Patent Publication Number: US-2021173292-A1

Title: Projection system and projector

Description:
The present application is based on, and claims priority from JP Application Serial Number 2019-221006 filed Dec. 6, 2019, the disclosure of which is hereby incorporated by reference herein in its entirety. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a projection system and a projector. 
     2. Related Art 
     JP-A-2010-20344 describes a projector that enlarges and projects a projection image formed by an image formation section via a projection system. The projection system described in JP-A-2010-20344 is formed of a first optical system and a second optical system sequentially arranged from the reduction side toward the enlargement side. The first optical system includes a refractive system. The second optical system is formed of one mirror having a concave curved shape. The image formation section includes a light source and a light valve. The image formation section forms a projection image in the reduction-side image formation plane of the projection system. The projection system forms an intermediate image in a position between the first optical system and the reflection surface of the mirror and projects a final image conjugate with the intermediate image on a screen disposed on the enlargement-side image formation plane of the projection system. The mirror reflects the light rays from the light source in an upward direction that intersects the optical axis of the first optical system. 
     When the projector described in JP-A-2010-20344 projects the final image on the screen, the distance between an upper portion of the screen and the mirror is longer than the distance between a lower portion of the screen and the mirror. Further, in the description of JP-A-2010-20344, in which the final image conjugate with the intermediate image is formed on the screen based on the effect of only one mirror, the difference in distance described above causes the light ray that reaches the upper portion of the screen and the light ray that reaches the lower portion of the screen to form the intermediate image in different positions in the direction of the optical axis of the first optical system. That is, the light ray that reaches the upper portion of the screen has a longer distance between the intermediate image and the mirror, and the light ray that reaches the lower portion of the screen has a shorter distance between the intermediate image and the mirror. The intermediate image therefore inclines in the direction along the optical axis of the first optical system. 
     When the projection distance of the projection system is shortened, the intermediate image inclines in the direction along the optical axis of the first optical system by a greater amount and expands in the direction of the optical axis, resulting in an increase in the size of the intermediate image. This causes a problem of the necessity of increasing the distance between the first optical system and the second optical system in correspondence with the size of the intermediate image. Further, since the light flux formed of the light rays diverges in the segment from the position where the intermediate image is formed toward the enlargement side, the increase in the size of the intermediate image causes a problem of the necessity of increasing the size of the mirror to capture the outside portion of the light flux. 
     SUMMARY 
     To solve the problems described above, a projection system according to an aspect of the present disclosure includes a first optical system, a second optical system disposed at an enlargement side of the first optical system, and a third optical system disposed at the enlargement side of the second optical system. An intermediate image conjugate with a reduction-side image formation plane is formed between the first optical system and the second optical system. The first optical system includes a first lens disposed in a position closest to the enlargement side in the first optical system. The second optical system includes a mirror having a concave curved surface. The third optical system includes a second lens disposed in a position closest to the reduction side in the third optical system, the second lens having negative power. An effective range of the first lens is located at one side of an optical axis of the first optical system. An effective range of the second lens is located at other side of the optical axis. 
     A projector according to another aspect of the present disclosure includes a light source, a light modulator modulating light emitted from the light source to form an image on the reduction-side image formation plane, and the projection system described above, which projects the image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic configuration diagram of a projector including a projection system according to the present disclosure. 
         FIG. 2  is a light ray diagram of the light rays passing through the entire projection system according to Example 1. 
         FIG. 3  is a light ray diagram of the light rays passing through the projection system according to Example 1. 
         FIG. 4  is a light ray diagram in the vicinity of a second optical system and a third optical system. 
         FIG. 5  shows the enlargement-side MTF of the projection system according to Example 1. 
         FIG. 6  is a light ray diagram of the light rays passing through the entire projection system according to Example 2. 
         FIG. 7  is a light ray diagram of the light rays passing through the projection system according to Example 2. 
         FIG. 8  is a light ray diagram in the vicinity of the second optical system and the third optical system. 
         FIG. 9  shows the enlargement-side MTF of the projection system according to Example 2. 
         FIG. 10  is a light ray diagram of the light rays passing through the entire projection system according to Example 3. 
         FIG. 11  is a light ray diagram of the light rays passing through the projection system according to Example 3. 
         FIG. 12  is a light ray diagram in the vicinity of the second optical system and the third optical system. 
         FIG. 13  shows the enlargement-side MTF of the projection system according to Example 3. 
         FIG. 14  is a light ray diagram of the light rays passing through the entire projection system according to Example 4. 
         FIG. 15  is a light ray diagram of the light rays passing through the projection system according to Example 4. 
         FIG. 16  is a light ray diagram in the vicinity of the second optical system and the third optical system. 
         FIG. 17  shows the enlargement-side MTF of the projection system according to Example 4. 
         FIG. 18  is a light ray diagram of the light rays passing through the entire projection system according to Example 5. 
         FIG. 19  is a light ray diagram of the light rays passing through the projection system according to Example 5. 
         FIG. 20  is a light ray diagram in the vicinity of the second optical system and the third optical system. 
         FIG. 21  shows the enlargement-side MTF of the projection system according to Example 5. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     A projection system and a projector according to embodiments of the present disclosure will be described below in detail with reference to the drawings. 
     Projector 
       FIG. 1  is a schematic configuration diagram of a projector including a projection system  3  according to the present disclosure. A projector  1  includes an image formation section  2 , which generates a projection image to be projected on a screen S, a projection system  3 , which enlarges the projection image and projects the enlarged image on the screen S, and a controller  4 , which controls the action of the image formation section  2 , as shown in  FIG. 1 . 
     Image Generation Optical System and Controller 
     The image formation section  2  includes a light source  10 , a first optical integration lens  11 , a second optical integration lens  12 , a polarization converter  13 , and a superimposing lens  14 . The light source  10  is formed, for example, of an ultrahigh-pressure mercury lamp or a solid-state light source. The first optical integration lens  11  and the second optical integration lens  12  each include a plurality of lens elements arranged in an array. The first optical integration lens  11  divides the light flux from the light source  10  into a plurality of light fluxes. The lens elements of the first optical integration lens  11  focus the light flux from the light source  10  in the vicinity of the lens elements of the second optical integration lens  12 . 
     The polarization converter  13  converts the light from the second optical integration lens  12  into predetermined linearly polarized light. The superimposing lens  14  superimposes images of the lens elements of the first optical integration lens  11  on one another in a display area of each of liquid crystal panels  18 R,  18 G, and  18 B, which will be described later, via the second optical integration lens  12 . 
     The image formation section  2  further includes a first dichroic mirror  15 , a reflection mirror  16 , a field lens  17 R, and the liquid crystal panel  18 R. The first dichroic mirror  15  reflects R light, which is part of the light rays incident via the superimposing lens  14 , and transmits G light and B light, which are part of the light rays incident via the superimposing lens  14 . The R light reflected off the first dichroic mirror  15  travels via the reflection mirror  16  and the field lens  17 R and is incident on the liquid crystal panel  18 R. The liquid crystal panel  18 R is a light modulator. The liquid crystal panel  18 R modulates the R light in accordance with an image signal to form a red projection image. 
     The image formation section  2  further includes a second dichroic mirror  21 , a field lens  17 G, and the liquid crystal panel  18 G. The second dichroic mirror  21  reflects the G light, which is part of the light rays via the first dichroic mirror  15 , and transmits the B light, which is part of the light rays via the first dichroic mirror  15 . The G light reflected off the second dichroic mirror  21  passes through the field lens  17 G and is incident on the liquid crystal panel  18 G. The liquid crystal panel  18 G is a light modulator. The liquid crystal panel  18 G modulates the G light in accordance with an image signal to form a green projection image. 
     The image formation section  2  further includes a relay lens  22 , a reflection mirror  23 , a relay lens  24 , a reflection mirror  25 , a field lens  17 B, and the liquid crystal panel  18 B. The B light having passed through the second dichroic mirror  21  travels via the relay lens  22 , the reflection mirror  23 , the relay lens  24 , the reflection mirror  25 , and the field lens  17 B and is incident on the liquid crystal panel  18 B. The liquid crystal panel  18 B is a light modulator. The liquid crystal panel  18 B modulates the B light in accordance with an image signal to form a blue projection image. 
     The liquid crystal panels  18 R,  18 G, and  18 B surround a cross dichroic prism  19  in such a way that the liquid crystal panels  18 R,  18 G, and  18 B face three sides of the cross dichroic prism  19 . The cross dichroic prism  19 , which is a prism for light combination, produces a projection image that is the combination of the light modulated by the liquid crystal panel  18 R, the light modulated by the liquid crystal panel  18 G, and the light modulated by the liquid crystal panel  18 B. 
     The cross dichroic prism  19  forms part of the projection system  3 . The projection system  3  enlarges and projects the combined projection image (images formed by liquid crystal panels  18 R,  18 G, and  18 B) from the cross dichroic prism  19  on the screen S. The screen S is the enlargement-side image formation plane of the projection system  3 . 
     The controller  4  includes an image processor  6 , to which an external image signal, such as a video signal, is inputted, and a display driver  7 , which drives the liquid crystal panels  18 R,  18 G, and  18 B based on image signals outputted from the image processor  6 . 
     The image processor  6  converts the image signal inputted from an external apparatus into image signals each containing grayscales and other factors of the corresponding color. The display driver  7  operates the liquid crystal panels  18 R,  18 G, and  18 B based on the color projection image signals outputted from the image processor  6 . The image processor  6  thus causes the liquid crystal panels  18 R,  18 G, and  18 B to display projection images corresponding to the image signals. 
     Projection System 
     The projection system  3  will next be described. Examples 1 to 5 will be hereinafter described as examples of the configuration of the projection system  3  incorporated in the projector  1 . In the light ray diagram of the light rays passing through the projection system in each of Examples, the liquid crystal panels  18 R,  18 G, and  18 B are expressed as light modulation devices  18 . 
     Example 1 
       FIG. 2  is a light ray diagram diagrammatically showing the entire projection system according to Example 1.  FIG. 2  diagrammatically shows light fluxes that exit out of a projection system  3 A according to the present example and reach the screen S in the form of light fluxes F 1  to F 3 . The light flux F 1  is a light flux that reaches a smallest image height position. The light flux F 3  is a light flux that reaches a largest image height position. The light flux F 2  is a light flux that reaches a position between the position that the light flux F 1  reaches and the position that the light flux F 3  reaches.  FIG. 3  is a light ray diagram of the light rays passing through the projection system  3 A according to Example 1.  FIG. 4  is a light ray diagram of the light rays passing through the lens located in a position closest to the enlargement side in a first optical system, a second optical system, and a third optical system. 
     The projection system  3 A according to the present example is formed of a first optical system  31 , a second optical system  32 , and a third optical system  33  sequentially arranged from the reduction side toward the enlargement side, as shown in  FIG. 3 . The first optical system  31  is a refractive optical system including a plurality of lenses. The second optical system  32  includes a mirror M having a concave curved surface. The third optical system  33  has negative power. The first optical system  31  forms an intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 , as shown in  FIG. 4 . The second optical system  32  and the third optical system  33  form a final image conjugate with the intermediate image  35  in the enlargement-side image formation plane. 
     The liquid crystal panels  18  of the image formation section  2  are disposed in the reduction-side image formation plane. The liquid crystal panels  18  form projection images on one side of an optical axis N of the first optical system  31 . The intermediate image  35  is formed at the other side of the optical axis N of the first optical system  31 . The enlargement-side image formation plane is provided at the one side of the optical axis N of the first optical system  31 . The screen S is disposed in the enlargement-side image formation plane. 
     In the following description, three axes perpendicular to one another are called axes X, Y, and Z for convenience. The optical axis direction along the optical axis N of the first optical system  31  is called an axis-Z direction. One side of the optical axis N is called an upper side Y 1  of the axis-Y direction, and the other side of the optical axis Y is called a lower side Y 2  of the axis-Y direction. A plane perpendicular to the axis X and containing the axes Y and Z is called a plane YZ. The liquid crystal panels  18  therefore form projection images at the upper side Y 1  of the optical axis N. The intermediate image  35  is formed at the lower side Y 2  of the optical axis N. The screen S is located at the upper side Y 1  of the optical axis N. The lateral direction of the screen S coincides with the axis-X direction. The intermediate image  35  is the image formed on the screen S that is not enlarged but turned upside down in the axis-Y direction.  FIGS. 2, 3, and 4  are light ray diagrams in the plane YZ. 
     The first optical system  31  includes the cross dichroic prism  19  and  16  lenses L 1  to L 16 , as shown in  FIG. 3 . The lenses L 1  to L 16  are arranged in the presented order from the reduction side toward the enlargement side. In the present example, the lenses L 2  and L 3  are bonded to each other to form a first doublet L 21 . The lenses L 4  and L 5  are bonded to each other to form a second doublet L 22 . The lenses L 11  and L 12  are bonded to each other to form a third doublet L 23 . The lenses L 13  and L 14  are bonded to each other to form a fourth doublet L 24 . A light flux passage area of the lens L 16  (first lens) is located at the lower side Y 2  of the optical axis N. 
     The second optical system  32  is formed of one mirror M, as shown in  FIG. 4 . The mirror M reflects the light rays from the first optical system  31  toward the upper side Y 1 . 
     The third optical system  33  is formed of one lens L 17  (second lens) having a meniscus shape. The lens L 17  is disposed at the upper side Y 1  of the optical axis N of the first optical system  31 . The reduction-side surface of the lens L 17  has a concave curved surface recessed toward the enlargement side. The reduction-side surface of the lens L 17  has negative power. The reduction-side surface of the lens L 17  is an aspheric surface. The enlargement-side surface of the lens L 17  is a convex curved surface protruding toward the enlargement side. The enlargement-side surface of the lens L 17  is an aspheric surface. The thickness of the lens L 17  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . In other words, the light rays reflected off the mirror M and passing through the lens L 17  each travel along an optical path length in the lens L 17  that increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . 
     The lens L 16  of the first optical system  31  and the lens L 17  of the third optical system  33  are each provided as part of one optical element O, which is disposed at the opposite side of the second optical system  32  with respect to the intermediate image  35  along the optical axis N of the first optical system  31 . That is, the lens L 16  of the first optical system  31  is a first optical element section O 1  of the optical element O, which is the section on the lower side Y 2  of the optical axis N of the first optical system  31 . The lens L 17  of the third optical system  33  is a second optical element section O 2  of the optical element O, which is the section on the upper side Y 1  of the optical axis N of the first optical system  31 . 
     Lens Data 
     Data on the lenses of the projection system  3 A are as follows: The surfaces of the lenses are numbered sequentially from the reduction side toward the enlargement side. Reference characters are given to the lenses and the mirror. Data labeled with surface numbers that do not correspond to the lenses or the mirror are dummy data. Reference character R denotes the radius of curvature of a lens surface or a mirror surface. Reference character D denotes the on-axis distance between surfaces. Reference character C denotes the effective diameter of a lens surface or a mirror surface. Reference characters R, D, and C are each expressed in millimeters. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Reference 
                 Surface 
                   
