Abstract:
A lens system ( 46 ) that can be used in a digital camera includes, in sequence, a first lens element ( 20 ), a second lens element ( 30 ) and a third lens element ( 40 ). The first lens element is biconvex and includes a first spherical surface ( 22 ) and a second spherical surface ( 24 ). The second lens is concavo-convex and includes a first aspheric surface ( 32 ) and a second aspheric surface ( 34 ). The first aspheric surface is a diffractive surface. The third lens includes a wave-shaped third aspheric surface ( 42 ) and a wave-shaped fourth aspheric surface ( 44 ). The lens has a compact volume and provides stable imaging performance and good image quality.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention generally relates to lenses for devices such as digital cameras and, more particularly, to a lens that has lens elements with a diffractive surface. 
   2. Discussion of the Related Art 
   Digital cameras utilizing high-resolution electronic imaging sensors typically require high resolution optical components such as lenses. In addition, the lenses generally must be very compact, so that they can be incorporated into devices such as palm-sized computers, cellular telephones, and the like. 
   Lenses for digital cameras generally have several individual lens elements. The lens elements are typically spherical and usually create spherical aberration. Chromatic aberration, coma aberration, distortion, and field curvature are also common optical aberrations that occur in the imaging process of a typical lens (http://www.astrosurf.org/lombry/report-aberrations2.htm). A large number of lens elements are generally required in order to balance the inherent optical aberrations. Lenses having a large number of lens elements tend to be large, heavy, and expensive to manufacture. The manufacturing costs involve both significant material costs and the cost of assembling and mounting the lens elements into a lens cell. 
   Further, conventional lenses commonly use one or more aspheric lens elements, each of which has one or two non-spherical surfaces. The aspheric lens elements are made of plastic or glass. Aspheric plastics lens elements may be produced by means of plastic injection molding and are therefore relatively inexpensive. However, the optical characteristics of most plastic lens elements change with changes in temperature and humidity, such as when the digital camera is used outdoors on very hot or very cold days. Furthermore, the hardness of optical plastic material is lower than that of an optical glass material. The surfaces of such lens elements are easily scraped or abraded, which affects the precision of the imaging. In comparison, glass aspheric lens elements have good optical properties and are less easily scraped or abraded. However, glass aspheric lenses generally cannot be easily produced by traditional glass grinding and polishing techniques. In addition, glass lens elements are heavier than plastic lens elements and thus go against the trend toward lightweight digital cameras. 
   A typical lens having both spherical lens elements and aspheric lens elements is disclosed in China Patent Number 02258384. The lens includes a first spherical lens element, a second spherical lens element, and a third lens element. The first lens element and the second lens element are made of glass. The third lens element has two aspheric surfaces and is made of plastic. Although the lens may satisfy the requirements for imaging, the resolution of the lens is low and may affect the image performance. 
   Accordingly, what is needed is a lens system for a digital camera which is compact and which provides good imaging quality. 
   SUMMARY 
   A lens system for a digital camera of a preferred embodiment consecutively includes a first lens element, a second lens element, and a third lens element. The first lens element is biconvex and has a first spherical surface and a second spherical surface. The second lens element is concavo-convex and includes a first aspheric surface and a second aspheric surface. The first aspheric surface is a diffractive surface. A third lens element has a third aspheric surface and a fourth aspheric surface. The third aspheric surface and the fourth aspheric surface are wave-shaped. 
