Abstract:
The present invention provides a light redirecting article for redirecting light toward a target angle, the light redirecting article comprising: an input surface comprising a plurality of light redirecting structures each light redirecting structure having a near surface having two slopes, sloping away from normal in one direction as defined by a first inclination base angle β 1 , a second inclination angle β 2 , and a first half apex angle α 2 , for accepting incident illumination over a range of incident angles and a far surface sloping away from normal, in the opposite direction relative to the input surface, as defined by a second base angle γ 1  and a second half apex angle α 1 . The invention further provides an output surface opposing to the input surface wherein the near and far surfaces are opposed to each other at an angle (α 1 +α 2 ) that is in the range from 60 to 70 degrees, and the base angle β 1  is in the range from 82 to 87 degrees.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention generally relates to display illumination articles for enhancing luminance from a surface and more particularly relates to a turning film having multiple slopes that redirects light from a light guiding plate. 
       BACKGROUND OF THE INVENTION 
       [0002]    Liquid crystal displays (LCDs) continue to improve in cost and performance, becoming a preferred display type for many computer, instrumentation, and entertainment applications. The transmissive LCD used in conventional laptop computer displays is a type of backlit display, having a light providing surface positioned behind the LCD for directing light outwards, towards the LCD. The challenge of providing a suitable backlight apparatus having brightness that is sufficiently uniform while remaining compact and low cost has been addressed following one of two basic approaches. In the first approach, a light-providing surface is used to provide a highly scattered, essentially Lambertian light distribution, having an essentially constant luminance over a broad range of angles. Following this first approach, with the goal of increasing on-axis and near-axis luminance, a number of brightness enhancement films have been proposed for redirecting a portion of this light having Lambertian distribution in order to provide a more collimated illumination. 
         [0003]    A second approach to providing backlight illumination employs a light guiding plate (LGP) that accepts incident light from a lamp or other light source disposed at the side and guides this light internally using Total Internal Reflection (TIR) so that light is emitted from the LGP over a narrow range of angles. The output light from the LGP is typically at a fairly steep angle with respect to normal, such as 70 degrees or more. With this second approach, a turning film, one type of light redirecting article, is then used to redirect the emitted light output from the LGP toward normal. Directional turning films, broadly termed light-redirecting articles or light-redirecting films, such as that provided with the HSOT (Highly Scattering Optical Transmission) light guide panel available from Clarex, Inc., Baldwin, N.Y., provide an improved solution for providing a uniform backlight of this type, without the need for diffusion films or for dot printing in manufacture. HSOT light guide panels and other types of directional turning films use arrays of prism structures, in various combinations, to redirect light from a light guiding plate toward normal, or toward some other suitable target angle that is typically near normal relative to the two-dimensional surface. As one example, U.S. Pat. No. 6,746,130 (Ohkawa) describes a light control sheet that acts as a turning film for LGP illumination. 
         [0004]    Referring to  FIG. 1 , the overall function of a light guiding plate  10  in a display apparatus  100  is shown. Light from a light source  12  is incident at an input surface  18  and passes into light guiding plate  10 , which is typically wedge-shaped as shown. The light propagates within light guiding plate  10  until Total Internal Reflection (TIR) conditions are frustrated and then, possibly reflected from a reflective surface  142 , exits light guiding plate at an output surface  16 . This light then goes to a turning film  20  and is directed to illuminate a light-gating device  120  such as an LCD or other type of spatial light modulator or other two-dimensional backlit component that modulates the light. For optimized viewing under most conditions, the emitted light should be provided over a range of relatively narrow angles about a normal V. A polarizer  124  is typically disposed in the illumination path in order to provide light-gating device  120  such as a liquid crystal cell with suitably polarized light for modulation. A reflective polarizer  125  is often provided between absorptive polarizer  124  and turning film  20 . 
         [0005]    Referring to  FIG. 2 , there is shown a schematic cross-sectional view of a conventional turning film  20   a  used with light guiding plate  10 , showing key angles and geometric relationships. Turning film  20   a  has a number of prismatic structures facing downward toward light guiding plate  10 , each structure having a near surface  24  (being near relative to light source  12 , as shown in the embodiment of  FIG. 1 ) and a far surface  26 , both sides slanted from a film normal direction V as determined by an apex angle α, and base angles β 1  and β 2 , relative to a horizontal S. Light from light guiding plate  10  is incident over a small range of angles about a central input angle θ in . The output angle θ out  of light delivered to the LC display element at a flat surface  22  of turning film  20   a  is determined by a number of factors including the central input angle θ in , the refractive index n of turning film  20   a , and the base angle β 1  at which far surface  26  is slanted. Output angle θ out  for emitted light is preferably normal with respect to turning film  20   a , however output angle θ out  can be considered a target angle, which may be at some inclination with respect to normal for some applications. For most conventional turning films, the target angle is normal. In a typical arrangement, base angles β 1  and β 2  are about 56 degrees, and apex angle α, 68 degrees. The primary ray  50   a  having an input angle around θ in ≈70° is redirected to near normal direction. However, some secondary rays  50   c ,  50   c   1  having an input angle around θ in &lt;70° may take paths as shown in  FIG. 2 . Secondary ray  50   c   1  is redirected toward a relative large angle from the normal direction. Further, secondary ray  50   c  is totally reflected back by the light exiting surface  92 . Consequently, the light utilization of this existing turning film is not satisfactory. 
         [0006]    Thus, while there have been solutions proposed for turning films suitable for some types of display apparatus and applications, there remains a need for improved turning films. 
       SUMMARY OF THE INVENTION 
       [0007]    The present invention provides a light redirecting article for redirecting light toward a target angle, the light redirecting article comprising: (a) an input surface comprising a plurality of light redirecting structures each light redirecting structure having: (i) a near surface having two slopes, sloping away from normal in one direction as defined by a first inclination base angle β 1 , a second inclination angle β 2 , and a first half apex angle α 2 , for accepting incident illumination over a range of incident angles; (ii) a far surface sloping away from normal, in the opposite direction relative to the input surface, as defined by a second base angle γ 1  and a second half apex angle α 1 ; and (b) an output surface opposing to the input surface wherein the near and far surfaces are opposed to each other at an angle (α 1 +α 2 ) that is in the range from 60 to 70 degrees, and the base angle β 1  is in the range from 82 to 87 degrees. 
