Abstract:
A Fresnel light emitting diode (LED) Lens and a LED Assembly thereof are provided. The Fresnel LED Lens is a lens disposed with a plurality of Fresnel optical surfaces. Each Fresnel optical surface includes a zone area having a plurality of drafts with vertical shape. Each Fresnel optical surface is arranged linearly along a center of a corresponding LED, and each Fresnel optical surface can used to focus light emitted from a LED chip so as to generate a quasi-circle distribution pattern of light with uniform light intensity and satisfy special optical requirements. A LED assembled formed by the Fresnel LED lens and a corresponding LED is used as a light source applied to illumination, mobile phone flashlights or camera flashlights.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to a Fresnel LED lens and a LED assembly thereof, especially to a Fresnel LED lens with a plurality of Fresnel optical surfaces that is arranged linearly, and it can be assembled with other components to form a light source to apply to illumination, flashlights of mobile phones or cameras. 
         [0002]    LED with features of low voltage, low power consumption and long operation life has been broadly applied to indicators, illuminators and so on. Compared with conventional light sources, light emitted from the LED chip is scattered. Thus optical lenses are required to concentrate light in small area or to uniformize light in large area. In lens design of LED, there are two lens types—primary optical lens and secondary optical lens. The primary optical lens is a lens directly packaged on the LED chip and it is used for concentrating light. The secondary optical lens is an LED array formed by signal chip or a plurality of LED chips, and it is used for spreading or unifying light beams. As to the design of the secondary optical lens, Fresnel lens is used so as to reduce thickness of the secondary optical lens. The Fresnel lens with a single LED is shown in  FIG. 1  and  FIG. 2 , light is emitted from a LED  21 , concentrated by a Fresnel lens  23 , and projected onto a target, as revealed in JP 2005257953, Taiwan Pat. No. M347533, M347534 and U.S. Pat. No. 6,726,859. The Fresnel lens with a LED array is shown in  FIG. 3  and  FIG. 4 , as revealed in US2007/0275344, US2008/0158854, US2002/0025157, US2007/0034890, EP1091167 etc. 
         [0003]    In order to meet requirements of power saving and compact design, LED is applied to flashlights of digital still cameras, PC cameras, network cameras, mobile phones etc. The LED lights or flashlight applied to such products are formed by a single LED or a LED array having a plurality of LED. Then a secondary optical lens is added so as to enable illumination and light intensity as uniform as possible. The light distribution pattern requires uniform light intensity and quasi-circle distribution pattern is most suitable to be applied to lighting or flashlights. The Fresnel-type secondary optical lens makes light emitted from LED achieve maximum efficiency. Thus there is a need to provide a secondary optical lens formed by a Fresnel lens that generates quasi-circle distribution pattern and a LED assembly thereof to apply to lighting, mobile flashlights or camera flashlights. 
       SUMMARY OF THE INVENTION 
       [0004]    Therefore it is a primary object of the present invention to provide a Fresnel LED lens and a LED assembly thereof. The LED assembly includes a plurality of LED arranged in a line at an equal interval, a circuit board for mounting the plurality of LEDs, and a Fresnel LED lens for concentrating light and forming a quasi-circle distribution pattern with uniform light intensity. The Fresnel LED lens is made from optical material and it has a source-side optical surface and an object-side optical surface. Both optical surfaces are flat surfaces. Moreover, the object-side optical surface is disposed with a plurality of Fresnel optical surfaces corresponding to the LED. Each central axis formed by a center of each LED connected with a center of a corresponding Fresnel optical surface is parallel to one another. Furthermore, the Fresnel convex surface is aspherical or spherical surface and it has a zone area having a plurality of drafts with vertical shape and equal zone pitch. The Fresnel convex surface satisfies the following conditions: 
         [0000]    
       
         
           
             
               
                 
                   0.7 
                   ≤ 
                   
                     
                       f 
                       s 
                     
                     
                       r 
                       n 
                     
                   
                   ≤ 
                   2.2 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   0.1 
                   ≤ 
                   
