Abstract:
A spatial light modulator includes a prism group and satisfies either of the following conditions
 
 d &lt;0.95×λ/(2×( n −1)),
 
 d &gt;1.05×λ/(2×( n −1))
 
where d is a distance between a reference surface and a flat surface, λ is a wavelength of an incident light, and n is a refractive index of the prism group.

Description:
BACKGROUND OF THE INVENTION 
   1) Field of the Invention 
   The present invention relates to a spatial light modulator and a projector, and more particularly, to a liquid-crystal spatial light modulator. 
   2) Description of the Related Art 
   A dot-matrix display device is widely used as an image display device, such as a liquid crystal panel (a liquid crystal display device), a cathode ray tube (CRT) display device, and a plasma display device. The dot-matrix display device displays an image by a number of pixels that are arranged periodically in two dimensional arrays. However, the periodic arrangement of the pixels causes a sampling noise that deteriorates quality of the image, which makes the image rough and less smooth. One of the methods to reduce deterioration of the quality of the image is disclosed in, for example, Japanese Patent Application Laid-Open No. H8-122709. 
   The dot-matrix image display device has a light-shielding portion called a black matrix. The black matrix is an area between each of the pixels to suppress an unnecessary light. In recent years, it is getting more popular to watch a large screen from comparatively close distance. For this reason, a watcher may recognize a black matrix image in a conventional dot-matrix image display device, resulting in the deterioration of the quality of the image. The conventional technology disclosed in the Japanese Patent Application Laid-Open No. H8-122709 can hardly reduce the deterioration of the quality of the image caused by the black matrix image. 
   One of the ideas to prevent the black matrix image from appearing is to input a light from the image display device into a prism group. Flat surfaces of the prism group transmit the light as it is; while refracting surfaces refracts the light. The light transmitted the prism group includes a straight light from the flat surfaces and a refracted light from the refracting surfaces. The refracted light is deflected and forms a pixel image on the black matrix area. As a result, the black matrix image becomes hard to recognize. 
   However, the characteristics of each prism element that composes the prism group sometimes cause a diffraction due to a variety of factors such as periodic arrangement, depth, arrangement pattern, arrangement pitch. A diffracted light from the prism group is dispersed and irradiated to undesired directions. The diffracted light makes the image blurred, resulting in the deterioration of the quality of the image. Furthermore, when the diffraction occurs in one region of the image display device and does not occur in other region, the displayed image becomes an image having an uneven light intensity in a lattice-pattern, a further deterioration of the quality of the image. 
   The present invention is made to solve the above problems. The object of the present invention is to provide a spatial light modulator and a projector that display a smooth image of a high-quality without having an image of the light shield portion such as the black matrix. 
   SUMMARY OF THE INVENTION 
   The spatial light modulator according to one aspect of the present invention includes a modulating unit that modulates a light based on an image signal and outputs a modulated light, a refracting part that refracts the modulated light, and a flat part that transmits the modulated light. The modulating unit includes a plurality of pixels that are arranged in a matrix, and a light-shielding portion between each of the pixels. The refracting part is a prism group that is composed of a plurality of prism elements, each of the prism elements having at least a refracting surface. The modulated light from one of the pixels is incident on at least a portion of the prism group. The refracting surface is oriented to project an image of the pixel over an image of the light-shielding portion on a screen at a predetermined distance, making an apex with an angle with respect to a reference surface that is orthogonal to an optical axis at the apex. A distance d between the reference surface and the flat part satisfies either of the following conditions
 
 d&lt; 0.95×λ/(2×( n− 1))  (1)
 
 d&gt; 1.05×λ/(2×( n− 1))  (2)
 
where λ is a wavelength of the light, and n is a refractive index of the prism elements.
 
   After passing through the pixel part, the light enters into the prism group and is refracted on the refracting surface. The direction of the refraction and the angle of the refraction respectively depend on the direction of the refraction surface and the angle between the refraction surface and the reference surface. In the technology of this invention, the light refracted is configured to form the images of the pixels, so that the images of the pixels are superposed on the images of the light-shielding portions on the screen at predetermined distance from the refraction surface. Consequently, the watchers see the smooth and less-rough image without seeing the image of the light-shielding portion. 
   In the prism group, the light is refracted on the refracting surface and the light is diffracted by the depth of the prism element. The technology of the present invention satisfies any one of the conditions (1) and (2) 
   If the depth d between the reference surface and the refracting surface satisfies the following condition (A)
 
 d =λ/(2×( n− 1))  (A)
 
the diffraction efficiency improves. In the technology of the present invention, preferably, the depth d does not cause the diffraction light, or the diffraction light is weak enough to get blurred. To lessen the effect of the diffraction, the value of the depth d may be various as far as the depth d satisfies any one of the conditions (1) or (2). Consequently, the diffraction light lessens and watcher sees the high-quality and smooth image without seeing the image of the black matrix.
 