                   
                   
                 Glass 
                 Refraction/ 
                   
               
               
                 character 
                 number 
                 Shape 
                 R 
                 D 
                 material 
                 reflection 
                 C 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 0.0000 
               
               
                   
                 1 
                 Spherical 
                 Infinity 
                 9.5000 
                   
                 Refraction 
                 11.7000 
               
               
                 19 
                 2 
                 Spherical 
                 Infinity 
                 25.9100 
                 SBSL7 
                 Refraction 
                 13.8197 
               
               
                   
                 3 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 17.5754 
               
               
                 L1 
                 4 
                 Spherical 
                 34.5867 
                 9.5095 
                 SFPL51 
                 Refraction 
                 18.8176 
               
               
                   
                 5 
                 Spherical 
                 −90.8873 
                 0.2000 
                   
                 Refraction 
                 18.6592 
               
               
                 L2 
                 6 
                 Spherical 
                 30.5520 
                 15.0000 
                 SFSL5 
                 Refraction 
                 16.9634 
               
               
                 L3 
                 7 
                 Spherical 
                 −57.2273 
                 1.2000 
                 STIH6 
                 Refraction 
                 14.0000 
               
               
                   
                 8 
                 Spherical 
                 173.6241 
                 0.2000 
                   
                 Refraction 
                 13.2517 
               
               
                 L4 
                 9 
                 Spherical 
                 22.4842 
                 8.6756 
                 SBSL7 
                 Refraction 
                 12.1460 
               
               
                 L5 
                 10 
                 Spherical 
                 −22.0071 
                 1.2000 
                 TAFD25 
                 Refraction 
                 11.2705 
               
               
                   
                 11 
                 Spherical 
                 51.1513 
                 0.8782 
                   
                 Refraction 
                 10.3777 
               
               
                 L6 
                 12 
                 Aspheric 
                 49.6558 
                 1.2000 
                 LBAL35 
                 Refraction 
                 10.3900 
               
               
                   
                   
                 surface 
               
               
                   
                 13 
                 Aspheric 
                 25.2762 
                 0.2000 
                   
                 Refraction 
                 10.2218 
               
               
                   
                   
                 surface 
               
               
                 L7 
                 14 
                 Spherical 
                 22.2953 
                 5.5069 
                 SFSL5 
                 Refraction 
                 10.2632 
               
               
                   
                 15 
                 Spherical 
                 −846.7643 
                 0.2000 
                   
                 Refraction 
                 9.8443 
               
               
                   
                 16 
                 Spherical 
                 Infinity 
                 3.5109 
                   
                 Refraction 
                 9.7876 
               
               
                 L8 
                 17 
                 Spherical 
                 35.2243 
                 4.9014 
                 STIH53 
                 Refraction 
                 11.4321 
               
               
                   
                 18 
                 Spherical 
                 −66.1835 
                 2.7394 
                   
                 Refraction 
                 11.4134 
               
               
                 L9 
                 19 
                 Aspheric 
                 −318.9262 
                 1.6426 
                 LLAM60 
                 Refraction 
                 10. 9985 
               
               
                   
                   
                 surface 
               
               
                   
                 20 
                 Aspheric 
                 26.3290 
                 16.1984 
                   
                 Refraction 
                 11.4618 
               
               
                   
                   
                 surface 
               
               
                   
                 21 
                 Spherical 
                 Infinity 
                 9.5039 
                   
                 Refraction 
                 17.3660 
               
               
                 L10 
                 22 
                 Spherical 
                 37.9392 
                 7.8029 
                 STIM22 
                 Refraction 
                 27.0207 
               
               
                   
                 23 
                 Spherical 
                 37.9749 
                 14.8804 
                   
                 Refraction 
                 25.7801 
               
               
                 L11 
                 24 
                 Spherical 
                 69.0185 
                 28.4144 
                 STIM2 
                 Refraction 
                 29.7336 
               
               
                 L12 
                 25 
                 Spherical 
                 −32.3562 
                 1.2000 
                 STIH6 
                 Refraction 
                 29.7945 
               
               
                   
                 26 
                 Spherical 
                 −202.3140 
                 0.2000 
                   
                 Refraction 
                 33.8303 
               
               
                 L13 
                 27 
                 Spherical 
                 91.9413 
                 14.9604 
                 STIL25 
                 Refraction 
                 36.6890 
               
               
                 L14 
                 28 
                 Spherical 
                 −172.7823 
                 7.6862 
                 STIH6 
                 Refraction 
                 36.6662 
               
