# Patent

## Title
Imaging lens

## Abstract

A four element lens system for use with an imaging sensor includes first, second, third, and fourth 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.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. application Ser. No. 13/757,634, filed Feb. 1, 2013, entitled “Imaging Lens,” which claims priority to Chinese Patent Application No. 201210328950.8, filed Sep. 7, 2012. The disclosure of U.S. application Ser. No. 13/757,634 is incorporated herein by reference.


BACKGROUND
The present disclosure relates to an imaging lens and an imaging lens system having the same, more particularly to an imaging lens with four 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 image 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) image 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. 7,453,654 discloses imaging lenses with four lens elements. Each of the imaging lenses has a unique combination and arrangement of lens elements with different 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 comprised. Therefore, the need to develop other imaging lenses with better combinations of optical characteristics still exists in the market.
SUMMARY
Certain 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, and fourth lens elements arranged sequentially in order from an object side to an imaging side, each of the first, second, third, and fourth 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 vd1−vd2>30, 0.5<d1avg/d2avg<0.9, 0.4 <d3avg/d4avg<0.7, wherein vd1 and vd2 are Abbe numbers of the respective first and second lens elements, and d1avg, d2avg, d3avg, and d4avg are average diameters of the first, second, third, and fourth lens elements.
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, and a fourth 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 is equal to or smaller than the imaging-side diameter. The aperture stop is configured to pass light and has a circular-shaped opening. The circular-shaped opening has a diameter that is 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 30. 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, and fourth lens elements that are arranged in order from an object side to an imaging side. The four lens elements are sequentially arranged on an optical axis. The lens system further includes an optical filter disposed between the fourth lens element and the imaging sensor along the optical axis. Each of the first, second, third, and fourth 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 0.4 mm from the imaging-side of the fourth 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 0.07 mm, the imaging-side surface of the second lens element and the object-side surface of the third lens element have an air gap of 0.34 mm, and the imaging-side surface of the third lens element and the object-side surface of the fourth lens element has an air gap of 0.06 mm. In an embodiment, the first lens element may have a thickness of 0.42 mm, the second lens element may have a thickness of 0.26 mm, the third lens element may have a thickness of 0.435 mm, and the fourth lens element may have a thickness of 0.3 mm. In an embodiment, the optical filter may have a thickness of 0.3 mm and may be disposed at a distance about 0.4 mm of the imaging-side surface of the forth 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 illustrating lens elements, filter, imaging sensor and the optical axis in accordance with an imaging lens system.
FIG. 3 is a schematic diagram defining the terminology used in an imaging lens system.
FIG. 4 is a cross-sectional view of a lens element to define sag values.
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 element” is herein defined as a single transparent mass of refractive material having two opposed refracting surfaces. The term “diameter” is referred to as the “clear aperture” or “clear aperture diameter” of a lens element. The term “clear aperture”, “clear aperture diameter”, and “diameter” will be alternatively 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. A “sag” is the displacement of the surface of the lens from a 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 perpendicular plane.
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, and fourth lens elements 3, 4, 5, 6, and an optical filter 7 arranged in the given order from an object side to an imaging side. Each of the first, second, third, and fourth lens elements 3, 4, 5, 6 has an object-side surface 31, 41, 51, 61, facing toward the object side, and an imaging-side surface 32, 42, 52, 62, 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 6, and optical filter 7 in the given order, and forms an image at an imaging plane 8 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 0.91 mm and the diameter of object-side surface 31 of the first lens element is about 1.01 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 7 has an object-side surface 71 facing toward the object side, and an imaging-side surface 72 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 four 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, and fourth 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, and s4 is an air gap between the imaging-side surface of the fourth lens element and the object-side surface of the optical filter. Additionally, imaging plane 8 is placed at a distance s5 from optical filter 7, 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 28 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, and t4 is a thickness of fourth lens element 6 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 lens barrel (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 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.
Table 1 provides design parameters of a lens system according to an embodiment of the present invention.











TABLE 1






Refractive





lens
index
Thickness (mm)
Air gap (mm)
Diameter (mm)