   Preferably, any one of the following conditions (3) or (4) is satisfied
 
 d&lt; 0.9×λ/(2×( n− 1))  (3)
 
 d&gt; 1.1×λ/(2×( n− 1))  (4)
 
More preferably, any one of the following conditions (5) or (6) is satisfied
 
 d&lt; 0.7×λ/(2×( n− 1))  (5)
 
 d&gt; 1.3×λ/(2×( n− 1))  (6)
 
Satisfying any one of the conditions (3) to (6) lessens the diffraction light more, so that the watcher sees the higher-quality image.
 
   The spatial light modulator according to another aspect of the present invention includes a modulating unit that modulates a light based on an image signal and outputs a modulated light, a refracting part that refracts the modulated light, and a flat part that transmits the modulated light. The modulating unit includes a plurality of pixels that are arranged in a matrix, and a light-shielding portion between each of the pixels. The refracting part is a prism group that is composed of a plurality of prism elements, each of the prism elements having at least a refracting surface. The modulated light from one of the pixels is incident on at least a portion of the prism group. The refracting surface is oriented to project an image of the pixel over an image of the light-shielding portion on a screen at a predetermined distance, making an apex with an angle with respect to a reference surface that is orthogonal to an optical axis at the apex. A distance between the reference surface and the flat part and a distance between the reference surface and a predetermined point on the refracting surface are arranged in aperiodic. 
   The prism group causes the diffraction light and one of the causes is the periodic arrangement of the prism elements. In the technology of the second invention, the distance between the reference surface and the refracting surface and the distance between the reference surface and the flat surface are aperiodic so that the diffraction light ascribable to the periodic arrangement of the prism elements lessens. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   The spatial light modulator according to still another aspect of the present invention includes a modulating unit that modulates a light based on an image signal and outputs a modulated light, a refracting part that refracts the modulated light, and a flat part that transmits the modulated light. The modulating unit includes a plurality of pixels that are arranged in a matrix, and a light-shielding portion between each of the pixels. The refracting part is a prism group that is composed of a plurality of prism elements, each of the prism elements having at least a refracting surface. The modulated light from one of the pixels is incident on at least a portion of the prism group. The refracting surface is oriented to project an image of the pixel over an image of the light-shielding portion on a screen at a predetermined distance, making an apex with an angle with respect to a reference surface that is orthogonal to an optical axis at the apex. The prism group is arranged in a substantially periodic manner, with number of the periods per a unit area of 15 or less. 
   One of the causes of that the prism group causes the diffraction light is the periodic arrangement of the prism elements. In the technology of the third invention, when the prism elements are arranged along by the lines that are substantially straight, the number of the substantial lines (periods) per unit area is 15 or less, so that the diffraction light ascribable to the periodic arrangement of the prism elements lessens. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   Preferably, the number of the substantial lines (periods) per unit area is 10 to 12. More preferably, the number is 7 to 9. The smaller number of the lines lessens the diffraction light ascribable to the periodic arrangement of the prism elements more certainly. 
   According to still another aspect of the present invention, the unit area is determined based on numerical apertures of an illumination optical system that supplies the light to the modulating unit and a projection optical system on which the modulated light is incident. Therefore, in the minimal unit area, the periodic arrangement of the prism elements may be limited, so that the light is refracted on the refracting surface of the prism group and the diffraction light ascribable to the periodic arrangement of the prism elements lessens. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   The projector according to still another aspect of the present invention includes a light source that supplies a light, the spatial light modulator according to the above aspects, and a projection lens that projects the light from the spatial light modulator to display an image on a screen. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   The other objects, features, and advantages of the present invention are specifically set forth in or will become apparent from the following detailed descriptions of the invention when read in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic of a projector according to a first embodiment of the present invention; 
       FIG. 2  is a perspective view of a liquid crystal panel according to the first embodiment; 
       FIG. 3  is a schematic of a black matrix according to the first embodiment; 
       FIG. 4  is a schematic of the black-matrix image according to a conventional image display device; 
       FIG. 5  is a cross section of the liquid crystal panel according to the first embodiment; 
       FIG. 6A  is a schematic for illustrating a refracting in a prism element according to the first embodiment; 
       FIG. 6B  is a top view of the prism element; 
       FIG. 7A  to  FIG. 7D  are schematics of projection images according to the first embodiment; 
       FIG. 8A  to  FIG. 8D  are cross sections of various prism groups; 
       FIG. 9  is a cross section of a prism group according to the first embodiment; 
       FIG. 10  is a cross section of a prism group according to a second embodiment of the present invention; 
       FIG. 11A  and  FIG. 11B  are schematics of a prism group according to a third embodiment of the present invention; 
       FIG. 12  is a schematic for explaining a unit area according to the third embodiment; 
       FIG. 13A  and  FIG. 13B  are cross sections of various prism groups with different depths; 
       FIG. 14A  to  FIG. 14D  are schematics of a prism group according to a fourth embodiment of the present invention; and 
