# Patent

## Title
Screen for projection display in which the light is uniformly transmitted throughout the screen

## Abstract

A screen for a projection display is provided. The screen includes a Fresnel lens sheet which converges light emitted from a light source, and a lenticular lens sheet which disperses in a horizontal direction the light transmitted by the Fresnel lens sheet. The Fresnel lens sheet includes a first Fresnel lens on one surface and a second Fresnel lens on an opposite surface.

## Background
BACKGROUND OF THE INVENTION
This application claims the priority of Korean Patent Application No. 2003-48428, filed on Jul. 15, 2003, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference.
1. Field of the Invention
The present invention relates to a screen for a projection display and, more particularly, to a projection display with a high definition view, slim structure and a large screen in which the light is uniformly transmitted throughout the screen even when an incident angle of light emitted from an optical projection system onto the screen is different depending on the position on the screen to which the light is transmitted.
2. Description of the Related Art
Referring to FIG. 1, a projection screen usually includes a Fresnel lens sheet 10 which collects light flux projected by an optical projection system toward a viewer, and a lenticular lens sheet 20 which disperses the light output from the Fresnel lens sheet 10 at a predetermined angle with respect to a horizontal direction of the screen, to widen a viewing angle.
A lenticular lens 20a is formed on an incident surface of the lenticular lens sheet 20 to disperse light in the horizontal direction. A black stripe 20b is formed on an exit surface of the lenticular lens sheet 20 to absorb the diverging light and to block the externally incident light, thereby increasing a contrast ratio.
Recently, projection displays having a large screen, a high definition view, and a slim structure have been researched and developed. In FIG. 2A, an optical projection system 25 is disposed at the same level as a center of the Fresnel lens sheet 10, with a plane incident surface 10a and an exit surface 10b. With this arrangement, it is necessary to decrease the height of a quadrangular pyramid of a light flux output from the optical projection system 25 to make the projection displays slim. However, when the optical projection system 25 is disposed at the same level as the center of the screen, the light flux output from the optical projection system 25 cannot be decreased to an optimal height of the quadrangular pyramid.
To solve this problem, the optical projection system 25 is disposed obliquely below the screen, as shown in FIG. 2B. However, in this case, the light loss increases due to a reflection at a peripheral portion of the Fresnel lens sheet 10, and the brightness at the peripheral portion of the screen decreases, thereby deteriorating a picture quality.
FIG. 3 is a graph illustrating the relationship between the transmittance of the Fresnel lens sheet 10 and an incident angle of light for the Fresnel lens sheet 10. Referring to FIG. 3, as the incident angle increases, the transmittance of the Fresnel lens sheet 10 rapidly decreases. In the graph illustrated in FIG. 3, T1 denotes an amount of light passing through a plane incident surface 10a of the Fresnel lens sheet 10 shown in FIG. 2, T2 denotes an amount of light passing through an exit surface 10b, i.e., a Fresnel lens surface, and TT denotes a product of T1 and T2.
As the light approaches the top of the screen, the incident angle of light increases more significantly in a system shown in FIG. 2B (referred to as a second system) than in a system shown in FIG. 2A (referred to as a first system). Accordingly, referring to FIG. 3, the light loss due to the reflection of light in the peripheral portion of the screen is greater in the second system than in the first system.
Consequently, when the light from an optical projection system 25 is obliquely incident onto a screen, as shown in FIG. 2B, a projection display can be made slim, but the picture quality deteriorates since a dark area and a bright area occur on the screen.
SUMMARY OF THE INVENTION
The present invention has been made in view of the above-mentioned problems. Accordingly, it is an aspect of the present invention to provide a screen which has uniform luminance by evenly distributing the light transmittance in the horizontal and vertical directions of the screen, which further increases the light transmittance, and which makes a projection system slim.
To accomplish the aforementioned aspect, a screen for a projection display is provided. The screen includes a Fresnel lens sheet which converges light emitted from a light source and a lenticular lens sheet which disperses in a horizontal direction the light transmitted by the Fresnel lens sheet. The Fresnel lens sheet includes a first Fresnel lens on one surface and a second Fresnel lens on an opposite surface.
The first Fresnel lens may further include a number of Fresnel lens units. Each of these Fresnel lens units may include a first Fresnel lens surface and a second Fresnel lens surface, where a first angle (of the first Fresnel lens surface with respect to a central line between the first and second Fresnel lens surfaces) and a second angle (of the second Fresnel lens surface with respect to the central line) are changed according to the incident angles of the light.
To further solve the above-described problems, the first angle has a range of




  
    
      π
      2
    
    -
    
      α
      1
    
  
  ≤
  
    θ
    1
  
  ≤
  
    π
    2
  




where θ1 is the first angle and α1 is a first incident angle of the light with respect to a normal line of the screen.

