Abstract:
A convex-Fresnel LED lens and a LED assembly thereof are revealed. The lens is a Fresnel lens whose optical surface on a forward side thereof is a convex surface having draft with vertical shape so that the lens in the LED assembly concentrates light emitted from a LED chip to generate light whose peak intensity is an elliptic distribution pattern. Moreover, the lens and the LED assembly thereof satisfy certain conditions. Thereby, light from the LED chip is gathered by a single lens to form a preset specific distribution pattern and is satisfying requirement of the ratio of the luminous flux that is larger than 85%. The convex-Fresnel LED lens and a LED assembly thereof are applied to lights and flashlights in mobile phones or cameras.

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates to a LED lens and a LED assembly thereof, especially to a Fresnel LED lens whose peak intensity is an elliptic distribution pattern in a LED assembly, being applied to LED lighting devices, flashlights of mobile phones or cameras. 
   LED with features of low voltage, low power consumption and long operation life has been broadly applied to indicators, illuminators and so on. Moreover, due to pure light color, compact volume and flat package, LED is also used on flashlight of mobile phones. Yet light emitted from LED chip is a point source with uneven brightness. Thus a lot of studies focus on light collection. Besides minimization of chip size, improvement of light emitting efficiency, the lens used is also an important direction of technical development. 
   Along with development of modern technology, electronics are getting more miniature, compact and multi-functional. A lot of electronic products such as digital still cameras, PC cameras, network cameras, mobile phones and even personal digital assistant (PDA) are equipped with a lens. The LED lights or flashlight applied to such products are formed by a single or multiple LED array(s). For convenience of easy carrying and humanized design, LED flashlights or lighting devices not only meet requirements of luminous flux such as combinations of LED elements with different distribution patterns but also require miniature and lower cost. 
   In lens design of LED, there are two types-primary optical lens and secondary optical lens. The primary optical lens is a lens directly packaged on the LED chip and is for concentrating light while the secondary optical lens is an LED array formed by signal chip or a plurality of LED chips for spreading light beams. The conventional design of the primary optical lens is shown in ES2157829, symmetrical aspherical lens is used. Refer to JP3032069, JP2002-111068, JP2005-203499, US2006/187653, and CN101013193, spherical lens is used as primary optical lens. In JP2002-221658, spherical lens is applied to Bulk-type LED. In high-level applications, the primary optical lens not only concentrates light but also generates specific distribution pattern with even peak intensity such as large angle, small angle, round or elliptic distribution pattern. The primary optical lens is used in combination with the LED array so as to achieve optimal optical effects. 
   The application of the primary optical lens is shown in  FIGS. 1A  &amp;  FIG. 1B . A lens  23  is covered over a LED chip  21 . Light emitted from the LED chip  21  passes through the lens  23  to be concentrated to form a preset light pattern. Or a layer of secondary optical lens is added over the primary optical lens for brightness uniformity. There are various designs of the primary optical lens and some of them use a Fresnel optical surface, as revealed in WO/2003/083943, JP2005-049367, U.S. Pat. No. 6,726,859, US2007/0275344, US2008/0158854, EP1091167, and TW200711186 etc. 
   However, above conventional technique uses Fresnel lens covered over a plurality of LEDs, working as a secondary optical lens like a projector. Due to fast development of LED light emitting efficiency, the applications of a single LED have become more important. In the LED array or light sources formed by a plurality of LEDs, the brightness become in uniformity due to compensation of cross light beams through the lens. 
   As to the single LED, the design of the primary optical lens is more complicated than that of the LED array or light sources formed by multiple LEDs because both the light concentration efficiency and the uniformity of brightness of the primary optical lens should be considered. A set of Fresnel zone plates is disposed on surface of the Fresnel lens and a zone pitch thereof is increasing gradually from the inside to the outside or from the outside to the inside. Besides light guiding and light collection, the Fresnel lens with features of light weight, compact volume and plastic nature and lower cost is suitable for being applied to lighting systems. For example, in JP2005-257953 and US 2006/0027828, a Fresnel lens with a single-side or double-side is disposed over a LED light source so as to generate uniform brightness, as shown in  FIG. 1A  &amp;  FIG. 1B . Refer to TW560085, by a paraboloid surface and a Fresnel lens, reducing the divergent light and uniform brightness may be formed. Furthermore, refer to Korean 1020070096368 and TW I261654, a LED primary lens is made by a Fresnel lens but the distribution pattern thereof is a round distribution pattern. 
   However, as to multiple point LED lighting systems, brightness uniformity of both illuminance and light intensity should be considered. Conventional techniques usually use a certain ratio of the zone pitch to the zone height or changing zone pitch with changing zone height. For lighting system formed by a plurality of LEDs, changing zone pitch is better for matching requirements of uniform illuminance/light intensity. As to a single LED primary optical lens, the zone pitch depends on optical properties of the lens. Although the Fresnel lens with complicated surface and higher manufacturing cost, it provides better light efficiency and brightness uniformity, especially being applied to lighting devices with a single LED. In order to make light from single LED achieve higher efficiency, the present invention provide a primary optical lens of the LED made by Fresnel lens so as to concentrate light from surface of the LED chip and generate an Elliptic distribution pattern with uniform peak intensity. 
   SUMMARY OF THE INVENTION 
   Therefore it is a primary object of the present invention to provide a convex Fresnel LED lens and a LED assembly thereof. The LED assembly having a LED chip for emitting light, a Fresnel lens for concentrating light and generating Elliptic distribution pattern with uniform peak intensity and a gel layer filled between the Fresnel lens and the LED chip for sealing. Wherein, the Fresnel lens can be a meniscus lens whose outer surface is tapered or perpendicular. A concave surface of the meniscus lens is an optical surface facing the light source and is able to be aspherical or spherical while a convex surface thereof is an optical surface on forward side and is a Fresnel optical surface. Moreover, the Fresnel convex surface can be aspherical or spherical surface and its zone can be draft with vertical shape and equal zone pitch and satisfying the following conditions: 
   