         [0008]    The present invention further provides a light redirecting article for redirecting light toward a target angle, the light redirecting article comprising: (a) an input surface comprising a plurality of light redirecting structures each light redirecting structure having: (i) a near surface having two slopes, sloping away from normal in one direction as defined by a first inclination base angle β 1 , a second inclination angle β 2 , and a first half apex angle α 2 , for accepting incident illumination over a range of incident angles, the first inclination base angle β 1  being the angle nearest to the substrate of the film, the second inclination angle β 2  being the angle farthest from the substrate of the film; (ii) a far surface sloping away from normal, in the opposite direction relative to the input surface, as defined by a second base angle γ 1  and a second half apex angle α 1 ; and (b) an output surface wherein β 2 −β 2  is at least 20 degrees. 
         [0009]    The present invention further provides a light redirecting article for redirecting light toward a target angle, the light redirecting article comprising: (a) an input surface comprising a plurality of light redirecting structures having a pitch P, each light redirecting structure having: (i) a near surface having two slopes, sloping away from normal in one direction as defined by a first inclination base angle β 1 , a second inclination angle β 2 , a first projection segment onto the substrate having a length L 1 , and a second projection segment onto the substrate having a length L 2 , and a first half apex angle α 2 , for accepting incident illumination over a range of incident angles, the first inclination base angle β 1  being the angle nearest to the substrate of the film, the second inclination angle β 2  being the angle farthest from the substrate of the film; (ii) a far surface sloping away from normal, in the opposite direction relative to the input surface, as defined by a second base angle γ 1  and a second half apex angle α 1 ; and (b) an output surface wherein the ratio L 1 /P is in the range of 0.06 and 0.08 and the ratio L 2 /P is in the range of 0.152 and 0.238. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a cross sectional view showing components of a conventional display apparatus; 
           [0011]      FIG. 2  is a schematic cross-sectional view showing a turning film with prismatic structure facing downward, toward the light guiding plate; 
           [0012]      FIG. 3A  is a schematic cross-sectional view showing a single unit of a turning film having two slopes on the near surface of the prismatic structures according to the present invention; 
           [0013]      FIG. 3B  is a schematic cross-sectional view showing a single unit of a turning film having four slopes on the near surface of the prismatic structures according to the present invention; 
           [0014]      FIG. 3C  is a schematic cross-sectional view showing a single unit of a turning film having a curved surface and two slopes on the near surface of the prismatic structures according to the present invention; 
           [0015]      FIG. 3D  is a schematic cross-sectional view showing a single unit of a turning film having two slopes on the near surface and two slopes on the far surface of the prismatic structures according to the present invention; 
           [0016]      FIG. 4  show data of comparative and inventive examples; 
           [0017]      FIG. 5  is a schematic cross-sectional view showing a turning film of the present invention in an LCD display system; 
           [0018]      FIG. 6A  is a schematic top view showing an LCD with a pair of polarizers oriented at 45 degrees relative to the grooves of the light redirecting structure of the turning film; 
           [0019]      FIG. 6B  is a schematic top view showing an LCD with a pair of polarizers oriented at parallel or perpendicular to the grooves of the light redirecting structure of the turning film; and 
           [0020]      FIG. 6C  is a schematic top view showing a turning film with arcuate grooves. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0021]    The apparatus of the present invention uses light-redirecting structures that are generally shaped as prisms. True prisms have at least two planar faces. Because, however, one or more surfaces of the light-redirecting structures need not be planar in all embodiments, but may be curved or have multiple sections, the more general term “light redirecting structure” is used in this specification. 
         [0022]    Referring to  FIG. 3A-3D , key features of the improved turning film of the present invention are shown.  FIG. 3A  shows one unit of a turning film  90   a  according to the present invention, which comprises a substrate having a light inputting surface  94  and a light exiting surface  92 . On the side of the light inputting surface  94  of the film  90   a  is a prismatic structure which is described by points P 1 , P 2 , P 3 , and P 4  and characterized by a near surface  24  and a far surface  26 , and the near surface is composed of at least first flat segment  24   a  and second flat segment  24   b , the angle β 2  between the first segment  24   a  and the horizontal direction S is smaller than the angle β 1  between the second segment  24   b  and the horizontal direction S. The prismatic structure can be further described by two half apex angles α 1  and α 2 , the pitch P and height H, and three projection dimensions L 1 , L 2 , and L 3 . The prismatic structure is made of a material of refractive index n, and the substrate may have its index of refraction greater than, equal to, or less than n. The shape and the refractive index n of the prismatic structure are chosen so that the primary ray  50   a  from the light guide plate  10 , secondary ray  50   b  having larger incident angle than the primary ray  50   a , and secondary ray  50   c  having smaller incident angle than the primary ray  50   a  are characterized as following: the primary ray  50   a  is refracted by the first segment  24   a  of the near surface  24 , subsequently reflected due to the total internal reflection at the far surface  26 , and finally emerges out toward the target angle (normally within 5 degrees from the normal of the film); the secondary ray  50   b  is also refracted by the first segment  24   a  of the near surface  24 , subsequently reflected due to the total internal reflection at the far surface  26 , and finally emerges out in a direction that is bent more from its original direction than the primary ray  50   a ; and the secondary ray  50   c  is refracted by the second segment  24   b  of the near surface  24 , subsequently reflected due to the total internal reflection at the far surface  26 , and finally emerges out in a direction that is closer to the target direction than it would if the second segment  24   b  has the same slope as the first segment  24   a.    
         [0023]    Inventive (denoted as “I”) and comparative examples (denoted as “C”) of turning film  90   a  are shown in Table 1-Table 5. In all of these examples, refractive index n is held constant at 1.5, and pitch P of the prisms is about 50 μm, though it can be in the range of 15 to 150 μm, preferably in the range of 20 to 75 μm, more preferably in the range of 25 to 50 μm. When n and P are held constant, there are 4 independent parameters to specify the shape of turning film  90   a , which are chosen to be L 1 /P, L 2 /P, β 1 , and β 2 . The height H and angles can be calculated as 
         [0000]    
       