       FIG. 15A  and  FIG. 15B  are schematics of a prism group according to a fifth embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
   Exemplary embodiments of a spatial light modulator and a projector according to the present invention are explained in detail with reference to the accompanying drawings. 
     FIG. 1  is a schematic of a projector according to a first embodiment of the present invention. A super-high pressure mercury lamp  101  generates a light that includes a red light, a green light, and a blue light (hereinafter, “R-light”, “G-light”, and “B-light”, respectively). An integrator  104  uniforms an illuminance distribution of the light. A polarization converter  105  changes the light with the uniform illuminance-distribution into a polarized light such as an s-polarized light. The s-polarized light enters into a red-light transmitting dichroic mirror  106 R. The red-light transmitting dichroic mirror  106 R transmits the R-light, but reflects the G-light and the B-light. The dichroic mirrors separate the light into the R-light, the G-light, and the B-light in order. 
   After the R-light passes through the red-light transmitting dichroic mirror  106 R, a reflecting mirror  107  bends the R-light by 90 degrees. Then a first-color spatial light modulator  110 R, which is a transparent liquid-crystal display device, modulates the R light based on an image signal corresponding to red. The R-light is still s-polarized when the R-light enters into the first-color spatial light modulator  110 R, because the dichroic mirrors do not change the polarization direction. 
   The first-color spatial light modulator  110 R includes a λ/2 wave plate  123 R, a glass plate  124 R, a first polarizing plate  121 R, a liquid crystal panel  120 R, and a second polarizing plate  122 R. The λ/2 wave plate  123 R and the first polarizing plate  121 R sandwich a glass plate  124 R, so that the heat does not distort the λ/2 wave plate  123 R and the first polarizing plate  121  R. The glass plate  124 R is transparent and does not affect the polarization. The second polarizing plate  122 R may be attached to the emergent surface of the liquid crystal panel  120 R or the incident surface of a cross dichroic prism  112 . 
   The first-color spatial light modulator  110 R modulates the R-light as follows. The λ/2 wave plate  123 R changes the s-polarized R light into a p-polarized R light. After passing though the glass plate  124 R and the first polarizing plate  121 R, the p-polarized R-light enters into the liquid crystal panel  120 R. The liquid crystal panel  120 R modulates the p-polarized R-light based on the image signal corresponding to red and changes the p-polarized R-light into an s-polarized R-light. Then the second polarizing plate  122 R outputs the s-polarized R-light to the cross dichroic prism  112 . 
   The red-light transmitting dichroic mirror  106 R deflects the G-light and the B-light by 90 degrees. The blue-light transmitting mirror  106 G reflects the G-light, but transmits the B-light. Then a second-color spatial light modulator  110 G, which is a transparent liquid-crystal display device, modulates the G-light based on an image signal corresponding to green. The second-color spatial light modulator  110 G includes a liquid crystal panel  120 G, a first polarizing plate  121 G, and a second polarizing plate  122 G. 
   The G-light is s-polarized when the G-light enters into the second-color spatial light modulator  110 G. After passing though the first polarizing plate  121 G, the s-polarized G-light enters into the liquid crystal panel  120 G. The liquid crystal panel  120 G modulates the s-polarized G-light based on an image signal corresponding to green and changes the s-polarized G-light into a p-polarized G-light. Then the second polarizing plate  122 G outputs the p-polarized G-light to the cross dichroic prism  112 . 
   After passing through the blue-light transmitting mirror  106 G, the B-light enters into a third-color spatial light modulator  110 B via two relay lenses  108  and two reflecting mirrors  107 . The third-color spatial light modulator  110 B, which is a transparent liquid-crystal display device, modulates the B-light based on an image signal corresponding to blue. 
   The B-light goes via the relay lenses  108  because the optical path of the B-light is longer than those of the R-light and the G-light. The relay lenses  108  are configured to transmit the B-light to the third-color spatial light modulator  110 B as it is. The third-color spatial light modulator  110 B includes a λ/2 wave plate  123 B, a glass plate  124 B, a first polarizing plate  121 B, a liquid crystal panel  120 B, and a second polarizing plate  122 B. The configuration of the third-color spatial light modulator  110 B is same as that of the first-color spatial light modulator  110 R and the explanation is omitted. 
   The B-light is s-polarized when the B-light enters into the third-color spatial light modulator  110 B. The λ/2 wave plate  123 B changes the s-polarized B-light into a p-polarized B-light. After passing though the glass plate  124 B and the first polarizing plate  121 B, the p-polarized B-light enters into the liquid crystal panal  120 B. The liquid crystal panel  120 B modulates the p-polarized B-light based on an image signal corresponding to blue and changes the p-polarized B-light into a s-polarized B-light. Then the second polarizing plate  122 B outputs the s-polarized B-light to the cross dichroic prism  112 . Thus, the red-light transmitting dichroic mirror  106 R and the blue-transmitting dichroic mirror  106 G separate the light from the super-high pressure mercury lamp  101  into the R-light, the G-light, and the B-light. 
   The dichroic prism  112  includes two dichroic layers  112   a ,  112   b  that are crossed each other. The dichroic layer  112   a  reflects the B-light and transmits the R-light and the G-light, while the dichroic layer  112   b  reflects the R-light and transmits the B-light and the G-light. In this manner, the dichroic prism  112  synthesizes the R-light, the G-light, and the B-light that are modulated by the first-color spatial light modulator, the second-color spatial light modulator, and the third-color spatial light modulator, respectively. Then a projection lens  114  projects the light combined by the dichroic prism  112  onto a screen  166  to display a full-color image. 