Another aspect of the present invention provides a screen where each Fresnel lens unit is a total internal reflection prism.
Moreover, a condition of




  0
  ≤
  
    
      θ
      2
    
    -
    
      π
      2
    
    +
    
      (
      
        
          θ
          1
        
        +
        
          θ
          2
        
      
      )
    
    -
    
      
        sin
        
          -
          1
        
      
      (
      
        sin
        (
        
          
            
              α
              1
            
            -
            
              π
              2
            
            +
            
              θ
              1
            
          
          
            n
            2
          
        
        )
      
      )
    
  
  ≤
  
    
      2
      ⁢
      
        
      
      ⁢
      π
    
    9
  




is satisfied, where α1 is a first incident angle of the light with respect to a normal line of the screen, n2 is a refractive index of a medium through which the light passes after being incident onto the first Fresnel lens surface, θ1 is the first angle, and θ2 is the second angle.

Preferably, the first Fresnel lens and the screen are eccentric such that the center of the first Fresnel lens is below the center of the screen.
The first Fresnel lens may also include two or more of the following elements: a plate, a refraction prism, and a total internal reflection prism based on the incident angles of light.
Preferably, the first Fresnel lens includes the plate in an area where the incident angle of light α1 with respect to a normal line of the screen, has a range of 0≦α1<20, the refraction prism in an area where 20≦α1<50, and the total internal reflection prism in an area where 50≦α1≦80.



BRIEF DESCRIPTION OF THE DRAWINGS
The above and other features and advantages of the present invention will become more apparent by describing in detail illustrative, non-limiting embodiments thereof with reference to the attached drawings in which:
FIG. 1 is a perspective view of a conventional screen for a projection display;
FIG. 2A illustrates a conventional structure in which an optical projection system is disposed at the same level as the center of a screen;
FIG. 2B illustrates another conventional structure in which an optical projection system is disposed below the screen;
FIG. 3 is a graph showing the relationship between the transmittance of light and the incident angle of light in a conventional Fresnel lens sheet;
FIG. 4A is a perspective view of a screen for a projection display, according to a first illustrative, non-limiting embodiment of the present invention;
FIG. 4B is a side view of a Fresnel lens sheet employed in the screen according to the first embodiment of the present invention;
FIG. 5 is a partial enlarged view of a Fresnel lens employed in the screen according to the first embodiment of the present invention;
FIG. 6 illustrates a relationship between the incident light and a prism unit of the Fresnel lens when the light is incident onto the Fresnel lens employed in the screen according to the first embodiment of the present invention;
FIG. 7 is a graph comparing the light transmittance, according to incident position, between the screen according to the first embodiment of the present invention and the conventional screen; and
FIG. 8 illustrates a structure of a Fresnel lens employed in the screen according to a second illustrative, non-limiting embodiment of the present invention.



DETAILED DESCRIPTION OF THE ILLUSTRATIVE, NON-LIMITING EMBODIMENTS OF THE PRESENT INVENTION
The present invention will now be described in detail by describing illustrative, non-limiting embodiments thereof with reference to the accompanying drawings. In the drawings, the same reference characters denote the same elements.
Referring to FIGS. 4A and 4B, a screen for a projection display according to the first illustrative, non-limiting embodiment of the present invention includes a Fresnel lens sheet 40 and a lenticular lens sheet 55. The Fresnel lens sheet 40 includes a first Fresnel lens 42 on one surface and a second Fresnel lens 45 on an opposite surface. The lenticular lens sheet 55 disperses in a horizontal direction light transmitted by the Fresnel lens sheet 40. The first and second Fresnel lenses 42 and 45 may have their centers at the same level or at a different level as the center of the screen.
Referring to FIG. 5, the first Fresnel lens 42 includes a number of ridges. Each ridge is a a Fresnel lens unit. In other words, the first Fresnel lens 42 has a number of units 43. Each Fresnel lens unit 43 has a first Fresnel lens surface 43a and a second Fresnel lens surface 43b. FIG. 5 is an enlarged view of the first and second Fresnel lens surfaces 43a and 43b included in the Fresnel lens unit 43. In FIG. 5, θ1 denotes a first angle of the first Fresnel lens surface 43a with respect to a central line “c” between the first and second Fresnel lens surfaces 43a and 43b, θ2 denotes a second angle of the second Fresnel lens surface 43b with respect to the central line “c”, α1 denotes a first incident angle with respect to a normal line of the screen, and α2 denotes a second incident angle with respect to a normal line of the second Fresnel lens surface 43b. In this case, the second incident angle α2 can be expressed by Formula (1).