         
           
             
               H 
               = 
               
                 P 
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                         l 
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                     + 
                     
                       
                         l 
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                           ( 
                           
                             β 
                             2 
                           
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                   ] 
                 
               
             
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                 α 
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               = 
               
                 
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                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       1 
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                         l 
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                         l 
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                     h 
                   
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               = 
               
                 
                   90 
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                   ° 
                 
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             α 
             ≡ 
             
               
                 α 
                 1 
               
               + 
               
                 α 
                 2 
               
             
           
         
       
       
         
           
             
               
                 γ 
                 1 
               
               = 
               
                 
                   90 
                    
                   ° 
                 
                 - 
                 
                   α 
                   1 
                 
               
             
             , 
             
               
 
             
              
             
               
                 where 
                  
                 
                     
                 
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                   l 
                   1 
                 
               
               ≡ 
               
                 
                   L 
                   1 
                 
                 P 
               
             
             , 
             
               
                 l 
                 2 
               
               ≡ 
               
                 
                   L 
                   2 
                 
                 P 
               
             
             , 
             
               h 
               ≡ 
               
                 
                   H 
                   P 
                 
                 . 
               
             
           
         
       
     
         [0000]    When α 1 =α 2 , it follows 
         [0000]    
       
         
           
             
               
                 l 
                 2 
               
               = 
               
                 
                   
                     1 
                     - 
                     
                       l 
                       1 
                     
                   
                   2 
                 
                 - 
                 
                   
                     
                       l 
                       1 
                     
                     2 
                   
                    
                   
                     
                       tan 
                        
                       
                         ( 
                         
                           β 
                           1 
                         
                         ) 
                       
                     
                     
                       tan 
                        
                       
                         ( 
                         
                           β 
                           2 
                         
                         ) 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
              
             or 
           
         
       
       
         
           
             
               l 
               1 
             
             = 
             
               
                 1 
                 - 
                 
                   2 
                    
                   l 
                 
               
               
                 1 
                 + 
                 
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         1 
                       
                       ) 
                     
                   
                   
                     tan 
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                       ( 
                       
                         β 
                         2 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0024]    In Table 1-4, Columns L 1 /P, α 1 , and α 2  are independent parameters. 
         [0000]    
       
         
           
             
               
                 L 
                 2 
               
               / 
               P 
             
             = 
             
               
                 l 
                 2 
               
               = 
               
                 
                   
                     1 
                     - 
                     
                       l 
                       1 
                     
                   
                   2 
                 
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                     l 
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                   2 
                 
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                       ( 
                       
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                       ) 
                     
                   
                   
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                       ( 
                       
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                         2 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0000]    to ensure α 1 =α 2 =90°−β 2 , and α≡2α 1 . The four right most columns represent the output of turning film in terms of total power, maximum intensity ratio, maximum intensity angle, and on-axis intensity ratio. The turning film of the present invention has: Power≧85%, Maximum intensity ratio≧1.1 and Maximum intensity angle is within −5° and −5°. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Impact of β 1   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 β 1   
                 β 2   
                 α 1   
                 α 2   
                 α 
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 L 1 /P 
                 L 2 /P 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C1.1 
                 0.077 
                 0.31422 
                 80 
                 56 
                 34 
                 34 
                 68 
                 0.856 
                 0.967 
                 3.5 
                 0.940 
               
               
                 C1.2 
                 0.077 
                 0.27672 
                 82 
                 56 
                 34 
                 34 
                 68 
                 0.872 
                 1.035 
                 4.5 
                 0.920 
               
               
                 C1.3 
                 0.077 
                 0.25000 
                 83 
                 56 
                 34 
                 34 
                 68 
                 0.882 
                 1.094 
                 3.5 
                 0.997 
               
               
                 I1.1 
                 0.077 
                 0.21443 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.154 
                 2.5 
                 1.074 
               
               
                 I1.2 
                 0.077 
                 0.16633 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.195 
                 0.5 
                 1.172 
               
               
                 C1.4 
                 0.077 
                 0.09013 
                 86 
                 56 
                 34 
                 34 
                 68 
                 0.896 
                 1.034 
                 −4.5 
                 0.961 
               
               
                   
               
             
          
         
       
     
         [0025]    In Table 1, Ex. C1.1-C1.4 and 11.1-11.2 show the impact of β 1 , given L 1 /P=0.077, and β 2 =56°. Turning films of inventive examples 11.1 and 11.2 meet the criteria: high power (&gt;0.88), large maximum peak intensity ratio (&gt;1.15), and small maximum intensity angle from the normal (≦±3°). When β 1  is out of the preferred range between 83.5° and 85.5°, other parameters being equal except L 2 /P, which is determined by 
         [0000]    
       
         
           
             
               
                 L 
                 2 
               
               / 
               P 
             
             = 
             
               
                 
                   1 
                   - 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                 
                 2 
               
               - 
               
                 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                   2 
                 
                  
                 
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         1 
                       
                       ) 
                     
                   
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         2 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0000]    to keep
 
α 1 =α 2 =α/2, the outputs from comparative examples C1.1-C1.4 do not meet all of the criteria, in terms of power (&gt;0.85), maximum intensity ratio (&gt;1.10), and maximum intensity angle (≦±5°), indicating inferior performance.
 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Impact of L 1 /P 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 β 1   
                 β 2   
                 α 1   
                 α 2   
                 α 
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 L 1 /P 
                 L 2 /P 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C2.1 
                 0.04 
                 0.32581 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.860 
                 0.988 
                 2.5 
                 0.911 
               
               
                 C2.2 
                 0.05 
                 0.28226 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.874 
                 1.075 
                 4.5 
                 0.934 
               
               
                 I2.1 
                 0.06 
                 0.23871 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.886 
                 1.133 
                 3.5 
                 1.010 
               
               
                 I2.2 
                 0.062 
                 0.23000 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.887 
                 1.113 
                 4.5 
                 1.043 
               
               
                 I2.3 
                 0.064 
                 0.22129 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.133 
                 2.5 
                 1.051 
               
               
                 I2.4 
                 0.066 
                 0.21258 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.889 
                 1.157 
                 2.5 
                 1.069 
               
               
                 I2.5 
                 0.068 
                 0.20387 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.890 
                 1.164 
                 3.5 
                 1.093 
               
               
                 I2.6 
                 0.07 
                 0.19516 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.891 
                 1.185 
                 2.5 
                 1.100 
               
               
                 I2.7 
                 0.072 
                 0.18645 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.218 
                 2.5 
                 1.134 
               
               
                 I2.8 
                 0.074 
                 0.17774 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.180 
                 1.5 
                 1.152 
               
               
                 I2.9 
                 0.075 
                 0.17339 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.204 
                 1.5 
                 1.158 
               
               
                 I2.10 
                 0.076 
                 0.16903 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.198 
                 0.5 
                 1.165 
               
               
                 I2.11 
                 0.077 
                 0.16468 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.184 
                 0.5 
                 1.174 
               
               
                 I2.12 
                 0.078 
                 0.16032 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.188 
                 0.5 
                 1.184 
               
               
                 I2.13 
                 0.079 
                 0.15597 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.893 
                 1.192 
                 −0.5 
                 1.175 
               
               
                 I2.14 
                 0.08 
                 0.15161 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.893 
                 1.171 
                 −0.5 
                 1.167 
               
               
                 C2.5 
                 0.09 
                 0.10806 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.895 
                 1.096 
                 −2.5 
                 1.024 
               
               
                 C2.6 
                 0.1 
                 0.06452 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.898 
                 0.982 
                 −5.5 
                 0.883 
               
               
                 C2.7 
                 0.114 
                 0.00355 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.900 
                 1.089 
                 2.5 
                 1.036 
               
               
                 I2.15 
                 0.075 
                 0.22184 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.150 
                 3.5 
                 1.056 
               
               
                 I2.16 
                 0.076 
                 0.21813 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.142 
                 2.5 
                 1.053 
               
               
                 I2.17 
                 0.077 
                 0.21443 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.154 
                 2.5 
                 1.074 
               
               
                 I2.18 
                 0.078 
                 0.21072 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.145 
                 2.5 
                 1.071 
               