   The cross dichroic prism  112  synthesizes the R-light, G-light, and B-light effectively. To synthesize the lights effectively, each spatial-light modulator is configured to output the light with the different polarization direction. When each light enters into the cross dichroic prism  112 , the R-light and the B-light is s-polarized while the G-light is p-polarized. This configuration comes from the reflection characteristic of the dichroic layers  112   a  and  112   b . The dichroic layers  112   a  and  112   b  usually have the better reflection characteristic in an s-polarized light, so that the dichroic layers  112   a  and  112   b  are configured to reflect the R-light and the B-light that are s-polarized and transmit the G-light that is p-polarized. 
     FIG. 2  is a perspective view of a liquid crystal panel according to the first embodiment. The liquid crystal panel is explained in details with the liquid crystal panel  120 R. The other two liquid display panels  120 G,  120 B have the same configuration except the wave-length region. 
   The liquid crystal panel  120 R includes six layers. The incident R-light goes toward a screen  116  passing the layers from the bottom side to the upper side. The layers are in the bottom-up order: an incident-side dust-proof transparent plate  201 ; an opposed substrate  202 ; a black matrix layer  203 ; a liquid crystal layer  204 ; a TFT substrate  205 ; and an exit-side dust-proof transparent plate  206 . The opposed substrate  202  is formed on the incident-side dust-proof transparent plate  201  while the TFT substrate  205  is formed on the exit-side dust-proof transparent plate  206 . The opposed substrate  202  includes transparent electrodes and so on, and the TFT substrate  205  includes thin film transistors (TFT), transparent electrodes, and so on. The opposed substrate  202  and the TFT substrate  205  sandwich the black matrix layer  203  and the liquid crystal layer  204 . The black matrix layer  203  is formed on the incident side of the liquid crystal layer  204  and used to decrease the leakage of the light to the outside. The liquid crystal layer  204  is used to display an image. 
   A prism group  210  is composed of a plurality of prism elements  211  and formed on the exit-side surface of the exit-side dust-proof transparent plate  206 , however, may be formed on the second polarizing plate,  122 R or on the incident-side surface of the cross dichroic prism  112 . Similarly, the first polarizing plate and the second polarizing plate may be inserted between other layers, such as between the incident-side dust-proof transparent plate  201  and the opposed substrate  202 , between the exit-side dust-proof transparent plate  206  and the TFT substrate  205 , and so on as an alternative to the structure shown in  FIG. 1 . 
     FIG. 3  is a schematic of the black matrix layer  203  that includes a black matrix part  220  and an opening part  230 . The black matrix part  220  blocks out the incident R-light so that the incident R-light does not go toward the screen  116 . The black matrix part  220  has predetermined widths W 1 , W 2  and is formed with an orthogonal lattice-pattern. The opening part  230  is a rectangular area that is surrounded by the black matrix parts  220  and transmits the incident R-light. After passing through the opposed substrate  202  to the TFT substrate  205  while being modulated by the liquid crystal layer  204 , the incident R-light forms the image of the pixel (hereinafter, “pixel image”). The position and the size of the pixel image are corresponding to those of the opening part  230 . CL is a center line of the black matrix part  220 , and the center lines surrounds an area  240  that appears periodically, which is shown within a heavy-line frame. 
     FIG. 4  is a schematic of an image projected on the screen  116  by a conventional projector. A zonal black-matrix image  220 P surrounds an opening image  230 P. An image  240 P that appears periodically, which is shown within a heavy-line frame, is corresponding to the area  240 . An intersection point CP is an intersection point of central-line images CLPs. All the following embodiments are explained with the images that the projection lens  114  projects on the screen  116 , because the images that are projected on the screen  116  using the projection lens  114  are considered to be essentially same as the images that are projected on a virtual screen without using the projection lens  114 , except a magnification. The virtual screen is assumed to be laid at a predetermined distance from the prism group  210 . The former image is projected by the projector  100  and the latter image is projected by the first-color spatial light modulator  110 R and the like. 
     FIG. 5  is a cross section of the liquid crystal panel according to the first embodiment. To give a clear explanation, the other components are not shown. After passing through the opening part  230 , the R-light diverges conically and enters into the prism group  210  partially. The prism group  210  includes a refracting surface  212  and a flat surface  213 . The flat surface  213  is substantially parallel with a surface  230   a  where the opening parts  230  are formed. A plurality of prism elements  211  are arranged periodically and compose the prism group  210 . 
     FIG. 6A  is a schematic for illustrating a refracting in a prism element according to the first embodiment. The refractive index of the media between the prism group  210  and the screen  116  (such as the air) is n 1 , the refractive index of the material of the prism group  210  is n 2 , and the angle between the refracting surface  212  and a reference surface  213   a , which is called the angle of gradient, is θ. The reference surface  213   a  corresponds to the flat surface  213  expanded. 
   The parallel light of the incident light to the prism group  210  is used to give a clear explanation. Some lights enter into the flat surface  213  and some lights enter into the refracting surface  212 . The light that enters into the flat surface  213  orthogonally goes as it is and projects the image on the screen without being refracted. On the other hand, the light that enters into the refracting surface  212  is refracted while satisfying with the following conditional equation
 
