|vd3−vd2|≦5, 20<vd4−vd3, and 0≦|vd4−vd5|≦5, wherein vd1, vd2, vd3, vd4, and vd5 are Abbe numbers of the first, second, third, fourth, and fifth lens elements, respectively.
According to another embodiment of the present invention, an imaging lens system has in order from an object side to an imaging side an aperture stop, a first lens element, a second lens element, a third lens element, a fourth lens element, and a fifth lens element arranged behind the aperture stop in sequence. Each lens element has an object-side diameter and an imaging-side diameter. The object-side diameter may be equal to or smaller than the imaging-side diameter. The aperture stop is configured to pass light and may have a circular-shaped opening. The circular-shaped opening has a diameter that may be equal to or smaller than the object-side diameter of the first lens element. The first lens element has a first Abbe number and the second lens element has a second Abbe number. The first Abbe number is greater than the second Abbe number by at least 20. The object-side and imaging-side surfaces of each lens element can be coated with an anti-reflective coating.
According to yet another embodiment of the present invention, a lens system includes first, second, third, fourth, and fifth lens elements that are arranged in order from an object side to an imaging side. The five lens elements are sequentially arranged on an optical axis. The lens system further includes an optical filter disposed between the fifth lens element and the imaging sensor along the optical axis. Each of the first, second, third, fourth and fifth lens elements has an object-side surface facing toward the object side, and an imaging-side surface facing toward the imaging side. The optical filter has an object-side surface and disposed at a distance of about 0.441 mm from the imaging-side of the fifth lens element. In an embodiment, the imaging-side surface of the first lens element and the object-side surface of the second lens element have an air gap of 0.070 mm, the imaging-side surface of the second lens element and the object-side surface of the third lens element have an air gap of 0.288 mm, the imaging-side surface of the third lens element and the object-side surface of the fourth lens element has an air gap of 0.260 mm, and the imaging-side surface of the fourth lens element and the object-side surface of the fifth lens element has an air gap of 0.131 mm. In an embodiment, the first lens element may have a thickness of 0.49 mm, the second lens element may have a thickness of 0.27 mm, the third lens element may have a thickness of 0.465 mm, the fourth lens element may have a thickness of 0.4 mm, and the fifth lens element may have a thickness of 0.35 mm. In an embodiment, the optical filter may have a thickness of 0.3 mm and may be disposed at a distance about 0.441 mm of the imaging-side surface of the fifth lens element.
The following detailed description together with the accompanying drawings will provide a better understanding of the nature and advantages of the present invention.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram illustrating some terms used in the present description.
FIG. 2 is a schematic diagram defining certain characteristics of an imaging lens system according to the present invention.
FIG. 3 is a schematic diagram defining certain characteristics of an imaging lens system according to the present invention.
FIGS. 4A and 4B are cross-sectional views illustrating different total track lengths of a lens system for explaining the lens system's operations.
FIG. 5 is a schematic diagram illustrating TV distortion of an imaging lens system.
FIG. 6 is a schematic diagram illustrating a relationship between an imaging sensor, an associated image sensor circle and a maximum image circle according to an embodiment of the present invention.



DETAILED DESCRIPTION
The term “lens” or “lens system” will be used to describe a complete lens that may include multiple lens elements, an aperture stop, optical filter, and the like. The term “lens element” is herein defined as a single transparent mass of refractive material having two opposed refracting surfaces. The term “diameter” refers to the “clear aperture” or “clear aperture diameter” of a lens element. The term “clear aperture”, “clear aperture diameter,” and “diameter” will be interchangeably used throughout the specification. The term “total track length” or “TTL” is defined as a distance from an object-side surface of the first lens element to an imaging plane. The term “focal length” is defined as the distance from the optical center of the lens to the focal point that is located on an imaging sensor. A “sag” is the displacement of the surface of the lens from a reference plane transverse (perpendicular) to the optical axis and can be measured at different radial distances from the optical axis. FIG. 1 shows an example of two different lens elements having different sag values at the 25 percent point, 50 percent point, 75 percent point, and at the 100 percent point from the optical axis, where the percentages are relative to the radius of the lens in the plane perpendicular to the optical axis. The radius is defined as one-half of the clear aperture diameter of a lens element. Since the lens elements described herein are rotationally symmetric about the optical axis, the lower half is a mirror image of the upper half. The sag value can be zero, positive, or negative depending on the surface shape of the lens element and whether the surface is an object-side or imaging side surface. In the example shown in FIG. 1, the sag values are positive.
Referring to FIG. 2, an imaging lens system 200, according to an embodiment of the present invention, may include a cover glass or window 2, first, second, third, fourth and fifth lens elements 3, 4, 5, 6, 7, and an optical filter 8 arranged in the given order from an object side to an imaging side. Each of the first, second, third, fourth, and fifth lens elements 3, 4, 5, 6, 7 has an object-side surface 31, 41, 51, 61, 71, facing toward the object side, and an imaging-side surface 32, 42, 52, 62, 72 facing toward the imaging side. In some embodiments, aperture stop 1 may be disposed at object-side surface 21 of cover glass or window 2. When light from a target object enters imaging lens system 200, it passes through aperture stop 1, cover glass or window 2, lens elements 3 through 7, and optical filter 8 in the given order, and forms an image at an imaging plane 9 which may be a surface of an imaging sensor.
In some embodiments, aperture stop 1 is made of an opaque material. A central opening 11 through aperture stop 1 may be circular shaped and have a diameter that is smaller than the diameter of the object-side surface 31 of the first lens element. In an exemplary embodiment, the diameter of the aperture stop is about 1.36 mm and the diameter of object-side surface 31 of the first lens element is about 1.377 mm. In another embodiment, aperture stop 1 may be disposed between cover glass 2 and object-side surface 31 of the first lens element 3.
Each lens element has two shaped surfaces that converge or diverge light. Each lens element is made out of an optically transparent material, such as glass or plastic. The refractive index of the lens material and curvature of the shaped surface define the light refraction. The surface curvature of each lens element can be defined by a set of sag values. In an embodiment, the set of sag values of each lens element can be provided in a table format to a computer database for manufacturing a lens element.
Referring still to FIG. 2, optical filter 8 has an object-side surface 81 facing toward the object side, and an imaging-side surface 82 facing toward the imaging side. In some embodiments, the optical filter may be an infrared filter that passes light having a wavelength lower than 0.8 microns and suppresses transmission of light having wavelengths greater than 0.8 microns. Each of the five lens elements may have a refractive index greater than 1.5. In some embodiments, the object-side surface and the imaging-side surface of the first, second, third, fourth and fifth lens elements are coated with an anti-reflective coating.
In some embodiments, the relative position of the lens elements to each other, the diameter to thickness ratio of each lens element, the ratio between the sum of the air gaps and the total track length are factors in achieving good optical performance. In some embodiments an air gap between the lens elements is needed to facilitate proper focusing of incident light. Referring to FIG. 3, s1 is an air gap between the imaging-side surface of the first lens element and the object-side surface of the second lens element, s2 is an air gap between the imaging-side surface of the second lens element and the object-side surface of the third lens element, s3 is an air gap between the imaging-side surface of the third lens element and the object-side surface of the fourth lens element, s4 is an air gap between the imaging-side surface of the fourth lens element and the object-side surface of the fifth lens element, and s5 is an air gap between the imaging-side surface of the fifth lens element and the object-side surface of the optical filter. Additionally, imaging plane 9 is placed at a distance s6 from the imaging-side of optical filter 8, as shown in FIG. 3. If the imaging plane is placed at a distance larger than 0.4 mm from the optical filter, the imaging sensor may generate an inaccurate image due to possible loss of light with a given chief ray angle (CRA). In an embodiment, the chief ray angle is less than 31 degrees.
Referring still to FIG. 3, t1 is a thickness of first lens element 3 that is measured from the object-side surface at the optical axis to the imaging-side surface at the optical axis. Similarly, t2 is a thickness of second lens element 4 measured at the optical axis, t3 is a thickness of third lens element 5 measured at the optical axis, t4 is a thickness of fourth lens element 6 measured at the optical axis, and t5 is a thickness of fifth lens element 7 measured at the optical axis. Each lens element may have one or more flanges formed around its periphery and extending outwardly away from the optical axis. The flanges may be used to mount the lens element to a holding member (not shown). The effective diameter (i.e., the “clear aperture” or “clear aperture diameter”) of the object-side surface of first lens element 3 is designated d1, and the effective diameter of the imaging-side surface of first lens element 3 is designated d2. The effective diameter is defined as the diameter of the surface of the lens element that may contribute to the optical performance of the lens element. In other words, the effective diameter may not include the flange at the outer periphery of the lens element. Hereinafter, the effective diameter is referred to as the diameter. Similarly, the diameter of the object-side surface of second lens element 4 is designated d3, and the diameter of the imaging-side surface of second lens element 4 is designated d4; the diameter of the object-side surface of third lens element 5 is designated d5, and the diameter of the imaging-side surface of third lens element 5 is designated d6; the diameter of the object-side surface of fourth lens element 6 is designated d7, and the diameter of the imaging-side surface of fourth lens element 6 is designated d8. Likewise, the diameter of the object-side surface of fifth lens element 7 is designated d9, and the diameter of the imaging-side surface of fifth lens element 7 is designated d10.
Table 1 provides design parameters of a lens system according to an embodiment of the present invention.











