Abstract:
A lens system is particularly designed for use in an image reading device, essentially including three lenses elements, wherein two or three of them are plastic lenses.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a triplet lens system constructed with glass and plastic lenses. Although not limited thereto, it is particularly suitable to lens systems for being used with an image reading device. 
     2. Description of the Related Art 
     An image reading device generally consists of a glass lens system, but the glass lens system has its disadvantage of high manufacturing cost that refrains from number of elements of glass lenses. In lower cost without losing resolution, spherical glass lenses with three elements are widely used. Whereas aberration still exists and cannot be completely removed by only using three-element-spherical-glass lenses due to its limited controllable factors. Moreover, the field angle to an optical system may get larger as the whole system becomes smaller. As the field angle gets larger, it is more difficult to get rid of the aberration. In addition, high resolution is maintained by reducing the aperture size though incurring insufficient lightness of the lens system and lower diffractive limit from smaller size of the aperture. Therefore, the manufacturing cost, the field angle, the resolution, the illumination, and the diffractive limit become trade-off variables in the optical design. 
     The use of the plastic lenses may be considered as a solution to the above-mentioned problems. 
     First of all, the plastic lens made by injection molding of an injection machine is considered to decrease the cost, easier to be produced into aspheric surface or diffractive surface. Unlike the spherical surface, the aspheric and diffractive surfaces have more controllable factors than the spherical surface to eliminate the image aberration and chromatic aberration so as to improve the resolution and to uplift the field angle. Moreover, the aperture can be larger so as to resolve the illumination and diffractive limit problems. 
     Second, the use of plastic lens can create new lens layout that differ with common triplet lens system. Usually, a lens system with three elements is suggested positioning with positive-negative-positive allocation, or called Cook Triplet System. In such lens system, position of lenses has the following three types: the first lens with forwarded convex surface, positive meniscus or bi-convex lens; the second lens with bi-concave surface; the third lens with bi-convex surface. 
     During the manufacturing of the glass lens, it is not easy to control the centering error. Considering the cost of production, in design of the lens, the curvature of the two sides of the lens cannot be too close. The plastic lens is made of injection so that it is easy to control the centering error of the meniscus lens. At the same time, during development of the plastic mold, the meniscus lens can reach a precision better than that of glass lens, thereby enhancing the resolution. Therefore, the meniscus positive or negative lens can be adapted to co-operate with an aspherical or diffractive surface so as to obtain a greater field angle. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the present invention, the main objective of this invention is to completely resolve aberration by means of applying more than two plastic lenses in a three-element lens system. 
     In order to achieve the primary objective, the lens system according to a first embodiment of the present invention uses a positive-negative-positive arrangement. The first lens uses a positive meniscus plastic lens instead of the positive meniscus glass lens in the prior art. The second lens uses a forward concave surface and negative meniscus plastic lens instead of the bi-concave glass lens in the prior art. The third lens uses a forward concave surface and positive meniscus glass lens instead of the bi-convex glass lens in the prior art. At least one aspheric surface is mounted on one of the plastic lenses, and a diffractive surface is mounted on the first lens. The focal length of the lens system and the plastic lenses satisfy the following equation: 
     
       
         0.2&lt;| f   2   /f   1 |&lt;0.7  [1] 
       
     
     
       
         0.2&lt;| f   2   /f   s |&lt;0.6  [2] 
       
     
     wherein, f 1  is the focal length of the first lens, f 2  is the focal length of the second lens, and f s  is the focal length of the optical lens system. 
     The reasons for applying the plastic-plastic-glass arrangement are explained as follows. 
     In the so-called “Cook Triplet System”, the focus of the third lens is desired to be shorter than that of the first lens. In other words, it is desirable that the refractive rate of the third lens is higher than that of the first lens for facilitating the design. In addition, it is easier to find a glass material with a high refractive index so that the plastic material is to be applied in the first lens. 
     The first lens is made of plastic material in that the plastic material is easier to be made into an aspheric or a diffractive surface so that it has a greater ability to resolve the aberration. Relatively, in addition to be provided with a bi-concave shape, the second lens may also be designed to have a meniscus shape so as to increase the precision of the plastic lens, thereby enhancing the image quality. Equation [1] and equation [2] are thus derived for resolving the aberration problem. It is desired that the first lens has a higher Abbe-number so that the diffractive surface was designed to be mounted in the first lens for improving the chromatic aberration. 
     The lens system according to a second embodiment of the present invention is the opposite case of the first embodiment. Because the allocation of the lenses was reversed, the relationship between the focal length of the second and the third lenses, and the relationship between the focal length of the second lens and the whole optical system are changed and should to satisfy the following condition. 
     
