# Patent

## Title
Lens system

## Abstract

A lens system includes a positive refractive power first lens, a positive refractive power second lens, and a negative refractive power third lens in that order from the object side of the lens system. Wherein the lens system satisfies the following conditions: (1) 0.25<R1F/F<0.5; (2) R2F<R2R<0; and (3) 0<R1F<R1R, wherein, R1R and R1F are radius of curvature of object side surface and image side surface of the first lens respectively, R2R and R2F are radius of curvature of object side surface and image side surface of the second lens respectively, and F is a focal length of the lens system.

## Background
TECHNICAL FIELD
The present invention relates to a lens system and, particularly, to a compact lens system having a small number of lens components and a short overall length.
DESCRIPTION OF RELATED ART
Conventionally, there is a technical field of lenses where a short overall length is demanded for use in lens modules for image acquisition that are mounted in relatively thin equipment, such as simple digital cameras, webcams for personal computers, and portable imaging systems in general. In order to satisfy this demand, previous imaging lenses have been formed using a one-piece lens construction. Because the electronic image sensing chips previously used with the lens modules were compact and had low resolution, maintaining a small image size on the image sensing chips and miniaturizing the lens systems with a small number of lens components was a priority. In previous arrangements, even with one-piece lens construction, aberrations were acceptable and the incident angle of light rays onto the image sensing chip was not so large as to be a problem.
However, in recent years, because the resolution and the size of the image sensing chips have increased, aberrations occurring in one-piece lenses are too large to achieve the desired optical performance. Therefore, it has become necessary to develop a lens system with a short overall length and with an optical performance that matches image sensing chips having enhanced resolution and size.
What is needed, therefore, is a lens system with a short overall length and with relatively good optical performance.
SUMMARY
In accordance with one present embodiment, a lens system includes a positive refractive power first lens, a positive refractive power second lens, and a negative refractive power third lens in that order from the object side of the lens system. Wherein the lens system satisfies the following conditions:

0.25<R1F/F<0.5;  (1)

R2F<R2R<0; and  (2)

0<R1F<R1R,  (3)

wherein, R1R is the radius of curvature of a surface of the first lens facing the image side of the lens system, R1F is the radius of curvature of the surface of the first lens facing the object side of the lens system, R2R is the radius of curvature of a surface of the second lens facing the image side of the lens system, R2F is the radius of curvature of the surface of the second lens facing the object side of the lens system, and F is a focal length of the lens system.




BRIEF DESCRIPTION OF THE DRAWING
Many aspects of the present lens system can be better understood with reference to the following drawings. The components in the drawing are not necessarily drawn to scale, the emphasis instead being placed upon clearly illustrating the principles of the present lens system. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.
FIG. 1 is a schematic view of a lens system in accordance with an embodiment.
FIGS. 2-4 are graphs respectively showing spherical aberration, field curvature and distortion for a lens system in accordance with a first exemplary embodiment of the present invention.
FIGS. 5-7 are graphs respectively showing spherical aberration, field curvature and distortion for a lens system in accordance with a second exemplary embodiment of the present invention.



DETAILED DESCRIPTION OF THE EMBODIMENTS
Embodiments will now be described in detail below, with reference to the drawings.
Referring to FIG. 1, a lens system 100, according to an embodiment, is shown. The lens system 100 includes a positive refractive power first lens 10, a positive refractive power second lens 20, and a negative refractive power third lens 30 in that order from the object side of the lens system 100. The lens system 100 can be used in digital cameras, mobile phones, personal computer cameras and so on. The lens system 100 can be used for capturing images by disposing an image sensor at an image plane 40 of the lens system 100.
In order that the lens system 100 has a short overall length and excellent optical performance, the lens system 100 satisfies the following conditions:

0.25<R1F/F<0.5;  (1)

R2F<R2R<0; and  (2)