  
    
      
        
          α
          2
        
        =
        
          
            α
            1
          
          -
          
            π
            2
          
          +
          
            θ
            1
          
        
      
    
    
      
        (
        1
        )
      
    
  




In addition, n1 denotes a refractive index of a first medium through which the light passes before being incident onto the first Fresnel lens 42, n2 denotes a refractive index of a second medium through which the light passes after being incident onto the first Fresnel lens 42, and β denotes a refraction angle of the light after being incident onto the first Fresnel lens surface 43a. Using these four values, Formula (2) is derived according to Snell's law.

n1 sin α2=n2 sin β  (2)

In particular, when the refractive index of the first medium is 1, β is obtained by Formula (3).




  
    
      
        β
        =
        
          
            sin
            
              -
              1
            
          
          ⁡
          
            (
            
              
                sin
                ⁢
                
                  
                
                ⁢
                
                  α
                  2
                
              
              
                n
                2
              
            
            )
          
        
      
    
    
      
        (
        3
        )
      
    
  




When the light refracted by the first Fresnel lens surface 43a is further reflected by the second Fresnel lens surface 43b, the angle formed between the second Fresnel lens surface 43b and the reflected light is denoted by δ. In this case, δ can be derived using Formula (4).




  
    
      
        δ
        =
        
          
            π
            2
          
          +
          β
          -
          
            (
            
              
                θ
                1
              
              +
              
                θ
                2
              
            
            )
          
        
      
    
    
      
        (
        4
        )
      
    
  




In addition, “m” denotes an incident angle or a reflection angle of the light with respect to the second Fresnel lens surface 43b and is obtained by Formula (5).




  
    
      
        m
        =
        
          
            π
            2
          
          -
          δ
        
      
    
    
      
        (
        5
        )
      
    
  




When an angle between the normal line of the screen and the reflected light, i.e., an exit angle of the light with respect to the normal line of the screen, is denoted by θt, the exit angle θt can be defined using θ1, θ3, and α2 based on Formulae (4) and (5) as follows.




  
    
      
        
          
            
              
                θ
                t
              
              =
              
                
                  θ
                  2
                
                -
                δ
              
            
          
        
        
          
            
              =
              
                
                  θ
                  2
                
                -
                
                  π
                  2
                
                +
                m
              
            
          
        
        
          
            
              =
              
                
                  θ
                  2
                
                -
                
                  π
                  2
                
                +
                
                  (
                  
                    
                      θ
                      1
                    
                    +
                    
                      θ
                      2
                    
                  
                  )
                
                -
                
                  
                    sin
                    
                      -
                      1
                    
                  
                  ⁡
                  
                    (
                    
                      
                        sin
                        ⁢
                        
                          
                        
                        ⁢
                        
                          α
                          2
                        
                      
                      
                        n
                        2
                      
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        (
        6
        )
      
    
  




In addition, the exit angle θt can be defined using θ1, θ2, and α1 based on the Formula (1) as follows.




  
    
      
        
          θ
          t
        
        =
        
          
            θ
            2
          
          -
          
            π
            2
          
          +
          
            (
            
              
                θ
                1
              
              +
              
                θ
                2
              
            
            )
          
          -
          
            
              sin
              
                -
                1
              
            
            (
            
              sin
              (
              
                
                  
                    α
                    1
                  
                  -
                  
                    π
                    2
                  
                  +
                  
                    θ
                    1
                  
                
                
                  n
                  2
                
              
              )
            
            )
          
        
      
    
    
      
        (
        7
        )
      
    
  




The first Fresnel lens 42 increases light transmittance throughout the screen and also increases the uniformity of luminance throughout the screen. In particular, as the incident angle of light α1 with respect to the normal line of the screen increases, the uniformity of luminance also effectively increases.
To increase the light transmittance and the uniformity of luminance, the first angle θ1 and the second angle θ2 are changed according to a vertical position on the screen. It is preferable that the first angle θ1 and the second angle θ2 satisfy the following conditions.
Firstly, referring to FIG. 3, the transmittance of light is over 90% when the incident angle is in a range from 0E to 30E. Accordingly, it is preferable for the second incident angle α2 with respect to the first Fresnel lens surface 43a to have a range of 0≦α2≦30. Based on this fact, it is preferable for the second incident angle α2 to have a range of 0≦α2≦π/6 in order to decrease the amount of light reflected when the light is incident onto the first Fresnel lens 42. The value of the first angle θ1 so as to allow the second incident angle α2 to have the preferable range, can be derived using Formula (1) as follows.