                     
                       ( 
                       
                         
                           N 
                           
                             d 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                      
                     
                       
                         d 
                         2 
                       
                       
                         f 
                         s 
                       
                     
                   
                   ≤ 
                   1.25 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     φ 
                                     x 
                                   
                                   - 
                                   
                                     ω 
                                     x 
                                   
                                 
                                 π 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     φ 
                                     y 
                                   
                                   - 
                                   
                                     ω 
                                     y 
                                   
                                 
                                 π 
                               
                               ) 
                             
                             2 
                           
                         
                       
                       · 
                       
                         f 
                         g 
                       
                     
                     ≤ 
                     0.6 
                   
                    
                   
                     
 
                   
                    
                   
                     wherein 
                      
                     
                       : 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     g 
                   
                   = 
                   
                      
                     
                       
                         ( 
                         
                           
                             1 
                             
                               R 
                               1 
                             
                           
                           - 
                           
                             1 
                             
                               R 
                               F 
                             
                           
                         
                         ) 
                       
                       · 
                       
                         f 
                         s 
                       
                     
                      
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     ω 
                     x 
                   
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                      
                     
                       ( 
                       
                         D 
                         
                           
                             d 
                              
                             
                                 
                             
                              
                             0 
                           
                           + 
                           
                             d 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             d 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           Lx 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     ω 
                     y 
                   
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                      
                     
                       ( 
                       
                         D 
                         
                           
                             d 
                              
                             
                                 
                             
                              
                             0 
                           
                           + 
                           
                             d 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             d 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           Ly 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein f s  is effective focal length of the lens, d 0  is thickness of the LED chip, d 1  is thickness of seal gel on the central axis, d 2  is thickness of the LED lens on the central axis, r n  is radius of a last draft of a Fresnel optical surface R2, 2φ x , (deg.) is an angle of a place where light intensity is half highest light intensity (I 1/2 ) in the X direction of the light emitted from the Fresnel LED lens, 2φ y  (deg.) is an angle of a place where light intensity is half highest light intensity (I 1/2 ) in the Y direction of the light emitted from the Fresnel LED lens, 2 Lx is length of the LED chip in the X direction, 2 Ly is length of the LED chip in the Y direction, fg is a equivalent focal length of the Fresnel LED lens, R 1  is a radius of the source-side optical surface, R F  is a radius of the object side optical surface, and D is a maximum radius of a single Fresnel optical surface on the Fresnel LED lens. 
         [0005]    For convenience of use, the Fresnel lens of the present invention can be made from optical glass or optical glass. 
         [0006]    It is another object of the present invention to provide a LED assembly that includes at least two LED that is assembled on the circuit board linearly at an equal interval. Each central axis formed by a center of each LED connected with a center of a corresponding Fresnel optical surface is parallel to one another. The light pattern of the LED assembly is quasi-circle distribution pattern. In the cross section of the light pattern, the ratio of the length of the short axis to that of the long axis is larger than 0.8, or the ratio of the length of the long axis to that of the short axis is smaller than 1.25, as the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     0.8 
                     ≤ 
                     κ 
                   
                   = 
                   
                     
                       
                         φ 
                         y 
                       
                       
                         φ 
                         x 
                       
                     
                     ≤ 
                     1.25 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein 2φ x  (deg.) is an angle of a place where light intensity is half of highest light intensity (I 1/2 ) in the X direction of the light emitted from the Fresnel LED lens, 2φ y  (deg.) is an angle of a place where light intensity is half of highest light intensity (I 1/2 ) in the Y direction of the light emitted from the Fresnel LED lens, κ is ratio of φ y  to φ x . 
         [0007]    It is a further object of the present invention to provide a LED assembly that includes a Fresnel LED lens, generates a quasi-circle distribution pattern and satisfies following condition (ratio of luminous flux is larger than 60%): 
         [0000]    
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       β 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                           α 
                           i 
                         
