Abstract:
Compact wide angle lens designs are described. The lens has three lens groups and includes complex aspherical lens elements. The lens designs have a field of view of 80° or greater and satisfies at least one of the conditional equations a) BFL/EFL&lt;=0.6 where BFL is the distance from the image surface vertex of the complex aspheric lens element to the image plane, EFL is the effective focal length of the optical lens, and,
       b) BFL/CA&lt;=0.3 where CA is the clear aperture of the complex aspheric lens element, EFL is the effective focal length of the optical lens, and,   c) 3=&lt;TTL/EFL&lt;=6.6 where TTL is the distance from the vertex of the first element of group 1 to the image plane of the lens assembly when focused at infinity, EFL is the effective focal length of the optical lens.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to U.S. Provisional Application 62/271321, titled Compact wide angle lens, filed Dec. 28, 2015, by the same inventor and currently pending. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable. 
       BACKGROUND OF THE INVENTION 
       [0003]    Technical Field 
         [0004]    The invention relates to wide-angle lenses, having high quality images across the entire field of view in a compact form factor. 
         [0005]    Related Background Art 
         [0006]    Digital imaging cameras use solid-state image sensors such as CCD or CMOS imagers to convert optical images into electronic signals. As the resolution of the imagers increases, there is a continuous need for optical lenses with increased performance. An important characteristic of the lens is the ability to produce high-resolution images across a wide field of view. Another important characteristic is to produce such high-resolution images using a lens that is of a compact size. The lenses are increasing being incorporated into a variety of electronic devices including mobile phones, cameras, sports cameras, computers and computer peripherals. Incorporation of the lenses into new devices also places new environmental performance requirements upon the lens. The lens must be compact and light, to be used in portable devices, and must maintain high performance characteristics. 
         [0007]    The quality and pixel density of very small imaging sensors is continuously improving. The sensors are used in machine vision, medical, cell phone and automotive applications. In many cases low distortion is critical to proper functioning in the intended application. These lenses are being used more and more in consumer application where literally millions of such lens systems must be easily produced at consistent high quality and at low cost. Custom lens features required to produce low distortion must be designed such that they are also easy to manufacture. 
         [0008]    Lateral chromatic aberration is the separation of image height on the focal plane at off-axis field points between light rays of different wavelengths. This aberration becomes more significant and difficult to correct for wide-angle lenses. Similarly optical distortion is separation of image features on the focal plane at off-axis field points resulting in distortion of shapes and inconsistency of image feature detail location across the image plane. 
         [0009]    Both types distortion cannot be fully corrected through mathematical manipulation of the digital images, in order for such corrections to be effective requires that the lens designer produces a well behaved lens. Optical distortion aka fisheye distortion is a departure from f-tan condition (where the image height is equal to the product of the effective focal length and tangent of the field angle). A distortion free lens would follow the f-tan relationship perfectly. Optical distortion is more difficult with wide angle lens that are designed to be compact. 
         [0010]    There is a need for new lens designs that exhibit low color aberration and low optical distortion that follow the f-tan relationship and the lens is a compact lens. 
         [0011]    There is a need for new lens designs that exhibit low color aberration and low optical distortion that follow the f-tan relationship, especially for wide-angle (field of view greater than 80o) and super wide-angle lens designs (field of view greater than 170o). 
         [0012]    There is also need to provide super wide-angle and fisheye lens designs that can be manufactured cheaply, consistently and can be automatically assembled. 
       BRIEF SUMMARY OF THE INVENTION 
       [0013]    The present invention comprises 3 lens groups counting from the object side: Group 1, Group 2 and Group 3. The Groups are each described as: Group 1: This is the first lens group facing the object space. This group comprises at least 2 lens elements wherein the first element has a negative power. In the first preferred embodiment, at least one of the two elements is a positive lens element. In the second preferred embodiment, an aspheric element is included in this group. An aspheric element defined as lens element having at least one aspheric surface, which is generally described by the following well-known equation: 
         [0000]    
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         cr 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                                
                               
                                 c 
                                 2 
                               
                                
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         α 
                         1 
                       
                        
                       
                         r 
                         2 
                       
                     
                     + 
                     
                       
                         α 
                         2 
                       
                        
                       
                         r 
                         4 
                       
                     
                     + 
                     
                       
                         α 
                         3 
                       
                        
                       
                         r 
                         6 
                       
                     
                     + 
                     
                       
                         α 
                         4 
                       
                        
                       