   Other objects, advantages and novel features of the present lens system will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Many aspects of the lens system can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, the emphasis instead being placed upon clearly illustrating the principles of the present lens system and its potential applications. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
       FIG. 1  is a schematic, side cross-sectional view of a lens system for a digital camera according to a preferred embodiment; 
       FIG. 2  is a schematic, side cross-sectional view of a diffractive surface of the second lens element shown in  FIG. 1 , wherein y represents a depth of a groove and x represents a position on a first aspheric surface of the second lens element; 
       FIG. 3  is a graph of Modulation Transfer Function (MTF) of the lens system of  FIG. 1 ; 
       FIG. 4  is another graph of Modulation Transfer Function (MTF) of the lens system of  FIG. 1 ; 
       FIG. 5  is a graph of tangential and sagittal field curvatures of the lens system of  FIG. 1 ; 
       FIG. 6  is a graph of optical distortion of the lens system of  FIG. 1 ; and 
       FIG. 7  is a graph of relative illuminance of the lens system of  FIG. 1 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Referring to  FIG. 1 , an optical module  100  of a digital camera of a preferred embodiment includes an aperture stop  10 , a first lens element  20 , a second lens element  30 , a third lens element  40 , an flat optical structure  50 , and an imaging sensor  60 , which are consecutively arranged in that order from an object side designated as “Z obj ” to an image side designated as “Z img ”. An “O” line represents an optical axis of the lens. The first lens element  20 , the second lens element  30 , and the third lens element  40  together may be considered, as a group, to constitute the lens system  46  of the optical module  100 . 
   The aperture stop  10  includes a stop plane  12 , which faces the first lens element  20 . The aperture stop  10  is the first component to receive light rays when the lens is used. Therefore, it is convenient to selectively control the light rays using the aperture stop  10 . 
   The first lens element  20  is biconvex and spherical. The first lens element  20  includes a first spherical surface  22  and a second spherical surface  24 . The second lens element  30  is concavo-convex and includes a first aspheric surface  32  and a second aspheric surface  34 . The first surface  32  is a diffractive surface and is schematically represented in  FIG. 2 . The third lens element  40  includes a third aspheric surface  42  and a fourth aspheric surface  44 . The configurations of the third and fourth surfaces  42 ,  44  are wave-shaped. All of the lens elements  20 ,  30 ,  40  of the lens system  46  are symmetrically disposed about the O line, respectively. 
   The first lens element  20  is advantageously made of optical glass. A refractive index, designated as “n”, and a dispersion coefficient, designated as “v”, of the first lens element  20  need to satisfy the following requirements: 1.5&lt;n&lt;1.65, 50&lt;v&lt;70. The first lens element  20  is preferably made from BACD5. The refractive index of BACD5 is 1.589, and its dispersion coefficient is 61.25. 
   The second lens element  30  is advantageously made of optical plastic since optical plastic can be more readily shaped/machined into the desired complex shape desired for the second lens element. A refractive index and a dispersion coefficient of the second lens element  30  need to satisfy the following requirements: 1.65&lt;n&lt;1.65,20&lt;v&lt;30. The second lens element  30  is preferably made from OKP4. The refractive index of OKP4 is 1.609, and its dispersion coefficient is 26.64. 
   Referring to  FIG. 2 , the first aspheric surface  32  of the second lens element  30  is a diffractive surface. The diffractive surface is toward the object side and is substantially serrated. The serrated diffractive surface may advantageously be engraved in the first aspheric surface  32  of the second lens element  30  by means of cutting tools. The largest serration depth is about 0.967 microns, and the smallest distance of a serration from the optical axis is about 26.7 millimeters. The diffractive surface is designed according to optics principles. Because the light rays are made up of different wavelengths of light, the diffractive surface may change an image phase of different wavelength of light, so as to make the light rays conform. An image phase of the diffractive surface  32  is defined as “Φ”. “Φ” is determined by the formula:
 