                       
                     
                     ≥ 
                     
                       60 
                        
                       % 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein α i  is luminous flux of light emitted from ith LED, 
         [0000]    
       
         
           
             
               ∑ 
               
                 i 
                 = 
                 1 
               
               n 
             
              
             
               α 
               i 
             
           
         
       
     
         [0000]    is total luminous flux of light emitted from a number n of LED, β is luminous flux at infinity (100×f s ) of the object side without consideration of attenuation. 
         [0008]    Thereby the Fresnel LED lens and the LED assembly thereof according to the present invention produce a quasi-circle distribution pattern and satisfy the condition that the ratio of luminous flux is larger than 60%. Moreover, the LED assembly features on thin thickness so as to be applied to lighting devices or flashlights of mobile phones and cameras. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  is a LED assembly with a Fresnel lens and a LED of a prior art; 
           [0010]      FIG. 2  is a LED assembly with a Fresnel lens and a LED of a prior art; 
           [0011]      FIG. 3  is a LED assembly having a Fresnel lens and a LED array of a prior art; 
           [0012]      FIG. 4  is a LED assembly having a Fresnel lens and a LED array of a prior art; 
           [0013]      FIG. 5  is a lateral cross sectional view of an embodiment of a LED assembly according to the present invention; 
           [0014]      FIG. 6  is a schematic drawing showing a Fresnel lens and a LED assembly according to the present invention; 
           [0015]      FIG. 7  is a perspective view of an embodiment of a Fresnel LED lens according to the present invention; 
           [0016]      FIG. 8  is a top view of the embodiment in  FIG. 7 ; 
           [0017]      FIG. 9  is a cross sectional view of the embodiment along a  9 - 9  line in  FIG. 8 ; 
           [0018]      FIG. 10  is a lateral cross sectional view of another embodiment of a LED assembly according to the present invention; 
           [0019]      FIG. 11  is a top view of the embodiment in  FIG. 10 ; 
           [0020]      FIG. 12  is a cross sectional view of the embodiment along a  12 - 12  line in  FIG. 11 ; 
           [0021]      FIG. 13  shows a relationship between light intensity distribution and grazing angle in a polar coordinate system light of an embodiment of a LED according to the present invention; 
           [0022]      FIG. 14  shows a relationship between light intensity distribution and grazing angle in a polar coordinate system light of an embodiment of a LED assembly according to the present invention; 
           [0023]      FIG. 15  shows a relationship between light intensity distribution and grazing angle in a polar coordinate system light of another embodiment of a LED according to the present invention; 
           [0024]      FIG. 16  shows a relationship between light intensity distribution and grazing angle in a polar coordinate system light of another embodiment of a LED assembly according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0025]    Refer to  FIG. 5 , a LED assembly  10  of the present invention includes a plurality of LEDs  11  arranged in a line at an equal distance, a circuit board  12  and a Fresnel LED lens  13 . The Fresnel LED lens  13  has a source-side optical surface  130  and an object-side optical surface  131 . The object-side optical surface  131  is disposed with a plurality of Fresnel optical surfaces  131   a - 131   e  and the amount of Fresnel optical surfaces is equal to that of the LEDs  11 . 
         [0026]    Two conductive plates  121  that transmit power to each LED  11  for emitting light are connected to the circuit board  12 . Each LED  11  includes a LED chip  111  and seal gel  112 , and it can emit light. The light emitted from the LED chip  111  passes through the seal gel  112 , air, the source-side optical surface  130  in sequence and then it is concentrated by the Fresnel optical surfaces  131   a - 131   e  to form a light beam with quasi-circle distribution pattern. 
         [0027]    Refer to  FIG. 6 , a central axis Zb is formed by a center of the LED  11  connected with a center of the corresponding Fresnel optical surface  131   b , d 0  is thickness of the seal gel  112 , d 1  is thickness of air layer, and d 2  is distance between the source-side optical surface  130  and the Fresnel optical surface  131   b . The Fresnel optical surface  131   b  is an optical surface having a zone area, and the zone area includes several surrounding drafts. Each draft has vertical shape and equal zone height, wherein r 1  is radius of the first draft (the diameter is 2 r 1 ), r n  is radius of the last draft, h d  is height of the draft, and r t  is an interval between two adjacent drafts. The Fresnel optical surface  131   b  also must satisfy the equation (1) and equation (2). 
         [0028]    The material of the seal gel  12  is not restricted while optical resin or silicon gel is often used in the LED  11 . The Fresnel LED lens  13  is made from optical glass or optical plastic resin. 
         [0029]    Refer from  FIG. 7  to  FIG. 9 , the Fresnel LED lens  13  includes a concave slot  132  and a locking slot  133 . The concave slot  132  is used to receive and locate the circuit board  12  so as to make the plurality of LEDs  11  on the circuit board  12  align with a center of the Fresnel optical surfaces  131   a - 131   e  of the Fresnel LED lens  13  respectively. The locking slot  133  is used to assemble with cameras or other devices. 
         [0030]    The light emitted from the LED chip  111  passes through the Fresnel optical surfaces  131   a - 131   e  for concentration and refraction, and then a required quasi-circle distribution pattern of light is formed. The required quasi-circle distribution pattern of light satisfies the condition of β/α≧85% at an angle of 2ψ (2 φ x  in the X direction and 2 φ y  in the Y direction), wherein α is luminous flux emitted from the LED chip and β is luminous flux at infinity (100×f s ) of the object side without consideration of air refraction and scattering. 
         [0031]    If the Fresnel optical surface is an aspherical optical surface, the aspherical surface formula is the equation (9): 
         [0000]    
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       
                         ch 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     K 
                                   