TABLE 1






Refractive
Thickness
Air gap
Diameter


lens
index
(mm)
(mm)
(mm)







first
1.54
t1 = 0.490
s1 = 0.070
d1 = 1.377






d2 = 1.393


second
1.65
t2 = 0.270
s2 = 0.288
d3 = 1.388






d4 = 1.390


third
1.54
t3 = 0.465
s3 = 0.260
d5 = 1.494






d6 = 1.906


fourth
1.54
t4 = 0.400
s4 = 0.131
d7 = 2.078






d8 = 2.431


fifth
1.53
t5 = 0.350
s5 = 0.441
d9 = 2.870






d10 = 3.402









Referring to Table 1 and FIG. 3, the thickness of the lens element is measured from the object-side surface to the imaging-side surface at the optical axis. The air gap is measured from the imaging-side of a lens element to the object-side of an adjacent lens element along the optical axis. In an embodiment, the first lens element 3 has a thickness of 0.490 mm along the optical axis, and the air gap distance (measured at the optical axis) from the imaging-side surface of first lens element 3 to the object-side surface of second lens element 4 is 0.070 mm along the optical axis. The second lens element 4 has a thickness of 0.270 mm along the optical axis. The third lens element 5 has a thickness of 0.465 mm along the optical axis. The fourth lens element 6 has a thickness of 0.400 mm along the optical axis, and the fifth lens element 7 has a thickness of 0.350 mm along the optical axis. In an embodiment, the optical filter is interposed between fifth lens element 7 and imaging sensor 9. The optical filter may have a thickness of about 0.300 mm and disposed at a distance of about 0.441 mm from the imaging-side surface of fifth lens element 7 (measured at the optical axis) and at a distance of about 0.3 to 0.4 mm from the imaging sensor. In a preferred embodiment, the distance or air gap between the imaging-side surface of fifth lens element 7 (measured at the optical axis) and the optical filter is about 0.441 mm.
In an embodiment, the diameter d1 of the object-side surface of first lens element 3 is 1.377 mm. The diameter d2 of the imaging-side surface of first lens element 3 is 1.393 mm. Similarly, the diameter d3 of the object-side surface of second lens element 4 is 1.388 mm and the diameter d4 of the imaging-side surface of second lens element 4 is 1.390 mm. Likewise, the diameter d5 of the object-side surface of third lens element 5 is 1.494 mm and the diameter d6 of the imaging-side surface of third lens element 5 is 1.906 mm. The last 4 rows of Table 1 provide the respective object-side and imaging-side diameters d7 (2.078 mm), d8 (2.431 mm), d9 (2.870 mm), and d10 (3.402 mm) of fourth and fifth lens elements. In an embodiment, the thickness of the lens elements has a manufacturing tolerance of less than ±2 to less than ±6 microns depending on the power of the lens. In an embodiment, the tilt of the lens elements is less than ±0.1 degree.
A lens system may be characterized by the diameter ratios of the object-side surface of the lens elements. In an exemplary embodiment, the diameter ratios of the object-side surface of the lens elements are:

d1/d3=0.992  (1a)

d3/d5=0.929  (1b)

d5/d7=0.719  (1c)

d7/d9=0.724  (1d)

where d1, d3, d5, d7, and d9 are the object-side diameters of lens elements 3, 4, 5, 6, and 7, respectively.

A lens system may also be characterized by thickness ratios between lens elements. For example, in some embodiments of the present invention, the design of lens elements 3 and 4 and lens elements 5 and 6 may be characterized by the thickness ratio of t1/t2 of 1.81 and t3/t4 of 1.162, where t1, t2, t3, and t4 are the thickness of respective lens elements 3, 4, 5, and 6. Similarly, the design of lens elements 6 and 7 may be characterized by the thickness ratio t4/t5 of 1.143, where t5 is the thickness of lens element 7.
In some embodiments, the air gap ratios between lens elements may satisfy the following conditions:

0<s2/s1<5.0  (2a)

0<s4/s3<0.7  (2b)

0<s3/s2<1.0  (2c)

where s1 is the an air gap between the imaging-side surface of first lens element 3 and the object-side surface of second lens element 4, s2 is the air gap between the imaging-side surface of second lens element 4 and the object-side surface of third lens element 5, s3 is the air gap between the imaging-side surface of third lens element 5 and the object-side surface of fourth lens element 6, s4 is the air gap between the imaging-side surface of fourth lens element 6 and the object-side surface of fifth lens element 7.

Referring still to FIG. 3, the lens elements are rotationally symmetric about the optical axis. The optical performance of lens system 300 is generally related to the particular object-side and imaging-side surface shapes of the lens elements. These surfaces can be characterized by sag values at various radial distances from the optical axis.
Tables 2 through 6 include sag values of the lens elements 3, 4, 5, 6 and 7, respectively. The sag values are in millimeters. The “Normalized Lens Height” in the first and fourth columns of the Tables denotes the normalized relative distance of a location on the surface of the lens elements from the optical axis. In other words, 0.0% corresponds to the location at the optical axis, 50.0% and 100.0% correspond to the respective one half and the full radius of the lens elements in relation to the optical axis. The full radius is half the effective diameter. As the lens elements are rotationally symmetric about the optical axis, the surface of the lens elements is sufficiently represented by sag values for the normalized lens height from the optical axis. The sag tables are provided in sufficient detail to be used for the fabrication of the lens elements using a numerically controlled machining tool. The thus obtained lens elements may have a sag tolerance less than ±2 microns to less than ±6 microns depending on the lens power. It should be noted that, in actual manufacturing, a slope function is used to assure that surface slopes and tolerance variations do not cause step functions in the shape of the lens surface.
Table 2 contains sag data for fabricating lens element 3. The “Min Sag 3” and the “Max Sag 3” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 3. Similarly, the “Min Sag 4” and the “Max Sag 4” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 3. In an embodiment, the lens element 3 needs to be within the minimum and maximum sag values to ensure a given optical performance. The sag values are given in millimeters (mm).












TABLE 2





Normal-


Normal-




ized Lens
Min
Max
ized Lens
Min
Max


Height
Sag 3
Sag 3
Ht
Sag 4
Sag 4




















0.0%
−0.001000
0.001000
0.0%
−0.001000
0.001000


1.4%
−0.000957
0.001043
1.4%
−0.000995
0.001005


2.9%
−0.000828
0.001172
2.9%
−0.000979
0.001021


4.3%
−0.000613
0.001386
4.3%
−0.000952
0.001048


5.8%
−0.000312
0.001687
5.7%
−0.000915
0.001085


7.2%
0.000075
0.002073
7.1%
−0.000868
0.001132


8.7%
0.000548
0.002546
8.6%
−0.000811
0.001189


10.1%
0.001108
0.003104
10.0%
−0.000744
0.001256


11.6%
0.001754
0.003749
11.4%
−0.000668
0.001332


13.0%
0.002487
0.004481
12.9%
−0.000582
0.001418


14.5%
0.003306
0.005298
14.3%
−0.000488
0.001512


15.9%
0.004212
0.006203
15.7%
−0.000385
0.001614


17.4%
0.005205
0.007194
17.1%
−0.000275
0.001725


18.8%
0.006286
0.008273
18.6%
−0.000157
0.001843


20.3%
0.007454
0.009439
20.0%
−0.000033
0.001967


21.7%
0.008710
0.010693
21.4%
0.000098
0.002098


23.2%
0.010054
0.012035
22.9%
0.000235
0.002235


24.6%
0.011486
0.013465
24.3%
0.000377
0.002377


26.1%
0.013008
0.014984
25.7%
0.000524
0.002524


27.5%
0.014618
0.016591
27.1%
0.000676
0.002675


29.0%
0.016319
0.018289
28.6%
0.000831
0.002830


30.4%
0.018109
0.020076
30.0%
0.000989
0.002989


31.9%
0.019990
0.021954
31.4%
0.001150
0.003150


33.3%
0.021962
0.023922
32.9%
0.001314
0.003313


34.8%
0.024025
0.025982
34.3%
0.001479
0.003479


36.2%
0.026181
0.028134
35.7%
0.001646
0.003645


37.7%
0.028429
0.030379
37.1%
0.001813
0.003813


39.1%
0.030771
0.032716
38.6%
0.001982
0.003982


40.6%
0.033206
0.035148
40.0%
0.002151
0.004150


42.0%
0.035737
0.037673
41.4%
0.002319
0.004319


43.5%
0.038362
0.040294
42.9%
0.002488
0.004488


44.9%
0.041083
0.043011
44.3%
0.002656
0.004656


46.4%
0.043901
0.045824
45.7%
0.002823
0.004823


47.8%
0.046817
0.048734
47.1%
0.002989
0.004989


49.3%
0.049830
0.051743
48.6%
0.003154
0.005154


50.7%
0.052943
0.054850
50.0%
0.003317
0.005317


52.2%
0.056156
0.058058
51.4%
0.003479
0.005479


53.6%
0.059470
0.061366
52.9%
0.003639
0.005639


55.1%
0.062886
0.064776
54.3%
0.003797
0.005797


56.5%
0.066405
0.068288
55.7%
0.003953
0.005952


58.0%
0.070027
0.071905
57.1%
0.004106
0.006105


59.4%
0.073755
0.075626
58.6%
0.004256
0.006255


60.9%
0.077589
0.079454
60.0%
0.004402
0.006402


62.3%
0.081531
0.083389
61.4%
0.004545
0.006545


63.8%
0.085581
0.087432
62.9%
0.004684
0.006684


65.2%
0.089742
0.091585
64.3%
0.004818
0.006818


66.7%
0.094014
0.095849
65.7%
0.004945
0.006945


68.1%
0.098398
0.100226
67.1%
0.005066
0.007066


69.6%
0.102897
0.104717
68.6%
0.005179
0.007179


71.0%
0.107511
0.109323
70.0%
0.005282
0.007282


72.5%
0.112242
0.114046
71.4%
0.005374
0.007374


73.9%
0.117092
0.118887
72.9%
0.005453
0.007453


75.4%
0.122061
0.123848
74.3%
0.005517
0.007517


76.8%
0.127152
0.128931
75.7%
0.005562
0.007562


78.3%
0.132366
0.134136
77.1%
0.005586
0.007586


79.7%
0.137705
0.139465
78.6%
0.005585
0.007585


81.2%
0.143169
0.144920
80.0%
0.005555
0.007555


82.6%
0.148760
0.150502
81.4%
0.005491
0.007491


84.1%
0.154480
0.156212
82.9%
0.005388
0.007388


85.5%
0.160330
0.162052
84.3%
0.005239
0.007239


87.0%
0.166310
0.168022
85.7%
0.005038
0.007037


88.4%
0.172422
0.174124
87.1%
0.004775
0.006774


89.9%
0.178666
0.180358
88.6%
0.004442
0.006440


91.3%
0.185042
0.186723
90.0%
0.004028
0.006026


92.8%
0.191549
0.193221
91.4%
0.003520
0.005517


94.2%
0.198187
0.199849
92.9%
0.002907
0.004902


95.7%
0.204953
0.206605
94.3%
0.002171
0.004164


97.1%
0.211843
0.213486
95.7%
0.001295
0.003286


98.6%
0.218852
0.220486
97.1%
0.000261
0.002248


100.0%
0.224758
0.226385
98.6%
−0.000955
0.001028





100.0%
−0.001879
0.000100









Table 3 contains sag data for fabricating lens element 4. The “Min Sag 5” and the “Max Sag 5” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 4. Similarly, the “Min Sag 6” and the “Max Sag 6” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 4. In an embodiment, the lens element 4 needs to be within the minimum and maximum sag values to ensure a given optical performance. The sag values are given in mm.