                         r 
                         8 
                       
                     
                     + 
                     
                       
                         α 
                         5 
                       
                        
                       
                         r 
                         10 
                       
                     
                     + 
                     
                       
                         α 
                         6 
                       
                        
                       
                         r 
                         12 
                       
                     
                     + 
                     
                       
                         α 
                         7 
                       
                        
                       
                         r 
                         14 
                       
                     
                     + 
                     
                       
                         α 
                         8 
                       
                        
                       
                         
                           r 
                           16 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0014]    Where z is the sag height measured from the vertex at radial distance of r. C is the curvature of the surface. K is the conic constant and the alphas are the aspheric coefficients. The first element (L1) is a meniscus element with a convex surface facing the object. 
         [0015]    Group 2: This group has positive power comprising at least 3 lens elements including a cemented doublet formed by two of the 3 elements, and an aperture stop. In preferred embodiment the first and the second elements have positive power. The third element has negative power having a double concave shape. The 2nd and 3rd elements form a cemented doublet. An aperture is located adjacent to this group. In some embodiments, an aperture stop is located between the 1st and 2nd element. 
         [0016]    Group 3: This lens group comprises at least 2 elements. At least one of them is an aspherical element. In preferred embodiment this aspheric element is the last element that faces the image space. One surface of the aspheric element has a complex surface profile. The definition of a complex aspheric surface is that the local surface derivative of the surface profile changes sign at least once going from center to the edge of the lens element. In preferred embodiment the complex aspheric surface is the last optically powered surface facing the image plane (not including any flat filter or sensor cover glass). The distance from the image side surface vertex of the last lens element to the image plane is back focal length (BFL). The overall effective focal length of the lens assembly is EFL. The clear aperture diameter of this complex aspheric surface is CA. TTL is the distance from the vertex of the first element of group 1 to the image plane of the lens assembly when focused at infinity. At least one of the following conditions are satisfied: 
         [0000]      BFL/EFL&lt;=0.6   (2)
 
         [0000]      BFL/CA&lt;=0.3   (3)
 
         [0000]      3=&lt;TTL/EFL&lt;=6.6   (4)
 