                                   ) 
                                 
                                  
                                 
                                   c 
                                   2 
                                 
                                  
                                 
                                   h 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         A 
                         4 
                       
                        
                       
                         h 
                         4 
                       
                     
                     + 
                     
                       
                         A 
                         6 
                       
                        
                       
                         h 
                         6 
                       
                     
                     + 
                     
                       
                         A 
                         8 
                       
                        
                       
                         h 
                         8 
                       
                     
                     + 
                     
                       
                         A 
                         10 
                       
                        
                       
                         h 
                         10 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein c is curvature, h is height of the lens, K is conic constant, and A 4  to A 10  respectively are 4 th , 6 th , 8 th , and 10 th  Order Aspherical Coefficients. 
         [0032]    The curvature radius R F  of the Fresnel optical surfaces  131   a - 131   e  is also defined by the equation (9), wherein Conic Constant is −1 (K=−1) for paraboloid surface, and 0 (K=0) for spherical surface, respectively. 
         [0033]    The present invention will be best description by following embodiments. Each of the Fresnel optical surfaces having a zone area, and the zone area includes several surrounding drafts. Each draft has vertical shape and equal zone. The seal gel  12  is made from transparent optical silicon gel with refractive index of 1.41. As to the general LED assembly, other components except the Fresnel LED lens of the present invention are obvious to those skilled in the art. Thus the size and material of each component of the LED assembly, wavelength and emitting angle of LED, patterns, the zone pitch and the zone height of the Fresnel optical surfaces all can be changed, modified and even substituted with equal effect parts. 
       Embodiment One 
       [0034]    Refer to  FIG. 5 ,  FIG. 7-FIG .  9 ,  FIG. 13  and  FIG. 14 , table one includes data of radius R of the seal gel  112  of the LED chip  111 , the curvature radius R F  (unit:mm) of the Fresnel optical surfaces  131   a - 131   e , and the on-axis surface spacing di (unit:mm) along a central axis Z from the source side to the object side, respective refractive index (N d ), and the effective focal length f s  of the Fresnel optical surface, wherein the surface labeled with * is an aspherical Fresnel optical surface. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE ONE 
               