       
         0.4&lt;| f   2   /f   3 |&lt;0.8  [3] 
       
     
     
       
         0.2&lt;| f   2   /f   s |&lt;0.6  [4] 
       
     
     wherein, f 2  is the focal length of the second lens, f 3  is the focal length of the third lens, and f s  is the focal length of the whole optical system. 
     The lens system according to a third embodiment of the present invention uses a positive-negative-positive arrangement, and all of the lenses are made of plastic. A diffractive surface is allocated in the second lens, and the aspheric surfaces are allocated in the plastic lenses. The focal length of the second lens and the whole lens system should to satisfy the following equation: 
     
       
           |f   2   /f   s |&lt;0.6  [5] 
       
     
     wherein, f 2  is the focal length of the second lens, f s  the focal length of the whole optical system. 
     In the equation [5], the aberration problem can be easily rectified. Because the kinds of the optical plastic material are limited, the diffractive surface is used to reinforce the capability of chromatic aberration reduction. 
     Further benefits and advantages of the present invention will become apparent after a careful reading of the detailed description with appropriate reference to the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a front plan view of a lens system in accordance with a first embodiment of the present invention; 
     FIG. 2 shows a spherical aberration curve of the first embodiment as shown in FIG. 1; 
     FIG. 3 shows a astigmatism curve of the first embodiment as shown in FIG. 1; 
     FIG. 4 shows a distortion curve of the first embodiment as shown in in FIG. 1; 
     FIG. 5 is a front plan view of a lens system in accordance with a second embodiment of the present invention; 
     FIG. 6 shows a spherical aberration curve of the second embodiment as shown in FIG. 5; 
     FIG. 7 shows a astigmatism curve of the second embodiment as shown in FIG. 5; 
     FIG. 8 shows a distortion curve of the second embodiment as shown in FIG. 5; 
     FIG. 9 is a front plan view of a lens system in accordance with a third embodiment of the present invention; 
     FIG. 10 shows a spherical aberration curve of the third embodiment as shown in FIG. 9; 
     FIG. 11 shows a astigmatism curve of the third embodiment as shown in FIG. 9; and 
     FIG. 12 shows a distortion curve of the third embodiment as shown in FIG.  9 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to the drawings and initially to FIGS. 1-4, in accordance with a first embodiment of the present invention, the optical lens system  100  comprises three juxtaposed lenses  10 ,  20  and  30 . The first lens  10  is a positive lens made of plastic having a front side formed with a convex surface S 1  and a rear side formed with a concave surface S 2 . The second lens  20  is a negative lens made of plastic having a front side formed with a concave surface S 3  and a rear side formed with a convex surface S 4 . The third lens  30  is a positive lens made of glass having a front side formed with a concave surface S 5  and a rear side formed with a convex surface S 6 . Aspheric surfaces were built on the lenses  10  and  20 , and a diffractive surface is mounted on lens  10 . This optical system includes two plate glasses  40  and  50  respectively located at its front and rear sides, which both are ineffective to the focal length of the lens system. 
     The equation for aspheric surface is expressed as below: 
     
       
           X ( Y )=( Y   2   /R )/(1+sqrt(1−(1+ K )×( Y/R ) 2 ))+ A   4   ×Y   4   +A   6   ×Y   6 + . . .   [6] 
       
     
     Wherein, 
     X(Y) is the distance along the optical axis at the height from the optical axis Y. 
     Y is the height from the optical axis. 
     K is the conic coefficient. 
     A 4 , A 6 , . . . , are the aspheric coefficients of 4 th , 6 th , . . . order. 
     The equation for a phase difference of the diffractive surface is expressed as below: 
     
       
           Ph ( Y )=2×π/( WL )×(C 1   ×Y   2   +C   2   ×Y   4 +. . . )  [7] 
       
     
     Where, 
     Ph(Y) is the phase difference. 
     WL is the reference wavelength. 
     Y is the height from the optical axis. 
     C 1 , C 2 , . . . is the aspheric phase coefficient of 2 nd , 4 th , . . . order. 
     Table 1 shows a demonstrated example of the first embodiment. 
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 The first demonstrated example of Embodiment I. 
               