         [0017]    In the preferred embodiment all three conditional equations 2-4 are satisfied. All of the lenses have a field of view of 80° or greater. The specific examples are not intended to limit the inventive concept to the example application. Other aspects and advantages of the invention will be apparent from the accompanying drawings and detailed description. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1  is a diagram of a complex aspheric lens element. 
           [0019]      FIG. 2  is a diagram of a first embodiment of the compact wide angle lens. 
           [0020]      FIG. 3  is a diagram of a second embodiment of the compact wide angle lens. 
           [0021]      FIG. 4  is a diagram of a third embodiment of the compact wide angle lens. 
           [0022]      FIG. 5  is a diagram of a fourth embodiment of the compact wide angle lens. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0023]    The radius of curvature in all examples is measured at the point on the lens intersecting the optical axis of the wide-angle lens. The description of the lens elements as flat, convex or concave refers to the curvature at this point on the lens surface that intersects the optical axis. A lens surface may also be aspherical thus a lens element surface that is described as flat and aspherical implies it is flat at the point on the lens surface that intersects the optical axis but curved elsewhere. The term lens or wide-angle lens refers to the wide-angle lens that is comprised of a plurality of lens elements. Each lens element by itself is also known in the literature as a lens. Here, lens refers to the multi-component system. 
         [0024]    Referring to  FIG. 1  a complex aspheric surface on a lens element is shown. The lens element  101  is shown in a cross-sectional profile, as are all of the subsequent lens designs. The lens element  101  is centered on the optical axis  104 . The lens is oriented such that the object side  102  is to the left and the image side  103  is to the right the surface  107  is a complex aspherical surface in that it is non-spherical and the slope of tangents  105 ,  106  have opposite signs. A complex aspherical surface is one in which the local derivative of the surface profile changes sign at least once going from center or optical axis  104  to the edge  109  of the lens element. That is dy/dx is positive for tangent line  106  and negative for tangent line  105 . The example shows a single sign change for the surface derivative. Other embodiments may have more than one sign change. 
         [0025]      FIG. 2  shows a first embodiment of the invented compact wide angle lens. The Figure is used both to show the general features of the invented wide angle lens as well as a specific example. The lens  201 , in going from object  202  to image  203 , is comprised of three (3) lens groups  205 ,  206 ,  207 . The first lens group  205  has negative power and is comprised of at least 2 lens elements  208 ,  209 . In the first preferred embodiment, at least one of the two elements  209  is a positive lens element. In other preferred embodiments shown in later Figures, an aspheric element is included in this first group  205 . 
         [0026]    The second lens group  206  has positive power comprising at least 3 lens elements  210 ,  211 ,  212  including a cemented doublet formed by two of the 3 elements  211 ,  212 , and an aperture stop  217 . In preferred embodiment the first  210  and the second  211  elements have positive power. The third element  212  has negative power having a double concave shape. The 2nd and 3rd elements  211 ,  212  form a cemented doublet. An aperture stop  217  is located between the first  210  and second  211  element. 
         [0027]    The third lens group  207  comprises at least 2 elements  213 ,  214 . At least one of them is an aspherical element. In preferred embodiment an aspheric element  214  is the last element that faces the image plane  219 . One surface  218  of the aspheric element has a complex surface profile. In a preferred embodiment the complex aspheric surface  218  is the last optically powered surface facing the image plane  219  (not including any flat filter or sensor cover glass). The distance  220  from the image side surface  218  vertex of the last lens element  214  to the image plane  219  is back focal length (BFL). The overall effective focal length of the lens assembly is EFL. The clear aperture diameter  221  of this complex aspheric surface  218  is CA. The lens elements are selected and placed to satisfy the equations 2 and 3 shown above. 
         [0028]    Each of the lens examples include a specification for each lens element. The specification includes material properties such as index of refraction and Abbe number as well as dimensions, formulas for each surface curvature, thickness of the lens elements and spacing between lens elements 
         [0029]    The radius of curvature for each lens element is measured at the intersection of each surface with the optical axis  204  of the wide-angle lens. Surfaces are numbered consecutively from object to image. Thus surface  1  is the first surface  215  of the first lens element  208 . Surface is the second or image side surface  216  of the same lens element. Surface  3  is the first, object side, surface  223  off the second lens element  209  and so forth through all elements of the lens  201 . Thickness is defined as the distance from the surface to the next labeled surface measured along the optical axis  204 . For example, in the Table 1A the thickness  223  of the lens element  208 , the distance between the first surface  215  and the second surface  216  of that lens element, is 1.00 mm. The distance  224  from the image side surface  216  to third surface  222  is 8.515 mm. 
         [0030]    Index in Table 1A is the index of refraction, and, Abbe # is the Abbe Number for the lens element corresponding to the designated surface at 578 nm (d-line). For example, the index of refraction of the first lens element  208  is 1.618 and the Abbe Number of the first element  208  is 63.417. The values for Radius and Thickness values are all given in mm. The values may be scaled by the effective focal length and the design may therefore be scaled for a lens of any focal length. 
         [0031]    Four specific examples satisfying the description of the invented wide angle lens follow. Each of the examples represent a wide angle lens with a field of view of 90° or greater, comprised of three lens groups as described above, satisfy equation 2 and 3, and include a complex aspheric surface as the last lens element surface prior to the image plane. 
       EXAMPLE 1 
       [0032]      FIG. 2  shows the layout of Example 1. This design has a field angle of +/−47°, for a total field of view 94°, with a relative aperture of F/2.8. The lens is comprised, from object to image, of three lens groups. Group 1,  205  comprises two lens elements  208 ,  209 . Group 2,  206  comprises three lens elements  210 ,  211 ,  212  with an aperture stop between the first  210  and second  211  element of the group and the second and third elements  211 ,  212  of the group are a cemented doublet. Group 3 comprises two lens elements  213 ,  214  and are aspheric elements. All four surfaces of these two lens elements  213 ,  214  are aspheric The image space facing side  218  the last lens element  214  is a complex aspheric surface. Table 1A shows the optical specification for this first example. The surfaces are numbered as already described. The radiuses of curvature are measured at the optical axis  204 . Table 1B shows the optical specifications for the aspheric lens by providing the constants for Equation 1. The conic constant for all surfaces in this example is 0. The EFL of this example 1 is 8.28 mm. BFL is 3.41 mm and the CA of 14.42 mm. The conditional expression (2) and (3) are satisfied. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1A 
               
             
             
               
                   
               
               
                 The optical prescription of Example 1. 
               