first
1.54
t1 = 0.420
s1 = 0.07
d1 = 1.011






d2 = 1.194


second
1.63
t2 = 0.26
s2 = 0.34
d3 = 1.302






d4 = 1.336


third
1.54
t3 = 0.435
s3 = 0.06
d5 = 1.457






d6 = 1.714


fourth
1.53
t4 = 0.3
s4 = 0.40
d7 = 2.711






d8 = 2.903









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 0.42 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 0.07 mm along the optical axis. The second lens element 4 has a thickness of 0.26 mm along the optical axis. The third lens element 5 has a thickness of 0.435 mm along the optical axis, and the fourth lens element 6 has a thickness of 0.3 mm along the optical axis. In an embodiment, the optical filter is interposed between fourth lens element 6 and imaging sensor 8. The optical filter may have a thickness of about 0.3 mm and disposed at a distance of about 0.4 mm from the imaging-side surface of fourth lens element 6 and at a distance of about 0.3 to 0.4 mm from the imaging sensor.
In an embodiment, the diameter d1 of the object-side surface of first lens element 3 is 1.011 mm. The diameter d2 of the imaging-side surface of first lens element 3 is 1.194 mm. Similarly, the diameter d3 of the object-side surface of second lens element 4 is 1.302 mm and the diameter d4 of the imaging-side surface of second lens element 4 is 1.336 mm. The last 4 rows of Table 1 provide the respective object-side and imaging-side diameters d5, d6, d7, and d8 of third and fourth 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.
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 5 include sag values of the lens elements 3, 4, 5 and 6, respectively. The sag values are in microns. The “normalized lens Ht” in the first and fourth columns denotes the normalized relative distance of lens element 3 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 lens element 3 in relation to the optical axis. As the lens element is rotationally symmetric about the optical axis, the surface of the lens element is sufficient 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 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. It should be noted that the tolerance between adjacent sag values may alternate between positive and negative values for not causing steps on the surface of the lens element.
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. Sag data in Table 2 is given in mm.












TABLE 2





Normal-


Normal-




ized


ized


Lens Ht
Min Sag 3
Max Sag 3
Lens Ht
Min Sag 4
Max Sag 4




















0.0%
−0.001000
0.001000
0.0%
−0.001000
0.001000


2.0%
−0.000969
0.001031
1.7%
−0.001018
0.000982


3.9%
−0.000875
0.001125
3.3%
−0.001071
0.000929


5.9%
−0.000718
0.001282
5.0%
−0.001159
0.000841


7.8%
−0.000499
0.001501
6.7%
−0.001283
0.000717


9.8%
−0.000217
0.001782
8.3%
−0.001443
0.000556


11.8%
0.000127
0.002125
10.0%
−0.001640
0.000360


13.7%
0.000533
0.002531
11.7%
−0.001873
0.000127


15.7%
0.001000
0.002998
13.3%
−0.002143
−0.000144


17.6%
0.001530
0.003526
15.0%
−0.002451
−0.000452


19.6%
0.002120
0.004116
16.7%
−0.002797
−0.000798


21.6%
0.002771
0.004767
18.3%
−0.003182
−0.001184


23.5%
0.003483
0.005478
20.0%
−0.003608
−0.001610


25.5%
0.004255
0.006249
21.7%
−0.004074
−0.002077


27.5%
0.005087
0.007079
23.3%
−0.004583
−0.002585


29.4%
0.005978
0.007970
25.0%
−0.005134
−0.003137


31.4%
0.006928
0.008918
26.7%
−0.005729
−0.003733


33.3%
0.007936
0.009926
28.3%
−0.006370
−0.004374


35.3%
0.009002
0.010990
30.0%
−0.007057
−0.005063


37.3%
0.010126
0.012112
31.7%
−0.007793
−0.005799


39.2%
0.011305
0.013291
33.3%
−0.008578
−0.006585


41.2%
0.012540
0.014525
35.0%
−0.009415
−0.007423


43.1%
0.013830
0.015813
36.7%
−0.010305
−0.008313


45.1%
0.015174
0.017155
38.3%
−0.011249
−0.009259


47.1%
0.016570
0.018550
40.0%
−0.012250
−0.010261


49.0%
0.018017
0.019996
41.7%
−0.013310
−0.011321


51.0%
0.019515
0.021492
43.3%
−0.014430
−0.012443


52.9%
0.021060
0.023036
45.0%
−0.015612
−0.013627


54.9%
0.022653
0.024627
46.7%
−0.016859
−0.014876


56.9%
0.024290
0.026263
48.3%
−0.018173
−0.016191


58.8%
0.025969
0.027941
50.0%
−0.019556
−0.017576


60.8%
0.027689
0.029659
51.7%
−0.021010
−0.019032


62.7%
0.029446
0.031416
53.3%
−0.022537
−0.020561


64.7%
0.031239
0.033207
55.0%
−0.024140
−0.022166


66.7%
0.033064
0.035031
56.7%
−0.025819
−0.023848


68.6%
0.034917
0.036883
58.3%
−0.027578
−0.025610


70.6%
0.036796
0.038761
60.0%
−0.029418
−0.027453


72.5%
0.038696
0.040661
61.7%
−0.031342
−0.029379


74.5%
0.040614
0.042578
63.3%
−0.033349
−0.031390


76.5%
0.042546
0.044509
65.0%
−0.035443
−0.033487


78.4%
0.044485
0.046449
66.7%
−0.037623
−0.035671


80.4%
0.046428
0.048391
68.3%
−0.039893
−0.037944


82.4%
0.048368
0.050331
70.0%
−0.042251
−0.040306


84.3%
0.050298
0.052262
71.7%
−0.044699
−0.042759


86.3%
0.052211
0.054176
73.3%
−0.047238
−0.045302


88.2%
0.054099
0.056065
75.0%
−0.049868
−0.047936


90.2%
0.055951
0.057918
76.7%
−0.052589
−0.050661


92.2%
0.057757
0.059726
78.3%
−0.055402
−0.053479


94.1%
0.059502
0.061473
80.0%
−0.058309
−0.056391


96.1%
0.061171
0.063145
81.7%
−0.061310
−0.059398


98.0%
0.062744
0.064722
83.3%
−0.064409
−0.062502


100.0%
0.063612
0.065591
85.0%
−0.067610
−0.065708





86.7%
−0.070918
−0.069023





88.3%
−0.074345
−0.072457





90.0%
−0.077904
−0.076024





91.7%
−0.081617
−0.079748





93.3%
−0.085518
−0.083663





95.0%
−0.089656
−0.087818





96.7%
−0.094106
−0.092293





98.3%
−0.098990
−0.097214





100.0%
−0.103022
−0.101288









In accordance with Table 2, lens element 3 may have an average sag value of 20 microns (0.020 mm) at 50 point and an average sag value of 65 microns (0.065 mm) at 100 point of the clear aperture of the object-side. The ratio between the sag value at 50 point and at 100 point satisfies the following conditions: 0.2<sag3(50)/sag3(100)<0.6 or preferably 0.25<sag3(50)/sag3(100)<0.50.
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 3. 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. Sag values in Table 3 are given in mm.