 n   1 ·sin β= n   2 ·sin α
 
where α is the angle of the incidence and β is the exit angle that are based on the normal N of the refracting surface  212 .
 
   When the screen  116  is laid at a distance L from the prism group  210 , and the light is refracted and moves a distance S on the screen  116 , the distance S satisfies the following equation:
 
 S=L ×tan(Δβ)
 
Δβ=β−α.
 
The distance S is the moving distance of the opening image  240 P on the screen  116  and configured by the angle θ of the gradient of the refracting surface  212 .
 
   Moreover, the direction where the light beam LL 2  is refracted depends on the direction of the refracting surface  212 . In other words, the direction where the opening image is formed on the screen  116  is configured by the direction of the refracting surface  212 . 
   The images that are projected on the screen  116  by the R-light are explained with reference to  FIGS. 7(   a ) to  7 ( d ).  FIG. 7A  shows an image  240 P of an area that appears periodically on the screen  116 . The light that enter into the flat surface  213  substantially orthogonally goes straight without being refracted and forms the opening image  230 P (a direct transmitted image) in the center of the image  240 P. 
   The relationship between the refracting surface and the direction of the refraction is explained with reference to  FIG. 6B  and  FIG. 7 .  FIG. 6B  is a top view of the prism element  211 . When the light enters into a refracting surface  212   a , the light is refracted with the direction of the refraction, the angle of the refraction, and the quantity of the refraction that are respectively corresponding to the direction of the refracting surface  212   a , the angle θ of the graduation, and the area P 1 . The angle between a side  211   a  and the central line CL on the black matrix layer is formed to be 45 degrees, so that the opening image  230 Pa, shown in  FIG. 7A , is formed to the direction of an arrow and at the distance S from the opening image  230 P (a direct transmitted image). To give a clear explanation, the following two things are assumed in all the explanations: 1) the projection lens  114  does not bring about a flip vertical and a flip horizontal, 2) the watcher always sees the projector  100  from the opposite direction that the light is traveling to. For example, the watcher sees an image projected on the screen  116  from the backside of the screen  116  to see the super-high pressure mercury lamp  101 . 
     FIG. 7A  to  FIG. 7D  show the identical image  240 P and each opening image:  230 Pa;  230 Pb;  230 Pc; and  230 Pd. The same explanation as the refracting surface  212   a  and the opening image  230 Pa is applied to: the refracting surface  212   b  and the opening image  230 Pb that are shown in  FIG. 7B ; the refracting surface  212   c  and the opening image  230 Pc that are shown in  FIG. 7C ; and the refracting surface  212   d  and the opening image  230 Pd that are shown in  FIG. 7D . 
     FIG. 8A  to  FIG. 8D  are cross sections of various prism groups. The direction of the refracting surface, the angle of the graduation, and the area determine the shape.  FIG. 8A  is a sectional view of a prism group  810  with a trapezoidal form that includes a refracting surface  810   a  and a flat surface  810   b .  FIG. 8B  is a sectional view of a prism group  820  with a triangular form that includes a refracting surface  820   a  and a flat surface  820   b .  FIG. 8C  is a sectional view of a prism group  830  with a triangular form that includes a refracting surface  830   a  and a flat surface  830   b .  FIG. 8D  is a sectional view of a prism group  840  with a blaze form that includes a refracting surface  840   a.    
   In this manner, the black-matrix image  220  gets blurred  220  using the light refracted on refracting surfaces  212   a ,  212   b ,  212   c , and  212   d . Next, the way to decrease the diffraction light is explained With reference to  FIG. 9 . To give a clear explanation, the shape of the prism element shown in  FIG. 8B  is used. 
   Two refracting surfaces  920   a  form a V-shaped depression that is periodic. A reference surface  901  is defined to be substantially orthogonal to an optical axis of the incident light and includes an apex of the V-shaped depression. A distance between the reference surface  901  and a flat surface  920   b  is d. The distance d corresponds to the depth of the V-shaped depression and may be called the depth d. The distance d satisfies any one of the following conditions
 
 d&lt; 0.95×λ/(2×( n− 1))  (1)
 
 d&gt; 1.05×λ/(2×( n− 1))  (2)
 
where n is the refractive index of the material of a prism group  920  and λ is the wavelength of the incident light to the prism group  920 . In the present embodiment, the distance d is 1100 nm and, if the depth d satisfies the following condition (A)
 
 d=λ/( 2×( n− 1))  (A)
 
the diffraction efficiency improves.
 