             
          
           
               
                 Surface 
                 Type 
                 Radius 
                 Thickness 
                 Nd 
                 Abbe# 
                 Diameter 
               
               
                   
               
             
          
           
               
                 1 
                 STD. 
                 66.377 
                 1.000 
                 1.618 
                 63.417 
                 17.035 
               
               
                 2 
                 STD. 
                 7.286 
                 8.515 
                   
                   
                 12.403 
               
               
                 3 
                 STD. 
                 14.003 
                 1.991 
                 1.911 
                 35.256 
                 10.429 
               
               
                 4 
                 STD. 
                 Infinity 
                 3.341 
                   
                   
                 9.892 
               
               
                 5 
                 STD. 
                 127.726 
                 1.214 
                 1.618 
                 63.417 
                 5.881 
               
               
                 6 
                 STD. 
                 −17.653 
                 0.100 
                   
                   
                 5.206 
               
               
                 STO 
                 STD. 
                 8.998 
                 2.080 
                 1.729 
                 54.669 
                 4.282 
               
               
                 8 
                 STD. 
                 −5.867 
                 0.442 
                 1.728 
                 28.315 
                 4.612 
               
               
                 9 
                 STD. 
                 9.228 
                 2.582 
                   
                   
                 4.916 
               
               
                 10 
                 ASPH. 
                 −4.957 
                 2.994 
                 1.535 
                 56.197 
                 6.114 
               
               
                 11 
                 ASPH. 
                 −5.065 
                 1.865 
                   
                   
                 8.655 
               
               
                 12 
                 ASPH. 
                 12.975 
                 2.167 
                 1.633 
                 23.327 
                 13.997 
               
               
                 13 
                 ASPH. 
                 14.115 
                 3.407 
                   
                   
                 14.420 
               
               
                 IMA 
                 STD. 
                 Infinity 
                   
                   
                   
                 16.028 
               
               
                   
               
               
                 STD. = SPHERICAL LENS SURFACE, 
               
               
                 ASPH. = ASPHERIC LENS SURFACE 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1B 
               
             
             
               
                   
               
               
                 The aspheric coefficients for the aspheric 
               
               
                 surfaces of Example 1 as per Equation (1). 
               
             
          
           
               
                   
                 Surface Number 
                 Coefficients 
               
               
                   
                   
               
             
          
           
               
                   
                 Surface 10: 
                   
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00083533472 
               
               
                   
                 Coeff on r 6: 
                 9.7714702e−005 
               
               
                   
                 Coeff on r 8: 
                 6.5201738e−006 
               
               
                   
                 Surface 11: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.00022411518 
               
               
                   
                 Coeff on r 6: 
                 4.7708268e−005 
               
               
                   
                 Coeff on r 8: 
                 3.8503953e−006 
               
               
                   
                 Surface 12: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0017036826 
               
               
                   
                 Coeff on r 6: 
                 2.7989386e−005 
               
               
                   
                 Coeff on r 8: 
                 −1.5069974e−007 
               
               
                   
                 Surface 13: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0018493911 
               
               
                   
                 Coeff on r 6: 
                 6.8877976e−006 
               
               
                   
                 Coeff on r 8: 
                 2.4459406e−007 
               
               
                   
                 Coeff on r 10: 
                 −2.1121465e−009 
               
               
                   
                   
               
             
          
         
       
     
       EXAMPLE 2 
       [0033]      FIG. 3  shows the layout of Example 2. This design has a field angle of +/−50° (for a total field of view)100° with a relative aperture of F/2.8. The lens  301 , in going from object  302  to image  303 , is comprised of three (3) lens groups  305 ,  306 ,  307 . The first lens group  305  has negative power and is comprised of at least 2 lens elements and in this example is comprised of three lens elements  307 ,  308 ,  309 . At least one of the elements  309  is a positive lens element. An aspheric element  308  is included in this first group  305 . 
         [0034]    The second lens group  306  has positive power comprising at least 3 lens elements  310 ,  311 ,  312  including a cemented doublet formed by two of the 3 elements  311 ,  312 , and an aperture stop  317 . The first  310  and the second  311  elements have positive power. The third element  312  has negative power having a double concave shape. The 2nd and 3rd elements  311 ,  312  form a cemented doublet. An aperture stop  317  is located between the first  310  and second  311  element of the second lens group  306 . 
         [0035]    The third lens group  307  comprises at least 2 elements  313 ,  314 . At least one of them is an aspherical element. In this case, both lens elements  313 ,  314  of the third group  307  are aspheric. An aspheric element  314  is the last element that faces the image plane  316 . One surface  315  of the aspheric element  314  has a complex surface profile. The complex aspheric surface  315  is the last optically powered surface facing the image plane  316  (not including any flat filter or sensor cover glass). The distance  318  from the image side surface  315  vertex of the last lens element  314  to the image plane  316  is back focal length (BFL). The overall effective focal length of the lens assembly is EFL. The clear aperture diameter of this complex aspheric surface is CA. The lens elements are selected and placed to satisfy the equations 2 and 3 shown above. Table 2A shows the optical specification for this second example. The surfaces are numbered as already described. The radiuses of curvature are measured at the optical axis  304 . Table 2B shows the optical specifications for the aspheric lens by providing the constants for Equation 1. The EFL of this example is 7.45 mm. BFL is 3.55 mm and the CA of 14.2 mm. The conditional expression (2) and (3) are satisfied. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2A 
               