TABLE 3





Normal-


Normal-




ized


ized


Lens Ht
Min Sag 5
Max Sag 5
Lens Ht
Min Sag 6
Max Sag 6




















0.0%
−0.001000
0.001000
0.0%
−0.001000
0.001000


1.5%
−0.000989
0.001011
1.5%
−0.000963
0.001037


3.0%
−0.000957
0.001043
3.0%
−0.000854
0.001146


4.5%
−0.000903
0.001097
4.5%
−0.000671
0.001329


6.1%
−0.000827
0.001173
6.0%
−0.000414
0.001585


7.6%
−0.000731
0.001269
7.5%
−0.000085
0.001914


9.1%
−0.000613
0.001387
9.0%
0.000318
0.002316


10.6%
−0.000475
0.001525
10.4%
0.000794
0.002791


12.1%
−0.000317
0.001683
11.9%
0.001343
0.003340


13.6%
−0.000138
0.001861
13.4%
0.001966
0.003962


15.2%
0.000059
0.002059
14.9%
0.002663
0.004658


16.7%
0.000275
0.002275
16.4%
0.003433
0.005426


18.2%
0.000509
0.002508
17.9%
0.004276
0.006269


19.7%
0.000760
0.002759
19.4%
0.005193
0.007184


21.2%
0.001027
0.003026
20.9%
0.006184
0.008173


22.7%
0.001309
0.003308
22.4%
0.007248
0.009236


24.2%
0.001605
0.003604
23.9%
0.008384
0.010371


25.8%
0.001913
0.003912
25.4%
0.009594
0.011579


27.3%
0.002233
0.004232
26.9%
0.010877
0.012860


28.8%
0.002562
0.004561
28.4%
0.012232
0.014213


30.3%
0.002899
0.004898
29.9%
0.013659
0.015638


31.8%
0.003243
0.005242
31.3%
0.015157
0.017134


33.3%
0.003592
0.005590
32.8%
0.016727
0.018701


34.8%
0.003943
0.005942
34.3%
0.018366
0.020339


36.4%
0.004295
0.006294
35.8%
0.020076
0.022046


37.9%
0.004646
0.006645
37.3%
0.021854
0.023822


39.4%
0.004995
0.006994
38.8%
0.023701
0.025666


40.9%
0.005339
0.007337
40.3%
0.025614
0.027577


42.4%
0.005676
0.007675
41.8%
0.027594
0.029555


43.9%
0.006005
0.008004
43.3%
0.029639
0.031597


45.5%
0.006325
0.008324
44.8%
0.031747
0.033703


47.0%
0.006633
0.008632
46.3%
0.033919
0.035872


48.5%
0.006930
0.008929
47.8%
0.036153
0.038103


50.0%
0.007214
0.009213
49.3%
0.038447
0.040395


51.5%
0.007485
0.009485
50.7%
0.040800
0.042746


53.0%
0.007744
0.009743
52.2%
0.043212
0.045155


54.5%
0.007990
0.009990
53.7%
0.045682
0.047622


56.1%
0.008226
0.010226
55.2%
0.048208
0.050146


57.6%
0.008453
0.010452
56.7%
0.050789
0.052725


59.1%
0.008673
0.010673
58.2%
0.053426
0.055359


60.6%
0.008891
0.010890
59.7%
0.056118
0.058048


62.1%
0.009109
0.011109
61.2%
0.058864
0.060791


63.6%
0.009334
0.011333
62.7%
0.061665
0.063590


65.2%
0.009571
0.011570
64.2%
0.064522
0.066443


66.7%
0.009826
0.011826
65.7%
0.067434
0.069353


68.2%
0.010109
0.012108
67.2%
0.070405
0.072321


69.7%
0.010427
0.012426
68.7%
0.073435
0.075348


71.2%
0.010791
0.012790
70.1%
0.076527
0.078437


72.7%
0.011211
0.013209
71.6%
0.079685
0.081591


74.2%
0.011697
0.013695
73.1%
0.082912
0.084813


75.8%
0.012263
0.014259
74.6%
0.086213
0.088110


77.3%
0.012921
0.014916
76.1%
0.089593
0.091485


78.8%
0.013683
0.015677
77.6%
0.093059
0.094946


80.3%
0.014563
0.016554
79.1%
0.096618
0.098500


81.8%
0.015573
0.017562
80.6%
0.100279
0.102154


83.3%
0.016726
0.018711
82.1%
0.104052
0.105919


84.8%
0.018031
0.020013
83.6%
0.107946
0.109806


86.4%
0.019500
0.021476
85.1%
0.111975
0.113826


87.9%
0.021138
0.023109
86.6%
0.116151
0.117992


89.4%
0.022950
0.024915
88.1%
0.120490
0.122319


90.9%
0.024937
0.026895
89.6%
0.125007
0.126824


92.4%
0.027094
0.029046
91.0%
0.129720
0.131523


93.9%
0.029410
0.031356
92.5%
0.134648
0.136435


95.5%
0.031870
0.033809
94.0%
0.139812
0.141581


97.0%
0.034446
0.036380
95.5%
0.145233
0.146982


98.5%
0.037103
0.039035
97.0%
0.150934
0.152661


100.0%
0.037460
0.039391
98.5%
0.156941
0.158644





100.0%
0.162236
0.163918









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 3. 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. Sag values in Table 4 are given in mm.