     
       
         
           
             
               
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   Wherein f s  is effective focal length of the lens, r n  is radius of a last zone of a Fresnel optical surface R 2 , d 2  is thickness of the lens on a central axis Z, N d2  is refractive index of the lens, 2φ x  (deg.) is an angle of a half of highest light intensity (I 1/2 ) in the X direction of the light emitted from the lens, 2φ y  (deg.) is an angle of a half of highest light intensity (I 1/2 ) in the Y direction of the light emitted from the lens, 2Lx is length of the LED chip in the X direction, 2Ly is length of the LED chip in the Y direction, fg is a relative focal length of the lens, R 1  is a radius of an optical surface on the source side, R F  is a radius of a Fresnel convex surface on the forward side, d 0  is thickness of the LED chip, d 1  is thickness of a gel layer on the central axis, D is radius of an optical surface on the forward side. 
   Moreover, in order to meet various requirements of distribution pattern and light concentration properties, a radius of Fresnel convex surface R F  can be set as a radius of a spherical surface or an aspherical surface. 
   In order to simplify the manufacturing of the device, the Fresnel lens may be a plano-convex lens made from optical material whose forward-side optical surface is a Fresnel convex surface and is satisfying from equation (1) to equation (3). Where the optical material may be selected by plastic resin or glass. 
   In order to improvement concentrating efficiency of LED assembly, the outer surface of the Fresnel lens may be tapered with taper ν whose forward-side optical surface is a Fresnel convex surface and is satisfying from equation (1) to equation (3). 
   It is another object of the present invention to provide a LED assembly that includes a plano-convex or a meniscus Fresnel LED lens and a LED chip and the LED assembly features on its elliptic distribution pattern and the ratio of luminous flux is larger than 85% (η=β/α≧85%) and is satisfying the following conditions:
 
 E   1/2 ≦0.5 E   d   (7)
 
wherein
 
                   E     1   /   2       =         I     1   /   2           (     π   ⁢           ⁢       r   n     ·   sin     ⁢           ⁢     ϕ   x       )     ·     (         r   n     ·   sin     ⁢           ⁢     ϕ   y       )         ·   η             (   8   )               
wherein r n  is radius of a last zone of the Fresnel optical surface R 2 , α is luminous flux of the LED chip, β is luminous flux at infinity (100X f s ) of the forward side without consideration of attenuation, η is ratio of the luminous flux, E d  is incidence of the LED chip, and E 1/2  is incidence at the half of highest light intensity from the Fresnel lens surface.
 