             
             
               
                   
               
               
                 Optical prescription of Example 2. 
               
             
          
           
               
                 Surf 
                 Type 
                 Radius 
                 Thickness 
                 Nd 
                 Abbe# 
                 Diameter 
                 Conic 
               
               
                   
               
             
          
           
               
                 1 
                 STD 
                 20.000 
                 1.000 
                 1.623 
                 56.952 
                 17.084 
                 0.000 
               
               
                 2 
                 STD 
                 6.204 
                 4.524 
                   
                   
                 11.680 
                 0.000 
               
               
                 3 
                 ASPH. 
                 110.703 
                 1.000 
                 1.535 
                 56.197 
                 11.639 
                 0.000 
               
               
                 4 
                 STD. 
                 6.942 
                 1.141 
                   
                   
                 11.099 
                 −2.189 
               
               
                 5 
                 STD. 
                 18.150 
                 2.793 
                 1.911 
                 35.256 
                 11.149 
                 0.000 
               
               
                 6 
                 STD. 
                 −19.740 
                 4.754 
                   
                   
                 11.045 
                 0.000 
               
               
                 7 
                 STD. 
                 14.485 
                 1.650 
                 1.535 
                 56.197 
                 6.142 
                 0.000 
               
               
                 8 
                 ASPH. 
                 −10.748 
                 0.100 
                   
                   
                 5.470 
                 0.000 
               
               
                 STO 
                 STD. 
                 8.203 
                 2.010 
                 1.729 
                 54.669 
                 4.148 
                 0.000 
               
               
                 10 
                 STD. 
                 −8.203 
                 0.450 
                 1.728 
                 28.315 
                 4.416 
                 0.000 
               
               
                 11 
                 STD. 
                 5.107 
                 4.424 
                   
                   
                 4.659 
                 0.000 
               
               
                 12 
                 ASPH. 
                 −7.986 
                 1.420 
                 1.535 
                 56.197 
                 9.530 
                 0.000 
               
               
                 13 
                 ASPH. 
                 −6.185 
                 0.100 
                   
                   
                 10.660 
                 0.000 
               
               
                 14 
                 ASPH. 
                 14.314 
                 2.792 
                 1.640 
                 23.522 
                 13.611 
                 0.000 
               
               
                 15 
                 ASPH. 
                 27.202 
                 3.549 
                   
                   
                 14.202 
                 0.000 
               
               
                 IMA 
                 STD. 
                 Infinity 
                   
                   
                   
                 16.019 
                 0.000 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 2B 
               
               
                   
               
               
                 The aspheric coefficients for the aspheric 
               
               
                 surfaces of Example 2 as per Equation (1). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface 3: 
                   
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00061525091 
               
               
                   
                 Coeff on r 6: 
                 8.1948189e−006 
               
               
                   
                 Coeff on r 8: 
                 −8.3082433e−008  
               
               
                   
                 Surface 8: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.0002179492 
               
               
                   
                 Coeff on r 6: 
                 −1.4912038e−006  
               
               
                   
                 Surface 12: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.0022010651 
               
               
                   
                 Coeff on r 6: 
                 −9.4364766e−005  
               
               
                   
                 Surface 13: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.0017457744 
               
               
                   
                 Coeff on r 6: 
                 −1.2657953e−005  
               
               
                   
                 Coeff on r 8: 
                 2.8577692e−007 
               
               
                   
                 Surface 14: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0016285282 
               
               
                   
                 Coeff on r 6: 
                 2.8354991e−005 
               
               
                   
                 Coeff on r 8: 
                 −2.0180218e−007  
               
               
                   