  
    
      
        
          
            
              0
              ≤
              
                
                  α
                  1
                
                -
                
                  π
                  2
                
                +
                
                  θ
                  1
                
              
              ≤
              
                π
                6
              
            
          
        
        
          
            
              
                
                  π
                  2
                
                -
                
                  α
                  1
                
              
              ≤
              
                θ
                1
              
              ≤
              
                
                  
                    2
                    3
                  
                  ⁢
                  π
                
                -
                
                  α
                  1
                
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




When the first angle θ1 has a range defined by Formula (8) with respect to the first incident angle α1, the first Fresnel lens 42 can obtain a transmittance of over 90%. In the meantime, since the first angle θ1 should be smaller than 90 degrees taking into account the usual structure of a Fresnel lens, it is preferable that the first angle θ1 has a range of




  
    
      π
      2
    
    -
    
      α
      1
    
  
  ≤
  
    θ
    1
  
  ≤
  
    
      π
      2
    
    .
  




Secondly, it is preferable to determine the second angle θ2 so as to minimize an area “f” of the first Fresnel lens surface 43a onto which the light is not incident due to the second Fresnel lens surface 43b. When the second angle θ2 is greater than the first incident angle α1, the light transmitted by the first Fresnel lens surface 43a may not be incident onto the second Fresnel lens surface 43b. Accordingly, it is preferable that the second angle θ2 is equal to or smaller than the first incident angle α1 such that the light transmitted by the first Fresnel lens surface 43a can be incident onto the second Fresnel lens surface 43b and then the light reflected by the second Fresnel lens surface 43b satisfies a third condition, i.e., total internal reflection, which will be described later. Considering the above-described requirements, the second angle θ2 can be defined by Formula (9). In FIG. 6, a reference character “e” denotes an area of the first Fresnel lens surface 43a onto which the light is incident.

θ2≦α1  (9)

Thirdly, it is preferable to subject the light to total internal reflection by the second Fresnel lens surface 43b. The condition expressed by Formula (10) must be satisfied to subject the light to total internal reflection by the second Fresnel lens surface 43b.




  
    
      
        m
        ≥
        
          
            sin
            
              -
              1
            
          
          ⁡
          
            (
            
              
                n
                1
              
              
                n
                2
              
            
            )
          
        
      
    
    
      
        (
        10
        )
      
    
  




Formula (10) provides a total internal reflection at the second Fresnel lens surface 43b. As a result, when n1=1, Formula (10) can be rearranged with respect to θ1 and θ2 using Formulae (4) and (5) as follows.




  
    
      
        
          
            sin
            
              -
              1
            
          
          ⁡
          
            [
            
              sin
              ⁡
              
                (
                
                  
                    
                      α
                      1
                    
                    -
                    
                      π
                      2
                    
                    +
                    
                      θ
                      1
                    
                  
                  
                    n
                    2
                  
                
                )
              
            
            ]
          
        
        ≥
        
          
            θ
            1
          
          +
          
            θ
            2
          
          -
          
            
              sin
              
                -
                1
              
            
            ⁡
            
              (
              
                1
                
                  n
                  2
                
              
              )
            
          
        
      
    
    
      
        (
        11
        )
      
    
  




When the first and second angles θ1 and θ2 satisfy the above-described total internal reflection condition, the Fresnel lens unit 43 can be a total internal reflection prism. In addition, the first and second angles θl and θ2 of the Fresnel lens unit 43 change according to the first incident angle α1.
Meanwhile, the exit angle θt of the first Fresnel lens 42 corresponds to an incident angle of the light onto the second Fresnel lens 45. Referring to FIG. 3, the second Fresnel lens 45 has a transmittance of over 90% when the incident angle of light onto the second Fresnel lens 45 is less than 30 degrees. However, taking into account the light loss at the first Fresnel lens 42, it is preferable for the exit angle θt of the first Fresnel lens 42 to have a range of 0≦θt≦20. As a result, the fourth condition is to have the exit angle θt satisfy the conditional expression 0≦θt≦20 using Formula (7).
It is preferable for the screen to have the first and second Fresnel lens surfaces 43a and 43b with the first and second angles θ1 and θ2 satisfy at least two of the above-described conditions. For example, the Fresnel lens unit 43 may be formed having the first and second angles θ1 and θ2 with respect to the first incident angle α1 satisfy Formulae (8) and (9), or satisfying Formula (8) and having the exit angle θt in a predetermined range based on the Formula (7), or satisfying Formulae (9) and (10) or (11). When Formulae (8) and (9) are satisfied, the Fresnel lens unit 43 functions as a refraction prism just refracting light. When Formulae (9) and (10) or (11) are satisfied, the Fresnel lens unit 43 functions as a total internal reflection prism.
More preferably, the amount of light reflected by the first Fresnel lens surface 43a can be minimized by making α2=0. When α2=0, Formula (1) can be rewritten as Formula (12).