Φ= p   2   *r   2   +p   4   *r   4   +p   6   *r   6   +p   8   *r   8   +p   10   *r   10  
 
Where:
         r is the distance from the optical axis; and   p 2 , p 4 , p 6 , p 8 , p 10  are the coefficients.
 
The image phase “Φ” will be a target function to satisfy a correction of optical aberrations. After the optical aberrations are optimized, the coefficients of p 2 , p 4 , p 6 , p 8 , p 10  are achieved. A depth of the groove is defined by “d”. A “d” is determined by the formula:
 
Φ=2*π/(λ*( n− 1)* d )
 
Where: π is the circumference coefficient; λ is the wavelength, n is the refractive power. Because “Φ” is known, accordingly
 
 p   2   *r   2   +p   4   *r   4   +p   6   *r   6   +p   8   *r   8   +p   10   *r   10  . . . =2*π/(λ*( n− 1)* d )
 
“d” will be determined by the above formula. The final result is p 2 =−161.01084, p 4 =137.96568, p 6 =−169.06449, p 8 =122.77371, p 10 =−36001241. Accordingly, the depth of the groove will be formulated. In  FIG. 2 , x represents the value of r, and y represents the value of the groove depth. After that, the depth will be added with the aspheric surface. Therefore, the diffractive structure will be determined.
       

   The third lens element  40  is advantageously made of optical plastic, facilitating formation of the third lens element  40 . A refractive index and a dispersion coefficient of the second lens element  40  need to satisfy the following requirements: 1.5&lt;n&lt;1.6, 50&lt;v&lt;70. The third lens element  40  is preferably made from ZEO-E48R. The refractive index of ZEO-E48R is 1.5299, and its dispersion coefficient is 55.866. 
   The flat optical structure  50  is usefully made of glass and includes a first plane  52  and a second plane  54 . The flat optical structure  50  is preferably made from B270. The refractive index of B270 is 1.585, and its dispersion coefficient is 29.9. 
   At least one surface of the first lens element  20 , the optical board  50  is coated an Infrared-cut (IR-cut) coating (not shown). The IR-cut coating can filter infrared rays and hence improving image quality. 
   The image sensor  60  is located at the image side of the flat optical structure  50 . The image sensor  60  includes an image plane  62 . The flat optical structure  50  can protect the image plane  62  of the image sensor  60 , so that dust or other contamination does not reach the image plane  62 . The image sensor  60  is usually a Charge Coupled Device (CCD) or a Complementary Metal Oxide Semiconductor (CMOS). If the image sensor  60  is used in a digital camera of a mobile phone, the image sensor  60  is usually a CMOS for cost reasons. A pixel size of the CMOS of the present embodiment is 3.18 μm, and a resolution of the CMOS is about 1600×1200 pixels. 
   Detailed structural parameters of the preferred embodiment of the lens are shown in  FIG. 1  and provided in Table 1. Surface radiuses and axial distances are shown in millimeters. The surfaces are identified according to the corresponding drawing reference, from the object side to the image side as shown. 
   
     
       
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               Radius 
               Thickness 
                 
                 
               Conic 
             
             
               Surface 
               Description 
               (R) 
               (d) 
               Material 
               Diameter 
               Constant (k) 
             
             
                 
             
           
           
             
               12 
               Stop plane 
               ∞ 
               0.02826331 
                 
               1.69643 
               0 
             
             
               22 
               First spherical surface 
                2.199789 
               1.286996 
               BACD5 
               2.044452 
               0 
             
             
               24 
               Second spherical surface 
               12.18765 
               0.6906032 
                 
               2.243178 
               0 
             
             
               32 
               First aspheric surface 
               −1.444906 
               0.6529131 
               OKP4 
               2.351006 
               0 
             
             
               34 
               Second aspheric surface 
               −1.555362 
               0.2138643 
                 
               2.709882 
               0 
             
             
               42 
               Third aspheric surface 
               15.82701 
               1.574585 
               ZEO-E48R 
               3.326867 
               0 
             
             
               44 
               Fourth aspheric surface 
                4.164333 
               0.35 
                 
               4.760408 
               0 
             
             
               52 
               First plane 
               ∞ 
               0.55 
               B270 
               5.160381 
               0 
             
             
               54 
               Second plane 
               ∞ 
               0.8160738 
                 
               5.378413 
               0 
             
             
                 
             
           
        
       
     
   
   The aspheric surfaces are the surfaces  32 ,  34 ,  42  and  44 , and describe the following equation: 
           z   =         cr   2       1   +       1   -       (     1   +   k     )     ⁢     c   2     ⁢     r   2               +       a   1     ⁢     r   2       +       a   2     ⁢     r   4       +       a   3     ⁢     r   6       +       a   4     ⁢       r   8     ++     ⁢     a   5     ⁢     r   10       +       a   6     ⁢     r   12     ⁢           ⁢   …             
Where:
         z is the surface sag;   C=1/R, where R is the radius of the surface;   K is the conic constant;   r is the distance from the optical axis; and   a 1 , a 2 , a 3 , a 4 , a 5 , and a 6  are the aspheric coefficients.
 