   The convex Fresnel LED lens and the LED assembly thereof according to the present invention have elliptic distribution pattern and satisfies the requirement of luminous flux larger than 85%. Moreover, the thickness of the lens is minimized so that the lens can be applied to a single LED, LED arrays for lighting, or flashlights on mobile phones and cameras. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1A  shows LED assembly of a conventional LED lens; 
       FIG. 1B  shows LED assembly of a conventional LED lens; 
       FIG. 2  is a perspective view of LED assembly of a Fresnel LED lens without taper according to the present invention; 
       FIG. 3  is a perspective view of LED assembly of a Fresnel LED lens with taper according to the present invention; 
       FIG. 4  shows a relationship between radius of a convex surface and a Fresnel LED lens having draft with vertical shape and equal zone pitch; 
       FIG. 5  shows a relationship between radius of a convex surface and a Fresnel LED lens having draft with vertical shape and equal zone height; 
       FIG. 6  is a schematic drawing showing LED assembly of an embodiment according to the present invention; 
       FIG. 7  is a schematic drawing showing taper of a Fresnel LED lens of an embodiment according to the present invention; 
       FIG. 8  shows light paths of LED assembly of an embodiment according to the present invention; 
       FIG. 9  shows refraction of group A light beams and group B light beams by a Fresnel LED lens; 
       FIG. 10  shows light path of group A light beams and group B light beams passing through a Fresnel LED lens; 
       FIG. 11  is a schematic drawing uniform light intensity formed by combination of group A light beams with group B light beams in  FIG. 9  &amp;  FIG. 10 ; 
       FIG. 12  shows relationship between light intensity distribution of the first embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 13  shows relationship between light intensity distribution of the second embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 14  shows relationship between light intensity distribution of the third embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 15  shows relationship between light intensity distribution of the fourth embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 16  shows relationship between light intensity distribution of the fifth embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 17  shows relationship between light intensity distribution of the sixth embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
       FIG. 18  shows relationship between light intensity distribution of the seventh embodiment of the LED assembly and grazing angle in a polar coordinate system light; and 
       FIG. 19  shows relationship between light intensity distribution of the eighth embodiment of the LED assembly and grazing angle in a polar coordinate system light. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Refer to  FIG. 6 , a LED assembly  10  according to the present invention comprises a LED chip  11 , a gel layer  12  and a lens  13  along a central axis Z from a source side to a forward side. When light is emitted from the LED chip  11 , passing through the gel layer  12  and being concentrated by the lens  13  to form a light beam with elliptic distribution pattern symmetrical to the central axis Z that projects onto the forward side. The lens  13  is made of optical material such as optical glass or optical plastic resin. A concave surface of the lens  13  is a source-side optical surface R 1  facing on the light source and is aspherical or spherical optical surface. The other side opposite to the concave surface is a Fresnel optical surface R 2  with vertical shape draft and facing on the forward side. The optical surface R 2 , the lens thickness d 2  and the effective focal length f s  of the lens  13  satisfy the equation (1) and the equation (2). The angle  2  (having 2φ x  in the X direction and 2φ y  in the Y direction) of distribution pattern of light intensity formed by the lens  13  satisfies the equation (3). 
   The material of the gel layer  12  is not restricted. In the LED assembly, optical resin or silicon gel is commonly used. 
   Refer to  FIG. 2 , the LED assembly  10  is a plano-convex Fresnel LED lens  13 . An optical surface R 1  of the lens  13  on source side is a flat surface (R 1 =∞) while the other optical surface R 2  (opposite surface) on forward side is a convex Fresnel optical surface with vertical shape draft. 
   Refer to  FIG. 3 , a further embodiment of the LED assembly  20  is revealed. Along with the central axis Z from the source side to the forward side, the LED assembly  20  comprises of a LED chip  21 , a gel layer  22  and a plano-convex Fresnel lens  23 . The difference between this LED assembly  20  and the LED assembly  10  in  FIG. 2  is in that an outer surface of the lens  23  is with taper ν, as shown in  FIG. 7  so as to reduce light divergent from the side surface of the lens  23  and improve the optical efficiency. 
   The forward-side optical surface R 2  of the lens  13  or the lens  23  is a convex Fresnel optical surface lens having draft with vertical shape, as shown in  FIG. 4  &amp;  FIG. 5 . The Fresnel optical surface R 2  is transformed by the radius of R F . By means of different ways of transformation the radius of R F , various Fresnel optical surface R 2  are formed, as equal zone pitch ( FIG. 4 ) and equal zone height ( FIG. 5 ). 
   Refer to  FIG. 4 , a Fresnel optical surface R 2  with equal zone pitch is shown. The zone pitch r t  thereof is a fixed value. The optical surface with radius of R F  is transformed into a multi-zone Fresnel optical surface R 2  by equal zone pitch r t  but with unequal zone height h d  ( FIG. 6 .). Refer to  FIG. 5 , a Fresnel optical surface R 2  with equal zone height is shown. That means the zone height h d  is a fixed value. The optical surface with radius of R F  is transformed into a multi-zone Fresnel optical surface R 2  by equal vertical zone height h d  but with unequal zone pitch r t . 
   Each zone on the forward-side Fresnel optical surface R 2  is formed by a slope and a vertical zone surface (ring-shaped surface) so that the zone is called draft with vertical shape. The radius of the first zone is r 1  and the radius of the last zone is r n . As shown in  FIG. 9 , when light emits into the Fresnel optical surface R 2 , the light is refracted by the slope of each zone so as to achieve similar optical effects of paraboloid optical surface. 
   Refer from  FIG. 9  to  FIG. 11 , after being refracted by the Fresnel optical surface R 2 , the angles of emergence of the group A light beams (such as A 1 , A 2 , A 3  light beam) on an object are different due to different incident angles of the light beams A 1 , A 2 , A 3 , as shown in  FIG. 10 . On the position parallel to the central axis toward vertical direction, the group A light beams have higher light intensity in the center thereof. Similarly, after being refracted by the Fresnel optical surface, a light-beam group B (such as B 1 , B 2 , B 3  light beam) is also a light-beam group whose light intensity is higher in the center thereof. By the combinations of group A and group B, as shown in  FIG. 11 , a light pattern with even light intensity is generated so as to improve brightness uniformity. 
   If the optical surface R 1  of the lens  13  or the optical surface R 1  of the lens  23  is formed by aspherical optical surface, the Aspherical Surface Formula is the equation (9): 
                 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   )               
wherein c is curvature, h is height of the lens, K is conic constant, and A 4  to A 10  respectively are Nth Order Aspherical Coefficients.
 