θ1=90−α1  (12)

Usually, the first incident angle α1 has a range of about 0≦α1≦80. For example, it is preferable that θ1=30 when α1=60 and θ1=50 when α1=40.
In addition, according to the Formula (10), when n2=1.585, m≧39.11. For example, when m=40 and θ2=60, the exit angle θt becomes 10 degrees according to the Formula (6).
As described above, when the first and second angles θ1 and θ2 change according to the first and second incident angles α1 and α2 onto the first Fresnel lens surface 43a, uniform light transmittance throughout the screen can be achieved even when the incident angle of light onto the screen changes according to a vertical position on the screen. In addition, the amount of light can be increased throughout the screen. In other words, the light transmittance can be increased in a portion of a conventional screen which typically has had a low transmittance, and an overall amount of light and uniformity of luminance throughout the screen can also be increased, by decreasing the incident angle θt of light onto the second Fresnel lens 45 and equalizing incident angles of the light onto the second Fresnel lens 45 throughout the screen.
FIG. 7 is a graph of the relative luminance at various positions i.e., a vertical position, on a quadrant I of the screen. In the graph shown in FIG. 7, a white bar indicates the light transmitted by a conventional Fresnel lens sheet, and a black bar indicates the light transmitted by a Fresnel lens sheet according to the first, illustrative, non-limiting embodiment of the present invention. Referring to the graph, an amount of light increases throughout the screen, and uniformity of luminance is remarkably increased in the peripheral portion of the screen.
The first Fresnel lens 42 may be formed on either the incident surface or the exit surface of the Fresnel lens sheet 40. The second Fresnel lens 45 may be a refraction Fresnel lens or a total reflection Fresnel lens. When the first Fresnel lens 42 is formed on the incident surface of the Fresnel lens sheet 40, the second Fresnel lens 45 converges light, which has uniform exit angles due to the first Fresnel lens 42. When the first Fresnel lens 42 is formed on the exit surface of the Fresnel lens sheet 40, light converged by the second Fresnel lens 45 is output at uniform angles due to the first Fresnel lens 42 so that luminance is uniformly distributed throughout the screen.
In the first embodiment of the present invention, the screen is designed such that the first and second angles θ1 and θ2 are changed according to the first and second incident angles α1 and α2. In this arrangement, since the first and second incident angles α1 and α2 change according to the horizontal and vertical positions on the screen, the first and second angles θ1 and θ2 also change according to the horizontal and vertical positions on the screen. As a result, luminance is uniformly distributed in both of the horizontal and vertical directions of the screen.
The following description relates to a screen for a projection display according to a second illustrative, non-limiting embodiment of the present invention.
The screen according to the second embodiment of the present invention includes a first Fresnel lens 50 and a second Fresnel lens 53. The first Fresnel lens 50 may have two or more of the following elements: a plate 46, a refraction prism 47, and a total internal reflection prism 48 depending on the incident angle of light. The second Fresnel lens 53 has a refraction Fresnel lens. The reflection prism has surfaces 48a and 48b. 
The first Fresnel lens 50 includes a number of Fresnel lens unit, each of which is implemented by the plate 46, the refraction prism 47, or the total internal reflection prism 48. For example, the first Fresnel lens 50 may have the plate 46 in an area where an incident angle α1 has a range of 0≦α1<20, the refraction prism 47 in an area where an incident angle α1′ has a range of 20≦α1′<50, and the reflection prism 48 in an area where an incident angle α1′′ has a range of 50≦α1′′≦80.
Referring to FIG. 3, since the light transmission loss is small in the area where the incident angle α1 has the range of 0≦α1<20, for the manufacturing efficiency, it is preferable to have the plate 46 as a Fresnel lens unit in this area. When the light is incident onto the plate 46 at the incident angle α1 having the range of 0≦α1<20, if a refractive index n1 of a first medium before the plate 46 is less than a refractive index n2 of a second medium through which the light passes after being incident onto the plate 46, a refraction angle (or an exit angle) θt of the light onto the plate 46 is less than the incident angle α1. Accordingly, the light passing through the plate 46 is incident onto the second Fresnel lens 53 at an angle of less than 20 degrees.
It is preferable that the refraction prism 47, which satisfies Formulae (8) and (9), is used as a Fresnel lens unit when the incident angle α1′ has a range of 20≦α1′<50. The refraction prism 47 has a first Fresnel lens surface 47a and a second Fresnel lens surface 47b. A first angle of the first Fresnel lens surface 47a with respect to a normal line of the screen is denoted by θ1, and a second angle of the second Fresnel lens surface 47b with respect to the normal line of the screen is denoted by θ2. In this arrangement, the light incident onto the first Fresnel lens surface 47a is set to output the light at the exit angle θt which is equal to or less than 20 degrees due to the refraction by the first Fresnel lens surface 47a. 
When the incident angle α1′ increases to be equal to or greater than 50 degrees, the first angle θ1 also increases. As a result, since a portion of the first Fresnel lens surface 47a shaded by the second Fresnel lens surface 47b increases, an area of the first Fresnel lens surface 47a substantially decreases and an area of the second Fresnel lens surface 47b substantially increases. Accordingly, when a Fresnel lens unit is formed to have a uniform thickness, the size of the first Fresnel lens surface 47a performing refraction decreases and a reduction of the exit angle θt due to the refraction also decreases. Consequently, it is preferable to use the refraction prism 47 when the incident angle α1′ is less than 50 degrees and to use a prism of a type other than a refraction type when the incident angle α1′ is greater than 50 degrees.
When the light is incident onto the refraction prism 47 at the incident angle α1′ having a range of 20≦α1′<50, it is preferable that the second angle θ2 is less than the incident angle α1 according to Formula (9). In this arrangement, it is preferable that an exit angle θt′ is equal to or less than 20 degrees. In this case, only refraction by the first Fresnel lens surface 47a without total internal reflection by the second Fresnel lens surface 47b is considered. The exit angle θt′ can be defined using Snell's law as follows, assuming g that n1=1.