   In the present embodiment, the incident light is the visible light of the light that the super-high pressure mercury lamp  101  generates. For example, when the wavelength λ of the incident light is 480 nm and the refractive index n of the prism group  920  is 1.46, the condition (A) is 
   
     
       
         
           
             
               
                 d 
                 = 
                   
                 ⁢ 
                 
                   480 
                   / 
                   
                     ( 
                     
                       2 
                       × 
                       
                         ( 
                         
                           1.46 
                           - 
                           1 
                         
                         ) 
                       
                     
                     ) 
                   
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   522 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     nm 
                     . 
                   
                 
               
             
           
         
       
     
   
   Another example is that when the wavelength λ of the incident light is 650 nm and the refractive index n of the prism group  920  is 1.46, the condition (A) is 
   
     
       
         
           
             
               
                 d 
                 = 
                   
                 ⁢ 
                 
                   650 
                   / 
                   
                     ( 
                     
                       2 
                       × 
                       
                         ( 
                         
                           1.46 
                           - 
                           1 
                         
                         ) 
                       
                     
                     ) 
                   
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   707 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     nm 
                     . 
                   
                 
               
             
           
         
       
     
   
   The diffraction occurs effectively if the wavelength λ of the incident light is 522 nm in the former case and if the wavelength λ of the incident light is 707 nm in the latter case. In the present embodiment, preferably, the depth d of the V-shaped depression does not cause the diffraction light, or lessens the diffraction to get blurred. 
   In the present embodiment, the value of the distance d may be various as far as the distance d satisfies any one of the conditions (1) or (2). For example, when the wavelength λ is 480 nm, the conditions (1) and (2) become 
   
     
       
         
           
             
               
                 
                   d 
                   &lt; 
                   
                     0.95 
                     × 
                     
                       λ 
                       / 
                       
                         ( 
                         
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                             ( 
                             
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                               - 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
                 = 
                   
                 ⁢ 
                 
                   0.95 
                   × 
                   
                     480 
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                         2 
                         × 
                         
                           ( 
                           
                             1.46 
                             - 
                             1 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
             
           
           
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     496 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     nm 
                   
                 
                 , 
                 and 
               
             
           
           
             
               
                 
                   d 
                   &gt; 
                   
                     1.05 
                     × 
                     
                       λ 
                       / 
                       
                         ( 
                         
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                             ( 
                             
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                 = 
                   
                 ⁢ 
                 
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                   × 
                   
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                       ( 
                       
                         2 
                         × 
                         
                           ( 
                           
                             1.46 
                             - 
                             1 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
             
           
           
             
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       548 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       nm 
                     
                   
                   , 
                   
                     respectively 
                     . 
                   
                 
                 ⁢ 
                 
                     
                 
               
             
           
         
       
     
   
   Another example is that when the wavelength λ is 650 nm, the conditions (1) and (2) become 
   
     
       
         
           
             
               
                 
                   d 
                   &lt; 
                   
                     0.95 
                     × 
                     
                       λ 
                       / 
                       
                         ( 
                         
                           2 
                           × 
                           
                             ( 
                             
                               n 
                               - 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
                 = 
                   
                 ⁢ 
                 
                   0.95 
                   × 
                   
                     650 
                     / 
                     
                       ( 
                       
                         2 
                         × 
                         
                           ( 
                           
                             1.46 
                             - 
                             1 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
             
           
           
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     671 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     nm 
                   
                 
                 , 
                 and 
               
             
           
           
             
               
                 
                   d 
                   &gt; 
                   
                     1.05 
                     × 
                     
                       λ 
                       / 
                       
                         ( 
                         
                           2 
                           × 
                           
                             ( 
                             
                               n 
                               - 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
                 = 
                   
                 ⁢ 
                 
                   1.05 
                   × 
                   
                     650 
                     / 
                     
                       ( 
                       
                         2 
                         × 
                         
                           ( 
                           
                             1.46 
                             - 
                             1 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
             
           
           
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     742 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     nm 
                   
                 
                 , 
                 
                   respectively 
                   . 
                 
               
             
           
         
       
     
   
   In the present embodiment, the depth d is 1100 nm and this length satisfies the condition (2) with any wavelengths of the incident light, so that the diffraction light lessens. Accordingly, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   In the present embodiment, it is preferable that the following condition (3) or (4) is satisfied
 
 d&lt; 0.9×λ/(2×( n− 1))  (3)
 
 d&gt; 1.1×λ/(2×( n− 1))  (4)
 
   It is more preferable that the following condition (5) or (6) is satisfied
 
 d&lt; 0.7×λ/(2×( n− 1))  (5)
 
 d&gt; 1.3×λ/(2×( n− 1))  (6)
 
Satisfying any one of the conditions (3) to (6) lessens the diffraction light more, so that the watcher sees the higher-quality and smoother image.
 
