Abstract:
A plano-Fresnel LED lens and a LED assembly thereof are revealed. The lens is a Fresnel lens whose optical surface on the forward side thereof is a plano surface having saw teeth with vertical taper (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 plano-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 Plano-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  FIG. 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 1261654, 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 plano-Fresnel LED lens and a LED assembly thereof. The LED assembly having a LED chip for emitting light, a Fresnel lens fort 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 plano-concave lens whose outer surface is tapered or perpendicular. A concave surface of the Fresnel lens is an optical surface facing the light source and is able to be aspherical or spherical while a plano-Fresnel surface thereof is an optical surface on forward side and is a Fresnel optical surface. Moreover, the light-collecting curved surface (R F ) for forming the plano-Fresnel 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: 
                   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           (   3   )               
wherein:
 
                     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   )               
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 plano-Fresnel 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, the radius R F  of the light-collecting curved surface (R F ) (a convex surface) for forming the plano-Fresnel surface of the Fresnel lens can be set as a radius of a spherical surface or an aspherical surface. 
     In order to simplify the manufacturing of the device, the plano-concave Fresnel lens can be replaced to be a plano-plano lens made from optical material whose forward-side optical surface is a plano-Fresnel 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-concave or a plano-plano 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 ≦0.6 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 surface R 2 , α is luminous flux of the LED chip, β is luminous flux at infinity (100×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 plano-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 the radius of a convex surface and a plano-Fresnel surface of a Fresnel LED lens having draft with vertical shape and equal zone pitch; 
         FIG. 5  shows a relationship between the radius of a convex surface and a plano-Fresnel surface of 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; 
         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; 
         FIG. 20  shows relationship between light intensity distribution of the ninth embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
         FIG. 21  shows relationship between light intensity distribution of the tenth embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
         FIG. 22  shows relationship between light intensity distribution of the eleventh embodiment of the LED assembly and grazing angle in a polar coordinate system light; 
         FIG. 23  shows relationship between light intensity distribution of the twelfth embodiment of the LED assembly and grazing angle in a polar coordinate system light; and 
         FIG. 24  shows relationship between light intensity distribution of the thirteenth 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 plano-Fresnel optical surface R 2  with draft with vertical shape and facing on the forward side. The plano-Fresnel 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 2φ (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-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 plano-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-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 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  of the invention is a plano-Fresnel optical surface 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 plano-Fresnel optical surface R 2  with equal zone pitch is shown. The zone pitch r t  thereof is a fixed value. The light optical surface with radius of R F  is transformed into a multi-zone plano-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 plano-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 plano-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 plano-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 φ 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 plano-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 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 plano-Fresnel optical surface R 2  is also defined by the equation (9), wherein Conic Constant of the curvature radius R F  of the paraboloid for collecting light 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-concave or plano-plano 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 blu-ray 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 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 all can be changed, modified and even substituted with equal effect parts. 
     As to the following thirteen embodiments, in the first to seventh embodiments, a LED assembly with a plano-plano Fresnel lens that is with no taper and equal zone height is used. In the eighth and ninth embodiments, a LED assembly with a plano-plano Fresnel lens that is with taper and equal zone height is used. In the tenth and eleventh embodiments, a LED assembly with a plano-plano Fresnel lens that is with no taper and equal zone pitch is used. In the twelfth and thirteenth embodiments, a LED assembly with a plano-concave 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 curvature 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 curvature 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 , FIG.  12   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE ONE 
               
             
             
               
                   
               
               
                 fs = 2.024 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.000 
                 2.00 
                 1.582 
               
               
                   
                   
               
               
                   
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE TWO 
               
               
                   
               
             
             
               
                   
                 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 Zone 
               
               
                   
                   
               
               
                   
                 Fesnel Surface 
                 0.1 
                 0.447 
                 2.490 
                 31 
               
               
                   
                 (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, 68° in the X direction, 30° in the Y direction and the luminous flux β=69.201 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
     
       
         
           
             η 
             = 
             0.8815 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             33.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             32.5 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             15.2 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             0.8130 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.5751 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.2394 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.4489 
           
         
       
     
     By the above table one and table two as well as  FIG. 12 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     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 
                 −8.5000E−01 
                 0.0000E+00 
                 2.4000E−05 
                 5.7000E−08 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                   
                 h d   
                 r 1   
                 r n   
                 No. of Zone 
               
               
                   
                   
               
               
                   
                 Fesnel Surface 
                 0.1 
                 0.499 
                 2.480 
                 30 
               
               
                   
                 (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, 33° in the Y direction and the luminous flux β=70.245 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
     
       
         
           
             η 
             = 
             0.8948 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             32.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             33.7 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             16.8 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0203 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             1.1410 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.1319 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.3915 
           
         
       