             
          
           
               
                 Surface 
                 Radius 
                 Thickness 
                 Index 
                 V number 
                 Notes 
               
               
                   
               
               
                 OBJ 
                 Infinity 
                  0.000 
                   
                   
                   
               
               
                   
                 Infinity 
                  3.000 
                 1.517 
                 64.2 
                 Platen Glass 
               
               
                   
                 Infinity 
                 316.489 
               
               
                 S1 
                   4.650 
                  1.616 
                 1.492 
                 57.4 
                 Aspheric 
               
               
                 S2 
                   7.361 
                  0.665 
                   
                   
                 Diffractive/Aspheric 
               
               
                 STO 
                 Infinity 
                  0.996 
               
               
                 S4 
                 −4.512 
                  1.000 
                 1.585 
                 29.9 
                 Aspheric 
               
               
                 S5 
                 −16.038  
                  0.521 
               
               
                 S6 
                 −16.689  
                  1.502 
                 1.773 
                 49.6 
               
               
                 S7 
                 −6.853 
                  26.224 
               
               
                   
                 Infinity 
                  0.700 
                 1.517 
                 64.2 
                 Sensor cover glass 
               
               
                   
                 Infinity 
                  1.300 
               
               
                 IMG 
                   
                  −0.025   
               
               
                   
               
               
                 Notes  
               
               
                 1. System focal length, fs = 27.70 mm, NA = 0.0714, HFOV = 18.62 degree  
               
               
                 G1 focal length, f1 = 21.41 mm  
               
               
                 G2 focal length, f2 = −11.00 mm  
               
               
                 |f2/f1| = 0.514; |f2/fs| = 0.397  
               
               
                 2. Coefficients for the aspheric surface S1:  
               
               
                 K = 1.5538  
               
               
                 3. Coefficients for the diffractive/aspheric surface S2:  
               
               
                 C1 = 7.5401B-5, C2 = −4.3112E-5  
               
               
                 K = 8.3749  
               
               
                 4. Coefficients for the aspheric surface S3:  
               
               
                 A4 = −1.0641E-3, A6 = −1.1197E-4  
               
             
          
         
       
     
     Referring to FIG. 2, it shows the spherical aberration curve of the first embodiment. 
     Referring to FIG. 3, it shows the astigmatism curve of the first embodiment. 
     Referring to FIG. 4, it shows the distortion curve of the first embodiment. 
     Referring to FIGS. 5-8, in accordance with a second embodiment of the present invention, the optical lens system  101  comprises three juxtaposed lenses  11 ,  21  and  31 . The first lens  11  is a positive lens made of glass. The second lens  21  is a negative lens made of plastic having a front side formed with a convex surface S 3  and rear side formed with a concave surface S 4 . The third lens  31  is a positive lens made of plastic having a rear side formed with a convex surface S 6 . Aspheric surfaces are built on the lenses  21  and  31 , and a diffractive surface is mounted on the lens  31 . This optical system includes two plate glasses  41  and  51  respectively located at its front and rear sides, which both are ineffective to the focal length of the lens system. 
     The equation for aspheric surface is expressed as equation [6], and the equation of phase difference of diffractive surface is expressed as equation [7]. 
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 The first demonstrated example of Embodiment II. 
               
             
          
           
               
                 Surface 
                 Radius 
                 Thickness 
                 Index 
                 V number 
                 Notes 
               
               
                   
               
               
                 OBJ 
                 Plano 
                 0.000 
                   
                   
                   
               
               
                   
                 Plano 
                 3.000 
                 1.517 
                 64.2 
                 Platen Glass 
               
               
                   
                 Plano 
                 316.985  
               
               
                 S1 
                 8.725 
                 1.424 
                 1.773 
                 49.6 
               
               
                 S2 
                 22.661  
                 0.477 
               
               
                 S3 
                 6.722 
                 1.000 
                   
                   
                 Aspheric 
               
               
                 S4 
                 3.405 
                 0.895 
                 1.585 
                 29.9 
                 Aspheric 
               