TABLE 3





Normal-


Normal-




ized Lens
Min
Max
ized Lens
Min
Max


Height
Sag 5
Sag 5
Height
Sag 6
Sag 6




















0.0%
−0.001000
0.001000
0.0%
−0.001000
0.001000


1.4%
−0.000992
0.001008
1.4%
−0.000974
0.001026


2.9%
−0.000968
0.001032
2.9%
−0.000894
0.001106


4.3%
−0.000929
0.001071
4.3%
−0.000762
0.001237


5.7%
−0.000875
0.001125
5.7%
−0.000578
0.001422


7.1%
−0.000805
0.001195
7.1%
−0.000341
0.001659


8.6%
−0.000720
0.001280
8.6%
−0.000051
0.001948


10.0%
−0.000621
0.001379
10.0%
0.000291
0.002289


11.4%
−0.000508
0.001492
11.4%
0.000684
0.002683


12.9%
−0.000382
0.001618
12.9%
0.001130
0.003128


14.3%
−0.000243
0.001756
14.3%
0.001627
0.003624


15.7%
−0.000093
0.001907
15.7%
0.002175
0.004172


17.1%
0.000069
0.002069
17.1%
0.002774
0.004770


18.6%
0.000242
0.002242
18.6%
0.003424
0.005420


20.0%
0.000425
0.002424
20.0%
0.004124
0.006119


21.4%
0.000616
0.002616
21.4%
0.004875
0.006869


22.9%
0.000815
0.002815
22.9%
0.005675
0.007668


24.3%
0.001022
0.003022
24.3%
0.006525
0.008517


25.7%
0.001236
0.003235
25.7%
0.007424
0.009415


27.1%
0.001455
0.003455
27.1%
0.008372
0.010362


28.6%
0.001679
0.003679
28.6%
0.009369
0.011358


30.0%
0.001908
0.003907
30.0%
0.010414
0.012403


31.4%
0.002139
0.004139
31.4%
0.011509
0.013497


32.9%
0.002374
0.004373
32.9%
0.012652
0.014639


34.3%
0.002611
0.004610
34.3%
0.013844
0.015830


35.7%
0.002849
0.004848
35.7%
0.015085
0.017069


37.1%
0.003088
0.005087
37.1%
0.016375
0.018358


38.6%
0.003328
0.005327
38.6%
0.017714
0.019696


40.0%
0.003567
0.005567
40.0%
0.019103
0.021083


41.4%
0.003806
0.005806
41.4%
0.020542
0.022521


42.9%
0.004045
0.006044
42.9%
0.022032
0.024009


44.3%
0.004282
0.006282
44.3%
0.023573
0.025549


45.7%
0.004519
0.006518
45.7%
0.025167
0.027141


47.1%
0.004754
0.006753
47.1%
0.026813
0.028786


48.6%
0.004988
0.006987
48.6%
0.028514
0.030484


50.0%
0.005220
0.007219
50.0%
0.030269
0.032238


51.4%
0.005450
0.007450
51.4%
0.032082
0.034049


52.9%
0.005680
0.007679
52.9%
0.033952
0.035917


54.3%
0.005907
0.007907
54.3%
0.035882
0.037845


55.7%
0.006134
0.008133
55.7%
0.037874
0.039834


57.1%
0.006359
0.008359
57.1%
0.039928
0.041886


58.6%
0.006583
0.008583
58.6%
0.042047
0.044003


60.0%
0.006807
0.008806
60.0%
0.044234
0.046187


61.4%
0.007029
0.009028
61.4%
0.046491
0.048441


62.9%
0.007250
0.009249
62.9%
0.048820
0.050766


64.3%
0.007470
0.009469
64.3%
0.051224
0.053167


65.7%
0.007688
0.009688
65.7%
0.053706
0.055646


67.1%
0.007905
0.009905
67.1%
0.056270
0.058205


68.6%
0.008120
0.010120
68.6%
0.058918
0.060850


70.0%
0.008333
0.010333
70.0%
0.061656
0.063582


71.4%
0.008543
0.010542
71.4%
0.064486
0.066408


72.9%
0.008748
0.010748
72.9%
0.067413
0.069330


74.3%
0.008948
0.010948
74.3%
0.070443
0.072354


75.7%
0.009142
0.011142
75.7%
0.073581
0.075486


77.1%
0.009327
0.011327
77.1%
0.076832
0.078731


78.6%
0.009502
0.011502
78.6%
0.080204
0.082096


80.0%
0.009664
0.011664
80.0%
0.083704
0.085588


81.4%
0.009811
0.011811
81.4%
0.087339
0.089215


82.9%
0.009939
0.011939
82.9%
0.091119
0.092985


84.3%
0.010045
0.012045
84.3%
0.095054
0.096910


85.7%
0.010125
0.012125
85.7%
0.099155
0.101000


87.1%
0.010174
0.012174
87.1%
0.103435
0.105268


88.6%
0.010186
0.012186
88.6%
0.107909
0.109728


90.0%
0.010157
0.012157
90.0%
0.112594
0.114398


91.4%
0.010081
0.012081
91.4%
0.117509
0.119296


92.9%
0.009950
0.011950
92.9%
0.122677
0.124445


94.3%
0.009758
0.011757
94.3%
0.128127
0.129872


95.7%
0.009497
0.011496
95.7%
0.133889
0.135610


97.1%
0.009161
0.011159
97.1%
0.140003
0.141696


98.6%
0.008740
0.010738
98.6%
0.146517
0.148177


100.0%
0.008535
0.010532
100.0%
0.149821
0.151464









Table 4 contains sag data for fabricating lens element 5. The “Min Sag 7” and the “Max Sag 7” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 5. Similarly, the “Min Sag 8” and the “Max Sag 8” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 5. In an embodiment, the lens element 5 needs to be within the minimum and maximum sag values to ensure a given optical performance. The sag values are given in mm.