               
                 I2.19 
                 0.079 
                 0.20701 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.889 
                 1.163 
                 4.5 
                 1.082 
               
               
                 I2.20 
                 0.08 
                 0.20330 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.890 
                 1.165 
                 2.5 
                 1.127 
               
               
                   
               
             
          
         
       
     
         [0026]    In Table 2, comparative examples C2.1-C2.7 and inventive examples 12.1-12.14 show the impact of L 1 /P when β 1 =85°, β 2 =56°. When L 1 /P is out of the preferred range between 0.06 and 0.08, other parameters being equal except L 2 /P, which is determined by 
         [0000]    
       
         
           
             
               
                 L 
                 2 
               
               / 
               P 
             
             = 
             
               
                 
                   1 
                   - 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                 
                 2 
               
               - 
               
                 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                   2 
                 
                  
                 
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         1 
                       
                       ) 
                     
                   
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         2 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0000]    to keep α 1 =α 2 =α/2, the output in terms of power (&gt;0.85), maximum intensity ratio (≧1.10), and maximum intensity angle (≦±5°) is not acceptable. Table 2 also includes inventive examples 12.15-12.20 when β 1 =84°, β 2 =56°. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Impact of β 2   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 β 1   
                 β 2   
                 α 1   
                 α 2   
                 α 
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 L 1 /P 
                 L 2 /P 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C3.1 
                 0.076 
                 0.21123 
                 85 
                 60 
                 30 
                 30 
                 60 
                 0.895 
                 1.081 
                 −9.5 
                 0.655 
               
               
                 C3.2 
                 0.076 
                 0.20102 
                 85 
                 59 
                 31 
                 31 
                 62 
                 0.894 
                 1.124 
                 −7.5 
                 0.859 
               
               
                 I3.1 
                 0.076 
                 0.19059 
                 85 
                 58 
                 32 
                 32 
                 64 
                 0.893 
                 1.144 
                 −2.5 
                 1.026 
               
               
                 I3.2 
                 0.076 
                 0.17994 
                 85 
                 57 
                 33 
                 33 
                 66 
                 0.892 
                 1.183 
                 −1.5 
                 1.140 
               
               
                 I3.3 
                 0.076 
                 0.16903 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.198 
                 0.5 
                 1.165 
               
               
                 I3.4 
                 0.076 
                 0.15787 
                 85 
                 55 
                 35 
                 35 
                 70 
                 0.893 
                 1.194 
                 2.5 
                 1.027 
               
               
                 I3.5 
                 0.076 
                 0.14643 
                 85 
                 54 
                 36 
                 36 
                 72 
                 0.893 
                 1.138 
                 4.5 
                 0.830 
               
               
                 C3.3 
                 0.076 
                 0.13470 
                 85 
                 53 
                 37 
                 37 
                 74 
                 0.890 
                 1.075 
                 7.5 
                 0.601 
               
               
                 C3.4 
                 0.076 
                 0.12265 
                 85 
                 52 
                 38 
                 38 
                 76 
                 0.888 
                 1.042 
                 9.5 
                 0.421 
               
               
                   
               
             
          
         
       
     
         [0027]    In Table 3, comparative examples C3.1-C3.4 and inventive examples 13.1-13.5 show the impact of β 2  when L 1 /P=0.076 and β 1 =85°. When L 1 /P is out of the preferred range between 58.5° and 53.5°, other parameters being equal except L 2 /P, which is determined by 
         [0000]    
       
         
           
             
               
                 L 
                 2 
               
               / 
               P 
             
             = 
             
               
                 
                   1 
                   - 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                 
                 2 
               
               - 
               
                 
                   
                     
                       L 
                       1 
                     
                     / 
                     P 
                   
                   2 
                 
                  
                 
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         1 
                       
                       ) 
                     
                   
                   
                     tan 
                      
                     
                       ( 
                       
                         β 
                         2 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0000]    to keep α 1 =α 2 α/2, the output in terms of power (&gt;0.85), maximum intensity ratio (≧1.10), and maximum intensity angle (≦±5°) is not acceptable. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Asymmetrical Turning Film Having α 1  ≠α 2   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 β 1   
                 β 2   
                 α 1   
                 α 2   
                   
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 L 1 /P 
                 L 2 /P 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 α (°) 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C4.1 
                 0.01 
                 0.17 
                 85 
                 56 
                 65.93 
                 34 
                 99.93 
                 0.732 
                 0.874 
                 27.5 
                 0.031 
               
               
                 C4.2 
                 0.03 
                 0.17 
                 85 
                 56 
                 53.36 
                 34 
                 87.36 
                 0.715 
                 0.640 
                 15.5 
                 0.063 
               
               
                 C4.3 
                 0.05 
                 0.17 
                 85 
                 56 
                 43.44 
                 34 
                 77.44 
                 0.858 
                 0.983 
                 29.5 
                 0.146 
               
               
                 C4.4 
                 0.07 
                 0.17 
                 85 
                 56 
                 35.84 
                 34 
                 69.84 
                 0.891 
                 1.177 
                 6.5 
                 0.837 
               
               
                 C4.5 
                 0.09 
                 0.17 
                 85 
                 56 
                 30.02 
                 34 
                 64.02 
                 0.897 
                 1.179 
                 −9.5 
                 0.628 
               
               
                 C4.6 
                 0.11 
                 0.17 
                 85 
                 56 
                 25.50 
                 34 
                 59.50 
                 0.898 
                 0.822 
                 −18.5 
                 0.171 
               
               
                 C4.7 
                 0.13 
                 0.17 
                 85 
                 56 
                 21.94 
                 34 
                 55.94 
                 0.886 
                 1.011 
                 23.5 
                 0.064 
               
               
                 C4.8 
                 0.15 
                 0.17 
                 85 
                 56 
                 19.07 
                 34 
                 53.07 
                 0.878 
                 1.055 
                 28.5 
                 0.038 
               
               
                 C4.9 
                 0.17 
                 0.17 
                 85 
                 56 
                 16.73 
                 34 
                 50.73 
                 0.872 
                 1.062 
                 30.5 
                 0.033 
               
               
                 C4.10 
                 0.19 
                 0.17 
                 85 
                 56 
                 14.79 
                 34 
                 48.79 
                 0.864 
                 1.038 
                 35.5 
                 0.109 
               
               
                 C4.11 
                 0.01 
                 0.19 
                 85 
                 56 
                 63.67 
                 34 
                 97.67 
                 0.687 
                 0.764 
                 23.5 
                 0.035 
               
               
                 C4.12 
                 0.03 
                 0.19 
                 85 
                 56 
                 51.31 
                 34 
                 85.31 
                 0.751 
                 0.544 
                 8.5 
                 0.086 
               