                 Coeff on r 10: 
                 3.2670732e−010 
               
               
                   
                 Surface 15: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00197103 
               
               
                   
                 Coeff on r 6: 
                 2.4326944e−005 
               
               
                   
                 Coeff on r 8: 
                 −2.2165103e−007  
               
               
                   
                 Coeff on r 10: 
                  1.661843e−009 
               
               
                   
                   
               
             
          
         
       
     
       EXAMPLE 3 
       [0036]      FIG. 4  shows the layout of Example 3. This design has a field angle of +/−45° (for a total field of view)90° with a relative aperture of F/2.9. The lens  401 , in going from object  402  to image  403 , is comprised of three (3) lens groups  405 ,  406 ,  407 . The first lens group  405  has negative power and is comprised of at least 2 lens elements and in this example is comprised of three lens elements  407 ,  408 ,  409 . At least one of the elements  409  is a positive lens element. An aspheric element  407  is included in this first group  405 . 
         [0037]    The second lens group  406  has positive power comprising at least 3 lens elements  410 ,  411 ,  412  including a cemented doublet formed by two of the 3 elements  411 ,  412 , and an aperture stop  417 . The first  410  and the second  411  elements have positive power. The third element  412  has negative power having a double concave shape. The 2nd and 3rd elements  411 ,  412  form a cemented doublet. An aperture stop  417  is located between the first  410  and second  411  element of the second lens group  406 . 
         [0038]    The third lens group  407  comprises at least 2 elements  413 ,  414 . At least one of them  414  is an aspherical element. An aspheric element  414  is the last element that faces the image plane  416 . At least one surface  415  of the aspheric element  414  has a complex surface profile. A complex aspheric surface  415  is the last optically powered surface facing the image plane  416  (not including any flat filter or sensor cover glass). In this example 3, both surfaces of the lens element  415  are complex aspheric surfaces. The distance  418  from the image side surface  415  vertex of the last lens element  414  to the image plane  416  is back focal length (BFL). The overall effective focal length of the lens assembly is EFL. The clear aperture diameter of this complex aspheric surface is CA. The lens elements are selected and placed to satisfy the equations 2 and 3 shown above. Table 3A shows the optical specification for this third example. The surfaces are numbered as already described. The radiuses of curvature are measured at the optical axis  404 . Table 3B shows the optical specifications for the aspheric lens by providing the constants for Equation 1. The EFL of this example is 8.88 mm. BFL is 3.51 mm and the CA of 14.4 mm. The conditional expression (2) and (3) are satisfied. Table 3A shows the optical specification for this second example. The surfaces are numbered as already described. The radiuses of curvature are measured at the optical axis  404 . Table 3B shows the optical specifications for the aspheric lens by providing the constants for Equation 1. The EFL of this example is 8.88 mm. BFL is 3.51 mm and the CA of 14.4 mm. The conditional expression (2) and (3) are satisfied. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3A 
               
             
             
               
                   
               
               
                 shows the optical prescription of Example 3. 
               
             
          
           
               
                 Surf 
                 Type 
                 Radius 
                 Thickness 
                 Nd 
                 Abbe# 
                 Diameter 
                 Conic 
               
               
                   
               
             
          
           
               
                 1.000 
                 ASPH. 
                 18.613 
                 1.000 
                 1.535 
                 56.197 
                 14.452 
                 0.000 
               
               
                 2.000 
                 ASPH. 
                 6.021 
                 2.961 
                   
                   
                 11.046 
                 −2.213 
               
               
                 3.000 
                 STD. 
                 Infinity 
                 0.750 
                 1.618 
                 63.417 
                 10.899 
                 0.000 
               
               
                 4.000 
                 STD. 
                 8.038 
                 1.504 
                   
                   
                 9.814 
                 0.000 
               
               
                 5.000 
                 STD. 
                 18.620 
                 2.447 
                 1.804 
                 46.568 
                 9.910 
                 0.000 
               
               
                 6.000 
                 STD. 
                 −18.620 
                 4.534 
                   
                   
                 9.752 
                 0.000 
               
               
                 7.000 
                 ASPH. 
                 10.844 
                 1.850 
                 1.535 
                 56.197 
                 6.272 
                 0.000 
               
               
                 8.000 
                 ASPH. 
                 −9.983 
                 0.100 
                   
                   
                 5.758 
                 0.000 
               
               
                 STO 
                 STD. 
                 13.318 
                 2.391 
                 1.618 
                 63.417 
                 4.744 
                 0.000 
               