TABLE 4





Normal-


Normal-




ized Lens
Min
Max
ized Lens
Min
Max


Height
Sag 7
Sag 7
Height
Sag 8
Sag 8




















0.0%
−0.001500
0.001500
0.0%
−0.001500
0.001500


1.3%
−0.001496
0.001504
1.0%
−0.001500
0.001500


2.7%
−0.001485
0.001515
2.1%
−0.001501
0.001499


4.0%
−0.001466
0.001534
3.1%
−0.001503
0.001497


5.3%
−0.001440
0.001560
4.2%
−0.001505
0.001495


6.7%
−0.001407
0.001593
5.2%
−0.001509
0.001491


8.0%
−0.001367
0.001633
6.3%
−0.001513
0.001487


9.3%
−0.001320
0.001680
7.3%
−0.001519
0.001481


10.7%
−0.001268
0.001732
8.3%
−0.001527
0.001473


12.0%
−0.001210
0.001790
9.4%
−0.001537
0.001463


13.3%
−0.001147
0.001853
10.4%
−0.001549
0.001451


14.7%
−0.001080
0.001920
11.5%
−0.001564
0.001436


16.0%
−0.001010
0.001990
12.5%
−0.001582
0.001418


17.3%
−0.000936
0.002064
13.5%
−0.001605
0.001395


18.7%
−0.000860
0.002140
14.6%
−0.001631
0.001369


20.0%
−0.000784
0.002216
15.6%
−0.001663
0.001337


21.3%
−0.000707
0.002293
16.7%
−0.001701
0.001299


22.7%
−0.000631
0.002369
17.7%
−0.001745
0.001255


24.0%
−0.000556
0.002444
18.8%
−0.001797
0.001203


25.3%
−0.000485
0.002515
19.8%
−0.001856
0.001144


26.7%
−0.000418
0.002582
20.8%
−0.001925
0.001075


28.0%
−0.000356
0.002644
21.9%
−0.002003
0.000996


29.3%
−0.000301
0.002699
22.9%
−0.002093
0.000907


30.7%
−0.000254
0.002746
24.0%
−0.002194
0.000806


32.0%
−0.000217
0.002783
25.0%
−0.002309
0.000691


33.3%
−0.000190
0.002810
26.0%
−0.002437
0.000562


34.7%
−0.000176
0.002824
27.1%
−0.002582
0.000418


36.0%
−0.000176
0.002824
28.1%
−0.002742
0.000257


37.3%
−0.000193
0.002807
29.2%
−0.002921
0.000078


38.7%
−0.000226
0.002774
30.2%
−0.003120
−0.000121


40.0%
−0.000279
0.002721
31.3%
−0.003339
−0.000340


41.3%
−0.000353
0.002646
32.3%
−0.003581
−0.000582


42.7%
−0.000451
0.002549
33.3%
−0.003847
−0.000848


44.0%
−0.000573
0.002426
34.4%
−0.004139
−0.001141


45.3%
−0.000723
0.002277
35.4%
−0.004459
−0.001460


46.7%
−0.000902
0.002097
36.5%
−0.004808
−0.001809


48.0%
−0.001112
0.001887
37.5%
−0.005188
−0.002190


49.3%
−0.001357
0.001642
38.5%
−0.005601
−0.002604


50.7%
−0.001637
0.001362
39.6%
−0.006050
−0.003054


52.0%
−0.001956
0.001042
40.6%
−0.006537
−0.003541


53.3%
−0.002316
0.000682
41.7%
−0.007063
−0.004068


54.7%
−0.002719
0.000278
42.7%
−0.007631
−0.004637


56.0%
−0.003169
−0.000172
43.8%
−0.008244
−0.005250


57.3%
−0.003667
−0.000671
44.8%
−0.008904
−0.005911


58.7%
−0.004218
−0.001223
45.8%
−0.009613
−0.006622


60.0%
−0.004823
−0.001829
46.9%
−0.010375
−0.007384


61.3%
−0.005485
−0.002492
47.9%
−0.011191
−0.008202


62.7%
−0.006209
−0.003217
49.0%
−0.012065
−0.009077


64.0%
−0.006996
−0.004006
50.0%
−0.013000
−0.010013


65.3%
−0.007850
−0.004862
51.0%
−0.013997
−0.011013


66.7%
−0.008774
−0.005788
52.1%
−0.015061
−0.012079


68.0%
−0.009773
−0.006789
53.1%
−0.016195
−0.013215


69.3%
−0.010849
−0.007867
54.2%
−0.017401
−0.014424


70.7%
−0.012005
−0.009026
55.2%
−0.018682
−0.015708


72.0%
−0.013246
−0.010270
56.3%
−0.020042
−0.017071


73.3%
−0.014575
−0.011603
57.3%
−0.021484
−0.018517


74.7%
−0.015995
−0.013027
58.3%
−0.023011
−0.020047


76.0%
−0.017512
−0.014548
59.4%
−0.024626
−0.021667


77.3%
−0.019127
−0.016168
60.4%
−0.026333
−0.023378


78.7%
−0.020845
−0.017891
61.5%
−0.028133
−0.025184


80.0%
−0.022670
−0.019722
62.5%
−0.030032
−0.027087


81.3%
−0.024605
−0.021663
63.5%
−0.032031
−0.029092


82.7%
−0.026653
−0.023718
64.6%
−0.034133
−0.031201


84.0%
−0.028819
−0.025891
65.6%
−0.036342
−0.033416


85.3%
−0.031105
−0.028185
66.7%
−0.038660
−0.035741


86.7%
−0.033515
−0.030603
67.7%
−0.041090
−0.038178


88.0%
−0.036050
−0.033147
68.8%
−0.043633
−0.040730


89.3%
−0.038714
−0.035820
69.8%
−0.046293
−0.043399


90.7%
−0.041507
−0.038623
70.8%
−0.049072
−0.046186


92.0%
−0.044433
−0.041559
71.9%
−0.051970
−0.049094


93.3%
−0.047491
−0.044627
72.9%
−0.054991
−0.052124


94.7%
−0.050681
−0.047828
74.0%
−0.058134
−0.055278


96.0%
−0.054002
−0.051161
75.0%
−0.061402
−0.058556


97.3%
−0.057454
−0.054624
76.0%
−0.064795
−0.061960


98.7%
−0.061032
−0.058214
77.1%
−0.068313
−0.065489


100.0%
−0.063691
−0.060881
78.1%
−0.071957
−0.069144





79.2%
−0.075725
−0.072924





80.2%
−0.079618
−0.076829





81.3%
−0.083634
−0.080857





82.3%
−0.087772
−0.085007





83.3%
−0.092030
−0.089276





84.4%
−0.096406
−0.093664





85.4%
−0.100897
−0.098167





86.5%
−0.105500
−0.102781





87.5%
−0.110213
−0.107505





88.5%
−0.115030
−0.112334





89.6%
−0.119950
−0.117264





90.6%
−0.124967
−0.122292





90.6%
−0.124967
−0.122292





90.6%
−0.124967
−0.122292





91.7%
−0.130079
−0.127413





92.7%
−0.135280
−0.132624





93.8%
−0.140567
−0.137920





94.8%
−0.145937
−0.143299





95.8%
−0.151386
−0.148756





96.9%
−0.156911
−0.154290





97.9%
−0.162512
−0.159899





99.0%
−0.168187
−0.165582





100.0%
−0.169863
−0.167261









Table 5 contains sag data for fabricating lens element 6. The “Min Sag 9” and the “Max Sag 9” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 6. Similarly, the “Min Sag 10” and the “Max Sag 10” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 6. In an embodiment, the lens element 6 needs to be within the minimum and maximum sag values to ensure a given optical performance. The sag values are given in mm.