   The curvature radius of R F  of the Fresnel optical surface R 2  is also defined by the equation (9), wherein Conic Constant is −1 (K=−1) for paraboloid surface, is 0 (K=0) for spherical surface, respectively. 
   Refer to  FIG. 8 , light from the LED chip  11  ( 21 ) is concentrated and refracted by the lens  13  ( 23 ) to form a required elliptic distribution pattern that satisfies the condition of β/α≧85% at an angle of 2φ (2φ x  in the X direction and 2φ y  in the Y direction). Neglecting attenuation such as air refraction and scattering, the equation (7) is satisfied. Therefore, by a plano-convex or meniscus Fresnel LED lens and a LED chip, the LED assembly  10  ( 20 ) can emit preset Elliptic distribution pattern with uniform light intensity. Moreover, the LED assembly can be used in the form of a single assembly or an array formed by the LED assemblies with different distribution patterns. 
   In an embodiment of the present invention, the LED chip  11  is a blue-ray chip whose size is 1.85×0.77 mm, 1st peak wave-length is 450 nm, and 2nd peak wave-length is 550 nm. The blue light has diverge angle of ω x =39.8° in the X direction and ω y =35.2° in the Y direction for last light beam, α=78.5 lm, and light intensity E d =23.97 Lux. The diameter of the lens  13  ( 23 ) is 5 mm (D=2.5 mm). The optical surface on the forward side R 2  is a Fresnel optical surface having vertical draft shape, and equal zone height/or equal zone pitch. The gel layer  12  is made from transparent optical silicon gel with refractive index of 1.491. As to the LED assembly with a primary optical lens, other components except the lens and LED assembly of the present invention are obvious to those in the art. Thus the size and material of the components, wavelength and emitting angle of LED, patterns, the zone pitch and the zone height of the Fresnel optical surfaces are all can be changed, modified and even substituted with equal effect parts. 
   In the following first to fourth embodiments, a LED assembly with a plano-convex Fresnel lens that is with no taper and equal zone height is used. In the fifth embodiment, a LED assembly with a plano-convex Fresnel lens that is with taper and equal zone height is used. In the sixth embodiment, a LED assembly with a plano-convex Fresnel lens that is with no taper and equal zone pitch is used. In the seventh and eighth embodiments, a LED assembly with a meniscus Fresnel lens that is with no taper and equal zone height is used. 
   Two tables are shown in the following each embodiment respectively, wherein the first table includes data of radius R (unit: mm) of the source-side optical surface R 1  as well as that of the optical surface on the source side R 2 , or radius R F  (unit: mm), along a central axis Z from the source side to the forward side, the on-axis surface spacing di (unit: mm), the taper ν of the lens ( 13               23 ), respective refractive index (N d ) and the optical surface number. Denoted that labeled with * is an aspherical Fresnel optical surface. The second table is shown the respective parameters in the equation (9) of the aspherical Fresnel optical surface, radius r 1  of a first Fresnel zone from the center of the lens, radius r n  of the last Fresnel zone, Fresnel zone height h d  and number of Fresnel zones.
   The First Embodiment 
   Refer to  FIG. 6  and  FIG. 12 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE ONE 
             