The aspheric coefficients a 1 , a 2 , a 3 , a 4 , a 5 , and a 6  are given by Table 2:
       
   
     
       
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
               Surface 
               Description 
               a 1   
               a 2   
               a 3   
               a 4   
               a 5   
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               32 
               First surface 
               0 
               0.042668744 
               0.045843703 
               0.023104266 
               −0.011218416 
             
             
               34 
               Second surface 
               0 
               0.016369603 
               0.061024975 
               −0.0039084828 
               0.0027731957 
             
             
               42 
               Third surface 
               0 
               −0.061949054 
               0.032381233 
               −0.012023059 
               0.0017581425 
             
             
               44 
               Fourth surface 
               0 
               −0.053218236 
               0.0090815367 
               −0.0013358709 
               0.000066713635 
             
             
                 
             
           
        
       
     
   
   The effective focal length of the lens system  46  is 4.750229 mm in air, and the maximum aperture is f/2.8. The total length of the lens system  46  is 6.163299 mm, and, as such, the total length thereof is advantageously less than 1 cm. The lens system  46  is well suited for use with state-of-the-art digital sensors having a resolution about 1280×960 pixels. 
   The performance of the lens system  46  of the preferred embodiment is illustrated in  FIG. 3  through  FIG. 7 . 
   Referring to  FIGS. 3 and 4 , Modulation Transfer Function (MTF) is the scientific means of evaluating the fundamental spatial resolution performance of an imaging system. When the MTF is measured, an imaging height is divided into 1.0, 0.8, 0.6, and 0 fields. For each field, the MTF is measured. Each curved line represents the performance of the lens. The higher the modulation transfer, the better the preservation of detail by the imaging system. In  FIG. 3 , when the spatial frequency is 100 lp/mm (line pairs/millimeter), the MTF is higher than 40%. This is considered satisfactory for general imaging requirements. 
   Referring to  FIG. 5 , field curvature represents the curved extent of the image plane when visible light is focused through a lens. Field curvature is very seldom totally eliminated, and it is not absolutely necessary to have the best correction, at least for most camera applications. When cost is important, it is often wise to select a more modestly priced configuration, rather than have a high degree of correction. For the lens system  46 , it can be seen that the tangential and sagittal field curvature is well under ±0.1 mm, at generally less than ±0.06 mm. 
   Referring to  FIG. 6 , distortion represents the inability of a lens to create a rectilinear image of the subject. Distortion does not modify the colors or the sharpness of the image, but rather the shape of the image. The maximum geometric distortion of the lens system  46  is typically higher than −1% and is lower than +1% (i.e., in the range of about −1% to about +1%) and, preferably, within about +/−0.10%. Based on the data provided in  FIG. 6 , the lens system  46  can provide crisp and sharp images with minimal field curvature. In fact, the lens system  46  with such a performance would be considered to be sufficient for over 90 percent of photography applications. 
   Referring to  FIG. 7 , the lowest value of the relative illuminance is about 50%. Usually when the value of relative illuminance is higher than 50%, it is considered satisfactory for general requirements. 
   The lens system  46  may be used in various digital camera applications, including in personal digital cameras and other very small electronic devices (e.g., web cams and cameras in mobile phones). 
   While certain specific relationships, materials and other parameters have been detailed in the above description of preferred embodiments, the described embodiments can be varied, where suitable, within the principles of the present invention. It should be understood that the preferred embodiments have been presented by way of example only and not by way of limitation. Thus the breadth and scope of the present invention should not be limited by the above-described exemplary embodiments, but should be defined according to the following claims and their equivalents.