TABLE 5





Normal-


Normal-




ized Lens
Min
Max
ized Lens
Min
Max


Height
Sag 9
Sag 9
Height
Sag 10
Sag 10




















0.0%
−0.003000
0.003000
0.0%
−0.003000
0.003000


1.0%
−0.003026
0.002974
0.8%
−0.003056
0.002944


1.9%
−0.003103
0.002896
1.6%
−0.003223
0.002776


2.9%
−0.003232
0.002767
2.5%
−0.003501
0.002496


3.8%
−0.003412
0.002586
3.3%
−0.003890
0.002104


4.8%
−0.003644
0.002354
4.1%
−0.004390
0.001601


5.8%
−0.003926
0.002071
4.9%
−0.005000
0.000987


6.7%
−0.004260
0.001736
5.7%
−0.005719
0.000263


7.7%
−0.004644
0.001351
6.6%
−0.006547
−0.000570


8.7%
−0.005077
0.000916
7.4%
−0.007483
−0.001512


9.6%
−0.005561
0.000431
8.2%
−0.008526
−0.002562


10.6%
−0.006095
−0.000104
9.0%
−0.009676
−0.003720


11.5%
−0.006677
−0.000688
9.8%
−0.010932
−0.004983


12.5%
−0.007309
−0.001322
10.7%
−0.012293
−0.006352


13.5%
−0.007989
−0.002004
11.5%
−0.013757
−0.007825


14.4%
−0.008718
−0.002735
12.3%
−0.015325
−0.009402


15.4%
−0.009495
−0.003514
13.1%
−0.016995
−0.011082


16.3%
−0.010319
−0.004341
13.9%
−0.018766
−0.012864


17.3%
−0.011192
−0.005216
14.8%
−0.020638
−0.014747


18.3%
−0.012113
−0.006140
15.6%
−0.022610
−0.016730


19.2%
−0.013082
−0.007111
16.4%
−0.024682
−0.018813


20.2%
−0.014099
−0.008131
17.2%
−0.026852
−0.020995


21.2%
−0.015164
−0.009199
18.0%
−0.029121
−0.023276


22.1%
−0.016277
−0.010315
18.9%
−0.031487
−0.025656


23.1%
−0.017439
−0.011481
19.7%
−0.033951
−0.028133


24.0%
−0.018650
−0.012695
20.5%
−0.036512
−0.030708


25.0%
−0.019911
−0.013960
21.3%
−0.039170
−0.033380


26.0%
−0.021221
−0.015274
22.1%
−0.041925
−0.036149


26.9%
−0.022582
−0.016639
23.0%
−0.044776
−0.039015


27.9%
−0.023995
−0.018056
23.8%
−0.047724
−0.041978


28.8%
−0.025459
−0.019525
24.6%
−0.050769
−0.045038


29.8%
−0.026976
−0.021046
25.4%
−0.053909
−0.048194


30.8%
−0.028546
−0.022622
26.2%
−0.057146
−0.051447


31.7%
−0.030171
−0.024251
27.0%
−0.060479
−0.054796


32.7%
−0.031851
−0.025937
27.9%
−0.063908
−0.058242


33.7%
−0.033587
−0.027679
28.7%
−0.067433
−0.061784


34.6%
−0.035380
−0.029478
29.5%
−0.071054
−0.065422


35.6%
−0.037232
−0.031336
30.3%
−0.074770
−0.069156


36.5%
−0.039142
−0.033253
31.1%
−0.078582
−0.072986


37.5%
−0.041114
−0.035231
32.0%
−0.082489
−0.076911


38.5%
−0.043146
−0.037270
32.8%
−0.086491
−0.080931


39.4%
−0.045241
−0.039373
33.6%
−0.090587
−0.085045


40.4%
−0.047400
−0.041540
34.4%
−0.094776
−0.089253


41.3%
−0.049624
−0.043772
35.2%
−0.099059
−0.093554


42.3%
−0.051915
−0.046071
36.1%
−0.103434
−0.097948


43.3%
−0.054273
−0.048438
36.9%
−0.107900
−0.102433


44.2%
−0.056699
−0.050874
37.7%
−0.112458
−0.107009


45.2%
−0.059196
−0.053380
38.5%
−0.117105
−0.111675


46.2%
−0.061764
−0.055958
39.3%
−0.121840
−0.116429


47.1%
−0.064404
−0.058608
40.2%
−0.126664
−0.121271


48.1%
−0.067117
−0.061333
41.0%
−0.131573
−0.126199


49.0%
−0.069905
−0.064132
41.8%
−0.136568
−0.131211


50.0%
−0.072768
−0.067006
42.6%
−0.141646
−0.136307


51.0%
−0.075707
−0.069957
43.4%
−0.146807
−0.141485


51.9%
−0.078722
−0.072985
44.3%
−0.152047
−0.146743


52.9%
−0.081814
−0.076090
45.1%
−0.157366
−0.152079


53.8%
−0.084984
−0.079271
45.9%
−0.162761
−0.157491


54.8%
−0.088229
−0.082530
46.7%
−0.168230
−0.162976


55.8%
−0.091551
−0.085865
47.5%
−0.173771
−0.168533


56.7%
−0.094949
−0.089275
48.4%
−0.179381
−0.174158


57.7%
−0.098419
−0.092759
49.2%
−0.185057
−0.179848


58.7%
−0.101962
−0.096314
50.0%
−0.190795
−0.185599


59.6%
−0.105575
−0.099939
50.8%
−0.196592
−0.191409


60.6%
−0.109254
−0.103630
51.6%
−0.202444
−0.197272


61.5%
−0.112997
−0.107384
52.5%
−0.208345
−0.203184


62.5%
−0.116799
−0.111197
53.3%
−0.214291
−0.209140


63.5%
−0.120656
−0.115064
54.1%
−0.220276
−0.215133


64.4%
−0.124564
−0.118980
54.9%
−0.226294
−0.221157


65.4%
−0.128515
−0.122940
55.7%
−0.232337
−0.227205


66.3%
−0.132506
−0.126937
56.6%
−0.238398
−0.233268


67.3%
−0.136528
−0.130964
57.4%
−0.244468
−0.239340


68.3%
−0.140575
−0.135015
58.2%
−0.250539
−0.245409


69.2%
−0.144639
−0.139082
59.0%
−0.256601
−0.251467


70.2%
−0.148714
−0.143159
59.8%
−0.262642
−0.257503


71.2%
−0.152793
−0.147236
60.7%
−0.268652
−0.263504


72.1%
−0.156866
−0.151308
61.5%
−0.274620
−0.269460


73.1%
−0.160928
−0.155367
62.3%
−0.280532
−0.275358


74.0%
−0.164971
−0.159406
63.1%
−0.286376
−0.281185


75.0%
−0.168989
−0.163419
63.9%
−0.292138
−0.286926


76.0%
−0.172977
−0.167400
64.8%
−0.297804
−0.292570


76.9%
−0.176929
−0.171345
65.6%
−0.303362
−0.298101


77.9%
−0.180843
−0.175251
66.4%
−0.308796
−0.303506


78.8%
−0.184715
−0.179115
67.2%
−0.314092
−0.308771


79.8%
−0.188545
−0.182937
68.0%
−0.319238
−0.313882


80.8%
−0.192334
−0.186719
68.9%
−0.324221
−0.318828


81.7%
−0.196084
−0.190463
69.7%
−0.329026
−0.323595


82.7%
−0.199802
−0.194174
70.5%
−0.333644
−0.328172


83.7%
−0.203493
−0.197862
71.3%
−0.338063
−0.332550


84.6%
−0.207167
−0.201535
72.1%
−0.342274
−0.336719


85.6%
−0.210838
−0.205206
73.0%
−0.346269
−0.340672


86.5%
−0.214520
−0.208892
73.8%
−0.350041
−0.344402


87.5%
−0.218231
−0.212610
74.6%
−0.353586
−0.347907


88.5%
−0.221992
−0.216383
75.4%
−0.356901
−0.351183


89.4%
−0.225827
−0.220235
76.2%
−0.359985
−0.354231


90.4%
−0.229763
−0.224194
77.0%
−0.362840
−0.357051


91.3%
−0.233830
−0.228290
77.9%
−0.365469
−0.359648


92.3%
−0.238060
−0.232557
78.7%
−0.367877
−0.362028


93.3%
−0.242488
−0.237030
79.5%
−0.370071
−0.364197


94.2%
−0.247150
−0.241745
80.3%
−0.372062
−0.366165


95.2%
−0.252082
−0.246740
81.1%
−0.373859
−0.367944


96.2%
−0.257318
−0.252047
82.0%
−0.375476
−0.369545


97.1%
−0.262891
−0.257698
82.8%
−0.376927
−0.370982


98.1%
−0.268821
−0.263712
83.6%
−0.378226
−0.372270


99.0%
−0.275122
−0.270097
84.4%
−0.379389
−0.373425


100.0%
−0.281059
−0.276105
85.2%
−0.380432
−0.374461





86.1%
−0.381371
−0.375395





86.9%
−0.382223
−0.376242





87.7%
−0.383002
−0.377018





88.5%
−0.383722
−0.377737





89.3%
−0.384399
−0.378411





90.2%
−0.385042
−0.379054





91.0%
−0.385665
−0.379676





91.8%
−0.386276
−0.380287





92.6%
−0.386884
−0.380895





93.4%
−0.387497
−0.381509





94.3%
−0.388122
−0.382134





95.1%
−0.388765
−0.382778





95.9%
−0.389432
−0.383446





96.7%
−0.390131
−0.384147





97.5%
−0.390870
−0.384887





98.4%
−0.391657
−0.385677





99.2%
−0.392503
−0.386526





100.0%
−0.392975
−0.387000









Table 6 contains sag data for fabricating lens element 7. The “Min Sag 11” and the “Max Sag 11” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 7. Similarly, the “Min Sag 12” and the “Max Sag 12” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 7. In an embodiment, the lens element 7 needs to be within the minimum and maximum sag values to ensure a given optical performance. The sag values are given in mm.