               
                   
                 29 
                 Spherical 
                 −211.4567 
                 1.7202 
                   
                 Refraction 
                 36.8449 
               
               
                 L15 
                 30 
                 Aspheric 
                 −334.1939 
                 1.3786 
                 □Z-E48R□ 
                 Refraction 
                 35.5825 
               
               
                   
                   
                 surface 
               
               
                   
                 31 
                 Aspheric 
                 38.6610 
                 13.9841 
                   
                 Refraction 
                 34.8094 
               
               
                   
                   
                 surface 
               
               
                 L16 
                 32 
                 Aspheric 
                 −547.4767 
                 1.2000 
                 □Z-E48R□ 
                 Refraction 
                 33.9637 
               
               
                   
                   
                 surface 
               
               
                   
                 33 
                 Aspheric 
                 70.0493 
                 61.6960 
                   
                 Refraction 
                 32.9483 
               
               
                   
                   
                 surface 
               
               
                 M 
                 34 
                 Aspheric 
                 −51.9308 
                 −61.6960 
                   
                 Reflection 
                 42.1244 
               
               
                   
                   
                 surface 
               
               
                   
                 35 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 68.6960 
               
               
                 L17 
                 36 
                 Aspheric 
                 31.5643 
                 −1.2000 
                 □Z-E48R□ 
                 Refraction 
                 27.1036 
               
               
                   
                   
                 surface 
               
               
                   
                 37 
                 Aspheric 
                 66.6691 
                 0.0000 
                   
                 Refraction 
                 40.5464 
               
               
                   
                   
                 surface 
               
               
                   
                 38 
                 Spherical 
                 Infinity 
                 −439.3040 
                   
                 Refraction 
                 101.5136 
               
               
                   
                 39 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 1371.0322 
               
               
                   
               
            
           
         
       
     
     The aspheric constants of each of the aspheric surfaces are listed below. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
             
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 49.65582381 
                 25.27621931 
                 −318.9262388 
                 26.32901912 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −1.90452E−04 
                 −1.65330E−04 
                 −7.75605E−05 
                 −4.50156E−05  
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                  1.41580E−06 
                  1.44462E−06 
                  9.01620E−09 
                 7.03003E−08 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −5.56606E−09 
                 −6.76700E−09 
                 −4.30650E−11 
                 1.75774E−11 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                  1.12856E−11 
                  1.47249E−11 
               
               
                 coefficient (D) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 S30 
                 S31 
                 S32 
                 S33 
               
               
                   
               
               
                 Radius of 
                 334.1939158 
                 38.66100388 
                 −547.476701 
                 70.0493315 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 80.93042591 
                 0 
                 −179329.1453 
                 2.476873572 
               
               
                 (K) 
               
               
                 Fourth-order 
                  1.56186E−05 
                 −1.08312E−05 
                  1.56783E−06 
                 3.01840E−07 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −1.62590E−08 
                  1.52873E−08 
                 −2.89746E−10 
                 3.71758E−09 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                  1.79446E−11 
                 −1.99997E−11 
                 −9.51446E−14 
                 −5.66030E−12  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −1.92132E−14 
                  4.71234E−15 
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                  1.18169E−17 
                  5.83566E−18 
               
               
                 coefficient (E) 
               
               
                 Fourteenth-order 
                 −2.76801E−21 
                 −2.98566E−21 
               
               
                 coefficient (F) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Surface number 
                 S34 
                 S36 
                 S37 
               
               
                   
               
               
                 Radius of 
                 −51.93079714 
                 31.56428165 
                 66.66912913 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 −1.119965114 
                 0.225510562 
                 −3.294841957 
               
               
                 (K) 
               
               
                 Fourth-order 
                 2.73444E−07 
                 9.66883E−06 
                 3.95104E−06 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −3.94761E−10  
                 −1.03190E−08  
                 4.69353E−10 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.46325E−13 
                 2.50100E−11 
                 −2.86696E−13  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −4.37368E−17  
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 4.91882E−21 
               
               
                 coefficient (E) 
               
               
                   
               
            
           
         
       
     
     A maximum object height, brightness, a mirror radius, a final lens radius, a lens overall length, and TR of the projection system  3 A are as follows: The maximum object height is the dimension to the farthest point from the optical axis N of the projection system  3 A in an image formation area on the surface of each of the liquid crystal panels  18 . The maximum object height is expressed in mm. The brightness is expressed in the form of NA. The mirror radius is the radius of the mirror M in millimeters. The final lens radius is the radius of the lens L 17  of the third optical system  33  in millimeters. The overall lens length of the projection system  3 A is the distance in millimeters from the lens L 1  to the mirror M along the axis Z of the first optical system  31 . TR stands for a throw ratio that is the quotient of the dimension of the screen S in the axis-X direction and the projection distance, specifically, the former divided by the latter. 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Maximum object height 
                 11.7 
               
               
                   
                 NA 
                 0.3125 
               
               
                   
                 Mirror radius 
                 42.1 
               
               
                   
                 Final lens radius 
                 40.5 
               
               
                   
                 Overall lens length 
                 273 
               
               
                   
                 TR (0.59□WXGA) 
                 0.29 
               
               
                   
                   
               
            
           
         
       
     
     Effects and Advantages 
     The projection system  3 A according to the present example is formed of the first optical system  31 , the second optical system  32 , and the third optical system  33  sequentially arranged from the reduction side toward the enlargement side. The first optical system  31  includes the lens L 16  disposed in a position closest to the enlargement side and forms the intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 . The second optical system  32  includes the mirror M formed of a concave curved surface. The third optical system  33  includes the lens L 17  disposed in a position closest to the enlargement side and having negative power. The effective range of the lens L 16  is located at the lower side Y 2  of the optical axis N of the first optical system  31 , and the effective range of the lens L 17  is located at the upper side Y 1  of the optical axis N. 
     That is, the projection system  3 A according to the present example includes the third optical system  33 , which has negative power, at the enlargement side of the mirror M. The lens L 17  of the third optical system  33  has negative power. The lens L 17  can therefore project the light rays outputted from the mirror M having the concave curved surface toward the enlargement side on the screen S with the light rays inclining with respect to the screen S. The projection distance of the projection system  3 A can thus be shortened. 
     Further, according to the present example, light ray tracing from the screen S shows that the effect provided by the lens L 17  reduces the angles of the light rays traveling toward the mirror M. When the light rays are traced from the screen S and the angles of the rays with respect to the mirror M decrease, the position where the light ray that reaches the upper portion of the screen S forms the intermediate image  35  and the position where the light ray that reaches the lower portion of the screen S forms the intermediate image  35  approach each other along the axis Z of the first optical system  31 . The intermediate image  35  is therefore erected in the direction perpendicular to the optical axis N of the first optical system  31  and decreases in size in the axis-Z direction. The size of the mirror M, which captures the light flux divergent in the segment from the position where the intermediate image  35  is formed toward the enlargement side, can therefore be reduced. Further, since the size of the intermediate image  35  decreases in the axis-Z direction, the first optical system  31  and the second optical system  32  are allowed to approach each other in the axis-Z direction. The overall lens length can therefore be shortened. 
     Further, in the present example, the optical element O, which is disposed at the opposite side of the second optical system  32  with respect to the intermediate image  35  along the optical axis N of the first optical system  31 , is provided. The lens L 16 , which is the final lens of the first optical system  31 , is the first optical element section O 1  of the optical element O, which is the section at the lower side Y 2  of the optical axis N of the first optical system  31 , and the lens L 17 , which forms the third optical system  33 , is the second optical element section O 2  of the optical element O, which is the section at the upper side Y 1  of the optical axis N of the first optical system  31 . The number of lenses that form the projection system  3 A can thus be suppressed. 
     The lens L 17  of the third optical system  33  has a meniscus shape. That is, the reduction-side surface of the lens L 17  has a concave curved shape recessed toward the enlargement side, and the enlargement-side surface of the lens L 17  has a convex curved shape protruding toward the enlargement side. The thickness of the lens L 17  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . In other words, the light rays reflected off the mirror M and passing through the lens L 17  each travel along an optical path length in the lens L 17  that increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . The negative power of the third optical system  33  can therefore be increased, whereby the projection distance of the projection system  3 A can be readily shortened. 
     In the projection system  3 A, an area A, where the optical density is maximized in the optical path from the reduction-side image formation plane to the enlargement-side image formation plane conjugate with the intermediate image  35 , is located between the second optical system  32  and the third optical system  33 . That is, the area A, where the optical density is maximized, is located outside the optical elements that form the projection system  3 A, such as the lenses. Therefore, in the projection system  3 A, a situation in which the optical elements are heated so that the optical characteristics thereof change can be avoided or suppressed. 
     In the present example, the lens L 17  of the third optical system  33  has an aspheric surface at the reduction side. Further, in the present example, the lens L 17  has an aspheric surface also at the enlargement side. Occurrence of distortion is therefore readily suppressed. 
     Further, since the third optical system  33  is formed of one lens, the number of lenses that form the projection system  3 A is readily suppressed. The third optical system  33  may further include a lens at the enlargement side of the lens L 17 . 
       FIG. 5  shows the enlargement-side MTF of the projection system  3 A. The horizontal axis of  FIG. 5 , which shows the MTF, represents the spatial frequency. The vertical axis of  FIG. 5  represents a contrast reproduction ratio (modulation). In  FIG. 5 , the black graphs represent tangential light rays (T), and the gray graphs represent radial light rays (R). Out of the tangential light rays (T) and the radial light rays (R), the solid lines represent the light flux F 1 , the long-line-segment broken lines represent the light flux F 2 , and the broken lines represent the light flux F 3 . The projection system  3 A according to the present example provides high resolution, as shown in  FIG. 5 . 
     Example 2 
       FIG. 6  is a light ray diagram diagrammatically showing the entire projection system according to Example 2.  FIG. 6  diagrammatically shows light fluxes that exit out of a projection system  3 B according to the present example and reach the screen S in the form of the light fluxes F 1  to F 3 .  FIG. 7  is a light ray diagram of the light rays passing through the projection system according to Example 2.  FIG. 8  is a light ray diagram of the light rays passing through the lens located in a position closest to the enlargement side in a first optical system, a second optical system, and a third optical system. The projection system  3 B according to Example 2 has a configuration corresponding to that of the projection system  3 A described above, and corresponding components therefore have the same reference characters in the description. 
     The projection system  3 B according to the present example is formed of the first optical system  31 , the second optical system  32 , and the third optical system  33  sequentially arranged from the reduction side toward the enlargement side, as shown in  FIG. 7 . The first optical system  31  is a refractive optical system including a plurality of lenses. The second optical system  32  includes the mirror M having a concave curved surface. The third optical system  33  has negative power. The first optical system  31  forms the intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 , as shown in  FIG. 8 . The second optical system  32  and the third optical system  33  form a final image conjugate with the intermediate image  35  in the enlargement-side image formation plane. The liquid crystal panels  18  located in the reduction-side image formation plane form projection images at the upper side Y 1  of the optical axis N. The intermediate image  35  is formed at the lower side Y 2  of the optical axis N. The screen S disposed in the enlargement-side image formation plane is located at the upper side Y 1  of the optical axis N. The lateral direction of the screen S coincides with the axis-X direction. The intermediate image  35  is the image formed on the screen S that is not enlarged but turned upside down in the axis-Y direction.  FIGS. 6, 7, and 8  are light ray diagrams in the plane YZ. 
     The first optical system  31  includes the cross dichroic prism  19  and  16  lenses L 1  to L 16 , as shown in  FIG. 7 . The lenses L 1  to L 16  are arranged in the presented order from the reduction side toward the enlargement side. In the present example, the lenses L 2  and L 3  are bonded to each other to form the first doublet L 21 . The lenses L 4  and L 5  are bonded to each other to form the second doublet L 22 . The lenses L 11  and L 12  are bonded to each other to form the third doublet L 23 . The lenses L 13  and L 14  are bonded to each other to form the fourth doublet L 24 . The light flux passage area of the lens L 16  (first lens) is located at the lower side Y 2  of the optical axis N. 
     The second optical system  32  is formed of one mirror M, as shown in  FIG. 8 . The mirror M reflects the light rays from the first optical system  31  toward the upper side Y 1 . 
     The third optical system  33  is formed of one lens L 17  (second lens) having a meniscus shape. The lens L 17  is disposed at the upper side Y 1  of the optical axis N of the first optical system  31 . The reduction-side surface of the lens L 17  has a concave curved surface recessed toward the enlargement side. The reduction-side surface of the lens L 17  has negative power. The reduction-side surface of the lens L 17  is an aspheric surface. The enlargement-side surface of the lens L 17  is a convex curved surface protruding toward the enlargement side. The enlargement-side surface of the lens L 17  is an aspheric surface. The thickness of the lens L 17  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . 
     In the projection system  3 B, the area A, where the optical density is maximized in the optical path from the reduction-side image formation plane to the enlargement-side image formation plane, is located between the second optical system  32  and the third optical system  33 . 
     The lens L 16  of the first optical system  31  and the lens L 17  of the third optical system  33  are each provided as part of one optical element O, which is disposed at the opposite side of the second optical system  32  with respect to the intermediate image  35  along the optical axis N of the first optical system  31 . That is, the lens L 16  of the first optical system  31  is the first optical element section O 1  of the optical element O, which is the section at the lower side Y 2  of the optical axis N of the first optical system  31 . The lens L 17  of the third optical system  33  is the second optical element section O 2  of the optical element O, which is the section at the upper side Y 1  of the optical axis N of the first optical system  31 . 
     Lens Data 
     Data on the lenses of the projection system  3 B are as follows: The surfaces of the lenses are numbered sequentially from the reduction side toward the enlargement side. Reference characters are given to the lenses and the mirror. Reference character R denotes the radius of curvature of a lens surface or a mirror surface. Reference character D denotes the on-axis distance between surfaces. Reference character C denotes the effective diameter of a lens surface or a mirror surface. Reference characters R, D, and C are each expressed in millimeters. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Reference 
                 Surface 
                   