TABLE 4





Normal-


Normal-




ized


ized


Lens Ht
Min Sag 7
Max Sag 7
Lens Ht
Min Sag 8
Max Sag 8




















0.0%
−0.001500
0.001500
0.0%
−0.001500
0.001500


1.4%
−0.001534
0.001466
1.2%
−0.001592
0.001407


2.7%
−0.001634
0.001365
2.3%
−0.001869
0.001129


4.1%
−0.001802
0.001197
3.5%
−0.002329
0.000667


5.5%
−0.002036
0.000963
4.7%
−0.002971
0.000020


6.8%
−0.002337
0.000661
5.8%
−0.003795
−0.000808


8.2%
−0.002704
0.000294
7.0%
−0.004799
−0.001817


9.6%
−0.003135
−0.000139
8.1%
−0.005980
−0.003004


11.0%
−0.003632
−0.000636
9.3%
−0.007335
−0.004366


12.3%
−0.004192
−0.001197
10.5%
−0.008863
−0.005902


13.7%
−0.004815
−0.001821
11.6%
−0.010561
−0.007607


15.1%
−0.005500
−0.002508
12.8%
−0.012424
−0.009479


16.4%
−0.006246
−0.003255
14.0%
−0.014450
−0.011515


17.8%
−0.007051
−0.004061
15.1%
−0.016635
−0.013709


19.2%
−0.007915
−0.004927
16.3%
−0.018976
−0.016060


20.5%
−0.008835
−0.005849
17.4%
−0.021468
−0.018563


21.9%
−0.009812
−0.006827
18.6%
−0.024108
−0.021213


23.3%
−0.010842
−0.007858
19.8%
−0.026893
−0.024008


24.7%
−0.011924
−0.008942
20.9%
−0.029817
−0.026943


26.0%
−0.013057
−0.010077
22.1%
−0.032877
−0.030014


27.4%
−0.014238
−0.011260
23.3%
−0.036070
−0.033218


28.8%
−0.015467
−0.012490
24.4%
−0.039391
−0.036550


30.1%
−0.016740
−0.013765
25.6%
−0.042836
−0.040006


31.5%
−0.018055
−0.015082
26.7%
−0.046403
−0.043583


32.9%
−0.019411
−0.016440
27.9%
−0.050087
−0.047277


34.2%
−0.020806
−0.017835
29.1%
−0.053884
−0.051085


35.6%
−0.022236
−0.019267
30.2%
−0.057791
−0.055002


37.0%
−0.023700
−0.020732
31.4%
−0.061805
−0.059026


38.4%
−0.025195
−0.022229
32.6%
−0.065921
−0.063153


39.7%
−0.026718
−0.023753
33.7%
−0.070137
−0.067378


41.1%
−0.028268
−0.025304
34.9%
−0.074450
−0.071700


42.5%
−0.029841
−0.026877
36.0%
−0.078855
−0.076115


43.8%
−0.031434
−0.028472
37.2%
−0.083349
−0.080618


45.2%
−0.033045
−0.030084
38.4%
−0.087930
−0.085207


46.6%
−0.034671
−0.031711
39.5%
−0.092593
−0.089879


47.9%
−0.036310
−0.033350
40.7%
−0.097335
−0.094629


49.3%
−0.037958
−0.034999
41.9%
−0.102153
−0.099454


50.7%
−0.039613
−0.036654
43.0%
−0.107042
−0.104351


52.1%
−0.041272
−0.038313
44.2%
−0.112000
−0.109316


53.4%
−0.042932
−0.039973
45.3%
−0.117021
−0.114344


54.8%
−0.044591
−0.041631
46.5%
−0.122103
−0.119432


56.2%
−0.046245
−0.043285
47.7%
−0.127241
−0.124575


57.5%
−0.047893
−0.044932
48.8%
−0.132429
−0.129770


58.9%
−0.049531
−0.046570
50.0%
−0.137665
−0.135010


60.3%
−0.051158
−0.048196
51.2%
−0.142942
−0.140291


61.6%
−0.052771
−0.049809
52.3%
−0.148255
−0.145608


63.0%
−0.054368
−0.051406
53.5%
−0.153599
−0.150955


64.4%
−0.055949
−0.052985
54.7%
−0.158969
−0.156327


65.8%
−0.057510
−0.054546
55.8%
−0.164357
−0.161717


67.1%
−0.059052
−0.056087
57.0%
−0.169757
−0.167118


68.5%
−0.060574
−0.057607
58.1%
−0.175163
−0.172524


69.9%
−0.062074
−0.059107
59.3%
−0.180568
−0.177928


71.2%
−0.063555
−0.060587
60.5%
−0.185963
−0.183322


72.6%
−0.065016
−0.062047
61.6%
−0.191342
−0.188698


74.0%
−0.066459
−0.063489
62.8%
−0.196695
−0.194048


75.3%
−0.067885
−0.064915
64.0%
−0.202015
−0.199364


76.7%
−0.069298
−0.066328
65.1%
−0.207293
−0.204637


78.1%
−0.070702
−0.067731
66.3%
−0.212519
−0.209857


79.5%
−0.072101
−0.069130
67.4%
−0.217684
−0.215015


80.8%
−0.073500
−0.070529
68.6%
−0.222779
−0.220102


82.2%
−0.074906
−0.071935
69.8%
−0.227794
−0.225107


83.6%
−0.076326
−0.073356
70.9%
−0.232719
−0.230022


84.9%
−0.077770
−0.074801
72.1%
−0.237544
−0.234836


86.3%
−0.079247
−0.076280
73.3%
−0.242260
−0.239540


87.7%
−0.080769
−0.077804
74.4%
−0.246856
−0.244123


89.0%
−0.082348
−0.079386
75.6%
−0.251322
−0.248576


90.4%
−0.083999
−0.081041
76.7%
−0.255650
−0.252889


91.8%
−0.085737
−0.082784
77.9%
−0.259830
−0.257054


93.2%
−0.087580
−0.084633
79.1%
−0.263853
−0.261062


94.5%
−0.089546
−0.086607
80.2%
−0.267712
−0.264905


95.9%
−0.091656
−0.088725
81.4%
−0.271399
−0.268576


97.3%
−0.093930
−0.091011
82.6%
−0.274908
−0.272069


98.6%
−0.096393
−0.093487
83.7%
−0.278233
−0.275378


100.0%
−0.098763
−0.095872
84.9%
−0.281370
−0.278499





86.0%
−0.284317
−0.281431





87.2%
−0.287071
−0.284171





88.4%
−0.289634
−0.286721





89.5%
−0.292008
−0.289082





90.7%
−0.294197
−0.291261





91.9%
−0.296210
−0.293264





93.0%
−0.298055
−0.295101





94.2%
−0.299746
−0.296784





95.3%
−0.301298
−0.298330





96.5%
−0.302731
−0.299759





97.7%
−0.304067
−0.301092





98.8%
−0.305335
−0.302358





100.0%
−0.306217
−0.303239









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 3. 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. Sag data in Table 5 is given in mm.