0<R1F<R1R,  (3)

wherein, R1R is the radius of curvature of a surface of the first lens 10 facing the image side of the lens system 100, R1F is the radius of curvature of the surface of the first lens 10 facing the object side of the lens system 100, R2R is the radius of curvature of a surface of the second lens 20 facing the image side of the lens system 100, R2F is the radius of curvature of the surface of the second lens 20 facing the object side of the lens system 100, and F is a focal length of the lens system 100. The first condition (1) is for limiting the overall length of the lens system 100. If the value of the R1F/F is bigger than 0.5, the lens system 100 cannot achieve a short overall length. If the value of the R1F/F is smaller than 0.25, the field curvature and spherical aberration caused by the first lens 10 will be difficult to compensate for. The second condition (2), is for limiting the direction of the second lens 20 in the lens system 100 in order to compensate lateral chromatic aberration, spherical aberration and coma caused by the first lens 10. The third condition (3) is for limiting the overall length of the lens system 100 and making the first lens 10 having a positive refractive power for compensating aberrations caused by the third lens 30. In the present embodiment, the first lens 10 is a meniscus-shaped lens with a convex surface facing the object side of the lens system 100. Preferably, the two surfaces of the first lens 10 are aspherical. The second lens 20 is a meniscus-shaped lens with a convex surface facing the image side of the lens system 100. Preferably, the two surfaces of the second lens 20 are aspherical.

Preferably, the first lens 10 also satisfies the following condition:

0.3<(R1R−R1F)/(R1F+R1R),  (4)

The fourth condition (4) is for limiting the relationship between the radius of curvature of two surfaces of the first lens 10 in order to correct distortion and astigmation of the lens system 100.

Preferably, the lens system 100 also satisfies the following condition:

R3F>0;  (5)

0.7<F1/F<1.5,  (6)

wherein, R3F is the radius of curvature of the surface of the third lens 30 facing the object side of the lens system 100, and F1 is a focal length of the first lens 10. Conditions (5) and (6) together limit the incident angle of the incident light on the image plane 40 to less than 25° and also can correct distortion of the lens system 100. Further, the sixth condition (6) is for correcting many types of aberrations, especially spherical aberration, of the lens system 100 and limiting the overall length of the lens system 100. If the value of the F1/F is bigger than 1.5, the refractive power of the first lens 10 will be too small and the distortion of the lens system 100 will be difficult to correct. The third lens 30 is a meniscus-shaped lens with a convex surface facing the object side of the lens system 100. Preferably, the two surfaces of the third lens 30 are aspherical.

Also, in order to appropriately correct the chromatic aberration of the lens system 100, the Abbe constant v2 of the second lens 20 preferably satisfies the following condition:

45<v2<60.  (7)

The lens system 100 further includes an aperture stop 50 and a infrared filter 60. The aperture stop 50 is arranged between the first lens 10 and the second lens 20 in order to reduce light flux into the second lens 20. For further cost reduction, the aperture stop 50 is preferably formed directly on the surface of the first lens 10 facing the image side of the lens system 100. In practice, a portion of the surface of the first lens 10 through which light rays should not be transmitted is coated with an opaque material, such as black material, which functions as the aperture stop 50. The infrared filter 60 is arranged between the third lens 30 and the image plane 40 for filtering infrared rays coming into the lens system 100.
Further, the first lens 10, the second lens 20, and the third lens 30 can be made from a resin or a plastic, which makes their manufacture relatively easy and inexpensive.
Examples of the system will be described below with reference to FIGS. 2-7. It is to be understood that the invention is not limited to these examples. The following are symbols used in each exemplary embodiment.

    FNo: F number
    2ω: field angle
    R: radius of curvature
    d: distance between surfaces on the optical axis of the system
    Nd: refractive index of lens
    v: Abbe constant


In each example, both surfaces of the first lens 10, both surfaces of the second lens 20, and both surfaces of the third lens 30 are aspheric. The shape of each aspheric surface is determined by expression 1 below. Expression 1 is based on a Cartesian coordinate system, with the vertex of the surface being the origin, and the optical axis extending from the vertex being the x-axis.