  
    
      
        
          θ
          t
          ′
        
        =
        
          
            π
            2
          
          -
          
            θ
            1
          
          -
          
            
              sin
              
                -
                1
              
            
            ⁡
            
              (
              
                sin
                ⁢
                
                  
                    
                      α
                      1
                    
                    -
                    
                      π
                      2
                    
                    +
                    
                      θ
                      1
                    
                  
                  
                    n
                    2
                  
                
              
              )
            
          
        
      
    
    
      
        (
        13
        )
      
    
  




A conditional expression for making the exit angle θt′ equal to or less than 20 degrees can be obtained using Formula (13) as follows.




  
    
      
        0
        ≤
        
          
            π
            2
          
          -
          
            θ
            1
          
          -
          
            
              sin
              
                -
                1
              
            
            ⁡
            
              (
              
                sin
                ⁢
                
                  
                    
                      α
                      1
                    
                    -
                    
                      π
                      2
                    
                    +
                    
                      θ
                      1
                    
                  
                  
                    n
                    2
                  
                
              
              )
            
          
        
        ≤
        20
      
    
    
      
        (
        14
        )
      
    
  




When




  
    -
    1
  
  ≤
  
    sin
    ⁢
    
      {
      
        (
        
          
            α
            1
          
          -
          
            π
            2
          
          +
          
            θ
            1
          
        
        )
      
      }
    
  
  ≤
  1




and n2 is about 1.5, the arcsin has a value ranging from −40 degrees to +40 degrees. When the arcsin is in the range of −40 to +40 degrees, the first angle θ1 is obtained as follows.

30≦θ1≦50

110≦θ1≦130  (15)

Meanwhile, since the first angle θ1 needs to be less than 90 degrees, it is preferable that the first angle θ1 has the range of 30≦θ1≦50 in Formula (15).
When the incident angle α1′′ has the range of 50≦α1′′≦80, the first and second angles θ1 and θ2 can be set to make the exit angle θt′ equal to or less than 20 degrees. When the incident angle α1′′ has the range of 50≦α1′′≦80, it is preferable to use the total internal reflection prism 48 as a Fresnel lens unit.
The first angle θ1 is set to make a second incident angle α2 zero in order to minimize the reflection of light by the first Fresnel lens 50. When




  
    
      α
      2
    
    =
    0
  
  ,
  
    
      θ
      1
    
    =
    
      
        π
        2
      
      -
      
        α
        1
      
    
  




according to the Formula (1). According to the Formula (3), β=0. In addition,





  m
  =
  
    
      
        θ
        1
      
      +
      
        θ
        2
      
    
    =
    
      
        π
        2
      
      -
      
        α
        1
      
      +
      
        θ
        2
      
    
  




in Formula (5).