TABLE 5





Normal-


Normal-




ized


ized
Min Sag
Max Sag


Lens Ht
Min Sag 9
Max Sag 9
Lens Ht
10
10




















0.0%
−0.003000
0.003000
0.0%
−0.003000
0.003000


0.7%
−0.002969
0.003031
0.7%
−0.002904
0.003095


1.5%
−0.002874
0.003125
1.4%
−0.002616
0.003380


2.2%
−0.002717
0.003281
2.1%
−0.002137
0.003853


2.9%
−0.002498
0.003500
2.7%
−0.001471
0.004512


3.7%
−0.002217
0.003780
3.4%
−0.000620
0.005354


4.4%
−0.001875
0.004121
4.1%
0.000411
0.006374


5.1%
−0.001471
0.004523
4.8%
0.001618
0.007569


5.9%
−0.001008
0.004985
5.5%
0.002995
0.008933


6.6%
−0.000485
0.005506
6.2%
0.004536
0.010459


7.4%
0.000096
0.006085
6.8%
0.006234
0.012143


8.1%
0.000735
0.006722
7.5%
0.008083
0.013976


8.8%
0.001430
0.007414
8.2%
0.010075
0.015952


9.6%
0.002179
0.008161
8.9%
0.012203
0.018064


10.3%
0.002983
0.008962
9.6%
0.014460
0.020306


11.0%
0.003838
0.009815
10.3%
0.016838
0.022669


11.8%
0.004745
0.010719
11.0%
0.019331
0.025146


12.5%
0.005701
0.011672
11.6%
0.021931
0.027732


13.2%
0.006704
0.012673
12.3%
0.024631
0.030417


14.0%
0.007754
0.013720
13.0%
0.027424
0.033197


14.7%
0.008848
0.014811
13.7%
0.030304
0.036064


15.4%
0.009984
0.015944
14.4%
0.033264
0.039012


16.2%
0.011161
0.017118
15.1%
0.036298
0.042035


16.9%
0.012377
0.018332
15.8%
0.039400
0.045126


17.6%
0.013629
0.019582
16.4%
0.042564
0.048281


18.4%
0.014917
0.020866
17.1%
0.045786
0.051493


19.1%
0.016237
0.022184
17.8%
0.049058
0.054757


19.9%
0.017588
0.023533
18.5%
0.052378
0.058069


20.6%
0.018968
0.024911
19.2%
0.055739
0.061423


21.3%
0.020375
0.026315
19.9%
0.059137
0.064815


22.1%
0.021806
0.027745
20.5%
0.062568
0.068241


22.8%
0.023260
0.029197
21.2%
0.066027
0.071695


23.5%
0.024734
0.030669
21.9%
0.069510
0.075175


24.3%
0.026227
0.032160
22.6%
0.073014
0.078675


25.0%
0.027735
0.033667
23.3%
0.076535
0.082194


25.7%
0.029258
0.035189
24.0%
0.080069
0.085725


26.5%
0.030792
0.036723
24.7%
0.083613
0.089268


27.2%
0.032337
0.038266
25.3%
0.087163
0.092817


27.9%
0.033889
0.039818
26.0%
0.090717
0.096370


28.7%
0.035447
0.041376
26.7%
0.094271
0.099924


29.4%
0.037009
0.042937
27.4%
0.097822
0.103476


30.1%
0.038573
0.044500
28.1%
0.101368
0.107023


30.9%
0.040136
0.046064
28.8%
0.104906
0.110563


31.6%
0.041697
0.047625
29.5%
0.108433
0.114092


32.4%
0.043254
0.049183
30.1%
0.111946
0.117608


33.1%
0.044805
0.050734
30.8%
0.115444
0.121109


33.8%
0.046349
0.052279
31.5%
0.118924
0.124592


34.6%
0.047883
0.053814
32.2%
0.122383
0.128055


35.3%
0.049405
0.055338
32.9%
0.125820
0.131496


36.0%
0.050916
0.056849
33.6%
0.129233
0.134913


36.8%
0.052411
0.058346
34.2%
0.132618
0.138303


37.5%
0.053891
0.059827
34.9%
0.135975
0.141665


38.2%
0.055354
0.061292
35.6%
0.139301
0.144997


39.0%
0.056798
0.062738
36.3%
0.142595
0.148296


39.7%
0.058223
0.064163
37.0%
0.145854
0.151561


40.4%
0.059626
0.065568
37.7%
0.149077
0.154790


41.2%
0.061007
0.066951
38.4%
0.152262
0.157981


41.9%
0.062364
0.068311
39.0%
0.155407
0.161134


42.6%
0.063698
0.069646
39.7%
0.158512
0.164245


43.4%
0.065006
0.070956
40.4%
0.161573