  
    
      
        x
        =
        
          
            
              ch
              2
            
            
              1
              +
              
                
                  1
                  -
                  
                    
                      (
                      
                        k
                        +
                        1
                      
                      )
                    
                    ⁢
                    
                      c
                      2
                    
                    ⁢
                    
                      h
                      2
                    
                  
                
              
            
          
          +
          
            ∑
            
              
                A
                i
              
              ⁢
              
                h
                i
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        1
      
    
  




wherein, h is a height from the optical axis to the surface, c is a vertex curvature, k is a conic constant, and Ai are i-th order correction coefficients of the aspheric surfaces.

EXAMPLE 1
Tables 1 and 2 show lens data of Example 1.











TABLE 1





Lens system 100
R (mm)
d (mm)
Nd
ν



















Object side surface of the first lens 10
1.142824
0.663186
1.54
56


Image side surface of the first lens 10
2.897551
0.04947936
1.54
56


Aperture stop 50
infinite
0.6687439


Object side surface of the second lens 20
−1.20516
0.8278974
1.53
56


Image side surface of the second lens 20
−0.81768
0.1
1.53
56


Object side surface of the third lens 30
14.01444
0.5215678
1.53
56


Image side surface of the third lens 30
1.369028
0.15
1.53
56


Object side surface of the infrared filter 60
infinite
0.3
1.5168
64.16734


Image side surface of the infrared filter 60
Infinite
0.41415
1.5168
64.16734


















TABLE 2









Surface














Object side
Image side
Object side
Image side
Object side




surface of the
surface of the
surface of the
surface of the
surface of the
Image side



first lens 10
first lens 10
second lens 20
second lens 20
third lens 30
surface of the third lens 30

















Aspherical
A2 = 0.5734400
A2 = 10.20508
A2 = 0.6121418
A2 = −0.4658288
A2 = −6687.413
A2 = −10.4658


coefficient
A4 = −0.038082183
A4 = −0.01524513
A4 = −0.19334272
A4 = 0.095586872
A4 = −0.24715187
A4 = −0.16668525



A6 = 0.26617946
A6 = 0.17622633
A6 = −0.71128885
A6 = −0.003293142
A6 = 0.1682316
A6 = 0.076842457



A8 = −0.27003972
A8 = −1.138302
A8 = 0.46720762
A8 = −0.005742858
A8 = −0.04475158$$
A8 = −0.28162178



A10 = 0.47036051
A10 = 1.8438515
A10 = −1.3879106
A10 = −0.17914532
A10 = 0.004060038
A10 = 0.005731356



A12 = −0.4519263
A12 = 2.6236165
A12 = 0.32719325
A12 = 0.26183762
A12 = 0.000101020
A12 = −0.000483753









FIGS. 2-4 are graphs of aberrations (spherical aberration, field curvature, and distortion) of the lens system 100 of Example 1. In FIG. 2, the curves c, d, and f show spherical aberration of the lens system 100 corresponding to three types of light with wavelengths of 656.3 nm, 587.6 nm, and 435.8 nm respectively. Generally, the spherical aberration of lens system 100 is limited to a range from −0.04 mm to 0.04 mm, the field curvature of the lens system 100 is limited to a range from −0.05 mm to 0.05 mm, and the distortion of the lens system 100 is limited to a range from −5% to 5%.
EXAMPLE 2
Tables 3 and 4 show lens data of Example 2.











TABLE 3





Lens system 100
R (mm)
d (mm)
Nd
ν



















Object side surface of the first lens 10
0.956381
0.704587
1.54
56


Image side surface of the first lens 10
1.847207
0.5423625
1.54
56


Object side surface of the second lens 20
−1.2
0.8836055
1.53
56


Image side surface of the second lens 20
−0.96075
0.1
1.53
56


Object side surface of the third lens 30
−11.7461
0.7269722
1.53
56


Image side surface of the third lens 30
2.645506
0.1
1.53
56


Object side surface of the infrared filter 60
infinite
0.3
1.5168
64.16734


Image side surface of the infrared filter 60
Infinite
0.2800699
1.5168
64.16734


















TABLE 4









Surface














Object side
Image side
Object side
Image side
Object side
Image side



surface of the
surface of the
surface of the
surface of the
surface of the
surface of the



first lens 10
first lens 10
second lens 20
second lens 20
third lens 30
third lens 30

