     
     By the above table three and table four as well as  FIG. 13 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Third Embodiment 
     Refer to FIG.  6  &amp; FIG.  14   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE FIVE 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
                   
               
               
                   
                 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 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                   
                 h d   
                 r 1   
                 r n   
                 No. of Zone 
               
               
                   
                   
               
               
                   
                 Fesnel Surface 
                 0.06 
                 0.387 
                 2.510 
                 42 
               
               
                   
                 (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, 64° in the X direction, 36° in the Y direction and the luminous flux β=69.816 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7): 
     
       
         
           
             η 
             = 
             0.8893 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             30.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             32.1 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             18.1 
           
         
       
       
         
           
             
               
                 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 
               
             
             = 
             0.2108 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.3406 
           
         
       
     
     By the above table five and table six as well as  FIG. 14 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     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 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                   
                 h d   
                 r 1   
                 r n   
                 No. of Zone 
               
               
                   
                   
               
               
                   
                 Fesnel Surface 
                 0.06 
                 0.387 
                 2.510 
                 41 
               
               
                   
                 (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, 68° in the X direction, 43° in the Y direction and the luminous flux β=72.48 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.9233 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             23.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             34.0 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             21.5 
           
         
       
       
         
           
             
               
                 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 
               
             
             = 
             0.1672 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.2231 
           
         
       
     
     By the above table seven and table eight as well as  FIG. 15 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Fifth Embodiment 
     Refer to FIG.  6  &amp; FIG.  16   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE NINE 
               
             
             
               
                   
               
               
                 fs = 5.061 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 2.500 
                 2.00 
                 1.582 
               
               
                   
                   
               
               
                   
                 *Spherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE TEN 
               
               
                   
                   
               
               
                   
                 r t   
                 r n   
                 No. of Zone 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Fesnel Surface 
                 0.0625 
                 2.500 
                 41 
               
               
                   
                 (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 (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.8980 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             22.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             43.0 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             34.5 
           
         
       
       
         
           
             
               
                 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 
               
             
             = 
             0.4536 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.1111 
           
         
       
     
     By the above table nine and table ten as well as  FIG. 16 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Sixth Embodiment 
     Refer to FIG.  6  &amp; FIG.  17   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE ELEVEN 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 4.96 
                 1.582 
               
               
                   
                   
               
               
                   
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE TWELVE 
               
               
                   
               
             
             
               
                   
                 K 
                 A 2   
                 A 4   
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −9.0000E−01 
                 0.0000E+00 
                 2.4000E−05 
                 5.7000E−08 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                 h d   
                 r 1   
                 r n   
                 No. of Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.387 
                 2.478 
                 46 
               
               
                   
               
             
          
         
       
     
     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 68° in the X direction, 43° in the Y direction and the luminous flux β=72.48 lm at infinity (100×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 
               
             
             = 
             32.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             31.0 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             17.0 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0213 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             1.1401 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.1030 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.4161 
           
         
       
     
     By the above table eleven and table twelve as well as  FIG. 17 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Seventh Embodiment 
     Refer to FIG.  6  &amp; FIG.  18   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE THIRTEEN 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 4.99 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE FOURTEEN 
               
               
                   
               
             
             
               
                   
                 K 
                 A 2   
                 A 4   
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −1.1000E+00 
                 0.0000E+00 
                 2.4000E−05 
                 5.7000E−08 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                 h d   
                 r 1   
                 r n   
                 No. of Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.388 
                 2.494 
                 38 
               
               
                   
               
             
          
         
       
     
     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, 40° in the Y direction and the luminous flux β=69.33 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.8832 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             27.5 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             33.7 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             19.5 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0146 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             1.1475 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.1252 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.2799 
           
         
       
     
     By the above table thirteen and table fourteen as well as  FIG. 18 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Eighth Embodiment 
     Refer to FIG.  6  &amp; FIG.  19   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE FIFTEEN 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 3.505 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 2.00 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE SIXTEEN 
               
               
                   
               
             
             
               
                   
                 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 Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.387 
                 2.387 
                 37 
               
               
                   
               
             
          
         
       
     
     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=69.588 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.8976 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             22.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             37.5 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             27.0 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0598 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.4601 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.2176 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.3022 
           
         
       
     
     By the above table fifteen and table sixteen as well as  FIG. 19 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Ninth Embodiment 
     Refer to FIG.  6  &amp; FIG.  20   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE SEVENTEEN 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 7.172 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 2.00 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE EIGHTEEN 
               
               
                   
               
             
             
               
                   
                 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 Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.387 
                 2.258 
                 33 
               
               
                   
               
             
          
         
       
     
     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, 33° in the Y direction and the luminous flux β=71.267 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.9078 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             34.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             33.8 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             16.8 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.2045 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.4601 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.2176 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.4998 
           
         
       