TABLE 6





Normal-


Normal-




ized Lens
Min
Max
ized Lens
Min
Max


Height
Sag 11
Sag 11
Height
Sag 12
Sag 12




















0.0%
−0.003000
0.003000
0.0%
−0.003000
0.003000


0.7%
−0.002983
0.003017
0.6%
−0.002940
0.003060


1.4%
−0.002933
0.003067
1.2%
−0.002759
0.003239


2.1%
−0.002849
0.003150
1.8%
−0.002458
0.003538


2.8%
−0.002733
0.003267
2.3%
−0.002038
0.003955


3.5%
−0.002584
0.003415
2.9%
−0.001500
0.004489


4.2%
−0.002403
0.003596
3.5%
−0.000846
0.005139


4.9%
−0.002191
0.003807
4.1%
−0.000077
0.005903


5.6%
−0.001950
0.004048
4.7%
0.000806
0.006780


6.3%
−0.001679
0.004318
5.3%
0.001798
0.007766


6.9%
−0.001381
0.004616
5.8%
0.002899
0.008860


7.6%
−0.001057
0.004940
6.4%
0.004105
0.010058


8.3%
−0.000708
0.005288
7.0%
0.005412
0.011358


9.0%
−0.000337
0.005658
7.6%
0.006819
0.012757


9.7%
0.000054
0.006050
8.2%
0.008321
0.014250


10.4%
0.000464
0.006459
8.8%
0.009914
0.015835


11.1%
0.000890
0.006884
9.4%
0.011595
0.017508


11.8%
0.001329
0.007323
9.9%
0.013359
0.019264


12.5%
0.001778
0.007772
10.5%
0.015203
0.021100


13.2%
0.002235
0.008229
11.1%
0.017122
0.023011


13.9%
0.002696
0.008690
11.7%
0.019112
0.024993


14.6%
0.003158
0.009151
12.3%
0.021168
0.027042


15.3%
0.003617
0.009611
12.9%
0.023286
0.029153


16.0%
0.004070
0.010064
13.5%
0.025462
0.031322


16.7%
0.004514
0.010508
14.0%
0.027690
0.033544


17.4%
0.004943
0.010938
14.6%
0.029966
0.035814


18.1%
0.005355
0.011350
15.2%
0.032287
0.038129


18.8%
0.005745
0.011740
15.8%
0.034646
0.040484


19.4%
0.006109
0.012105
16.4%
0.037040
0.042873


20.1%
0.006443
0.012440
17.0%
0.039464
0.045294


20.8%
0.006743
0.012741
17.5%
0.041915
0.047741


21.5%
0.007006
0.013004
18.1%
0.044387
0.050210


22.2%
0.007226
0.013225
18.7%
0.046876
0.052697


22.9%
0.007400
0.013400
19.3%
0.049379
0.055199


23.6%
0.007525
0.013524
19.9%
0.051891
0.057710


24.3%
0.007596
0.013595
20.5%
0.054409
0.060228


25.0%
0.007609
0.013609
21.1%
0.056929
0.062748


25.7%
0.007562
0.013562
21.6%
0.059448
0.065266


26.4%
0.007451
0.013450
22.2%
0.061961
0.067781


27.1%
0.007273
0.013271
22.8%
0.064466
0.070287


27.8%
0.007024
0.013022
23.4%
0.066959
0.072782


28.5%
0.006703
0.012699
24.0%
0.069438
0.075263


29.2%
0.006306
0.012300
24.6%
0.071899
0.077727


29.9%
0.005831
0.011823
25.1%
0.074340
0.080170


30.6%
0.005275
0.011264
25.7%
0.076758
0.082592


31.3%
0.004637
0.010624
26.3%
0.079151
0.084988


31.9%
0.003915
0.009898
26.9%
0.081515
0.087356


32.6%
0.003108
0.009086
27.5%
0.083850
0.089694


33.3%
0.002212
0.008186
28.1%
0.086152
0.092001


34.0%
0.001228
0.007196
28.7%
0.088420
0.094273


34.7%
0.000153
0.006116
29.2%
0.090651
0.096509


35.4%
−0.001012
0.004944
29.8%
0.092844
0.098707


36.1%
−0.002270
0.003679
30.4%
0.094998
0.100866


36.8%
−0.003621
0.002321
31.0%
0.097110
0.102982


37.5%
−0.005066
0.000868
31.6%
0.099178
0.105056


38.2%
−0.006606
−0.000680
32.2%
0.101202
0.107085


38.9%
−0.008241
−0.002324
32.7%
0.103180
0.109068


39.6%
−0.009971
−0.004064
33.3%
0.105111
0.111004


40.3%
−0.011798
−0.005901
33.9%
0.106992
0.112891


41.0%
−0.013721
−0.007835
34.5%
0.108823
0.114728


41.7%
−0.015742
−0.009867
35.1%
0.110603
0.116513


42.4%
−0.017859
−0.011996
35.7%
0.112331
0.118246


43.1%
−0.020074
−0.014223
36.3%
0.114005
0.119925


43.8%
−0.022386
−0.016548
36.8%
0.115624
0.121549


44.4%
−0.024797
−0.018971
37.4%
0.117188
0.123118


45.1%
−0.027304
−0.021492
38.0%
0.118694
0.124629


45.8%
−0.029910
−0.024111
38.6%
0.120143
0.126083


46.5%
−0.032612
−0.026828
39.2%
0.121533
0.127478


47.2%
−0.035412
−0.029643
39.8%
0.122863
0.128813


47.9%
−0.038309
−0.032555
40.4%
0.124132
0.130087


48.6%
−0.041303
−0.035563
40.9%
0.125340
0.131299


49.3%
−0.044392
−0.038668
41.5%
0.126485
0.132448


50.0%
−0.047577
−0.041869
42.1%
0.127567
0.133534


50.7%
−0.050857
−0.045165
42.7%
0.128584
0.134555


51.4%
−0.054230
−0.048555
43.3%
0.129536
0.135511


52.1%
−0.057697
−0.052038
43.9%
0.130422
0.136400


52.8%
−0.061256
−0.055613
44.4%
0.131240
0.137222


53.5%
−0.064907
−0.059280
45.0%
0.131991
0.137976


54.2%
−0.068647
−0.063037
45.6%
0.132673
0.138661


54.9%
−0.072476
−0.066882
46.2%
0.133286
0.139276


55.6%
−0.076392
−0.070815
46.8%
0.133828
0.139820


56.3%
−0.080395
−0.074834
47.4%
0.134299
0.140293


56.9%
−0.084482
−0.078938
48.0%
0.134697
0.140693


57.6%
−0.088652
−0.083124
48.5%
0.135023
0.141020


58.3%
−0.092903
−0.087391
49.1%
0.135274
0.141273


59.0%
−0.097234
−0.091738
49.7%
0.135451
0.141451


59.7%
−0.101642
−0.096161
50.3%
0.135552
0.141552


60.4%
−0.106126
−0.100661
50.9%
0.135577
0.141576


61.1%
−0.110684
−0.105233
51.5%
0.135523
0.141523


61.8%
−0.115312
−0.109876
52.0%
0.135392
0.141391


62.5%
−0.120009
−0.114587
52.6%
0.135180
0.141178


63.2%
−0.124772
−0.119363
53.2%
0.134889
0.140885


63.9%
−0.129597
−0.124201
53.8%
0.134516
0.140510


64.6%
−0.134482
−0.129098
54.4%
0.134060
0.140052


65.3%
−0.139423
−0.134051
55.0%
0.133521
0.139511


66.0%
−0.144416
−0.139054
55.6%
0.132897
0.138884


66.7%
−0.149456
−0.144104
56.1%
0.132187
0.138170


67.4%
−0.154539
−0.149196
56.7%
0.131391
0.137370


68.1%
−0.159661
−0.154324
57.3%
0.130507
0.136481


68.8%
−0.164814
−0.159484
57.9%
0.129533
0.135502


69.4%
−0.169993
−0.164668
58.5%
0.128469
0.134432


70.1%
−0.175192
−0.169870
59.1%
0.127313
0.133270


70.8%
−0.180403
−0.175083
59.6%
0.126065
0.132014


71.5%
−0.185619
−0.180299
60.2%
0.124721
0.130664


72.2%
−0.190832
−0.185511
60.8%
0.123283
0.129217


72.9%
−0.196034
−0.190709
61.4%
0.121747
0.127673


73.6%
−0.201217
−0.195886
62.0%
0.120113
0.126029


74.3%
−0.206370
−0.201033
62.6%
0.118378
0.124284


75.0%
−0.211487
−0.206140
63.2%
0.116543
0.122438


75.7%
−0.216557
−0.211198
63.7%
0.114604
0.120488


76.4%
−0.221571
−0.216200
64.3%
0.112561
0.118432


77.1%
−0.226521
−0.221134
64.9%
0.110411
0.116270


77.8%
−0.231398
−0.225995
65.5%
0.108154
0.113999


78.5%
−0.236193
−0.230772
66.1%
0.105787
0.111618


79.2%
−0.240900
−0.235459
66.7%
0.103309
0.109124


79.9%
−0.245510
−0.240049
67.3%
0.100718
0.106517


80.6%
−0.250018
−0.244535
67.8%
0.098012
0.103794


81.3%
−0.254416
−0.248911
68.4%
0.095190
0.100954


81.9%
−0.258701
−0.253173
69.0%
0.092248
0.097994


82.6%
−0.262869
−0.257316
69.6%
0.089186
0.094912


83.3%
−0.266915
−0.261339
70.2%
0.086002
0.091707


84.0%
−0.270837
−0.265237
70.8%
0.082692
0.088376


84.7%
−0.274634
−0.269011
71.3%
0.079256
0.084917


85.4%
−0.278305
−0.272659
71.9%
0.075691
0.081329


86.1%
−0.281849
−0.276181
72.5%
0.071994
0.077608


86.8%
−0.285268
−0.279577
73.1%
0.068165
0.073753


87.5%
−0.288561
−0.282850
73.7%
0.064199
0.069761


88.2%
−0.291731
−0.286000
74.3%
0.060096
0.065630


88.9%
−0.294778
−0.289028
74.9%
0.055852
0.061359


89.6%
−0.297706
−0.291937
75.4%
0.051466
0.056943


90.3%
−0.300516
−0.294730
76.0%
0.046935
0.052382


91.0%
−0.303210
−0.297407
76.6%
0.042258
0.047673


91.7%
−0.305791
−0.299972
77.2%
0.037430
0.042814


92.4%
−0.308261
−0.302428
77.8%
0.032452
0.037803


93.1%
−0.310623
−0.304776
78.4%
0.027319
0.032637


93.8%
−0.312880
−0.307020
78.9%
0.022031
0.027314


94.4%
−0.315035
−0.309163
79.5%
0.016585
0.021832


95.1%
−0.317092
−0.311209
80.1%
0.010979
0.016190


95.8%
−0.319056
−0.313163
80.7%
0.005211
0.010386


96.5%
−0.320933
−0.315031
81.3%
−0.000721
0.004417


97.2%
−0.322729
−0.316819
81.9%
−0.006817
−0.001717


97.9%
−0.324452
−0.318536
82.5%
−0.013081
−0.008019


98.6%
−0.326114
−0.320192
83.0%
−0.019513
−0.014490


99.3%
−0.327726
−0.321801
83.6%
−0.026114
−0.021131


100.0%
−0.328471
−0.322544
84.2%
−0.032887
−0.027944





84.8%
−0.039833
−0.034930





85.4%
−0.046952
−0.042089





86.0%
−0.054247
−0.049425





86.5%
−0.061718
−0.056936





87.1%
−0.069366
−0.064626





87.7%
−0.077193
−0.072494





88.3%
−0.085201
−0.080542





88.9%
−0.093389
−0.088772





89.5%
−0.101760
−0.097184





90.1%
−0.110314
−0.105780





90.6%
−0.119054
−0.114561





91.2%
−0.127979
−0.123527





91.8%
−0.137090
−0.132680





92.4%
−0.146388
−0.142019





93.0%
−0.155873
−0.151545





93.6%
−0.165545
−0.161257





94.2%
−0.175403
−0.171154





94.7%
−0.185446
−0.181237





95.3%
−0.195674
−0.191502





95.9%
−0.206084
−0.201950





96.5%
−0.216677
−0.212581





97.1%
−0.227455
−0.223397





97.7%
−0.238422
−0.234404





98.2%
−0.249590
−0.245613





98.8%
−0.260978
−0.257047





99.4%
−0.272618
−0.268741





100.0%
−0.273295
−0.269422









In an embodiment, the ratio between the sag values at 75 percent point and at 25 percent point of the object-side surface of fourth lens element 6 satisfies the following condition:

7.0<sag9(75)/sag9(25)<14.0  (3)

where sag9(75) is the sag value at 75 percent point of the clear aperture radius of the object-side of the fourth lens element measured from the optical axis, and sag9(25) is the sag value at 25 percent point of the clear aperture radius of the object-side of the fourth lens element 6. In some embodiments, the ratio between the sag values at 75 percent point and at 25 percent point of the object-side surface of fourth lens element 5 in relation (3) is preferably in a range from 8.0 to 12.5.

In an exemplary embodiment, the object-side surface of fourth lens element 6 has a minimum sag at the 25 percent point from the optical axis of about 19.9 microns and a maximum sag at the 75 percent point from the optical axis of about 163.4 microns. It is noted that the sag values are given in terms of absolute value. If the ratio in condition (3) exceeds the lower limit, the optical power of the fourth lens element and the lens system 300 may be reduced. If the ratio in condition (3) is greater than the upper limit, the optical performance of the lens system 300 may be affected.
Additionally, the object-side surface of fifth lens element 7 has a sag value at 100 percent point satisfying the following condition:

|sag11(100)|>320 microns  (4)

where |sag11(100)| is the absolute sag value at 100 percent point of the clear aperture radius measured from the optical axis of the object-side surface of the fifth lens element.

Furthermore, the imaging-side surface of fifth lens element 7 provides the largest sag value at a certain percentage point of the effective radius. In an embodiment, the largest absolute sag value is greater than 260 microns at 100 percentage point of the clear aperture radius of the fifth lens element. That is, the imaging-side surface of the fifth lens element satisfies the following condition:

|sag12(max)|>260 microns  (5)

where |sag12(max)| denotes the largest absolute sag value of the imaging-side surface of the fifth lens element.