     FIG. 10  is a cross section of a prism group  1020  of a spatial light modulator according to a second embodiment of the present invention. Except the prism group  1020 , the configuration of the second embodiment is basically same as that of the first embodiment and the explanations of the other components are omitted. In the present embodiment, a reference surface  1001  is defined to correspond to a flat surface of a substrate that includes the prism group  1020 , and to be substantially orthogonal to an optical axis of the incident light. The distances between the reference surface  1001  and a flat surface  1020   b  are d 1 , d 3 , d 5 . The distances between the reference surface  1001  and predetermined points are d 2 , d 4 , d 6 . The predetermined points are the nearest points to the reference surface  1001  on the refracting surface  1020   a . The distances d 1 , d 3 , d 5  and the distances d 2 , d 4 , d 6  are formed to be aperiodic. 
   One of the causes of that the prism group  1020  causes the diffraction light is the periodic arrangement of the prism elements. In the present embodiment, the arrangement of the prism elements is aperiodic, so that the diffraction light lessens. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
     FIG. 11A  is a perspective view of a liquid crystal panel  1100 R of a spatial light modulator according to a third embodiment of the present invention. The configuration of the third embodiment is basically same as that of the first embodiment, therefore, the same reference symbols as the first embodiment are applied. The liquid crystal panel  1100 R is an example of three liquid crystal panels that three special light modulators have respectively. 
   In the present embodiment, a prism group  1110  is composed of a plurality of prism elements  1111  and the prism elements  1111  are arranged along by lines La 1 , La 2 , La 3 , La 4 , and La 5  that are substantially straight. The number of the lines La 1 , La 2 , La 3 , La 4 , and La 5  per unit area aφ is five. The number of the lines La 1 , La 2 , La 3 , La 4 , and La 5  per unit area aφ may be 15 or less. 
     FIG. 11B  is a front view of the neighborhood of the unit area aφ. The prism elements  1111  are formed with substantially orthogonal lattice-pattern. The lines Lb 1 , Lb 2 , Lb 3 , Lb 4 , Lb 5 , and Lb 6  that are substantially straight are substantially orthogonal to the lines La 1  to La 5 . The unit area aφ may have 15 or less lines that are orthogonal to the lines La 1  to La 5 . 
     FIG. 12  is a schematic for explaining the unit area aφ with an optical path from the super-high pressure mercury lamp  101  to the screen  116 . For convenience, only the main components are shown, the projection lens  114  is illustrated to be a single biconvex lens, and the prism group  1110  is illustrated separately though the prism group  1110  is included in the liquid crystal panel  1100 R actually. The projector  100  includes the components that belong to optical systems such as the illumination optical system (hereinafter, “illumination system ILL”), the projection optical system (hereinafter, “projection system PL”), and the color-separation optical system. The super-high pressure mercury lamp  101  and the integrator belong to the illumination system ILL. The projection lens  114  belongs to the projection system PL and corresponds to the projection system PL in  FIG. 12 . Any components that belong to the color-separation optical system, such as the red-light transmitting dichroic mirror  106 , are not shown in  FIG. 12 . 
   The optical path from the super-high pressure mercury lamp  101  to the screen  116  is as follows. The super-high pressure mercury lamp  101  outputs the light to the integrator  104 . The integrator  104  illuminates the liquid crystal panel  1100 R with the superposed lights that have a predetermined angle distribution, that is, the superposed lights with the various incident angles illuminate a position OBJ that is on the liquid crystal panel. The liquid crystal panel  110 R outputs the light to the prism group  1110  while the light spreads with the F-number of the illumination system ILL. The projection lens  114  receives the light that passes through the prism group  1110  and projects the light on the screen  116  with the F-number that is same as or smaller than the F-number of the projection lens  114 . The image of the position OBJ is formed on the position IMG that is on the screen  116  because a position IMG is conjugated with the position OBJ. The F-number of the illumination system ILL (hereinafter, “F-number of ILL”) and that of the projection system PL (hereinafter, “F-number of PL”) satisfy any one of the following three relational expressions (B) to (D)
 
the F-number of ILL&gt;the F-number of PL  (B)
 
the F-number of ILL=the F-number of PL  (C)
 
the F-number of ILL&lt;the F-number of PL  (D)
 
   In any one of the relationships, the smaller F-number of ILL or F-number of PL determines the angular range, and the light within the angular range is projected on the screen  116  validly. For example, any one of the relational expressions (B) or (C) satisfies the following condition
 
1/(2 FILL )=sin θ a 
 
where FILL is the F-number of PL, θa is the angle between the optical axis and the emergent light of the position OBJ.
 