               
                 C4.13 
                 0.05 
                 0.19 
                 85 
                 56 
                 41.69 
                 34 
                 75.69 
                 0.864 
                 1.033 
                 24.5 
                 0.170 
               
               
                 I4.1 
                 0.07 
                 0.19 
                 85 
                 56 
                 34.37 
                 34 
                 68.37 
                 0.891 
                 1.175 
                 3.5 
                 1.075 
               
               
                 C4.14 
                 0.09 
                 0.19 
                 85 
                 56 
                 28.79 
                 34 
                 62.79 
                 0.898 
                 1.165 
                 −12.5 
                 0.464 
               
               
                 C4.15 
                 0.11 
                 0.19 
                 85 
                 56 
                 24.46 
                 34 
                 58.46 
                 0.898 
                 0.768 
                 15.5 
                 0.131 
               
               
                 C4.16 
                 0.13 
                 0.19 
                 85 
                 56 
                 21.04 
                 34 
                 55.04 
                 0.887 
                 1.013 
                 23.5 
                 0.054 
               
               
                 C4.17 
                 0.15 
                 0.19 
                 85 
                 56 
                 18.30 
                 34 
                 52.30 
                 0.878 
                 1.111 
                 29.5 
                 0.036 
               
               
                 C4.18 
                 0.17 
                 0.19 
                 85 
                 56 
                 16.05 
                 34 
                 50.05 
                 0.870 
                 1.109 
                 33.5 
                 0.039 
               
               
                 C4.19 
                 0.19 
                 0.19 
                 85 
                 56 
                 14.18 
                 34 
                 48.18 
                 0.864 
                 1.024 
                 36.5 
                 0.134 
               
               
                 I4.2 
                 0.076 
                 0.169 
                 85 
                 50 
                 35.2 
                 40 
                 75.2 
                 0.892 
                 1.124 
                 4.5 
                 0.809 
               
               
                 I4.3 
                 0.076 
                 0.169 
                 85 
                 51 
                 35 
                 39 
                 74 
                 0.892 
                 1.131 
                 3.5 
                 0.866 
               
               
                 I4.4 
                 0.076 
                 0.169 
                 85 
                 52 
                 34.8 
                 38 
                 72.8 
                 0.893 
                 1.138 
                 3.5 
                 0.940 
               
               
                 I4.5 
                 0.076 
                 0.169 
                 85 
                 53 
                 34.6 
                 37 
                 71.6 
                 0.893 
                 1.135 
                 3.5 
                 1.031 
               
               
                 I4.6 
                 0.076 
                 0.169 
                 85 
                 54 
                 34.4 
                 36 
                 70.4 
                 0.893 
                 1.159 
                 2.5 
                 1.083 
               
               
                 I4.7 
                 0.076 
                 0.169 
                 85 
                 55 
                 34.2 
                 35 
                 69.2 
                 0.892 
                 1.166 
                 1.5 
                 1.135 
               
               
                 I4.8 
                 0.076 
                 0.169 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.190 
                 0.5 
                 1.168 
               
               
                 I4.9 
                 0.076 
                 0.169 
                 85 
                 57 
                 33.8 
                 33 
                 66.8 
                 0.892 
                 1.192 
                 0.5 
                 1.173 
               
               
                 I4.10 
                 0.076 
                 0.169 
                 85 
                 58 
                 33.5 
                 32 
                 65.5 
                 0.892 
                 1.191 
                 0.5 
                 1.179 
               
               
                 I4.11 
                 0.076 
                 0.169 
                 85 
                 59 
                 33.3 
                 31 
                 64.3 
                 0.892 
                 1.187 
                 −2.5 
                 1.156 
               
               
                 I4.12 
                 0.076 
                 0.169 
                 85 
                 60 
                 33 
                 30 
                 63 
                 0.893 
                 1.172 
                 −1.5 
                 1.113 
               
               
                 C4.20 
                 0.076 
                 0.1 
                 85 
                 56 
                 39 
                 34 
                 73 
                 0.889 
                 1.045 
                 11.5 
                 0.339 
               
               
                 C4.21 
                 0.076 
                 0.12 
                 85 
                 56 
                 37.5 
                 34 
                 71.5 
                 0.891 
                 1.112 
                 7.5 
                 0.616 
               
               
                 C4.22 
                 0.076 
                 0.14 
                 85 
                 56 
                 36.1 
                 34 
                 70.1 
                 0.893 
                 1.156 
                 5.5 
                 0.887 
               
               
                 I4.13 
                 0.076 
                 0.16 
                 85 
                 56 
                 34.6 
                 34 
                 68.6 
                 0.892 
                 1.179 
                 1.5 
                 1.112 
               
               
                 I4.14 
                 0.076 
                 0.18 
                 85 
                 56 
                 33.2 
                 34 
                 67.2 
                 0.891 
                 1.180 
                 0.5 
                 1.177 
               
               
                 I4.15 
                 0.076 
                 0.2 
                 85 
                 56 
                 31.9 
                 34 
                 65.9 
                 0.892 
                 1.156 
                 −3.5 
                 1.054 
               
               
                 C4.23 
                 0.076 
                 0.22 
                 85 
                 56 
                 30.5 
                 34 
                 64.5 
                 0.894 
                 1.125 
                 −7.5 
                 0.861 
               
               
                 C4.24 
                 0.076 
                 0.24 
                 85 
                 56 
                 29.2 
                 34 
                 63.2 
                 0.895 
                 1.092 
                 −9.5 
                 0.631 
               
               
                 C4.25 
                 0.076 
                 0.26 
                 85 
                 56 
                 27.9 
                 34 
                 61.9 
                 0.895 
                 1.050 
                 −12.5 
                 0.465 
               
               
                 C4.26 
                 0.076 
                 0.28 
                 85 
                 56 
                 26.6 
                 34 
                 60.6 
                 0.895 
                 1.005 
                 −16.5 
                 0.352 
               
               
                 C4.27 
                 0.076 
                 0.3 
                 85 
                 56 
                 25.4 
                 34 
                 59.4 
                 0.894 
                 0.968 
                 −22.5 
                 0.261 
               
               
                 C4.28 
                 0.076 
                 0.32 
                 85 
                 56 
                 24.2 
                 34 
                 58.2 
                 0.893 
                 0.928 
                 −24.5 
                 0.184 
               
               
                 C4.29 
                 0.076 
                 0.34 
                 85 
                 56 
                 23 
                 34 
                 57 
                 0.890 
                 0.902 
                 −25.5 
                 0.127 
               
               
                   
               
             
          
         
       
     
         [0028]    Table 4 shows that it is possible to have asymmetrical turning film as shown in Inventive example 14.1-14.15 to provide acceptable output in terms of power (≧0.85), maximum intensity ratio (≧1.10), and maximum intensity angle (≦±5°), while randomly choosing parameters do not provide satisfactory results, as shown in comparative examples C4.1-C4.29. In general, the difference between α 1  and α 2  is preferably within 5°. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Impact of Refractive Index n 
               