Next, when the total internal reflection condition, i.e., Formula (10), is satisfied, Formula (16) is derived.




  
    
      
        
          θ
          2
        
        ≥
        
          
            
              sin
              
                -
                1
              
            
            ⁡
            
              (
              
                1
                
                  n
                  2
                
              
              )
            
          
          -
          
            π
            2
          
          +
          
            α
            1
          
        
      
    
    
      
        (
        16
        )
      
    
  




In this arrangement, it is assumed that n1=1. For example, when acryl medium having n2=1.585 is used, θ2>α1−50.89. In addition, since the condition of θ2>0 needs to be satisfied, α1′′ needs to be set to greater than 50.89 degrees. When n2=1.585, the condition of α1′′>50.89 is satisfied. In other words, the range of α1′′ can be changed based on the value of n2.
Next, when an exit angle θt′′ is set to have a range of 0≦θt′′≦20 using Formula (7), Formula (17) is derived.




  
    
      
        
          
            α
            1
            ′′
          
          2
        
        ≤
        
          θ
          2
        
        ≤
        
          10
          +
          
            
              α
              1
              ′′
            
            2
          
        
      
    
    
      
        (
        17
        )
      
    
  




As described above, when the incident angle α1′′ has the range of 50≦α1′′≦80, the total internal reflection prism 48 is used as a Fresnel lens unit and the first and second angles θ1 and θ2 change according to the incident angle α1′′. In this arrangement, since the incident angle α1′′ changes in the horizontal and vertical directions of the screen, the first and second angles θ1 and θ2 also change according to a vertical position and a horizontal position on the screen.
In addition, the first Fresnel lens 50 may have the refraction prism 47 and the total internal reflection prism 48 according to the incident angles. Alternatively, the first Fresnel lens 50 may have the plate 46 and the refraction prism 47 depending on the incident angles.
As described above, a screen for a projection display according to the illustrative, non-limiting embodiments of the present invention has Fresnel lenses on the opposite surfaces of a Fresnel lens sheet. The Fresnel lens has a number of total internal reflection prisms whose internal angles are different according to the incident angles of light. Alternatively, the Fresnel lens may have two or more of the following elements: a plate, a refraction prism, and a total internal reflection prism, based on the incident angles of light. The Fresnel leans has the above-described elements to obtain a uniform high luminance throughout the entire screen. In addition, the light obliquely incident onto a screen in a slim projection display is compensated in both the horizontal and vertical directions of the screen using a Fresnel lens sheet according to the illustrative, non-limiting embodiments of the present invention so that the luminance is uniformly or equally distributed throughout the screen. As a result, the picture quality of the screen can be improved.
The above and other features of the invention including various and novel details of the process and construction of the parts has been particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular process and construction of parts embodying the invention is shown by way of illustration only and not as a limitation of the invention. The principles and features of this invention may be employed in varied and numerous embodiments without departing from the scope of the invention.

## Claims

1. A screen for a projection display, the screen comprising:
a Fresnel lens sheet operable to converge light emitted from a light source; and
a lenticular lens sheet operable to disperse in a horizontal direction the light transmitted by the Fresnel lens sheet,
wherein the Fresnel lens sheet comprises a first Fresnel lens on one surface and a second Fresnel lens on an opposite surfaces,
wherein the first Fresnel lens comprises a plurality of Fresnel lens units, each of the plurality of Fresnel lens units comprises a first Fresnel lens surface and a second Fresnel lens surface,
wherein a first angle of the first Fresnel lens surface with respect to a central line between the first and second Fresnel lens surfaces, and a second angle of the second Fresnel lens surface with respect to the central line, are changed depending on incident angles of the light, and
wherein the first angle has a range of





  
    
      π
      2
    
    -
    
      α
      1
    
  
  ≤
  
    θ
    1
  
  ≤
  
    π
    2
  




where θ1 is the first angle and α1 is a first incident angle of the light with respect to a normal line of the screen.

2. The screen of claim 1, wherein the second angle satisfies a condition of θ2=α1 where θ2 is the second angle and α1 is a first incident angle of the light with respect to a normal line of the screen, and
wherein when the condition is satisfied, there is minimized an amount of the light which is incident onto the first Fresnel lens surface but is blocked by the second Fresnel lens surface, is minimized.