                   
                   
                 Glass 
                 Refraction/ 
                   
               
               
                 character 
                 number 
                 Shape 
                 R 
                 D 
                 material 
                 reflection 
                 C 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 0.0000 
               
               
                   
                 1 
                 Spherical 
                 Infinity 
                 9.5000 
                   
                 Refraction 
                 11.7000 
               
               
                 19 
                 2 
                 Spherical 
                 Infinity 
                 25.9100 
                 SBSL7 
                 Refraction 
                 13.3182 
               
               
                   
                 3 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 16.2020 
               
               
                 L1 
                 4 
                 Spherical 
                 30.3278 
                 9.3259 
                 SFPL51 
                 Refraction 
                 17.1016 
               
               
                   
                 5 
                 Spherical 
                 −71.8493 
                 0.2021 
                   
                 Refraction 
                 16.8620 
               
               
                 L2 
                 6 
                 Spherical 
                 39.9699 
                 8.5691 
                 SFSL5 
                 Refraction 
                 15.1975 
               
               
                 L3 
                 7 
                 Spherical 
                 −46.9494 
                 2.2341 
                 STIH6 
                 Refraction 
                 14.0000 
               
               
                   
                 8 
                 Spherical 
                 396.1335 
                 0.2000 
                   
                 Refraction 
                 13.2961 
               
               
                 L4 
                 9 
                 Spherical 
                 22.2287 
                 11.5106 
                 SBSL7 
                 Refraction 
                 12.3480 
               
               
                 L5 
                 10 
                 Spherical 
                 −21.5648 
                 1.2000 
                 TAFD25 
                 Refraction 
                 10.4773 
               
               
                   
                 11 
                 Spherical 
                 67.9160 
                 0.2000 
                   
                 Refraction 
                 9.8627 
               
               
                 L6 
                 12 
                 Aspheric 
                 20.2614 
                 1.1997 
                 LBAL35 
                 Refraction 
                 9.8479 
               
               
                   
                   
                 surface 
               
               
                   
                 13 
                 Aspheric 
                 13.0461 
                 1.7539 
                   
                 Refraction 
                 9.7302 
               
               
                   
                   
                 surface 
               
               
                 L7 
                 14 
                 Spherical 
                 21.8096 
                 5.2270 
                 SFSL5 
                 Refraction 
                 9.8583 
               
               
                   
                 15 
                 Spherical 
                 −811.2166 
                 0.2000 
                   
                 Refraction 
                 9.5143 
               
               
                   
                 16 
                 Spherical 
                 Infinity 
                 0.4916 
                   
                 Refraction 
                 9.4658 
               
               
                 L8 
                 17 
                 Spherical 
                 50.2350 
                 7.7354 
                 STIH53 
                 Refraction 
                 9.9074 
               
               
                   
                 18 
                 Spherical 
                 −35.2992 
                 0.2182 
                   
                 Refraction 
                 10.2091 
               
               
                 L9 
                 19 
                 Aspheric 
                 −229.6415 
                 1.2070 
                 LLAM60 
                 Refraction 
                 10.1014 
               
               
                   
                   
                 surface 
               
               
                   
                 20 
                 Aspheric 
                 23.3953 
                 7.1747 
                   
                 Refraction 
                 10.4338 
               
               
                   
                   
                 surface 
               
               
                   
                 21 
                 Spherical 
                 Infinity 
                 23.1237 
                   
                 Refraction 
                 12.6074 
               
               
                 L10 
                 22 
                 Spherical 
                 39.8368 
                 5.3358 
                 STIM22 
                 Refraction 
                 27.0000 
               
               
                   
                 23 
                 Spherical 
                 44.3376 
                 16.8499 
                   
                 Refraction 
                 26.4932 
               
               
                 L11 
                 24 
                 Spherical 
                 57.3488 
                 27.9599 
                 STIM2 
                 Refraction 
                 31.3567 
               
               
                 L12 
                 25 
                 Spherical 
                 −37.6257 
                 6.8632 
                 STIH6 
                 Refraction 
                 31.1522 
               
               
                   
                 26 
                 Spherical 
                 231.9361 
                 0.4054 
                   
                 Refraction 
                 32.9394 
               
               
                 L13 
                 27 
                 Spherical 
                 49.7771 
                 13.9592 
                 STIL25 
                 Refraction 
                 36.4799 
               
               
                 L14 
                 28 
                 Spherical 
                 159.8387 
                 2.5053 
                 STIH6 
                 Refraction 
                 35.9645 
               
               
                   
                 29 
                 Spherical 
                 176.9307 
                 1.5704 
                   
                 Refraction 
                 35.4864 
               
               
                 L15 
                 30 
                 Aspheric 
                 387.5955 
                 1.9078 
                 □Z-E48R□ 
                 Refraction 
                 35.0667 
               
               
                   
                   
                 surface 
               
               
                   
                 31 
                 Aspheric 
                 41.7328 
                 9.6693 
                   
                 Refraction 
                 34.4983 
               
               
                   
                   
                 surface 
               
               
                 L16 
                 32 
                 Aspheric 
                 176.3833 
                 1.2000 
                 □Z-E48R□ 
                 Refraction 
                 31.5775 
               
               
                   
                   
                 surface 
               
               
                   
                 33 
                 Aspheric 
                 48.6716 
                 67.6000 
                   
                 Refraction 
                 28.5952 
               
               
                   
                   
                 surface 
               
               
                 M 
                 34 
                 Aspheric 
                 −52.0669 
                 −67.6000 
                   