   The emergent light from the liquid crystal panel  1100 R spreads with the angle θa and illuminates the unit area aφ, which is a circular area on the prism group  1110 . Then, the projection lens  114  projects all the emergent light from the unit area on the screen  116 . On the other hand, in the relational expression (D), the F-number of ILL determines the unit area aφ that is projected on the screen  116  validly. 
   In any relational expressions (B), (C), and (D), the projection lens  114  projects the emergent light from the unit area aφ on the screen  116 . In the present embodiment, the prism group  1110  has the prism elements that are arranged along by the lines La 1  to La 5  and the lines Lb 1  to Lb 6  per the unit area aφ, and the number of the lines La 1  to La 5  and that of the lines Lb 1  to Lb 6  are not more than 15, so that the diffraction light ascribable to the periodic arrangement of the prism elements lessens. Consequently, the watcher sees the high-quality and smooth image without seeing the image of the black matrix. 
   In the unit areas aφ, the total area of the refracting surface  212  of a unit areas aφ is equal to those of any other unit areas aφ, and the total area of the flat surface of a unit areas aφ is equal to those of any other unit areas aφ. Therefore, the projection image has less diffraction light and the pixel images are superposed on the black-matrix images on the screen  116  at a predetermined distance from the prism group  1110 . Consequently, the watcher sees the smooth and less-rough images without seeing the image of the black matrix. 
   Preferably, the number of the lines that are substantially straight per the unit area is 10 to 12. More preferably, the number is 7 to 9. The smaller number of the lines lessens the diffraction light ascribable to the periodic arrangement of the prism elements more certainly. 
     FIG. 13A  is a cross section of the prism group  1320  that is made of glass. The depth d 1  is approximately 30 nm and the angle θ 1  between the reference surface  1001  and the refracting surface is approximately 0.06 degree.  FIG. 13B  is a cross section of the prism group  1320  made of acrylic or ZEONEX (a trade name). On the prism group  1320 , a resin substrate  1330 , which is optical transparent, and a glass substrate  1340  are formed. The depth d 2  is approximately 1 μm and the angle θ 2  is approximately 0.97 degree. The structure shown in  FIG. 13B  is made more easily than that shown in  FIG. 13A  because the former structure has the larger values of the depth and the angle than the latter structure. 
     FIG. 14A  to  FIG. 14D  are schematics of a prism group  1410  of a spatial light modulator according to a fourth embodiment of the present invention. Except the prism group  1410 , the configuration of the fourth embodiment is same as that of the first embodiment and the explanations of the other components are omitted. The prism group  1410  is composed of three types of prism elements  1411   a ,  1411   b , and  1411   c . When a set of is considered to have the prism elements  1411   a ,  1411   b ,  1411   c  and  1411   b  that are arranged in the described order and adhered to each other, a plurality of the sets are adhered to each other to compose the prism group  1410 . The prism elements  1411   a  is a zonal prism element with the refracting surfaces  1412   a , and the prism element  1411   c  with the refracting surface  1412   c  corresponds the prism element  1411   a  that is flipped horizontally. The prism element  1411   b  is a parallel flat plate that includes a flat surface  1412   b . The two prism groups  1410  may be overlapped substantially orthogonally to have the same function as the prism group that includes the flat surface  1411   b  and the refracting surfaces  1411   a ,  1411   c  that refract the lights that are substantially orthogonal each other. 
   In the present embodiment, the diffraction lessens in the following simple way: manufacturing the prism elements  1411   a ,  1411   b , and  1411   c  that are substantially flat plates; and arranging 15 or less prism elements  1411   a ,  1411   b , and  1411   c  per unit area aφ. 
     FIG. 15A  is a front view of a prism group  1510  of a spatial light modulator according to a fifth embodiment of the present invention. Except the prism group  1510 , the configuration of the fifth embodiment is same as that of the first embodiment and the explanations of the other components are omitted. Prism elements  1511   a ,  1511   b , and  1511   c  is formed to have the random depths and are arranged in the unit area aφ at random. In the unit areas aφ, the total area of the refracting surface  212  of a unit areas aφ is equal to those of any other unit areas aφ, and the total area of the flat surface  213  of a unit areas aφ is equal to those of any other unit areas aφ. 
   A manufacturing method of the prism group  1510  is explained with reference to  FIG. 15B . To form the prism elements that compose the prism group  1510 , a piezo actuator (not shown) or the like is used to press a substrate  1520  that is made of acrylic using a mold  1530  that has a pyramid-shaped tip. In the present method, the depth and the direction of the prism element respectively depend on the force and the direction with which the mold  1530  is pressed into the substrate  1520 . When the prism group  1510  is formed according to the present manufacturing method, the projection image has less diffraction light, and the pixel images are superposed on the black-matrix images on the screen at a predetermined distance from the prism group  1510 . Consequently, the watcher sees the smooth and less-rough images without seeing the black-matrix image. 
   The present invention does not limit the configurations to five embodiments described above. As far as the prism group does not cause the diffraction light, or the prism group lessens the diffraction light enough so that the diffraction light get blurred, any configurations may be any combinations of five embodiments. 
   Although the invention has been described with respect to a specific embodiment for a complete and clear disclosure, the appended claims are not to be thus limited but are to be construed as embodying all modifications and alternative constructions that may occur to one skilled in the art which fairly fall within the basic teaching herein set forth.