               
                 STO 
                 Plano 
                 0.900 
               
               
                 S5 
                 −6.876   
                 1.603 
                 1.492 
                 57.4 
                 Diffractive/Aspheric 
               
               
                 S6 
                 −4.437   
                 25.733  
                   
                   
                 Aspheric 
               
               
                   
                 Plano 
                 0.700 
                 1.517 
                 64.2 
                 Sensor cover glass 
               
               
                   
                 Plano 
                 1.300 
               
               
                 IMG 
                   
                 −0.012   
               
               
                   
               
               
                 Notes  
               
               
                 1. System focal length, fs = 27.85 mm, NA = 0.0714, HFOV = 18.51 degree  
               
               
                 G2 focal length, f2 = −13.18 mm  
               
               
                 G3 focal length, f3 = 20.46 mm  
               
               
                 |f2/f3| = 0.644; |f2/fs| = 0.473  
               
               
                 2. Coefficients for the aspheric surface S3:  
               
               
                 A4 = −1.7802E-3, A6 = 6.3932E-5  
               
               
                 3. Coefficients for the aspheric surface S4:  
               
               
                 A4 = −4.0522E-3, A6 = −7.6849E-5  
               
               
                 4. Coefficients for the diffractive/aspheric surface S5:  
               
               
                 C1 = −4.5259E-4, C2 = 2.7731E-5, C3 = −7.6811E-6  
               
               
                 A4 = −1.6987E-3, A6 = −1.3393E-4  
               
               
                 5. Coefficients for the aspheric surface S6:  
               
               
                 K = 1.359  
               
             
          
         
       
     
     Referring to FIG. 6, it shows the spherical aberration curve of the first embodiment. Referring to FIG. 7, it shows th e astigmatism curve of the first embodiment. Referring to FIG. 8, it shows the distortion curve of the first embodiment. 
     Referring to FIGS. 9-12, in accordance with a third embodiment of the present invention, the optical lens system  102  comprises three juxtaposed plastic lenses  12 ,  22  and  32 . The first lens  12  is a positive meniscus lens. The second lens  22  is a bi-concave meniscus lens. The third lens  32  is a positive lens. This lens system includes a diffractive surface. The equation for aspheric surface is expressed as equation [6], and the equation of phase difference of diffractive surface is expressed as equation [7]. 
     Table 3 shows the demonstrated example of the third Embodiment. 
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 The first demonstrated example of Embodiment III. 
               
             
          
           
               
                 Surface 
                 Radius 
                 Thickness 
                 Index 
                 V number 
                 Notes 
               
               
                   
               
               
                 OBJ 
                 Plano 
                 2963.85  
                   
                   
                   
               
               
                 S1 
                  7.3902 
                   3.450 
                 1.492 
                 57.4 
               
               
                 S2 
                 23.2662 
                   0.769 
               
               
                 S3 
                 −20.2089   
                   0.700 
                 1.492 
                 57.4 
                 Diffractive/Aspheric 
               
               
                 S4 
                  6.6084 
                   1.380 
               
               
                 S5 
                 13.0307 
                   1.380 
                 1.492 
                 57.4 
               
               
                 S6 
                 −16.5707   
                   0.17  
               
               
                 STO 
                 Plano 
                  28.294 
               
               
                 IMG 
                   
                   0.006 
               
               
                   
               
               
                 Notes  
               
               
                 1. System focal length, fs = 34.02 mm, NA = 0.089, HFOV = 30.6 degree  
               
               
                 G2 focal length, f2 = −10.48 mm  
               
               
                 |f2/fs| = 0.308  
               
               
                 2. Coefficients for the diffractive/aspheric surface S3:  
               
               
                 C1 = −2.1784E-3, C2 = 1.3305E-4, C3 = −4.8233E-6  
               
               
                 K = −7.561, A4 = 1.5854E-4, A6 = −5.0573E-6, A8 = −6.1205E-8  
               
             
          
         
       
     
     Referring to FIG. 10, it shows the spherical aberration curve of the first embodiment. Referring to FIG. 11, it shows the astigmatism curve of the first embodiment. Referring to FIG. 12, it shows the distortion curve of the first embodiment. 
     It should be clear to those skilled in the art that further embodiments may be made without departing from the scope of the present invention.