           
           
             
                 
             
             
               f = 5.466 υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               2.700 
               2.00 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE TWO 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −5.0000E−01 
               3.1000E−02 
               1.2600E−05 
               7.8000E−08 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.05 
               0.518 
               2.526 
               27 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index Nd2 of 1.582 and Abbe number νd2 of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 82° in the X direction, 65° in the Y direction and the luminous flux β=67.424 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
   
     
       
         
           η 
           = 
           0.8589 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           20.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           41.0 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           32.5 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           2.1640 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.2130 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.0331 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.1039 
         
       
     
   
   By the above Table one and Table two as well as  FIG. 12 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity. 
   The Second Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 13 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE THREE 
             
           
           
             
                 
             
             
               f = 2.530   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               2.00 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE FOUR 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               4.0000E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.510 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 67° in the X direction, 40° in the Y direction and the luminous flux β=70.245 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
   
     
       
         
           η 
           = 
           0.9219 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           29.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           33.0 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           19.1 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           1.0081 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.4601 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.1965 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.3216 
         
       
     
   
   By the above Table three and Table four as well as  FIG. 13 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Third Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 14 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE FIVE 
             
           
           
             
                 
             
             
               f = 2.530   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               2.00 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE SIX 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               1.1435E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.510 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 70° in the X direction, 42° in the Y direction and the luminous flux β=73.798 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
   
     
       
         
           η 
           = 
           0.9401 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           30.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           35.2 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           19.5 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           1.0081 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.4601 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.1839 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.3140 
         
       
     
   
   By the above Table five and Table six as well as  FIG. 14 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Fourth Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 15 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE SEVEN 
             
           
           
             
                 
             
             
               f = 2.530   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               2.00 
               1.491 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE EIGHT 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               4.0000E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.510 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from PMMA plastic with refractive index N d2  of 1.491 and Abbe number ν d2  of 32. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 62° in the X direction, 40° in the Y direction and the luminous flux β=74.069 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
   
     
       
         
           η 
           = 
           0.9435 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           24.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           31.0 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           20.0 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           1.0081 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.3881 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.1975 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.2766 
         
       
     
   
   By the above Table seven and Table eight as well as  FIG. 15 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Fifth Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 16   
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE NINE 
             
           
           
             
                 
             
             
               f = 2.530   υ = 6.17 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               2.00 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE TEN 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               4.0000E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.356 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern 68° in the X direction, 43° in the Y direction and the luminous flux β=72.48 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
   
     
       
         
           η 
           = 
           0.9219 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           32.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           33.0 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           19.0 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           1.0742 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.4601 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.0082 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.4043 
         
       
     
   
   By the above Table nine and Table ten as well as  FIG. 16 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Sixth Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 17 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE ELEVEN 
             
           
           
             
                 
             
             
               f = 5.061   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               ∞ 
               0.52 
               1.410 
             
             
                 
               S2* 
               2.500 
               2.00 
               1.582 
             
             
                 
                 
             
             
                 
               *Spherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
           
             
             
             
             
             
           
         
             
                 
               TABLE TWELVE 
             
             
                 
                 
             
             
                 
               r t   
               r n   
               No. of Zone 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
                 
               Fesnel Surface(mm) 
               0.125 
               2.500 
               19 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern 85° in the X direction, 70° in the Y direction and the luminous flux β=72.72 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
   
     
       
         
           η 
           = 
           0.8913 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           22.5 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           42.0 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           35.0 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           2.0243 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.2300 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.0248 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.1154 
         
       
     
   
   By the above Table eleven and Table twelve as well as  FIG. 17 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Seventh Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 18 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE THIRTEEN 
             
           
           
             
                 