If the imaging-side surface of the fifth lens element does not meet the condition (5), the lens system 200 of FIG. 2 may have astigmatism and aberration that exceeds the target design specifications. In some embodiments, the conditions (1a-1d), (2a-2c), (3), (4), and (5) allow the system to be constructed with a target total track length.
In an embodiment, first, second, third, fourth, and fifth lens elements can be made of plastic or glass. The Abbe number of first lens element 3 is vd1, the Abbe number of second lens element 4 is vd2, the Abbe number of third lens element 5 is vd3, the Abbe number of fourth lens element 6 is vd4, and the Abbe number of fifth lens element 7 is vd5. In an embodiment, they satisfy the following relations:

20<vd1−vd2  (6)

0≦|vd3−vd2|≦5  (7)

20<vd4−vd3  (8)

0≦|vd4−vd5|≦5  (9)

In an embodiment, vd1 is greater than 50, and preferably greater than 55; vd2 and vd3 can be in the range between 20 and 28, and vd4 and vd5 can be in the range between 51 and 57. In some embodiments, the difference between vd2 and vd3 may have an absolute value between 0 and 5. In other words, vd2 and vd3 may have the same Abbe number, or vd2 may have an Abbe number higher than that of vd3, or vd2 may have an Abbe number smaller than that of vd3 so that the absolute difference between them falls in the range between 0 and 5. Similarly, the absolute difference between vd4 and vd5 fall in the range between 0 and 5.
In a preferred embodiment, vd1 is 56.11, vd2 and vd3 each are 23.34, vd4 and vd5 each are 55.70 to satisfy the following conditions:

30<vd1−vd2  (6a)

|vd3−vd2|=0  (7a)

30<vd4−vd3  (8a)

|vd4−vd5|=0  (9a)

Optimizing air gaps between the lens elements and optical filter may minimize aberrations. In a preferred embodiment, the ratio between the sum of all air gaps from the imaging-side surface of the first lens element to the object-side surface of the optical filter and the total track length (TTL) is less than 0.4 in order for the lens system to be able to focus from infinity to portrait distances. In order words, the lens system 200 satisfies the following condition:

(Σ(air gaps))/TTL<0.4  (10)

where Σ(air gaps) is the sum of all air gaps from the imaging-side surface of the first lens element to the object-side surface of the optical lens and TTL is the total track length of the lens system. In some embodiments, the upper limit in condition (10) may be less than 0.4 such as less than 0.35 or preferably less than 0.3 to obtain a compact design of the lens system.

Similarly, air gaps between the lens elements may minimize aberrations. In some embodiments, the ratio between the sum of all air gaps between lens elements and the total track length (TTL) is less than 0.25 in order for the lens system to be able to focus from infinity to 10 cm. In a preferred embodiment, the sum of the air gaps from the imaging-side surface of the first lens element to the object-side surface of the fifth lens element is about 0.749 mm. The ratio of the sum of the air gaps between the lens elements to the total track length is about 0.25 or less, or preferably about 0.2 or less.
Further, the average diameter of each of the lens elements is related to its thickness as follows:

2.0<d1avg/t1<3.0;  (11a)

4.0<d2avg/t2<6.0  (11b)

2.0<d3avg/t3<5.0  (11c)

4.0<d4avg/t4<7.0  (11d)

7.0<d5avg/t5<11.0  (11e)

wherein t1, t2, t3, t4, and t5 are the respective thickness of the first, second, third, fourth, and fifth lens elements, and d1avg, d2avg, d3avg, d4avg and d5avg are the respective average diameters of the first, second, third, fourth and fifth lens elements. (As noted above, the average diameter is the sum of the object-side diameter and the imaging-side diameter of a lens element, divided by two.)

FIGS. 4A and 4B are cross-sectional views showing a lens system having variable total track lengths for explaining the lens operations. As shown in FIG. 4A, lens system 400 includes a lens arrangement 410 that comprises first, second, third, fourth, and fifth lens elements 3, 4, 5, 6, and 7. Lens system 400 may include an optical filter 8 that is disposed between lens arrangement 410 and an imaging sensor 9. Lens elements 3, 4, 5, 6, and 7 and optical filter 8 may have characteristics and optical performance described above in connection with FIGS. 2 and 3. In some embodiments, the diameters of the first and second lens elements may have a similar size. The diameters of the third lens element may be greater than the diameters of the first and second lens elements. The diameters of the fourth lens element may be greater than the diameters of the third lens element. The diameters of the fifth lens element may be greater than the diameters of the fourth lens element. And the active diameter of the optical filter may be greater than the diameters of the fifth lens elements.
In an embodiment, lens arrangement 410 may include a holding member (not shown) configured to hold lens elements 3, 4, 5, 6, and 7. The holding member may have a cylindrical shape having a plurality of grooves in the inside surface area to hold the lens elements by their flanges.
Lens arrangement 410 may be moveable along the optical axis toward and away from the imaging sensor. In some embodiments, lens arrangement 410 may include optical filter 8. In this case, the air gaps between the lens elements and optical filter remain constant and the air gap between the optical filter and the imaging plane of imaging sensor 9 may vary depending on the position of the lens arrangement. In other embodiments, optical filter 8 may not be part of lens arrangement 410 so that the air gap between optical lens 8 and the imaging plane of imaging sensor 9 remain constant while lens arrangement 410 moves toward and away from the imaging sensor, as shown in FIG. 4A and FIG. 4B. It should be noted that the FIG. 4A and FIG. 4B are merely examples. A person skilled in the art will appreciate that other embodiments can be within the claimed subject matter. In the following description, lens arrangement 410 may or may not include optical filter 8. For example, in case where lens arrangement 410 includes optical filter 8, air gap s5 between the imaging-side surface of fifth lens element 7 and optical lens 8 is constant while the lens arrangement moves along the optical axis relative to the imaging plane. In other words, optical lens 8 may be mounted to the holding member together with the lens elements.
To the extent that the focal length of lens arrangement 410 varies with distance to the object, moving lens arrangement 410 along the optical axis allows lens arrangement 410 to focus images of objects at different distances onto imaging sensor 9 at different times, providing variable focus. For example, in the embodiment shown, the focal length of lens arrangement 410 for an object at an infinite distance (or an effectively infinite distance, such as 10 m), denoted f∞, is shorter than the focal length of lens arrangement 410 for an object located in close proximity (e.g., 10 cm), denoted fmacro. Accordingly, when an object at infinity is to be imaged, it is desirable to move lens arrangement 410 closer to imaging sensor 9, and when an object in close proximity is to be imaged, it is desirable to move lens arrangement 410 farther from imaging sensor 9.
The holding member holding lens arrangement 410 can be movable along the optical axis within a limited range of motion. Moving lens arrangement 410 closer to imaging sensor 9 to get infinity focus results in shorter TTL, and moving farther away from imaging sensor 9 to get macro focus results in longer TTL. Thus, lens arrangement 410 may reach a closest position relative to the optical center of imaging sensor 9. The closest position between the lens arrangement and the imaging sensor provides the shortest total track length. The shortest total track length (TTL) allows an object located at a very long distance (e.g., at infinity) from the optical center of lens system 400 to be displayed on the focal plane on the imaging sensor. The shortest TTL is termed herein as TTL∞ and is shown in FIG. 4A.
Likewise, lens arrangement 410 may also reach a farthest position relative to the optical center of imaging sensor 9. The farthest position between the lens arrangement and the imaging sensor provides the longest total track length. The longest total track length (TTL) allows an object located at a very short distance (e.g., at a macro level) from the optical center of lens system 400 to be displayed on the focal plane on the imaging sensor. The longest TTL is termed herein as TTLmacro and is shown in FIG. 4B. In an embodiment, the shortest or close-up distance (macro) of the object from the optical center of imaging sensor can be 10 cm.
Lens system 400 can have variable focusing distance by changing the position of the lens arrangement in relation to the imaging sensor. In other words, the focus of lens system 400 can be varied by placing lens arrangement 410 at any positions between the two extremities corresponding to TTL∞ and TTLmacro. In an embodiment, the ratio of TTL∞ to TTLmacro is proportional to the ratio of focal length at the farthest extremity f∞ to focal length at the closest extremity fmacro (e.g., at 10 cm). Lens system 400 with variable focus satisfies the following conditions:

TTL∞/TTLmacro ̃f∞/fmacro  (12)

where the symbol “ ̃” means “is proportional to,” “f∞” designates the focal length of lens system 400 at the closest extremity (as shown in FIG. 4A) when an object of focus at an infinite distance from the optical center of imaging sensor 9 is in an in-focus state, and “fmacro” designates the focal length of lens system 400 at the farthest extremity (as shown in FIG. 4B) when a close-up object from the optical center of the imaging sensor is in an in-focus state, TTL∞ is the total track length of lens system 400 when an object of focus is at an effectively infinite distance from the optical center of imaging sensor 9, and TTLmacro is the total track length when the object of focus is at a close-up range from the optical center of imaging sensor 9. As shown in FIGS. 4A and 4B, the total track length TTL∞ is shorter than the total track length TTLmacro.

In an embodiment, the nominal total track length is about 3.91 mm, the minimum total track length (i.e., total track length of the lens system where the object of focus is at an infinite distance from the optical center of imaging sensor 9) is about 3.852 mm, and the maximum total track length (i.e., total track length where the object of focus is about 10 cm from the optical center of imaging sensor 9) is about 3.965 mm. In an embodiment, the ratio between the minimum TTL (TTL∞) and the maximum TTL (TTLmacro) is 0.99 or less, preferably 0.98 or less, more preferably from 0.965 to 0.975, to provide a compact lens system.
FIG. 5 is a schematic diagram illustrating TV distortion of an imaging lens system. TV distortion causes deviation from an ideal rectangular image field 500, which can occur as an inward distortion 502 or outward distortion 504. A TV distortion can be expressed with the following equation:

TV distortion(height)=±Δh/h  (13a)

TV distortion(width)=±Δw/w  (13b)

where TV distortion (height) is the distortion along the vertical height of the image field, TV distortion (width) is the distortion along the longitudinal length or width of the image field, h is the vertical height of the image field, Δh is the maximum deviation in the direction of the vertical height, w is the longitudinal length or width of the image field, and Δw is the maximum deviation in the direction of the longitudinal length of the image field.