               
                   
                   
               
               
                   
                 Surface No. 
                 R or R F   
                 d 
                 Nd 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 S0 
                 ∞ 
                 0.626 
                 1.410 
               
               
                   
                 S1 
                 ∞ 
                 0.85 
                 1.0 
               
               
                   
                 S2* 
                 2.0 
                 0.90 
                 1.587 
               
               
                   
                   
               
               
                   
                 *Aspherical Zone Fresnel 
               
             
          
         
       
     
         [0035]    The following table two shows respective parameters in the equation (9) of aspherical surface of Fresnel optical surface whose radius is R P , radius r 1  of a first Fresnel draft and radius r n  of the last Fresnel draft from the center of the lens, Fresnel zone height h d  and number of Fresnel drafts. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE TWO 
               
               
                   
               
               
                 Effective focal length fs = 4.4085 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 K 
                 A 2   
                 A 4   
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −1.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Surface 
               
               
                   
               
               
                   
                 h d   
                 r 1   
                 r n   
                 No. of draft 
               
               
                   
               
               
                 Fresnel 
                 0.125 
                 0.1414 
                 4.0 
                 8 
               
               
                 Surface(mm) 
               
               
                   
               
             
          
         
       
     
         [0036]    In this embodiment, the Fresnel LED lens  13  is made from plastic material with refractive index N d2  of 1.587 and five Fresnel optical surfaces  131   a - 131   e  are disposed on the object-side optical surface  131 . The size of the five LEDs  11  is 1.12×1.12 mm, diverge angles of the LEDs  11  are ω x =31.5° in the X direction and ω y =31.5° in the Y direction, and α is 6.9 lm. The relationship between LED  11  light intensity distribution and distribution angle in a polar coordinate system is shown in  FIG. 13 . The five LEDs  11  are disposed on the circuit board  12  in a linear form. The distance L between centers of two adjacent LED  11  is 3.0 (mm). That means the distance between two adjacent Fresnel optical surfaces  131   a - 131   e  L is 3.0 (mm). The circuit board  12  is mounted and fixed in the concave slot  132  of the Fresnel LED lens  13 . Each central axis Zb formed by centers of each LED  11  connected with center of the corresponding Fresnel optical surfaces  131   a - 131   e  is parallel to one another. The five central axis Zb are parallel to one another. The circuit board  12  is connected with external power sources by two conductive plates  121 . After the power is applied, the current passes through the conductive plates  121  and the circuit board  12  to make the five LED  11  emit light. After the light is concentrated by the Fresnel optical surfaces  131   a - 131   e  of the Fresnel LED lenses  13 , angles of a place where light intensity is half of the maximum luminance are 40.5° in the X direction and 35° in the Y direction so that a quasi-circle distribution pattern of the light is formed, and κ&gt;0.8. 
         [0037]    The relationship between light intensity distribution and distribution angle in a polar coordinate system of light of the LED assembly  10  is shown in  FIG. 14 . The luminous flux β is 32.5 μm at infinity (100×f s ) without consideration of air refraction and scattering. Equation (1), equation (2), equation (3), equation (7), and equation (8) respectively are as following: 
         [0000]    
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.102 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
                
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.1198 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             φ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             φ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.5397 
           
         
       
       
         
           
             
               φ 
               x 
             
             = 
             
               20.25 
                
               ° 
             
           
         
       
       
         
           
             
               φ 
               y 
             
             = 
             
               17.5 
                
               ° 
             
           
         
       
       
         
           
             κ 
             = 
             
               
                 
                   φ 
                   y 
                 
                 
                   φ 
                   x 
                 
               
               = 
               0.864 
             
           
         
       
       
         
           
             η 
             = 
             
               
                 β 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     n 
                   
                    
                   
                     α 
                     i 
                   
                 
               
               = 
               
                 94.2 
                  
                 % 
               
             
           