                 Reflection 
                 46.2470 
               
               
                   
                   
                 surface 
               
               
                   
                 35 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 60.7706 
               
               
                 L17 
                 36 
                 Aspheric 
                 48.6716 
                 −1.2000 
                 □Z-E48R□ 
                 Refraction 
                 32.0583 
               
               
                   
                   
                 surface 
               
               
                   
                 37 
                 Aspheric 
                 176.3833 
                 0.0000 
                   
                 Refraction 
                 43.8508 
               
               
                   
                   
                 surface 
               
               
                   
                 38 
                 Spherical 
                 Infinity 
                 −433.4000 
                   
                 Refraction 
                 81.8472 
               
               
                   
                 39 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                   
                 1382.1140 
               
               
                   
               
            
           
         
       
     
     The aspheric constants of each of the aspheric surfaces are listed below. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
             
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 20.26140547 
                 13.0461295 
                 −229.6414599 
                 23.39527788 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −3.45427E−04 
                 −2.79879E−04 
                 −6.71631E−05 
                 −4.16610E−05 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                  1.60875E−06 
                  2.03668E−06 
                 −1.00842E−07 
                 −9.53264E−10 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −5.30496E−09 
                 −9.51880E−09 
                 −7.34814E−11 
                  3.07082E−10 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −5.50717E−12 
                  1.66637E−11 
               
               
                 coefficient (D) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 S30 
                 S31 
                 S32 
                 S33 
               
               
                   
               
               
                 Radius of 
                 387.5955126 
                 41.73282202 
                 176.3832591 
                 48.67161757 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 90 
                 0 
                 11.80225283 
                 1.094322819 
               
               
                 (K) 
               
               
                 Fourth-order 
                 1.01203E−05 
                 −1.17185E−05  
                 2.87209E−06 
                 1.36690E−06 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −1.40448E−08  
                 1.19637E−08 
                 −1.14555E−09  
                 3.14586E−09 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.42478E−11 
                 −1.66915E−11  
                 1.98416E−13 
                 −2.66990E−12  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −1.86681E−14  
                 5.93763E−15 
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 1.42953E−17 
                 3.89540E−18 
               
               
                 coefficient (E) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Surface number 
                 S34 
                 S36 
                 S37 
               
               
                   
               
               
                 Radius of 
                 −52.06688058 
                 48.67161757 
                 176.3832591 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 −1 
                 1.094322819 
                 11.80225283 
               
               
                 (K) 
               
               
                 Fourth-order 
                 4.53933E−07 
                 1.36690E−06 
                 2.87209E−06 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −3.53577E−10  
                 3.14586E−09 
                 −1.14555E−09  
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.14681E−13 
                 −2.66990E−12  
                 1.98416E−13 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −2.76345E−17  
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 2.22920E−21 
               
               
                 coefficient (E) 
               
               
                   
               
            
           
         
       
     
     The maximum object height, the brightness, the mirror radius, the final lens radius, the lens overall length, and TR of the projection system  3 B are as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Maximum object height 
                 11.7 
               
               
                   
                 NA 
                 0.3125 
               
               
                   
                 Mirror radius 
                 46.3 
               
               
                   
                 Final lens radius 
                 43.9 
               
               
                   
                 Overall lens length 
                 273 
               
               
                   
                 TR (0.59□WXGA) 
                 0.29 
               
               
                   
                   
               
            
           
         
       
     
     Effects and Advantages 
     The projection system  3 B according to the present example can provide the same effects and advantages as those provided by the projection system  3 A described above. 
     In the projection system  3 B according to the present example, the lens L 16  of the first optical system  31  and the lens L 17  of the third optical system  33  are so shaped as to correspond to each other, as shown in the lens data. That is, the surface number  32 , which represents the reduction-side lens surface of the lens L 16  of the first optical system  31  and the surface number  37 , which represents the enlargement-side lens surface of the lens L 17  of the third optical system  33  represent shapes corresponding to each other. Further, the surface number  33 , which represents the enlargement-side lens surface of the lens L 16  of the first optical system  31  and the surface number  36 , which represents the reduction-side lens surface of the lens L 17  of the third optical system  33  represent shapes corresponding to each other. 
     Therefore, the optical element O, which is a meniscus lens, can be formed of the lens L 16 , which is the first optical element section O 1  at the lower side Y 2  of the optical axis N, and the lens L 17 , which is the second optical element section O 2  at the upper side Y 1  of the optical axis N. In other words, disposing one meniscus lens allows the lens L 16  of the first optical system  31  and the lens L 17  of the third optical system  33  to be provided. Further, to manufacture one meniscus lens as the optical element O, manufacturing an optical element formed of a portion located at the upper side Y 1  of the axis N and a portion located at the lower side Y 2  of the axis N and having a shape corresponding to that of the portion at the upper side Y 1  is more productive than manufacturing an optical element formed of a portion located at the upper side Y 1  of the axis N and a portion located at the lower side Y 2  of the axis N and having a shape different from that of the portion at the upper side Y 1 , whereby a decrease in yield can be suppressed. The projection system  3 B is readily produced in large quantities. 
     Further, in the present example, since the lens L 16  of the first optical system  31  and the lens L 17  of the third optical system  33  have shapes corresponding to each other, the lens L 16  has negative power as the lens L 17 . When the lens L 16  of the first optical system  31  has negative power, the lens L 16  can assist the power of the mirror M having a concave curved surface. The size of the mirror M along the optical axis N can thus be reduced. 
     The third optical system  33  may further include a lens at the enlargement side of the lens L 17 . 
       FIG. 9  shows the enlargement-side MTF of the projection system  3 B. The projection system  3 B according to the present example provides high resolution, as shown in  FIG. 9 . 
     Example 3 
       FIG. 10  is a light ray diagram diagrammatically showing the entire projection system according to Example 3.  FIG. 10  diagrammatically shows light fluxes that exit out of a projection system  3 C according to the present example and reach the screen S in the form of the light fluxes F 1  to F 3 .  FIG. 11  is a light ray diagram of the light rays passing through the projection system according to Example 3.  FIG. 12  is a light ray diagram in the vicinity of the second optical system and the third optical system. The projection system  3 C according to Example 3 has a configuration corresponding to that of the projection system  3 A described above, and corresponding components therefore have the same reference characters in the description. 
     The projection system  3 C according to the present example is formed of the first optical system  31 , the second optical system  32 , and the third optical system  33  sequentially arranged from the reduction side toward the enlargement side, as shown in  FIG. 11 . The first optical system  31  is a refractive optical system including a plurality of lenses. The second optical system  32  includes the mirror M having a concave curved surface. The third optical system  33  has negative power. The first optical system  31  forms the intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 , as shown in  FIG. 12 . The second optical system  32  and the third optical system  33  form a final image conjugate with the intermediate image  35  in the enlargement-side image formation plane. The liquid crystal panels  18  located in the reduction-side image formation plane form projection images at the upper side Y 1  of the optical axis N. The intermediate image  35  is formed at the lower side Y 2  of the optical axis N. The screen S disposed in the enlargement-side image formation plane is located at the upper side Y 1  of the optical axis N. The lateral direction of the screen S coincides with the axis-X direction. The intermediate image  35  is the image formed on the screen S that is not enlarged but turned upside down in the axis-Y direction.  FIGS. 10, 11, and 12  are light ray diagrams in the plane YZ. 
     The first optical system  31  includes the cross dichroic prisms  19  and  15  lenses L 1  to L 15 , as shown in  FIG. 11 . The lenses L 1  to L 15  are arranged in the presented order from the reduction side toward the enlargement side. In the present example, the lenses L 2  and L 3  are bonded to each other to form the first doublet L 21 . The lenses L 4  and L 5  are bonded to each other to form the second doublet L 22 . The lenses L 11  and L 12  are bonded to each other to form the third doublet L 23 . The lenses L 13  and L 14  are bonded to each other to form the fourth doublet L 24 . The light flux passage area of the lens L 15  (first lens) is located at the lower side Y 2  of the optical axis N. 
     The second optical system  32  is formed of one mirror M, as shown in  FIG. 12 . The mirror M reflects the light rays from the first optical system  31  toward the upper side Y 1 . 
     The third optical system  33  is formed of one lens L 16  (second lens) having a meniscus shape. The lens L 16  is disposed at the upper side Y 1  of the optical axis N of the first optical system  31 . The reduction-side surface of the lens L 16  has a concave curved surface recessed toward the enlargement side. The reduction-side surface of the lens L 16  has negative power. The reduction-side surface of the lens L 16  is an aspheric surface. The enlargement-side surface of the lens L 16  is a convex curved surface protruding toward the enlargement side. The enlargement-side surface of the lens L 16  is an aspheric surface. The thickness of the lens L 16  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . 
     In the projection system  3 C, the area A, where the optical density is maximized in the optical path from the reduction-side image formation plane to the enlargement-side image formation plane, is located between the second optical system  32  and the third optical system  33 . 
     The lens L 16  of the third optical system  33  is disposed in a position closer to the mirror M than the lens L 15 , which is located in the optical axis N of the first optical system  31  and in a position closest to the enlargement side in the first optical system  31 . 
     Lens Data 
     Data on the lenses of the projection system  3 C are as follows: The surfaces of the lenses are numbered sequentially from the reduction side toward the enlargement side. Reference characters are given to the lenses and the mirror. Reference character R denotes the radius of curvature of a lens surface or a mirror surface. Reference character D denotes the on-axis distance between surfaces. Reference character C denotes the effective diameter of a lens surface or a mirror surface. Reference characters R, D, and C are each expressed in millimeters. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Reference 
                 Surface 
                   
                   
                   
                 Glass 
                 Refraction/ 
                   
               
               
                 character 
                 number 
                 Shape 
                 R 
                 D 
                 material 
                 reflection 
                 C 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 0.0000 
               