             
          
           
               
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 n 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C5.1 
                 1.13 
                 0.881 
                 1.053 
                 7.5 
                 0.119 
               
               
                 I5.1 
                 1.14 
                 0.880 
                 1.202 
                 6.5 
                 0.147 
               
               
                 I5.2 
                 1.15 
                 0.879 
                 1.383 
                 5.5 
                 0.2 
               
               
                 I5.3 
                 1.16 
                 0.877 
                 1.482 
                 4.5 
                 0.262 
               
               
                 I5.4 
                 1.17 
                 0.877 
                 1.523 
                 4.5 
                 0.297 
               
               
                 I5.5 
                 1.18 
                 0.879 
                 1.491 
                 3.5 
                 0.413 
               
               
                 I5.6 
                 1.19 
                 0.883 
                 1.633 
                 2.5 
                 0.541 
               
               
                 I5.7 
                 1.2 
                 0.887 
                 1.467 
                 1.5 
                 0.938 
               
               
                 I5.8 
                 1.21 
                 0.894 
                 1.601 
                 0.5 
                 1.401 
               
               
                 I5.9 
                 1.22 
                 0.901 
                 1.690 
                 0.5 
                 1.612 
               
               
                 I5.10 
                 1.23 
                 0.909 
                 1.567 
                 −1.5 
                 1.431 
               
               
                 I5.11 
                 1.24 
                 0.912 
                 1.528 
                 0.5 
                 1.468 
               
               
                 I5.12 
                 1.25 
                 0.915 
                 1.476 
                 0.5 
                 1.427 
               
               
                 I5.13 
                 1.26 
                 0.917 
                 1.485 
                 −1.5 
                 1.359 
               
               
                 I5.14 
                 1.27 
                 0.921 
                 1.403 
                 0.5 
                 1.399 
               
               
                 I5.15 
                 1.28 
                 0.921 
                 1.335 
                 −1.5 
                 1.293 
               
               
                 I5.16 
                 1.29 
                 0.923 
                 1.326 
                 −0.5 
                 1.292 
               
               
                 I5.17 
                 1.3 
                 0.923 
                 1.269 
                 −0.5 
                 1.243 
               
               
                 I5.18 
                 1.31 
                 0.924 
                 1.302 
                 −1.5 
                 1.231 
               
               
                 I5.19 
                 1.32 
                 0.924 
                 1.257 
                 −2.5 
                 1.238 
               
               
                 I5.20 
                 1.33 
                 0.923 
                 1.287 
                 −1.5 
                 1.243 
               
               
                 I5.21 
                 1.34 
                 0.922 
                 1.254 
                 −0.5 
                 1.251 
               
               
                 I5.22 
                 1.35 
                 0.921 
                 1.240 
                 0.5 
                 1.238 
               
               
                 I5.23 
                 1.36 
                 0.920 
                 1.223 
                 1.5 
                 1.212 
               
               
                 I5.24 
                 1.37 
                 0.918 
                 1.227 
                 0.5 
                 1.222 
               
               
                 I5.25 
                 1.38 
                 0.917 
                 1.231 
                 −0.5 
                 1.22 
               
               
                 I5.26 
                 1.39 
                 0.914 
                 1.219 
                 −0.5 
                 1.204 
               
               
                 I5.27 
                 1.4 
                 0.912 
                 1.216 
                 0.5 
                 1.215 
               
               
                 I5.28 
                 1.41 
                 0.910 
                 1.231 
                 0.5 
                 1.224 
               
               
                 I5.29 
                 1.42 
                 0.909 
                 1.242 
                 0.5 
                 1.226 
               
               
                 I5.30 
                 1.43 
                 0.906 
                 1.213 
                 0.5 
                 1.202 
               
               
                 I5.31 
                 1.44 
                 0.905 
                 1.238 
                 0.5 
                 1.202 
               
               
                 I5.32 
                 1.45 
                 0.903 
                 1.227 
                 0.5 
                 1.199 
               
               
                 I5.33 
                 1.46 
                 0.900 
                 1.224 
                 0.5 
                 1.193 
               
               
                 I5.34 
                 1.47 
                 0.898 
                 1.205 
                 0.5 
                 1.188 
               
               
                 I5.35 
                 1.48 
                 0.896 
                 1.202 
                 1.5 
                 1.179 
               
               
                 I5.36 
                 1.49 
                 0.894 
                 1.196 
                 1.5 
                 1.179 
               
               
                 I5.37 
                 1.50 
                 0.892 
                 1.204 
                 1.5 
                 1.158 
               
               
                 I5.38 
                 1.51 
                 0.889 
                 1.191 
                 1.5 
                 1.140 
               
               
                 I5.39 
                 1.52 
                 0.887 
                 1.157 
                 0.5 
                 1.139 
               
               
                 I5.40 
                 1.53 
                 0.885 
                 1.155 
                 2.5 
                 1.132 
               
               
                 I5.41 
                 1.54 
                 0.884 
                 1.192 
                 1.5 
                 1.120 
               
               
                 I5.42 
                 1.55 
                 0.881 
                 1.149 
                 2.5 
                 1.091 
               
               
                 I5.43 
                 1.66 
                 0.861 
                 1.113 
                 3.5 
                 1.022 
               
               
                 C5.2 
                 1.67 
                 0.860 
                 1.074 
                 4.5 
                 0.991 
               
               
                   
               
             
          
         
       
     
         [0029]    Table 5 show the impact of refractive index n, when L 1 /P=0.075, β 1 =85°, β 2 =56°, and 
         [0000]    
       
         
           
             
               
                 
                   L 
                   2 
                 
                 / 
                 P 
               
               = 
               
                 
                   
                     
                       1 
                       - 
                       
                         
                           L 
                           1 
                         
                         / 
                         P 
                       
                     
                     2 
                   
                   - 
                   
                     
                       
                         
                           L 
                           1 
                         
                         / 
                         P 
                       
                       2 
                     
                      
                     
                       
                         tan 
                          
                         
                           ( 
                           
                             β 
                             1 
                           
                           ) 
                         
                       
                       
                         tan 
                          
                         
                           ( 
                           
                             β 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
                 = 
                 0.17339 
               
             
             , 
           
         
       
     
         [0000]    α 1 =α 2 =α/2=34°. Inventive examples 15.1-15.43 show that the index n is preferably in the range between 1.15 and 1.66, more preferably between 1.18 and 1.55, most preferably between 1.19 and 1.31, for a high power, and high maximum intensity ratio, while keeping the maximum intensity angle within 5° from the normal. When n is between 1.15 and 1.28, the maximum intensity ratio is greater than 1.3, sometimes is greater 1.6, which is significantly greater than the maximum intensity ratio of about 1.2 when n=1.5. For comparative examples C5.1 and C5.2, the maximum intensity is lower than 1.1. 
         [0030]    For the turning film  90   a  according to the present invention, the inclination angle of one of flat surfaces closest to light exit surface, is β 1 =85°, and the inclination angle of the other one of flat surfaces farthest from light exit surface, is β 2 =56°. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Comparison Between Prior Art Examples and Inventive Examples 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 β 1   
                 β 2   
                 α 1   
                 α 2   
                 α 
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 L 1 /P 
                 L 2 /P 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
          