         
       
     
         [0000]    Equation (1), equation (2), equation (3), equation (7) and equation (8) are satisfied. 
       Embodiment Two 
       [0038]    Refer from  FIG. 10  to  FIG. 12 ,  FIG. 15 , and  FIG. 16 , parameters in the following tables—table three and table four are the same with those in table one and table two. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE THREE 
               
               
                   
                   
               
               
                   
                 Surface No. 
                 R or R F   
                 d 
                 Nd 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 S0 
                 ∞ 
                 0 
                 1 
               
               
                   
                 S1 
                 ∞ 
                 0.4 
                 1 
               
               
                   
                 S2* 
                 2.7 
                 2 
                 1.8 
               
               
                   
                   
               
               
                   
                 *Aspherical Zone Fresnel 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE FOUR 
               
               
                   
               
               
                 Effective focal length fs = 5.4659 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 K 
                 A 2   
                 A4 
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −5.000E−01 
                 3.100E−02 
                 1.2600E−5 
                 7.8000E−8 
               
               
                 Surface 
               
               
                   
               
               
                   
                 h d   
                 r 1   
                 r n   
                 No. of draft 
               
               
                   
               
               
                 Fresnel 
                 0.05 
                 1.0368 
                 5.052 
                 27 
               
               
                 Surface(mm) 
               
               
                   
               
             
          
         
       
     
         [0039]    In this embodiment, the Fresnel LED lens  13  is made from glass with refractive index N d2  of 1.8 and six Fresnel optical surfaces  131   a - 131   f  are disposed on the object-side optical surface  131 . The size of the six LED  11  is 1.85×0.77 mm, diverge angles of the LEDs are ω x =38.25° in the X direction and ω y =29.25° in the Y direction, and α is 78.5 lm. The relationship between LED  11  light intensity distribution and distribution angle in a polar coordinate system is shown in  FIG. 15 . The six LEDs  11  are disposed on the circuit board  12  in a linear form. The distance L between centers of two adjacent LED  11  is 4.0 (mm). That means the distance between two adjacent Fresnel optical surfaces  131   a - 131   f  L is 4.0 (mm). After light emitted from the six LED  11  is concentrated by the Fresnel optical surfaces  131   a - 131   f , angles of a place where light intensity is half of the maximum luminance are 63° in the X direction and 54° in the Y direction so that a quasi-circle distribution pattern of the light is formed and κ&gt;0.8. 
         [0040]    The relationship between light intensity distribution and distribution angle in a polar coordinate system of light of the LED assembly  10  is shown in  FIG. 16 . The luminous flux β is 326.8 lm at infinity (100×f s ) without consideration of air refraction and scattering. Equation (1), equation (2), equation (3), equation (7), and equation (8) respectively are as following: 
         [0000]    
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.153 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
                
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.1145 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             φ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             φ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.2744 
           
         
       
       
         
           
             
               φ 
               x 
             
             = 
             
               31.5 
                
               ° 
             
           
         
       
       
         
           
             
               φ 
               y 
             
             = 
             
               27.0 
                
               ° 
             
           
         
       
       
         
           
             κ 
             = 
             
               
                 
                   φ 
                   y 
                 
                 
                   φ 
                   x 
                 
               
               = 
               0.873 
             
           
         
       
       
         
           
             η 
             = 
             
               
                 β 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     n 
                   
                    
                   
                     α 
                     i 
                   
                 
               
               = 
               
                 69.38 
                  
                 .2 
                  
                 % 
               
             
           
         
       
     
         [0000]    Equation (1), equation (2), equation (3), equation (7) and equation (8) are satisfied. 
         [0041]    In summary, the LED assembly  10  with the Fresnel LED lens  13  according to the present invention has high efficiency and provides quasi-circle distribution pattern with uniform light intensity. The applications of the present invention in lighting or camera flashlights etc. are increased. 
         [0042]    Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, and representative devices shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.