             
             
               f = 2.530   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               30.00 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               1.90 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE FOURTEEN 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               4.0000E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.510 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 68° in the X direction, 36° in the Y direction and the luminous flux β=72.929 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
   
     
       
         
           η 
           = 
           0.9163 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           29.0 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           33.9 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           18.1 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           
             
               1.0081 
               ⁢ 
               
                 
 
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       N 
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     - 
                     1 
                   
                   ) 
                 
                 ⁢ 
                 
                   
                     d 
                     2 
                   
                   
                     f 
                     s 
                   
                 
               
             
             = 
             
               
                 0.4361 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 ϕ 
                                 x 
                               
                               - 
                               
                                 ω 
                                 x 
                               
                             
                             π 
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               
                                 ϕ 
                                 y 
                               
                               - 
                               
                                 ω 
                                 y 
                               
                             
                             π 
                           
                           ) 
                         
                         2 
                       
                     
                   
                   · 
                   
                     f 
                     g 
                   
                 
               
               = 
               
                 
                   0.2193 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       E 
                       
                         1 
                         / 
                         2 
                       
                     
                     
                       E 
                       d 
                     
                   
                 
                 = 
                 0.3232 
               
             
           
         
       
     
   
   By the above Table thirteen and Table fourteen as well as  FIG. 17 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity. 
   The Eighth Embodiment 
   Refer to  FIG. 6  &amp;  FIG. 19 . 
   
     
       
             
           
             
             
             
             
             
           
         
             
               TABLE FIFTEEN 
             
           
           
             
                 
             
             
               f = 2.530   υ = 0 
             
           
        
         
             
                 
               Surface No. 
               R or R F   
               d i   
               Nd i   
             
             
                 
                 
             
             
                 
               S0 
               ∞ 
               0.10 
                 
             
             
                 
               S1 
               9.00 
               0.52 
               1.410 
             
             
                 
               S2* 
               1.250 
               1.65 
               1.582 
             
             
                 
                 
             
             
                 
               *Aspherical Zone Fesnel 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE SIXTEEN 
             
             
                 
             
           
           
             
                 
               K 
               A 2   
               A 4   
               A 6   
             
             
                 
             
             
               Aspherical 
               −1.0000E+00 
               4.0000E−02 
               0.0000E+00 
               0.0000E+00 
             
             
               Surface 
             
             
                 
             
           
        
         
             
                 
                 
               h d   
               r l   
               r n   
               No. of Zone 
             
             
                 
                 
             
             
                 
               Fesnel 
               0.06 
               0.387 
               2.510 
               41 
             
             
                 
               Surface (mm) 
             
             
                 
                 
             
           
        
       
     
   
   In this embodiment, the lens  13  is made from glass with refractive index N d2  of 1.582 and Abbe number ν d2  of 61.7. The light is concentrated by the lens  13  to form an elliptic distribution pattern, 65° in the X direction, 60° in the Y direction and the luminous flux β=70.245 lm at infinity (100X f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
   
     
       
         
           η 
           = 
           0.9096 
         
       
     
     
       
         
           
             I 
             
               1 
               / 
               2 
             
           
           = 
           30.1 
         
       
     
     
       
         
           
             ϕ 
             x 
           
           = 
           32.1 
         
       
     
     
       
         
           
             ϕ 
             y 
           
           = 
           18.1 
         
       
     
     
       
         
           
             
               f 
               s 
             
             
               r 
               n 
             
           
           = 
           1.0081 
         
       
     
     
       
         
           
             
               ( 
               
                 
                   N 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 - 
                 1 
               
               ) 
             
             ⁢ 
             
               
                 d 
                 2 
               
               
                 f 
                 s 
               
             
           
           = 
           0.3786 
         
       
     
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           x 
                         
                         - 
                         
                           ω 
                           x 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           ϕ 
                           y 
                         
                         - 
                         
                           ω 
                           y 
                         
                       
                       π 
                     
                     ) 
                   
                   2 
                 
               
             
             · 
             
               f 
               g 
             
           
           = 
           0.2721 
         
       
     
     
       
         
           
             
               E 
               
                 1 
                 / 
                 2 
               
             
             
               E 
               d 
             
           
           = 
           0.3484 
         
       
     
   
   By the above Table fifteen and Table sixteen as well as  FIG. 17 , it has been proved that the LED assembly with convex-Fresnel LED lens of the invention can achieve higher efficiency and generate an Elliptic distribution pattern with uniform peak intensity.