               
                 10.000 
                 STD. 
                 −4.753 
                 0.500 
                 1.620 
                 36.348 
                 4.998 
                 0.000 
               
               
                 11.000 
                 STD. 
                 5.570 
                 5.273 
                   
                   
                 5.324 
                 0.000 
               
               
                 12.000 
                 STD. 
                 Infinity 
                 2.506 
                 1.618 
                 63.417 
                 11.755 
                 0.000 
               
               
                 13.000 
                 STD. 
                 −12.945 
                 0.100 
                   
                   
                 12.444 
                 0.000 
               
               
                 14.000 
                 ASPH. 
                 17.045 
                 2.270 
                 1.535 
                 56.197 
                 12.731 
                 0.000 
               
               
                 15.000 
                 ASPH. 
                 12.359 
                 3.512 
                   
                   
                 14.396 
                 0.000 
               
               
                 IMA 
                 STD. 
                 Infinity 
                   
                   
                   
                 15.973 
                 0.000 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 3B 
               
               
                   
               
               
                 The aspheric coefficients for the aspheric 
               
               
                 surfaces of Example 3 as per Equation (1). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface 1: 
                   
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00027450861 
               
               
                   
                 Coeff on r 6: 
                  9.450237e−007 
               
               
                   
                 Coeff on r 8: 
                 −2.3065243e−009 
               
               
                   
                 Surface 2: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.00092691055 
               
               
                   
                 Coeff on r 6: 
                 −6.6716515e−006 
               
               
                   
                 Surface 7: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00016215002 
               
               
                   
                 Surface 8: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.0002461795 
               
               
                   
                 Coeff on r 6: 
                 −9.7401919e−007 
               
               
                   
                 Surface 14: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0014283981 
               
               
                   
                 Coeff on r 6: 
                 −1.0802005e−006 
               
               
                   
                 Coeff on r 8: 
                  2.5279061e−009 
               
               
                   
                 Surface 15: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0016443133 
               
               
                   
                 Coeff on r 6: 
                 −9.6586534e−006 
               
               
                   
                 Coeff on r 8: 
                  4.3176918e−007 
               
               
                   
                 Coeff on r 10: 
                 −4.1215076e−009 
               
               
                   
                   
               
             
          
         
       
     
       EXAMPLE 4 
       [0039]      FIG. 5  shows the layout of Example 4. This design has a field angle of +/−47° (for a total field of view)94° with a relative aperture of F/3.3. The lens  501 , in going from object  502  to image  503 , is comprised of three (3) lens groups  505 ,  506 ,  507 . The first lens group  505  has negative power and is comprised of at least 2 lens elements and in this example is comprised of three lens elements  507 ,  508 ,  509 . At least one of the elements  509  is a positive lens element. An aspheric element  507  is included in this first group  505 . 
         [0040]    The second lens group  506  has positive power comprising at least 3 lens elements  510 ,  511 ,  512  including a cemented doublet formed by two of the 3 elements  511 ,  512 , and an aperture stop  517 . The first  510  and the second  511  elements have positive power. The third element  512  has negative power having a double concave shape. The 2nd and 3rd elements  511 ,  512  form a cemented doublet. An aperture stop  517  is located between the first  510  and second  511  element of the second lens group  506 . 
         [0041]    The third lens group  507  comprises at least 2 elements  513 ,  514 . At least one of them is an aspherical element. In this 4 th  example both elements  513 ,  514  are aspherical. An aspheric element  514  is the last element that faces the image plane  516 . At least one surface  515  of the aspheric element  514  has a complex surface profile. A complex aspheric surface  515  is the last optically powered surface facing the image plane  516  (not including any flat filter or sensor cover glass). In this example 4, both surfaces of the lens element  515  are complex aspheric surfaces. The distance  518  from the image side surface  515  vertex of the last lens element  514  to the image plane  516  is back focal length (BFL). 
         [0042]    The overall effective focal length of the lens assembly is EFL. The clear aperture diameter of this complex aspheric surface is CA. The lens elements are selected and placed to satisfy the equations 2 and 3 shown above. Table 4A shows the optical specification for this third example. The surfaces are numbered as already described. The radiuses of curvature are measured at the optical axis  504 . Table 4B shows the optical specifications for the aspheric lens by providing the constants for Equation 1. The EFL of this example is 8.08 mm. BFL is 4.1 mm and the CA of 14.2 mm. The conditional expression (2) and (3) are satisfied. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4A 
               
             
             
               
                   
               
               
                 shows the optical prescription of Example 4. 
               