           
               
                 C1 
                 0.5 
                 0 
                 56 
                 56 
                 34 
                 34 
                 68 
                 0.786 
                 1.072 
                 0.5 
                 1.047 
               
               
                 C2 
                 0.122 
                 0.0 
                 84.4 
                 84.4 
                 35.2 
                 5.6 
                 40.8 
                 0.902 
                 1.174 
                 −1.5 
                 1.157 
               
               
                 I1.1 
                 0.077 
                 0.21443 
                 84 
                 56 
                 34 
                 34 
                 68 
                 0.888 
                 1.154 
                 2.5 
                 1.074 
               
               
                 I1.2 
                 0.077 
                 0.16633 
                 85 
                 56 
                 34 
                 34 
                 68 
                 0.892 
                 1.195 
                 0.5 
                 1.172 
               
               
                   
               
             
          
         
       
     
         [0031]    Comparative example C1 is the same as inventive example 11.1 except that it has only one slope. The comparative example C1 has much lower power of around 0.79, and lower maximum intensity ratio of about 1.07, compared to the power of about 0.89 and maximum intensity ratio of about 1.15 of inventive example 11.1. 
         [0032]    Comparative example C2 has almost the same power and maximum intensity ratio as inventive examples 11.1 and 11.2. However, comparative example C2 has much smaller apex angle (about 41°) compared to inventive examples 11.1 and 11.2 having apex of about 68°, which means an easier fabrication of the turning films of the present invention. 
         [0033]    The advantage of the turning film of the present invention is its high maximum intensity ratio (optical gain), and its large apex angle which enables its easy manufacture. 
       Turning Film Having 4 Slopes on the Near Surface 
       [0034]      FIG. 3B  shows another embodiment of the turning film  90   b  according to the present invention. One example is: 
         [0000]                                                                        Ex   L 1 /P   L 2 /P   L 3 /P   L 4 /P   β 1  (°)   β 2  (°)   β 3  (°)   β 4  (°)   α 1  (°)   α 2  (°)   α (°)                   I6   0.06535   0.02678   0.05680   0.09402   85   77.76   63.25   56   34   34   68                    
When n=1.5,
 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
               
               
                   
                 Maximum Intensity 
                 Maximum Intensity 
                 On-axis 
               
               
                 Power 
                 Ratio 
                 angle (°) 
                 Intensity ratio 
               
               
                   
               
             
             
               
                 0.893 
                 1.271 
                 −2.5 
                 1.214 
               
               
                   
               
             
          
         
       
     
         [0035]    The inclination angle of one of flat surfaces closest to light exit surface, is β 1 =85°, and the inclination angle of the other one of flat surfaces farthest from light exit surface, is β 4 =56°. Thus, the difference between them is 29°. In addition, the difference between the other two inclination angles is β 2 −β 3 =14.51°, which is greater than β 1 −β 2 =7.24°, β 3 −β 4 4=7.25°. Moreover, β 2 −β 3  is about twice of β 1 −β 2  and β 3 −β 4 . 
       Turning Film Having 2 Slopes and Curved Surface on the Near Surface 
       [0036]      FIG. 3C  shows another embodiment of the turning film  90   c  according to the present invention. The point P 2  in  FIG. 3A  is now replaced with a curved surface of radius R 2  (N=1.5). 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 L 1 /P 
                 L 2 /P 
                 β 1  (°) 
                 β 2  (°) 
                 α 1  (°) 
                 α 2  (°) 
                 α (°) 
               
               
                   
               
             
             
               
                 0.076 
                 0.16903 
                 85 
                 56 
                 34 
                 34 
                 68 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                   
                 Maximum 
                 Maximum 
                 On-axis 
               
               
                   
                   
                   
                 Intensity 
                 Intensity 
                 Intensity 
               
               
                 Ex 
                 R 2 /P 
                 Power 
                 Ratio 
                 angle (°) 
                 ratio 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 I7.1 
                 0.1 
                 0.892 
                 1.234 
                 −0.5 
                 1.227 
               
               
                 I7.2 
                 0.2 
                 0.893 
                 1.259 
                 0.5 
                 1.240 
               
               
                 I7.3 
                 0.3 
                 0.893 
                 1.272 
                 −2.5 
                 1.240 
               
               
                 I7.4 
                 0.4 
                 0.894 
                 1.292 
                 −1.5 
                 1.232 
               
               
                 I7.5 
                 0.5 
                 0.895 
                 1.312 
                 −1.5 
                 1.221 
               
               
                 I7.6 
                 0.6 
                 0.895 
                 1.300 
                 −1.5 
                 1.217 
               
               
                 I7.7 
                 0.8 
                 0.897 
                 1.274 
                 −1.5 
                 1.226 
               
               
                 I7.8 
                 1.0 
                 0.898 
                 1.216 
                 0.5 
                 1.207 
               
               
                 I7.9 
                 1.16882 
                 0.899 
                 1.175 
                 −1.5 
                 1.128 
               
               
                   
               
             
          
         
       
     