     
     By the above table seventeen and table eighteen as well as  FIG. 20 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Tenth Embodiment 
     Refer to FIG.  6  &amp; FIG.  21   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE NINETEEN 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 2.00 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE TWENTY 
               
               
                   
               
             
             
               
                   
                 K 
                 A 2   
                 A 4   
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −1.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                 r t   
                 r n   
                 No. of Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.5 
                 2.500 
                 5 
               
               
                   
               
             
          
         
       
     
     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, 70° in the Y direction and the luminous flux β=72.056 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.9214 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             26.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             40.5 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             35.0 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0121 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.4601 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.0081 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.1366 
           
         
       
     
     By the above table nineteen and table twenty as well as  FIG. 21 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Eleventh Embodiment 
     Refer to FIG.  6  &amp; FIG.  22   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-ONE 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 ∞ 
                 0.52 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 2.00 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-TWO 
               
               
                   
               
             
             
               
                   
                 K 
                 A 2   
                 A 4   
                 A 6   
               
               
                   
               
               
                 Aspherical 
                 −1.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Surface 
               
               
                   
               
             
          
           
               
                   
                   
                 r t   
                 r n   
                 No. of Zone 
               
               
                   
               
               
                   
                 Fesnel Surface (mm) 
                 0.0625 
                 2.500 
                 40 
               
               
                   
               
             
          
         
       
     
     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, 60° in the X direction, 80° in the Y direction and the luminous flux β=72.164 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.9192 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             30.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             39.4 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             30 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0121 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.4601 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.1147 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.2184 
           
         
       
     
     By the above table twenty-one and table twenty-two as well as  FIG. 22 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Twelfth Embodiment 
     Refer to FIG.  6  &amp; FIG.  23   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-THREE 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 30.00 
                 0.62 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 1.90 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-FOUR 
               
               
                   
               
             
             
               
                   
                 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 Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.387 
                 2.510 
                 42 
               
               
                   
               
             
          
         
       
     
     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, 60° in the X direction, 40° in the Y direction and the luminous flux β=69.506 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.8854 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             30.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             33.1 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             19.0 
           
         
       
       
         
           
             
               
                 f 
                 s 
               
               
                 r 
                 n 
               
             
             = 
             1.0008 
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     N 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               ⁢ 
               
                 
                   d 
                   2 
                 
                 
                   f 
                   s 
                 
               
             
             = 
             0.4361 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             x 
                           
                           - 
                           
                             ω 
                             x 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             ϕ 
                             y 
                           
                           - 
                           
                             ω 
                             y 
                           
                         
                         π 
                       
                       ) 
                     
                     2 
                   
                 
               
               · 
               
                 f 
                 g 
               
             
             = 
             0.2053 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.2188 
           
         
       
     
     By the above table twenty-three and table twenty-four as well as  FIG. 23 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention. 
     The Thirteenth Embodiment 
     Refer to FIG.  6  &amp; FIG.  24   
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-FIVE 
               
             
             
               
                   
               
               
                 fs = 2.530 υ = 0 
               
             
          
           
               
                   
                 Surface No. 
                 R or R F   
                 d i   
                 N di   
               
               
                   
               
               
                   
                 S0 
                 ∞ 
                 0.10 
                   
               
               
                   
                 S1 
                 9.00  
                 0.87 
                 1.410 
               
               
                   
                 S2* 
                 1.250 
                 1.65 
                 1.582 
               
               
                   
               
               
                 *Aspherical Zone Fesnel 
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE TWENTY-SIX 
               
               
                   
               
             
             
               
                   
                 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 Zone 
               
               
                   
               
               
                 Fesnel Surface (mm) 
                 0.06 
                 0.387 
                 2.510 
                 35 
               
               
                   
               
             
          
         
       
     
     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, 60° in the X direction, 40° in the Y direction and the luminous flux β=69.506 lm at infinity (100×f s ) without consideration of air refraction and scattering. The following values satisfy the equation (1), equation (2), equation (3) and equation (7). 
     
       
         
           
             η 
             = 
             0.8828 
           
         
       
       
         
           
             
               I 
               
                 1 
                 / 
                 2 
               
             
             = 
             29.0 
           
         
       
       
         
           
             
               ϕ 
               x 
             
             = 
             31.0 
           
         
       
       
         
           
             
               ϕ 
               y 
             
             = 
             20.2 
           
         
       
       
         
           
             
               
                 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 
               
             
             = 
             0.2227 
           
         
       
       
         
           
             
               
                 E 
                 
                   1 
                   / 
                   2 
                 
               
               
                 E 
                 d 
               
             
             = 
             0.2103 
           
         
       
     
     By the above table twenty-five and table twenty-six as well as  FIG. 24 , it has been proved that the LED assembly with plano-Fresnel LED lens of the invention can achieve higher efficiency and generate an elliptic distribution pattern with uniform peak intensity so as to increase the application of the invention.