0.167313


44.1%
0.066289
0.072241
41.1%
0.164590
0.170338


44.9%
0.067545
0.073499
41.8%
0.167562
0.173316


45.6%
0.068774
0.074730
42.5%
0.170486
0.176248


46.3%
0.069976
0.075934
43.2%
0.173361
0.179130


47.1%
0.071150
0.077110
43.8%
0.176186
0.181963


47.8%
0.072296
0.078258
44.5%
0.178959
0.184744


48.5%
0.073414
0.079378
45.2%
0.181679
0.187472


49.3%
0.074504
0.080469
45.9%
0.184345
0.190146


50.0%
0.075566
0.081533
46.6%
0.186956
0.192765


50.7%
0.076600
0.082569
47.3%
0.189509
0.195326


51.5%
0.077607
0.083577
47.9%
0.192004
0.197829


52.2%
0.078586
0.084559
48.6%
0.194440
0.200273


52.9%
0.079540
0.085514
49.3%
0.196815
0.202656


53.7%
0.080468
0.086443
50.0%
0.199128
0.204977


54.4%
0.081371
0.087348
50.7%
0.201378
0.207235


55.1%
0.082251
0.088228
51.4%
0.203564
0.209429


55.9%
0.083108
0.089087
52.1%
0.205684
0.211557


56.6%
0.083943
0.089923
52.7%
0.207737
0.213618


57.4%
0.084759
0.090739
53.4%
0.209723
0.215611


58.1%
0.085556
0.091537
54.1%
0.211639
0.217536


58.8%
0.086335
0.092318
54.8%
0.213486
0.219389


59.6%
0.087100
0.093083
55.5%
0.215261
0.221172


60.3%
0.087850
0.093834
56.2%
0.216963
0.222881


61.0%
0.088589
0.094573
56.8%
0.218592
0.224517


61.8%
0.089319
0.095303
57.5%
0.220147
0.226079


62.5%
0.090041
0.096025
58.2%
0.221625
0.227564


63.2%
0.090757
0.096742
58.9%
0.223027
0.228972


64.0%
0.091471
0.097455
59.6%
0.224351
0.230302


64.7%
0.092183
0.098168
60.3%
0.225596
0.231553


65.4%
0.092898
0.098882
61.0%
0.226761
0.232724


66.2%
0.093616
0.099601
61.6%
0.227845
0.233813


66.9%
0.094342
0.100326
62.3%
0.228848
0.234820


67.6%
0.095077
0.101060
63.0%
0.229767
0.235744


68.4%
0.095824
0.101807
63.7%
0.230603
0.236584


69.1%
0.096586
0.102568
64.4%
0.231353
0.237338


69.9%
0.097366
0.103347
65.1%
0.232019
0.238007


70.6%
0.098166
0.104146
65.8%
0.232597
0.238589


71.3%
0.098989
0.104968
66.4%
0.233089
0.239083


72.1%
0.099838
0.105816
67.1%
0.233493
0.239489


72.8%
0.100716
0.106692
67.8%
0.233808
0.239806


73.5%
0.101625
0.107599
68.5%
0.234034
0.240033


74.3%
0.102568
0.108540
69.2%
0.234170
0.240169


75.0%
0.103547
0.109518
69.9%
0.234215
0.240215


75.7%
0.104566
0.110534
70.5%
0.234170
0.240170


76.5%
0.105627
0.111592
71.2%
0.234034
0.240033


77.2%
0.106731
0.112694
71.9%
0.233807
0.239804


77.9%
0.107882
0.113841
72.6%
0.233487
0.239483


78.7%
0.109082
0.115037
73.3%
0.233076
0.239070


79.4%
0.110332
0.116283
74.0%
0.232574
0.238565


80.1%
0.111634
0.117582
74.7%
0.231979
0.237967


80.9%
0.112990
0.118934
75.3%
0.231293
0.237277


81.6%
0.114402
0.120341
76.0%
0.230516
0.236495


82.4%
0.115872
0.121806
76.7%
0.229647
0.235622


83.1%
0.117399
0.123328
77.4%
0.228688
0.234658


83.8%
0.118986
0.124909
78.1%
0.227639
0.233604


84.6%
0.120633
0.126551
78.8%
0.226501
0.232459


85.3%
0.122341
0.128252
79.5%
0.225274
0.231226


86.0%
0.124110
0.130015
80.1%
0.223960
0.229905


86.8%
0.125940
0.131839
80.8%
0.222559
0.228497


87.5%
0.127831
0.133723
81.5%
0.221072
0.227002


88.2%
0.129783
0.135669
82.2%
0.219500
0.225423


89.0%
0.131795
0.137674
82.9%
0.217845
0.223760