         [0037]    Though all of above inventive examples 17.1-17.9 meet the criteria, it has been found that R 2 /P is preferably in the range of 0.1 to 1.16882, more preferably in the range of 0.3 and 0.8, and most preferably in the range of 0.4 and 0.6 for further enhancement of maximum intensity ratio. 
         [0038]    The point P 3  can also be curved with radius of curvature R 3 . R 3 /P is preferably smaller than 0.2. 
       Turning Film Having 2 Slopes on the Near Surface and Curved Surface or Two Segments on Far Surface 
       [0039]      FIG. 3D  shows another embodiment of turning film  90   d  according to the present invention. The turning film  90   d  has the same features on the near surface  24  as one of turning films  90   a ,  90   b ,  90   c , and it also has one additional surface  26   a , which is either flat segment having different inclination as the other portion of  26 , or convex or concave curved surface. 
       Luminous Intensity Distribution for Example Embodiments 
       [0040]      FIG. 4  shows curves of maximum luminous intensity ratio vs polar angle for light passing through the turning films according to inventive example 11.1 and according to comparative example C1. Also shown is the luminous intensity distribution of light coming out from the light guide plate, which then is incident on the turning films. It is clearly seen that the turning film of inventive example 11.1 produces higher luminous intensity at almost every angle than the turning film of comparative example C1. 
       Display Apparatus and Orientation of Polarizers 
       [0041]    The apparatus and method of the present invention allow a number of possible configurations for support components to provide light for an LCD.  FIG. 5  is a schematic cross-sectional view showing a display apparatus  60  using turning film  90  according to the present invention, which can be either of turning films  90   a ,  90   b ,  90   c ,  90   d . An LC spatial light modulator  70  modulates light received from light guiding plate  10  and turning film  90 . A back polarizer  72  and a front polarizer  73  are provided for LC spatial light modulator  70 . 
         [0042]      FIG. 6A  is a schematic top view showing polarized light transmission axes  172  and  173  for LC spatial light modulator  70 , using a pair of polarizers that are oriented at 45 degrees relative to light redirecting structures  75  and grooves of turning film  90  that extend vertically in the view of  FIG. 6A . In this case, the LC spatial light modulator  70  can be a twisted nematic (TN) LCD, which is the dominant mode used in a notebook and monitor display. 
         [0043]      FIG. 6B  is a schematic top view showing polarized light transmission axes  172  and  173  for LC spatial light modulator  70 , using a pair of polarizers oriented at parallel or perpendicular relative to the grooves and light redirecting structures  75  of turning film  90 . In this case, the LC spatial light modulator  70  can use vertically aligned (VA) LCD or IPS LC elements. Rear polarizer transmission axis  172  is parallel to the plane of the cross section. 
         [0044]    In one embodiment the display apparatus comprises a pair of crossed polarizers, wherein the light redirecting structures are elongated in an elongation direction and wherein each of the crossed polarizers is oriented either substantially parallel or perpendicular to the elongation direction of the light redirecting article. In another embodiment the display apparatus comprises a pair of crossed polarizers, wherein the light redirecting structures are elongated in an elongation direction and wherein the polarizers are substantially oriented at +/−45 degrees relative to the elongation direction of the light redirecting article. 
         [0045]      FIG. 6C  is a schematic top view showing turning film  90  with arcuately elongated light redirecting structures  75  in another embodiment. This arrangement is advantageous for employing a point light source such as Light Emitting Diode (LED) at one or more corners of light guiding plate  10  in order to have a more compact design. The rear polarizer transmission axis  172  is more or less parallel to the plane of the cross section. 
         [0000]    Materials for Forming Turning Film  90   a - 90   d    
         [0046]    Turning film  90   a - 90   d  of the present invention can be fabricated using polymeric materials having indices of refraction ranging typically from about 1.40 to about 1.66. Possible polymer compositions include, but are not limited to: poly(methyl methacrylate)s, poly(cyclo olefin)s, polycarbonates, polysulfones and various co-polymers comprising various combinations of acrylate, alicyclic acrylate, carbonate, styrenic, sulfone and other moieties that are known to impart desirable optical properties, particularly high transmittance in the visible range and low level of haze. Various miscible blends of the aforementioned polymers are also possible material combinations that can be used in the present invention. The polymer compositions may be either thermoplastic or thermosetting. The former are manufacturable by an appropriate melt process that requires good melt processability while the latter can be fabricated by an appropriate UV cast and cure process or a thermal cure process. 
         [0047]    Turning film  90   a - 90   d  of the present invention may be fabricated using materials having an index of refraction in the range of 1.12 and 1.40. Example materials are inorganic materials, for example, MgF. Also, materials having a grating formed between a common polymeric material having refractive index in the range of 1.48 and 1.59 and air (n=1). Further, a mix of low index materials (n&lt;1.4) and materials having indices of refraction from about 1.40 to 1.50 may be used as well. 
       Maximum Intensity Ratio (or Optical Gain), Maximum Intensity Angle (or Peak Angle), and Power of a Turning Film 
       [0048]    In general, light distribution is specified in terms of spatial and angular distributions. The spatial distribution of light can be made quite uniform, achieved by careful placement of micro features on top and/or bottom sides of a light guide plate. The angular distribution of light is specified in terms of luminous intensity I as a function of polar angle θ and azimuthal angle. The angular distribution of light is measured with EZ Contrast 160 (available from Eldim, France). Polar angle θ is the angle between the light direction and the normal of the light guide plate V. The azimuthal angle is the angle between the projection of the light onto a plane that is perpendicular to the normal direction V and a direction that is parallel to the length direction of the light guide plate. The length direction of the light guide plate is perpendicular to the light source  12  and the normal direction V. The angular distribution of light can also be specified in terms of luminance L as a function of polar angle θ and azimuthal angle. The luminance L and the luminous intensity I are related by L=I/cos(θ). 
         [0049]    The maximum intensity angle, also referred as peak angle of a light distribution is defined as the polar angle at which the maximum luminous intensity occurs. Each luminous intensity distribution then defines a maximum (or peak) luminous intensity and a maximum intensity (or peak) angle. 
         [0050]    The maximum intensity ratio, also referred as optical gain, or normalized peak intensity, of a turning film, is defined as a ratio of the maximum luminous intensity of the light that is transmitted through the turning film over the maximum luminous intensity of the light that is emitted from a light guide plate. As a result, the maximum intensity ratio of a turning film is not dependent upon the absolute level of the light source, but is primarily dependent upon the turning film design itself. 
         [0051]    The power of a turning film is the ratio of the total amount of light passing through the turning film over the total amount of light incident upon the turning film. Thus, various turning film designs can be compared in terms of two critical quantities:maximum intensity ratio (or optical gain) and maximum intensity angle of the light that is transmitted through the turning film. 
       PARTS LIST 
       [0000]    
       
           10 . Light guiding plate 
           12 . Light source 
           14 . End surface 
           16 . Output surface 
           18 . Input surface 
           20 ,  20   a . Turning film 
           22 . Flat surface 
           24 . Near surface 
           24   a . First flat segment on Near surface 
           24   b . Second flat segment on Near surface 
           26 . Far surface 
           50   a . Primary rays 
           50   b . Secondary rays 
           50   c ,  50   c   1 . Secondary rays 
           52 . Reflective surface 
           60 . Display apparatus 
           70 . LC spatial light modulator 
           72 . Rear polarizer 
           73 . Front Polarizer 
           75 . Light redirecting structure 
           82 . Point light source 
           90 ,  90   a ,  90   b ,  90   c ,  90   d  Turning film 
           92 . Light exiting surface 
           94 . Light inputting surface 
           96 . Substrate 
           100 . Display apparatus 
           120 . Light-gating device 
           124 . Polarizer 
           125 . Reflective polarizer 
           142 . Reflective surface 
           172 ,  173 . Transmission axes 
         α. Apex angle 
         α 1 . Half apex angle 
         α 2 . Half apex angle 
         β 1 . base inclination angle 
         β 2 , β 3 , β 4 . inclination angle 
         γ 1 . Base inclination angle 
         n. Refractive index 
         θ in . Incident angle for a first light guide plate 
         θ out . Output angle 
         V. Film normal direction 
         S. Horizontal direction