               
                   
                 1 
                 Spherical 
                 Infinity 
                 9.5000 
                   
                 Refraction 
                 11.7000 
               
               
                 19 
                 2 
                 Spherical 
                 Infinity 
                 25.9100 
                 SBSL7 
                 Refraction 
                 13.3445 
               
               
                   
                 3 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 16.2743 
               
               
                 L1 
                 4 
                 Spherical 
                 26.2870 
                 9.8874 
                 SFPL51 
                 Refraction 
                 17.4163 
               
               
                   
                 5 
                 Spherical 
                 −114.0876 
                 0.2000 
                   
                 Refraction 
                 17.0589 
               
               
                 L2 
                 6 
                 Spherical 
                 27.4668 
                 8.3488 
                 SFSL5 
                 Refraction 
                 14.9069 
               
               
                 L3 
                 7 
                 Spherical 
                 −51.3244 
                 1.2000 
                 STIH6 
                 Refraction 
                 14.0000 
               
               
                   
                 8 
                 Spherical 
                 54.6395 
                 0.2098 
                   
                 Refraction 
                 12.8227 
               
               
                 L4 
                 9 
                 Spherical 
                 18.5782 
                 9.0874 
                 SBSL7 
                 Refraction 
                 12.0166 
               
               
                 L5 
                 10 
                 Spherical 
                 −24.5458 
                 1.2000 
                 TAFD25 
                 Refraction 
                 11.1356 
               
               
                   
                 11 
                 Spherical 
                 109.7598 
                 0.8616 
                   
                 Refraction 
                 10.2913 
               
               
                 L6 
                 12 
                 Aspheric 
                 53.3422 
                 1.2000 
                 LBAL35 
                 Refraction 
                 10.1819 
               
               
                   
                   
                 surface 
               
               
                   
                 13 
                 Aspheric 
                 22.4913 
                 0.2000 
                   
                 Refraction 
                 9.7741 
               
               
                   
                   
                 surface 
               
               
                 L7 
                 14 
                 Spherical 
                 18.5235 
                 4.4908 
                 SFSL5 
                 Refraction 
                 9.7606 
               
               
                   
                 15 
                 Spherical 
                 53.5909 
                 2.3051 
                   
                 Refraction 
                 9.2518 
               
               
                   
                 16 
                 Spherical 
                 Infinity 
                 0.2000 
                   
                 Refraction 
                 8.9283 
               
               
                 L8 
                 17 
                 Spherical 
                 28.6412 
                 4.3711 
                 STIH53 
                 Refraction 
                 9.7128 
               
               
                   
                 18 
                 Spherical 
                 −71.1586 
                 3.4903 
                   
                 Refraction 
                 9.7637 
               
               
                 L9 
                 19 
                 Aspheric 
                 −59.2915 
                 1.6422 
                 LLAM60 
                 Refraction 
                 9.5779 
               
               
                   
                   
                 surface 
               
               
                   
                 20 
                 Aspheric 
                 19.8927 
                 3.8576 
                   
                 Refraction 
                 10.5554 
               
               
                   
                   
                 surface 
               
               
                   
                 21 
                 Spherical 
                 Infinity 
                 0.2000 
                   
                 Refraction 
                 11.9089 
               
               
                 L10 
                 22 
                 Spherical 
                 50.3317 
                 4.5209 
                 STIM22 
                 Refraction 
                 13.8391 
               
               
                   
                 23 
                 Spherical 
                 −178.2940 
                 21.5104 
                   
                 Refraction 
                 14.3728 
               
               
                 L11 
                 24 
                 Spherical 
                 68.4656 
                 21.3878 
                 STIM2 
                 Refraction 
                 26.0000 
               
               
                 L12 
                 25 
                 Spherical 
                 −31.1606 
                 1.2000 
                 STIH6 
                 Refraction 
                 26.1591 
               
               
                   
                 26 
                 Spherical 
                 −177.1291 
                 2.5593 
                   
                 Refraction 
                 28.8624 
               
               
                 L13 
                 27 
                 Spherical 
                 −126.3867 
                 15.0000 
                 STIL25 
                 Refraction 
                 29.2250 
               
               
                 L14 
                 28 
                 Spherical 
                 −35.1022 
                 1.2000 
                 STIH6 
                 Refraction 
                 29.7095 
               
               
                   
                 29 
                 Spherical 
                 −51.0664 
                 0.2000 
                   
                 Refraction 
                 32.0278 
               
               
                 L15 
                 30 
                 Aspheric 
                 −1865.5094 
                 2.0076 
                 □Z-E48R□ 
                 Refraction 
                 33.3264 
               
               
                   
                   
                 surface 
               
               
                   
                 31 
                 Aspheric 
                 42.5160 
                 13.7457 
                   
                 Refraction 
                 32.8148 
               
               
                   
                   
                 surface 
               
               
                   
                 32 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 32.6126 
               
               
                   
                 33 
                 Spherical 
                 Infinity 
                 61.3064 
                   
                 Refraction 
                 32.6126 
               
               
                 M 
                 34 
                 Aspheric 
                 −44.3062 
                 −61.3064 
                   
                 Reflection 
                 38.8304 
               
               
                   
                   
                 surface 
               
               
                   
                 35 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 86.7508 
               
               
                 L16 
                 36 
                 Aspheric 
                 42.0853 
                 −1.2000 
                 □Z-E48R□ 
                 Refraction 
                 30.9008 
               
               
                   
                   
                 surface 
               
               
                   
                 37 
                 Aspheric 
                 118.6751 
                 0.0000 
                   
                 Refraction 
                 43.9961 
               
               
                   
                   
                 surface 
               
               
                   
                 38 
                 Spherical 
                 Infinity 
                 −439.6936 
                   
                 Refraction 
                 117.1750 
               
               
                   
                 39 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 1469.8039 
               
               
                   
               
            
           
         
       
     
     The aspheric constants of each of the aspheric surfaces are listed below. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
             
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 53.34221761 
                 22.49128344 
                 −59.29150676 
                 19.89273998 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −1.93783E−04  
                 −1.35859E−04  
                 −8.56185E−05 
                 −4.35212E−05 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 1.56223E−06 
                 1.61810E−06 
                 −6.83468E−08 
                  5.26818E−08 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −7.06670E−09  
                 −8.84670E−09  
                 −3.55359E−10 
                 −5.98134E−13 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 1.36669E−11 
                 1.88865E−11 
               
               
                 coefficient (D) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Surface number 
                 S30 
                 S31 
               
               
                   
                   
               
               
                   
                 Radius of 
                 1865.509356 
                 42.51598454 
               
               
                   
                 curvature in 
               
               
                   
                 axis-Y direction 
               
               
                   
                 Conic constant 
                 90 
                 0 
               
               
                   
                 (K) 
               
               
                   
                 Fourth-order 
                 2.07327E−05 
                 −1.60331E−06  
               
               
                   
                 coefficient (A) 
               
               
                   
                 Sixth-order 
                 −1.64003E−08  
                 1.39989E−08 
               
               
                   
                 coefficient (B) 
               
               
                   
                 Eighth-order 
                 1.19436E−11 
                 −2.06433E−11  
               
               
                   
                 coefficient (C) 
               
               
                   
                 Tenth-order 
                 −1.12644E−14  
                 4.23072E−15 
               
               
                   
                 coefficient (D) 
               
               
                   
                 Twelfth-order 
                 6.86665E−18 
                 3.30023E−18 
               
               
                   
                 coefficient (E) 
               
               
                   
                 Fourteenth-order 
                 −2.02644E−21  
                 −1.41483E−21  
               
               
                   
                 coefficient (F) 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 Surface number 
                 S34 
                 S36 
                 S37 
               
               
                   
               
               
                 Radius of 
                 −44.30622587 
                 42.08529774 
                 118.6750917 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 −1 
                 0.838596842 
                 5.9457377 
               
               
                 (K) 
               
               
                 Fourth-order 
                 1.02038E−06 
                 5.01374E−06 
                 3.63707E−06 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −6.59907E−10  
                 −2.50762E−09  
                 −8.15678E−10  
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.58870E−13 
                 4.76676E−12 
                 1.88373E−13 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 5.15051E−17 
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 −5.66805E−20  
               
               
                 coefficient (E) 
               
               
                 Fourteenth-order 
                 1.33892E−23 
               
               
                 coefficient (F) 
               
               
                   
               
            
           
         
       
     
     The maximum object height, the brightness, the mirror radius, the final lens radius, the lens overall length, and TR of the projection system  3 C are as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Maximum object height 
                 11.7 
               
               
                   
                 NA 
                 0.3125 
               
               
                   
                 Mirror radius 
                 38.8 
               
               
                   
                 Final lens radius 
                 44.0 
               
               
                   
                 Overall lens length 
                 233 
               
               
                   
                 TR (0.59□WXGA) 
                 0.27 
               
               
                   
                   
               
            
           
         
       