89.7%
0.133867
0.139739
83.6%
0.216108
0.222015


90.4%
0.135998
0.141863
84.2%
0.214290
0.220188


91.2%
0.138186
0.144044
84.9%
0.212392
0.218282


91.9%
0.140430
0.146281
85.6%
0.210416
0.216297


92.6%
0.142729
0.148574
86.3%
0.208362
0.214235


93.4%
0.145081
0.150919
87.0%
0.206233
0.212097


94.1%
0.147485
0.153316
87.7%
0.204029
0.209884


94.9%
0.149938
0.155762
88.4%
0.201752
0.207597


95.6%
0.152439
0.158257
89.0%
0.199401
0.205237


96.3%
0.154985
0.160797
89.7%
0.196979
0.202804


97.1%
0.157576
0.163382
90.4%
0.194484
0.200300


97.8%
0.160209
0.166008
91.1%
0.191918
0.197724


98.5%
0.162882
0.168676
91.8%
0.189280
0.195075


99.3%
0.165595
0.171383
92.5%
0.186569
0.192354


100.0%
0.167181
0.172966
93.2%
0.183784
0.189557





93.8%
0.180923
0.186685





94.5%
0.177984
0.183733





95.2%
0.174963
0.180698





95.9%
0.171855
0.177577





96.6%
0.168656
0.174362





97.3%
0.165360
0.171047





97.9%
0.161957
0.167625





98.6%
0.158439
0.164086





99.3%
0.154795
0.160417





100.0%
0.154190
0.159809









In an embodiment, the ratio between the sag values at 75 percent point and at 25 percent point of the imaging-side surface of third lens element 5 satisfies the following condition:

5.0<sag8(75)/sag8(25)<7.0   (1)

where sag8(75) is the sag value at 75 percent point of the clear aperture of the imaging-side of the third lens element measured from the optical axis, and sag8(25) is the sag value at 25 percent point of the clear aperture of the imaging-side of the third lens element. In some embodiments, the ratio between the sag values at 75 percent point and at 25 percent point of the imaging-side surface of third lens element 5 in Equation (1) is preferably in a range from 5.5 to 6.5.

In an exemplary embodiment, the imaging-side surface of third lens element 5 has a sag at the 25 percent point from the optical axis of about 38 microns and a sag at the 75 percent point from the optical axis of about 245 microns. If the ratio in condition (1) exceeds the upper limit, the optical power of the third lens element and the lens system 300 may be reduced. If the ratio in condition (1) is smaller than the lower limit, the compactness of the lens system 200 (FIG. 2) may be affected.
Additionally, the object-side surface of fourth lens element 6 has a sag value at 100 percent point satisfying the following condition:

sag9(100)>167 microns   (2)

where sag9(100) is the sag value at 100 percent point of the clear aperture measured from the optical axis of the object-side surface of the fourth lens element (see Table 5 and FIG. 4).

Furthermore, the imaging-side surface of fourth lens element 6 provides the largest sag value at a certain percentage point of the effective radius. In an embodiment, the largest sag value is 235 microns at 75 percentage point of the efficient radius of the fourth lens element. That is, the imaging-side surface of the fourth lens element satisfies the following condition:

sag10(max)>235 microns   (3)

where sag10(max) denotes the highest sag value of the imaging-side surface of the fourth lens element.