Aspherical
A2 = 0.358382
A2 = 9.366716
A2 = 1.925198
A2 = −0.6564744
A2 = −103.1109
A2 = −16.08475


coefficient
A4 = −0.03347
A4 = −0.02345
A4 = −0.19579
A4 = −0.02902
A4 = −0.15472
A4 = −0.11998



A6 = 0.074825
A6 = 0.11491001
A6 = −0.0830489
A6 = 0.03712748
A6 = 0.12202466
A6 = 0.03396535



A8 = −0.39767
A8 = −1.50568
A8 = −0.94961
A8 = −0.06658
A8 = −0.0393
A8 = −0.00901



A10 = 0.761948
A10 = 2.34376315
A10 = 0.813157
A10 = −0.01564
A10 = 0.005499
A10 = 0.001836



A12 = −0.73374
A12 = 2.133353
A12 = −1.146362
A12 = 0.053667
A12 = −0.00025
A12 = −0.00021









FIGS. 5-7 are graphs of aberrations (spherical aberration, field curvature, and distortion) of the lens system 100 of Example 1. In FIG. 5, the curve c, d, and f show spherical aberration of the lens system 100 corresponding to three types of light with wavelengths of 656.3 nm, 587.6 nm, and 435.8 nm respectively. Generally, the spherical aberration of lens system 100 is limited to a range from −0.04 mm to 0.04 mm, the field curvature of the lens system 100 is limited to a range from −0.05 mm to 0.05 mm, and the distortion of the lens system 100 is limited to a range from −5% to 5%.
As seen in the above-described examples, the distortion of the lens system 100 can also be limited to a range from −5% to 5% when keeping the field angle of the lens system bigger than 60°. The overall length of the lens system 100 is small, and the system 100 appropriately corrects fundamental aberrations.
While certain embodiments have been described and exemplified above, various other embodiments will be apparent to those skilled in the art from the foregoing disclosure. The present invention is not limited to the particular embodiments described and exemplified but is capable of considerable variation and modification without departure from the scope of the appended claims.

## Claims

1. A lens system comprising, in order from the object side:
a positive refractive power first lens;
a positive refractive power second lens; and
a negative refractive power third lens, the third lens being a meniscus-shaped lens with a convex surface facing the object side of the lens system, wherein the lens system satisfies the following conditions:


0.25<R1F/F<0.5  (1);



R2F<R2R<0  (2);



0<R1F<R1R  (3);



R3F>O  (4);



0.7<F1/F<1.5  (5); and



45<v2<60,



wherein, R1R is the radius of curvature of a surface of the first lens facing the image side of the lens system, R1F is the radius of curvature of the surface of the first lens facing the object side of the lens system, R2R is the radius of curvature of a surface of the second lens facing the image side of the lens system, R2F is the radius of curvature of the surface of the second lens facing the object side of the lens system, R3F is the radius of curvature of the surface of the third lens facing the object side of the lens system, F1 is a focal length of the first lens, F the focal length of the lens system, and v2 is the Abbe constant of the second lens.

2. The lens system as claimed in claim 1, wherein the following condition is satisfied: 0.3<(R1R−R1F)/(R1F+R1R).

3. The lens system as claimed in claim 1, wherein the lens system comprises an aperture stop arranged between the first lens and the second lens.

4. The lens system as claimed in claim 1, wherein the aperture stop is formed directly on the surface of the first lens facing the image side of the lens system.

5. The lens system as claimed in claim 4, wherein the aperture stop is formed by coating a peripheral portion of the surface of the first lens using an opaque material.

6. The lens system as claimed in claim 1, wherein the lens system further comprises an infrared filter arranged between the third lens and the image plane.

7. The lens system as claimed in claim 1, wherein the first lens is a meniscus-shaped lens with a convex surface facing the object side of the lens system.

8. The lens system as claimed in claim 1, wherein the second lens is a meniscus-shaped lens with a convex surface facing the image side of the lens system.

9. The lens system as claimed in claim 1, wherein each of the first lens, the second lens, and the third lens is an aspherical lens.