     
     Effects and Advantages 
     In the projection system  3 C according to the present example, the lens L 16 , which is disposed in a position closest to the enlargement side in the first optical system  31 , and the lens L 17 , which forms the third optical system  33 , cannot be so provided as to form one optical element. The projection system  3 C according to the present example, however, can provide the same effects and advantages as those provided by the projection system  3 A described above except the aforementioned effect and advantage of one optical element containing the lenses L 16  and L 17 . 
     In the present example, the lens L 15 , which is located in a position closest to the enlargement side in the first optical system  31 , has positive power. The divergence of the light flux that exits out of the first optical system and enters the second optical system  32  can thus be suppressed, whereby the size of the mirror M can be readily reduced. 
     The third optical system  33  may further include a lens at the enlargement side of the lens L 16 . 
       FIG. 13  shows the enlargement-side MTF of the projection system  3 C. The projection system  3 C according to the present example provides high resolution, as shown in  FIG. 13 . 
     Example 4 
       FIG. 14  is a light ray diagram diagrammatically showing the entire projection system according to Example 4.  FIG. 14  diagrammatically shows light fluxes that exit out of a projection system  3 D according to the present example and reach the screen S in the form of the light fluxes F 1  to F 3 .  FIG. 15  is a light ray diagram of the light rays passing through the projection system according to Example 4.  FIG. 16  is a light ray diagram in the vicinity of the second optical system and the third optical system. The projection system  3 D according to Example 4 has a configuration corresponding to that of the projection system  3 A described above, and corresponding components therefore have the same reference characters in the description. 
     The projection system  3 D according to the present example is formed of the first optical system  31 , the second optical system  32 , and the third optical system  33  sequentially arranged from the reduction side toward the enlargement side, as shown in  FIG. 15 . The first optical system  31  is a refractive optical system including a plurality of lenses. The second optical system  32  includes the mirror M having a concave curved surface. The third optical system  33  has negative power. The first optical system  31  forms the intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 , as shown in  FIG. 16 . The second optical system  32  and the third optical system  33  form a final image conjugate with the intermediate image  35  in the enlargement-side image formation plane. The liquid crystal panels  18  located in the reduction-side image formation plane form projection images at the upper side Y 1  of the optical axis N. The intermediate image  35  is formed at the lower side Y 2  of the optical axis N. The screen S disposed in the enlargement-side image formation plane is located at the upper side Y 1  of the optical axis N. The lateral direction of the screen S coincides with the axis-X direction. The intermediate image  35  is the image formed on the screen S that is not enlarged but turned upside down in the axis-Y direction.  FIGS. 14, 15, and 16  are light ray diagrams in the plane YZ. 
     The first optical system  31  includes the cross dichroic prism  19  and  15  lenses L 1  to L 15 , as shown in  FIG. 15 . The lenses L 1  to L 15  are arranged in the presented order from the reduction side toward the enlargement side. In the present example, the lenses L 2  and L 3  are bonded to each other to form the first doublet L 21 . The lenses L 4  and L 5  are bonded to each other to form the second doublet L 22 . The lenses L 11  and L 12  are bonded to each other to form the third doublet L 23 . The lenses L 13  and L 14  are bonded to each other to form the fourth doublet L 24 . The light flux passage area of the lens L 15  (first lens) is located at the lower side Y 2  of the optical axis N. 
     The second optical system  32  includes a meniscus lens L 16 , which is disposed in the optical axis N of the first optical system  31 , and the mirror M having a concave curved surface, as shown in  FIG. 16 . A surface of the meniscus lens L 16  that is the surface facing the first optical system  31  is recessed in the direction away from the first optical system  31 . A reflection coating layer  36  is provided on a surface of the meniscus lens L 16  that is the surface opposite the first optical system  31 . The mirror M is formed of the reflection coating layer  36 . The mirror M reflects the light rays incident thereon from the first optical system  31  via the meniscus lens L 16  toward the upper side Y 1 . The thickness of the meniscus lens L 16  decreases with distance from the optical axis N in the axis-Y direction. In other words, the light rays that exit out of the first optical system  31  and pass through the meniscus lens L 16  each travel along an optical path length in the meniscus lens L 16  that decreases with distance from the optical axis N of the first optical system  31  toward the lower side Y 2 . 
     The third optical system  33  is formed of one lens L 17  (second lens) having a meniscus shape. The lens L 17  is disposed at the upper side Y 1  of the optical axis N of the first optical system  31 . The reduction-side surface of the lens L 17  has a concave curved surface recessed toward the enlargement side. The reduction-side surface of the lens L 17  has negative power. The reduction-side surface of the lens L 17  is an aspheric surface. The enlargement-side surface of the lens L 17  is a convex curved surface protruding toward the enlargement side. The enlargement-side surface of the lens L 17  is an aspheric surface. The thickness of the lens L 17  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . 
     In the projection system  3 D, the area A, where the optical density is maximized in the optical path from the reduction-side image formation plane to the enlargement-side image formation plane, is located between the second optical system  32  and the third optical system  33 . 
     Lens Data 
     Data on the lenses of the projection system  3 D are as follows: The surfaces of the lenses are numbered sequentially from the reduction side toward the enlargement side. Reference characters are given to the lenses and the mirror. Reference character R denotes the radius of curvature of a lens surface or a mirror surface. Reference character D denotes the on-axis distance between surfaces. Reference character C denotes the effective diameter of a lens surface or a mirror surface. Reference characters R, D, and C are each expressed in millimeters. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Reference 
                 Surface 
                   
                   
                   
                 Glass 
                 Refraction/ 
                   
               
               
                 character 
                 number 
                 Shape 
                 R 
                 D 
                 material 
                 reflection 
                 C 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 0.0000 
               
               
                   
                 1 
                 Spherical 
                 Infinity 
                 9.5000 
                   
                 Refraction 
                 11.7000 
               
               
                 19 
                 2 
                 Spherical 
                 Infinity 
                 25.9100 
                 SBSL7 
                 Refraction 
                 13.3183 
               
               
                   
                 3 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 16.2023 
               
               
                 L1 
                 4 
                 Spherical 
                 27.0317 
                 9.8078 
                 SFPL51 
                 Refraction 
                 17.2638 
               
               
                   
                 5 
                 Spherical 
                 −91.7473 
                 0.2000 
                   
                 Refraction 
                 16.9375 
               
               
                 L2 
                 6 
                 Spherical 
                 30.0494 
                 7.6112 
                 SFSL5 
                 Refraction 
                 14.8572 
               
               
                 L3 
                 7 
                 Spherical 
                 −59.1281 
                 1.2000 
                 STIH6 
                 Refraction 
                 14.0000 
               
               
                   
                 8 
                 Spherical 
                 48.0144 
                 0.2000 
                   
                 Refraction 
                 12.8663 
               
               
                 L4 
                 9 
                 Spherical 
                 20.3285 
                 9.4745 
                 SBSL7 
                 Refraction 
                 12.3080 
               
               
                 L5 
                 10 
                 Spherical 
                 −21.8619 
                 1.2000 
                 TAFD25 
                 Refraction 
                 11.5903 
               
               
                   
                 11 
                 Spherical 
                 149.6514 
                 0.5716 
                   
                 Refraction 
                 11.0183 
               
               
                 L6 
                 12 
                 Aspheric 
                 42.1234 
                 1.2000 
                 LBAL35 
                 Refraction 
                 10.9502 
               
               
                   
                   
                 surface 
               
               
                   
                 13 
                 Aspheric 
                 20.5883 
                 0.2000 
                   
                 Refraction 
                 10.6377 
               
               
                   
                   
                 surface 
               
               
                 L7 
                 14 
                 Spherical 
                 19.5968 
                 4.7218 
                 SFSL5 
                 Refraction 
                 10.7462 
               
               
                   
                 15 
                 Spherical 
                 111.9897 
                 4.5451 
                   
                 Refraction 
                 10.4362 
               
               
                   
                 16 
                 Spherical 
                 Infinity 
                 0.3081 
                   
                 Refraction 
                 9.6833 
               
               
                 L8 
                 17 
                 Spherical 
                 32.4053 
                 4.4372 
                 STIH53 
                 Refraction 
                 10.2937 
               
               
                   
                 18 
                 Spherical 
                 −70.0786 
                 3.4909 
                   
                 Refraction 
                 10.3063 
               
               
                 L9 
                 19 
                 Aspheric 
                 −113.8987 
                 4.9584 
                 LLAM60 
                 Refraction 
                 10.0091 
               
               
                   
                   
                 surface 
               
               
                   
                 20 
                 Aspheric 
                 19.6728 
                 5.4182 
                   
                 Refraction 
                 11.0032 
               
               
                   
                   
                 surface 
               
               
                   
                 21 
                 Spherical 
                 Infinity 
                 3.0514 
                   
                 Refraction 
                 12.8961 
               
               
                 L10 
                 22 
                 Spherical 
                 49.7233 
                 5.3687 
                 STIM22 
                 Refraction 
                 16.9655 
               
               
                   
                 23 
                 Spherical 
                 −389.0832 
                 28.2696 
                   
                 Refraction 
                 17.2950 
               
               
                 L11 
                 24 
                 Spherical 
                 53.8480 
                 20.5720 
                 STIM2 
                 Refraction 
                 26.0000 
               
               
                 L12 
                 25 
                 Spherical 
                 −34.3085 
                 1.2000 
                 STIH6 
                 Refraction 
                 25.9611 
               
               
                   
                 26 
                 Spherical 
                 96.6824 
                 3.7817 
                   
                 Refraction 
                 27.6369 
               
               
                 L13 
                 27 
                 Spherical 
                 94.9435 
                 11.3569 
                 STIL25 
                 Refraction 
                 29.9356 
               
               
                 L14 
                 28 
                 Spherical 
                 −103.4216 
                 1.2000 
                 STIH6 
                 Refraction 
                 30.2208 
               
               
                   
                 29 
                 Spherical 
                 −117.6885 
                 0.2000 
                   
                 Refraction 
                 30.4963 
               
               
                 L15 
                 30 
                 Aspheric 
                 −336.4398 
                 3.3131 
                 □Z-E48R□ 
                 Refraction 
                 31.3723 
               
               
                   
                   
                 surface 
               
               
                   
                 31 
                 Aspheric 
                 75.2700 
                 7.0933 
                   
                 Refraction 
                 31.0996 
               
               
                   
                   
                 surface 
               
               
                   
                 32 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 30.8623 
               
               
                   
                 33 
                 Spherical 
                 Infinity 
                 56.5805 
                   
                 Refraction 
                 30.8623 
               
               
                 L16 
                 34 
                 Aspheric 
                 −60.2160 
                 3.0582 
                 □Z-E48R□ 
                 Refraction 
                 30.7960 
               