If the imaging-side surface of the fourth lens element does not meet the condition (3), the lens system 200 of FIG. 2 may have astigmatism and aberration that exceeds the target design specifications. In some embodiments, the conditions (1), (2) and (3) allow the system to be constructed with a target total track length.
In an embodiment, first, second, third and fourth lens elements can be made of plastic or glass and have an Abbe number of about 56, 23, 56, and 56, respectively. In an embodiment, the lens system 200 satisfies the following design characteristics and conditions:

vd1−vd2>30;   (4)

0.5<d1avg/d2avg<0.9;   (5)

0.4<d3avg/d4avg<0.7   (6)

wherein vd1, vd2 are the respective Abbe number of the first and second lens elements, and d1avg, d2avg, d3avg, and d4avg are the respective average diameters of the first, second, third, and fourth lens elements. The average diameter is the sum of the object-side and imaging-side diameters of a lens element, divided by two.

In order to obtain a high-performance lens system which is suitable ofr mega-pixels imaging sensors, the range in Equation (6) may be narrower such as 0.45<d3avg/d4avg<0.65, or preferably 0.50<d3avg /d4avg<0.60.
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   (7)

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 filter and TTL is the total track length of the lens system. In some embodiments, the upper limit in Equation (7) may be smaller such as less than 0.35 or preferably than 0.3 to obtain a compacter 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 portrait distances. 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 fourth lens element is about 0.5 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.
The relative positions of the lens elements to each other contribute to good optical performance. In some embodiments, the air gaps satisfy the following inequities:

0<s1/s2<0.4   (8)

0<s3/s4<0.2   (9)

wherein s1 is the 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, and s4 is the air gap between the imaging-side surface of fourth lens element 6 and the object-side surface of optical filter 7, as shown in FIG. 3.

Further, the average diameter of each of the lens elements is related to its thickness as follows:

2<d1avg/t1<3;   (10)

4<d2avg/t2<6   (11)

3<d3avg/t3<4   (12)

8<d4avg/t4<10   (13)

wherein t1, t2, t3, and t4 are the respective thickness of the first, second, third, and fourth lens elements, and d1avg, d2avg, d3avg, and d4avg are the respective average diameters of the first, second, third, and fourth 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.)

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=Δh/h   (16)

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 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 is equal to a diagonal size 603 of the rectangular imaging sensor. 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 3.22 mm, so that the sensor image circle also has a diameter of 3.22 mm, and the maximum image circle has a diameter of 3.44 mm. In an embodiment, the lens system has a chief ray angle of less than 28° 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   (17)

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 3.22 mm and the total track length can be 3.10 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, and fourth lens elements arranged in order from an object side to an imaging side, each of the first, second, third, and fourth lens elements having an object side surface facing toward the object side, and an imaging side surface facing toward the imaging side, wherein,
30<vd1−vd2, wherein vd1and vd2are Abbe numbers of the first and second lens elements, respectively;
0.4<d3avg/d4avg <0.7, wherein d3avg and d4avg are average diameters of the third and fourth lens elements, respectively; and
a ratio of a sag at 5 percent point and a sag at 100 percent point of the imaging-side surface of the first lens element is in a range from -0.0082 to 0.0114.

2. The lens system of claim 1 where in a ratio of a sag at 6 percent point and a sag at 100 percent point of the imaging-side surface of the second lens element is in a range from -0.0025 to 0.01.

3. The lens system of claim 1 wherein the first, second, third, and fourth lens elements have air gaps therebetween and a ratio of a total air gap to a total track length is about 0.25 or less.

4. The lens system of claim 1 further satisfying the following equations:


0<s1/s2<0.4; and



0<s3/s4<0.2;

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 optical filter.

5. The lens system of claim 4 wherein the imaging-side surface of the fourth lens element has a maximum sag in a range of 235 microns to 240 microns at the proximity of a 75 percent point in relation to the optical axis.

6. The lens system of claim 1 wherein the imaging-side surface of the fourth lens element has a maximum sag greater than 235 microns.

7. The lens system of claim 1 wherein the lens system has a maximum chief ray angle (CRA) smaller than 28° .

8. The lens system of claim 1 wherein the lens system has a TV distortion smaller than 1.0 percent.

9. An imaging lens comprising first, second, third, and fourth lens elements arranged in order from an object side to an imaging side, each of the first, second, third, and fourth 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:
30<vd1−vd2, wherein vd1and vd2are Abbe numbers of the first and second lens elements, respectively;
0.5<d1avg/d2avg <0.9, wherein d1avg and d2avg are average diameters of the first and second lens elements, respectively; and
0.4<d3avg/d4avg <0.7, wherein d3avg and d4avg are average diameters of the third and fourth lens elements, respectively.

10. The lens system of claim 9 wherein a sag at 100 percent point of the maximum clear aperture of the imaging-side surface of the third lens element is equal to or greater than 300 microns.

11. The lens system of claim 9 wherein the first lens element has a ratio of average diameter to thickness in a range from 2 to 3.

12. The lens system of claim 9 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.

13. The lens system of claim 9 further comprising a relative illumination greater than 40.0 percent across a full diagonal size of an imaging sensor.

14. The lens system of claim 9 wherein a ratio of a sag at 5 percent point and a sag at 100 percent point of the imaging-side surface of the first lens element is in a range from −0.0082 to 0.0114.

15. The lens system of claim 14 wherein a sag at 100 percent point of the maximum clear aperture of the object-side surface of the fourth lens element is equal to or greater than 167 microns.