             
          
           
               
                 Surf 
                 Type 
                 Radius 
                 Thickness 
                 Nd 
                 Abbe# 
                 Diameter 
                 Conic 
               
               
                   
               
             
          
           
               
                 1.000 
                 ASPH. 
                 15.172 
                 1.000 
                 1.535 
                 56.197 
                 13.750 
                 0.000 
               
               
                 2.000 
                 ASPH. 
                 4.686 
                 3.122 
                   
                   
                 9.753 
                 −0.740 
               
               
                 3.000 
                 STD. 
                 Infinity 
                 0.750 
                 1.593 
                 68.695 
                 9.682 
                 0.000 
               
               
                 4.000 
                 STD. 
                 5.965 
                 0.705 
                   
                   
                 8.464 
                 0.000 
               
               
                 5.000 
                 STD. 
                 8.502 
                 4.089 
                 1.743 
                 49.238 
                 8.496 
                 0.000 
               
               
                 6.000 
                 STD. 
                 −19.231 
                 2.879 
                   
                   
                 7.800 
                 0.000 
               
               
                 7.000 
                 ASPH. 
                 8.860 
                 1.533 
                 1.535 
                 56.197 
                 4.651 
                 0.000 
               
               
                 STO 
                 ASPH. 
                 −7.885 
                 0.100 
                   
                   
                 3.911 
                 0.000 
               
               
                 9.000 
                 STD. 
                 26.190 
                 2.133 
                 1.593 
                 68.695 
                 3.993 
                 0.000 
               
               
                 10.000 
                 STD. 
                 −3.907 
                 0.500 
                 1.620 
                 36.348 
                 4.091 
                 0.000 
               
               
                 11.000 
                 STD. 
                 5.569 
                 4.148 
                   
                   
                 4.276 
                 0.000 
               
               
                 12.000 
                 ASPH. 
                 −44.744 
                 2.670 
                 1.535 
                 56.197 
                 10.014 
                 0.000 
               
               
                 13.000 
                 ASPH. 
                 −7.366 
                 0.100 
                   
                   
                 11.206 
                 0.000 
               
               
                 14.000 
                 ASPH. 
                 10.912 
                 1.878 
                 1.535 
                 56.197 
                 13.525 
                 0.000 
               
               
                 15.000 
                 ASPH. 
                 8.131 
                 4.067 
                   
                   
                 14.172 
                 0.000 
               
               
                 IMA 
                 STD. 
                 Infinity 
                   
                   
                   
                 15.906 
                 0.000 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 4B 
               
               
                   
               
               
                 The aspheric coefficients for the aspheric 
               
               
                 surfaces of Example 4 as per Equation (1). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface 1: 
                   
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.00026172611 
               
               
                   
                 Coeff on r 6: 
                 1.1389733e−006 
               
               
                   
                 Coeff on r 8: 
                 −3.9695577e−009  
               
               
                   
                 Surface 2: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.00031331388 
               
               
                   
                 Coeff on r 6: 
                 8.2769362e−006 
               
               
                   
                 Surface 7: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0003692349 
               
               
                   
                 Surface 8: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.00051644976 
               
               
                   
                 Coeff on r 6: 
                 −9.716992e−006 
               
               
                   
                 Surface 12: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 5.9835381e−005 
               
               
                   
                 Coeff on r 6: 
                 −7.8711067e−006  
               
               
                   
                 Surface 13: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 0.00046012715 
               
               
                   
                 Coeff on r 6: 
                 2.4085634e−006 
               
               
                   
                 Surface 14: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0019509106 
               
               
                   
                 Coeff on r 6: 
                 1.8492481e−005 
               
               
                   
                 Surface 15: 
               
               
                   
                 Coeff on r 2: 
                 0 
               
               
                   
                 Coeff on r 4: 
                 −0.0027694282 
               
               
                   
                 Coeff on r 6: 
                  2.016481e−005 
               
               
                   
                 Coeff on r 8: 
                  −9.565005e−008  
               
               
                   
                   
               
             
          
         
       
     
       SUMMARY 
       [0043]    Compact wide angle lens designs are described. The lens has three lens groups and includes complex aspherical lens elements. The lens designs have a field of view of 80° or greater.