In some embodiments, an imaging lens system as described herein may have performance of astigmatism and distortion aberrations that meet certain target characteristics. Images taken with an imaging lens system disclosed above can be viewed on a TV screen with a vertical or longitudinal TV distortion of less than ±1 percent.
FIG. 6 shows a relation between a semiconductor imaging sensor (e.g., a CMOS imaging sensor), the associated sensor image circle and the maximum image circle according to an embodiment of the present invention. The sensor image circle (SIC) can be defined as a circle 600 that circumscribes a rectangular imaging sensor 602. In other words, the diameter of sensor image circle 600 is equal to a diagonal size 603 of rectangular imaging sensor 602. The maximum image circle for a lens system can be defined as a circle 604 that corresponds to a circular area in the imaging plane over which the lens produces acceptable image quality. In some embodiments, the ratio between the sensor image circle and the maximum image circle is greater than 0.9. For example, the imaging sensor may have a diagonal of about 4.534 mm, so that the sensor image circle also has a diameter of 4.536 mm, and the maximum image circle has a diameter of 4.736 mm. In an embodiment, the lens system has a chief ray angle of less than 31° and a relative illumination at full field diagonal image height greater than 40 percent. Embodiments of the present invention provide a compact lens system according to the following inequity:

DM/TTL≧1.0  (14)

where DM is the diameter of the sensor image circle and TTL is the total track length. For example, the sensor image circle can have a diameter of 4.536 mm and the total track length can be 3.90 mm in one embodiment.

In some embodiments, illumination of the surface area of the imaging sensor may depend on performance characteristics of an associated lens system. In general, an optical lens system may not illuminate the imaging sensor uniformly even when a uniform illuminating light is applied to it. A lens system may only partially pass through light that irradiates the lens system at a certain angle of incidence. The lens system may completely pass light that is substantially normal to the optical axis. As a result, the imaging sensor may receive more light in the center than around the edges. Therefore, a relative illumination may be used to characterize the optical performance of a lens system. The relative illumination can be defined as a percentage of a maximum illumination value. If the maximum illumination value of a surface region (e.g., the center) of the imaging sensor is 1.0 or 100%, the relative illumination values may decrease when moving away from the center of the imaging sensor. In an embodiment, the lens system 200 or 300 as shown in FIG. 2 or 3 may provide a relative illumination value greater than 40.0 percent across the diagonal of the imaging sensor.
While the invention has been described with respect to specific embodiments, one skilled in the art will recognize that variations and modifications are possible and that the invention is intended to cover all modifications and equivalents within the scope of the following claims.

## Claims

1. An imaging lens comprising first, second, third, fourth, and fifth lens elements arranged in order from an object side to an imaging side, each of the first, second, third, fourth, and fifth lens elements having an object-side surface facing toward the object side, and an imaging-side surface facing toward the imaging side, wherein the imaging lens satisfies the following conditions:


20<vd1−vd2;



0≦|vd3−vd2|≦5;



20<vd4−vd3; and



0≦|vd4−vd5|≦5,

wherein vd1, vd2, vd3, vd4, and vd5 are Abbe numbers of the respective first, second, third, fourth, and fifth lens elements, |vd3−vd2| is the absolute value of the difference between vd2 and vd3, and |vd4−vd5| is the absolute value of the difference between vd4 and vd5; and
wherein the object-side surface of the fourth lens element satisfies the following condition:


7.0<sag(75)/sag(25)<14.0,



where sag(25) is a sag value at a 25 percent point of a clear aperture radius of the object-side surface and sag(75) is a sag value at a 75 percent point of the clear aperture radius of the object-side surface.

2. The imaging lens of claim 1, wherein the first lens element has a ratio of average diameter to thickness in a range between 2 and 3, and the second lens element has a ratio of average diameter to thickness in a range between 4 and 6.

3. The imaging lens of claim 1, wherein the first lens element has an average diameter that is equal to an average diameter of the second lens element.

4. The imaging lens of claim 1, wherein each of the third, fourth, and fifth lens elements has an imaging-side diameter that is greater than an object-side diameter by at least 0.3 mm.

5. The imaging lens of claim 1, wherein the fourth lens element has a ratio of average diameter to thickness in a range between 4 and 7, and the fifth lens element has a ratio of average diameter to thickness in a range between 7 and 11.

6. The imaging lens of claim 1, wherein the object-side surface and the imaging-side surface of the first, second, third, and fourth lens elements are coated with an anti-reflective coating.

7. A lens system operable to operate in conjunction with an imaging sensor, the lens system comprising in order from an object side to an imaging side:
an aperture stop configured to pass light, the aperture stop having a circular-shaped opening in the center;
a first lens element having an object-side diameter and an imaging-side diameter;
a second lens element having an object-side diameter and an imaging-side diameter;
a third lens element having an object-side diameter and an imaging-side diameter;
a fourth lens element having an object-side diameter and an imaging-side diameter; and
a fifth lens element having an object-side diameter and an imaging-side diameter,
wherein the circular-shaped opening has a diameter smaller than the object-side diameter of the first lens element,
wherein a difference between a first Abbe number of the first lens element and a second Abbe number of the second lens element is greater than 20, and an absolute value of a difference between a third Abbe number of the third lens element and the second Abbe number of the second lens element falls in a range between 0 and 5,
wherein the lens system further satisfies the following conditions:


0<s2/s1<5.0;



0<s4/s3<0.7; and



0<s3/s2<1.0,



wherein s1 is an air gap between the imaging-side surface of the first lens element and the object-side surface of the second lens element, s2 is an air gap between the imaging-side surface of the second lens element and the object-side surface of the third lens element, s3 is an air gap between the imaging-side surface of the third lens element and the object-side surface of the fourth lens element, s4 is an air gap between the imaging-side surface of the fourth lens element and the object-side surface of the fifth lens element; and
wherein the first, second, third, fourth, and fifth lens elements are configured to focus images of objects located at distances ranging from 10 cm to infinity from the lens system by moving all of the lens elements from a first location to a second location in relation to the imaging sensor, while holding all of the lens elements in fixed relation to each other.

8. The lens system of claim 7 further comprising an optical filter disposed between the fifth lens element- and the imaging sensor and configured to suppress transmission of infrared light.

9. The lens system of claim 8, wherein the optical filter has a thickness of about 0.3 mm.

10. The lens system of claim 8, wherein the imaging sensor is disposed at a distance between about 0.3 mm and about 0.4 mm from the optical filter.

11. The lens system of claim 8, wherein the first, second, third, fourth, fifth lens elements, and the optical filter have air gaps therebetween and a ratio of a sum of the air gaps to a total track length is about 0.4 or less.

12. The lens system of claim 7, wherein the object-side diameter of each lens element is equal to or smaller than its imaging-side diameter.

13. The lens system of claim 7, wherein a ratio between a sag at 75 percent point and a sag at 25 percent point of the object-side surface of the fourth lens element is in a range from 7 to 14.

14. The lens system of claim 7, further comprising a holding member configured to hold the first, second, third, fourth, and fifth lens elements.

15. The lens system of claim 7 wherein the lens system has a maximum chief ray angle (CRA) smaller than 31 degrees.

16. The lens system of claim 7 wherein the lens system has a TV distortion less than ±1.0 percent.

17. The lens system of claim 7 wherein the lens system has a sensor image circle having a diameter of about 4.536 mm.

18. An imaging lens system comprising first, second, third, fourth, fifth lens elements, an optical filter, and an imaging sensor arranged sequentially in order from an object side to an imaging side, wherein:
the first lens element has an object-side surface and an imaging-side surface and a thickness along an optical axis of 0.49 mm;
the second lens element has an object-side surface and an imaging-side surface and a thickness along the optical axis of 0.27 mm;
the third lens element has an object-side surface and an imaging-side surface and a thickness along the optical axis of 0.465 mm;
the fourth lens element has an object-side surface and an imaging-side surface and a thickness along the optical axis of 0.4 mm;
the fifth lens element has an object-side surface and an imaging-side surface and a thickness along the optical axis of 0.35 mm; and
the optical filter has a thickness along the optical axis of 0.3 mm.

19. The lens system of claim 18, wherein:
the imaging-side surface of the first lens element and the object-side surface of the second lens element have an air gap along the optical axis of 0.07 mm;
the imaging-side surface of the second lens element and the object-side surface of the third lens element have an air gap along the optical axis of 0.288 mm;
the imaging-side surface of the third lens element and the object-side surface of the fourth lens element have an air gap along the optical axis of 0.26 mm;
the imaging-side surface of the fourth lens element and the object-side surface of the fifth lens element have an air gap along the optical axis of 0.13 mm, and
the imaging-side surface of the fifth lens element and the object-side surface of the optical filter have an air gap along the optical axis of 0.441 mm.

20. The lens system of claim 18, wherein the first lens element has a first Abbe number vd1, the second lens element has a second Abbe number vd2, the third lens element has a third Abbe number vd3, the fourth lens element has a fourth Abbe number vd4, and the fifth lens element has a fifth Abbe number vd5, wherein the Abbe numbers satisfy the following conditions:


20<vd1−vd2;



0≦|vd3−vd2|≦5;



20<vd4−vd3; and



0≦|vd4−vd5|≦5,

wherein |vd3−vd2| is the absolute value of the difference between vd2 and vd3, and |vd4−vd5| is tan absolute value of a difference between vd4 and vd5.

21. The lens system of claim 18 further satisfying the following condition:


DM/TTL≧1.0

wherein DM is a diameter of a sensor image circle and TTL is a total track length of the lens system.

22. The lens system of claim 18, wherein the lens system provides a relative illumination greater than 40.0 percent across a full diagonal size of an imaging sensor.

23. The lens system of claim 18 further satisfying the following conditions:


TTL∞TTLmacro ̃f∞/fmacro, and



0.96<TTL∞/TTLmacro<0.98,

where TTL∞ is a total track length of the lens system when an object of focus is at an effectively infinite distance from the optical center of the imaging sensor, TTLmacro is a total track length when the object of focus is at a close-up range from the optical center of the imaging sensor, f∞ is a focal length of the lens system when an object at an effectively infinite distance from the optical center of the imaging sensor is in an in-focus state, and fmacro is the focal length of the lens system at the farthest extremity when a close-up object from the optical center of the imaging sensor is in the in-focus state.

24. The lens system of claim 23, wherein the close-up range is about 10 cm.