3. The screen of claim 1, wherein each of said Fresnel lens units is a total internal reflection prism.

4. The screen of claim 1, wherein a condition of




  m
  ≥
  
    
      sin
      
        -
        1
      
    
    ⁡
    
      (
      
        
          n
          1
        
        
          n
          2
        
      
      )
    
  




is satisfied where “m” is an incident angle of the light onto the first Fresnel lens surface, n1 is a first refractive index of a medium through which the light passes before being incident onto the second Fresnel lens surface, and n2 is a second refractive index of a medium through which the light passes after being incident onto the first Fresnel lens surface.

5. The screen of claim 1, wherein a condition of




  0
  ≤
  
    
      θ
      2
    
    -
    
      π
      2
    
    +
    
      (
      
        
          θ
          1
        
        +
        
          θ
          2
        
      
      )
    
    -
    
      
        sin
        
          -
          1
        
      
      (
      
        sin
        (
        
          
            
              α
              1
            
            -
            
              π
              2
            
            +
            
              θ
              1
            
          
          
            n
            2
          
        
        )
      
      )
    
  
  ≤
  
    
      2
      ⁢
      
        
      
      ⁢
      π
    
    9
  




is satisfied where α1 is a first incident angle of the light with respect to a normal line of the screen, n2 is a refractive index of a medium through which the light passes after being incident onto the first Fresnel lens surface, θ1 is the first angle, and θ2 is the second angle.

6. The screen of claim 1, wherein the first Fresnel lens has a center at a different position from the second Fresnel lens.

7. The screen of claim 6, wherein the first Fresnel lens and the screen are eccentric such that the center of the first Fresnel lens is below a center of the screen.

8. The screen of claim 1, wherein the first Fresnel lens comprises at least two of a plate, a refraction prism, and a total internal reflection prism based on incident angles of the light.

9. The screen of claim 8, wherein the first Fresnel lens comprises:
the plate in an area where the incident angle α1 of the light with respect to a normal line of the screen has a first range of 0≦α1<20,
the refraction prism in an area where the incident angle α1 of the light with respect to the normal line of the screen has a second range of 20≦α1<50, and
the reflection prism in an area where the incident angle α1 of the light with respect to the normal line of the screen has a third range of 50≦α1≦80.

10. The screen of claim 9, wherein the refraction prism satisfies a condition of




  0
  ≤
  
    
      π
      2
    
    -
    
      θ
      1
    
    -
    
      
        sin
        
          -
          1
        
      
      (
      
        sin
        (
        
          
            
              α
              1
            
            -
            
              π
              2
            
            +
            
              θ
              1
            
          
          
            n
            2
          
        
        )
      
      )
    
  
  ≤
  20




where θ1 is a first angle of one surface of the refraction prism with respect to a central line of the refraction prism and θ2 is a second angle of the other surface of the refraction prism with respect to the central line.

11. The screen of claim 8, wherein the total internal reflection prism satisfies a condition of




  
    θ
    1
  
  =
  
    
      π
      2
    
    -
    
      α
      1
    
  




where θ1 is a first angle of one surface of the total internal reflection prism with respect to a central line of the total internal reflection prism and α1 is an incident angle of the light with respect to a normal line of the screen.

12. The screen of claim 11, wherein a condition of




  
    θ
    2
  
  ≥
  
    
      
        sin
        
          -
          1
        
      
      ⁡
      
        (
        
          1
          
            n
            2
          
        
        )
      
    
    -
    
      π
      2
    
    +
    
      α
      1
    
  




is satisfied, where θ2 is a second angle of a second surface of the total reflection prism with respect to the central line, and n2 is a refractive index of a medium through which the light passes after being incident onto the first Fresnel lens.

13. The screen of claim 8, wherein each of the refraction prism and the total internal reflection prism comprises a first angle and a second angle with respect to a central line of the prism, and the first angle and the second angle change based on the incident angles of the light.

14. The screen of claim 1, wherein the second angle satisfies a condition of θ2≦α1, where θ2 is the second angle, and α1 is a first incident angle of the light with respect to a normal line of the screen, and
wherein when the condition is satisfied, there is minimized an amount of the light which is incident onto the first Fresnel lens surface but is blocked by the second Fresnel lens surface.

15. The screen of claim 1, wherein the Fresnel lens sheet and the lenticular lens sheet are adjacent to each other without any other intervening components.