               
                   
                   
                 surface 
               
               
                 M 
                 35 
                 Aspheric 
                 −47.7619 
                 −3.0582 
                 □Z-E48R□ 
                 Reflection 
                 31.5806 
               
               
                   
                   
                 surface 
               
               
                 L16 
                 36 
                 Aspheric 
                 −60.2160 
                 0.0000 
                   
                 Refraction 
                 29.9102 
               
               
                   
                   
                 surface 
               
               
                   
                 37 
                 Spherical 
                 Infinity 
                 −56.5805 
                   
                 Refraction 
                 44.1961 
               
               
                 L17 
                 38 
                 Aspheric 
                 40.0796 
                 −1.2000 
                 □Z-E48R□ 
                 Refraction 
                 34.6026 
               
               
                   
                   
                 surface 
               
               
                   
                 39 
                 Aspheric 
                 197.8101 
                 0.0000 
                   
                 Refraction 
                 49.5049 
               
               
                   
                   
                 surface 
               
               
                   
                 40 
                 Spherical 
                 Infinity 
                 −444.4195 
                   
                 Refraction 
                 107.2002 
               
               
                   
                 41 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 1434.1834 
               
               
                   
               
            
           
         
       
     
     The aspheric constants of each of the aspheric surfaces are listed below. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
             
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 53.34221761 
                 22.49128344 
                 −59.29150676 
                 19.89273998 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −1.93783E−04  
                 −1.35859E−04  
                 −8.56185E−05 
                 −4.35212E−05 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 1.56223E−06 
                 1.61810E−06 
                 −6.83468E−08 
                  5.26818E−08 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −7.06670E−09  
                 −8.84670E−09  
                 −3.55359E−10 
                 −5.98134E−13 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 1.36669E−11 
                 1.88865E−11 
               
               
                 coefficient (D) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 42.12342595 
                 20.58825946 
                 −113.8986936 
                 19.67276682 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −1.99183E−04  
                 −1.55136E−04  
                 −6.79362E−05 
                 −3.70298E−05  
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 1.54723E−06 
                 1.63860E−06 
                 −3.30297E−08 
                 2.43777E−08 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −6.53371E−09  
                 −7.91622E−09  
                 −2.02085E−10 
                 1.85084E−11 
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 1.33431E−11 
                 1.75764E−11 
               
               
                 coefficient (D) 
               
               
                   
               
               
                 Surface number 
                 S30 
                 S31 
                 S34 
                 S35 
               
               
                   
               
               
                 Radius of 
                 −336.4398379 
                 75.27004202 
                 −60.21601377 
                 −47.76186481 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 90 
                 0 
                 −0.008892814 
                 −1 
               
               
                 (K) 
               
               
                 Fourth-order 
                 1.86571E−05 
                 −2.85543E−06  
                 −1.61721E−06  
                 2.65449E−07 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −1.53565E−08  
                 1.55346E−08 
                 5.23742E−10 
                 −3.00277E−10  
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.28759E−11 
                 −2.24983E−11  
                 −1.46010E−12  
                 −1.61591E−12  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −1.25944E−14  
                 5.64421E−15 
                 3.68162E−15 
                 3.44041E−15 
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 6.41997E−18 
                 5.23789E−18 
                 −2.59410E−18  
                 −2.53950E−18  
               
               
                 coefficient (E) 
               
               
                 Fourteenth-order 
                 −8.98575E−22  
                 −2.39098E−21  
                 1.53594E−22 
                 5.89213E−22 
               
               
                 coefficient (F) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface number 
                 S36 
                 S38 
                 S39 
               
               
                   
                   
               
               
                   
                 Radius of 
                 −60.21601377 
                 40.0795943 
                 197.8101186 
               
               
                   
                 curvature in 
               
               
                   
                 axis-Y direction 
               
               
                   
                 Conic constant 
                 −0.008892814 
                 0.115487402 
                 12.22664516 
               
               
                   
                 (K) 
               
               
                   
                 Fourth-order 
                 −1.61721E−06  
                 9.08015E−07 
                 2.46996E−06 
               
               
                   
                 coefficient (A) 
               
               
                   
                 Sixth-order 
                 5.23742E−10 
                 4.77696E−10 
                 −5.58940E−10  
               
               
                   
                 coefficient (B) 
               
               
                   
                 Eighth-order 
                 −1.46010E−12  
                 7.45508E−13 
                 1.09826E−13 
               
               
                   
                 coefficient (C) 
               
               
                   
                 Tenth-order 
                 3.68162E−15 
               
               
                   
                 coefficient (D) 
               
               
                   
                 Twelfth-order 
                 −2.59410E−18  
               
               
                   
                 coefficient (E) 
               
               
                   
                 Fourteenth-order 
                 1.53594E−22 
               
               
                   
                 coefficient (F) 
               
               
                   
                   
               
            
           
         
       
     
     The maximum object height, the brightness, the mirror radius, the final lens radius, the lens overall length, and TR of the projection system  3 D are as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Maximum object height 
                 11.7 
               
               
                   
                 NA 
                 0.3125 
               
               
                   
                 Mirror radius 
                 31.6 
               
               
                   
                 Final lens radius 
                 49.5 
               
               
                   
                 Overall lens length 
                 240 
               
               
                   
                 TR (0.59□WXGA) 
                 0.277 
               
               
                   
                   
               
            
           
         
       
     
     Effects and Advantages 
     In the projection system  3 D according to the present example, the lens L 16 , which is disposed in a position closest to the enlargement side in the first optical system  31 , and the lens L 17 , which forms the third optical system  33 , cannot be so provided as to form one optical element. The projection system  3 D according to the present example, however, can provide the same effects and advantages as those provided by the projection system  3 A described above except the aforementioned effect and advantage of one optical element containing the lenses L 16  and L 17 . 
     In the present example, the second optical system  32  includes the meniscus lens L 16  and the mirror M, which is formed of the reflection coating layer  36  provided on the meniscus lens L 16 . The light flux that exits out of the first optical system  31  and enters the second optical system  32  can therefore be refracted by the meniscus lens L 16  and then reach the mirror M. The light rays reflected off the mirror M are refracted by the meniscus lens L 16  and then caused to exit toward the third optical system  33 . Therefore, in the present example, not only the mirror M reflects the light rays, but the meniscus lens L 16  refracts the light rays twice. As described above, in the present example, the meniscus lens L 16  can increase the angle of reflection of the light rays, whereby the size of the mirror M can be readily reduced. 
     The thickness of the meniscus lens L 16  decreases with distance from the optical axis N in the axis-Y direction. The second optical system  32  is thus allowed to have power that causes the intermediate image  35  to be formed on the screen S. Further, since the meniscus lens L 16  has refractive power, the power of the mirror M can be reduced. The curved shape of the mirror M can thus be gentler, whereby the size of the mirror M can be readily reduced. 
     In the present example, the lens L 15 , which is located in a position closest to the enlargement side in the first optical system  31 , has positive power. The divergence of the light flux that exits out of the first optical system and enters the second optical system  32  can thus be suppressed, whereby the size of the mirror M can be readily reduced. 
     The third optical system  33  may further include a lens at the enlargement side of the lens L 17 . 
       FIG. 17  shows the enlargement-side MTF of the projection system  3 D. The projection system  3 D according to the present example provides high resolution, as shown in  FIG. 17 . 
     Example 5 
       FIG. 18  is a light ray diagram diagrammatically showing the entire projection system according to Example 5.  FIG. 18  diagrammatically shows light fluxes that exit out of a projection system  3 E according to the present example and reach the screen S in the form of the light fluxes F 1  to F 3 .  FIG. 19  is a light ray diagram of the light rays passing through the projection system according to Example 5.  FIG. 20  is a light ray diagram in the vicinity of the second optical system and the third optical system. The projection system  3 E according to Example 5 has a configuration corresponding to that of the projection system  3 D described above, and corresponding components therefore have the same reference characters in the description. 
     The projection system  3 E according to the present example is formed of the first optical system  31 , the second optical system  32 , and the third optical system  33  sequentially arranged from the reduction side toward the enlargement side, as shown in  FIG. 19 . The first optical system  31  is a refractive optical system including a plurality of lenses. The second optical system  32  includes the mirror M having a concave curved surface. The third optical system  33  has negative power. The first optical system  31  forms the intermediate image  35 , which is conjugate with the reduction-side image formation plane, between the first optical system  31  and the second optical system  32 , as shown in  FIG. 20 . The second optical system  32  and the third optical system  33  form a final image conjugate with the intermediate image  35  in the enlargement-side image formation plane. The liquid crystal panels  18  located in the reduction-side image formation plane form projection images at the upper side Y 1  of the optical axis N. The intermediate image  35  is formed at the lower side Y 2  of the optical axis N. The screen S disposed in the enlargement-side image formation plane is located at the upper side Y 1  of the optical axis N. The lateral direction of the screen S coincides with the axis-X direction. The intermediate image  35  is the image formed on the screen S that is not enlarged but turned upside down in the axis-Y direction.  FIGS. 18, 19, and 20  are light ray diagrams in the plane YZ. 
     The first optical system  31  includes the cross dichroic prism  19  and  15  lenses L 1  to L 15 , as shown in  FIG. 19 . The lenses L 1  to L 15  are arranged in the presented order from the reduction side toward the enlargement side. In the present example, the lenses L 2  and L 3  are bonded to each other to form the first doublet L 21 . The lenses L 4  and L 5  are bonded to each other to form the second doublet L 22 . The lenses L 11  and L 12  are bonded to each other to form the third doublet L 23 . The lenses L 13  and L 14  are bonded to each other to form the fourth doublet L 24 . The light flux passage area of the lens L 15  (first lens) is located at the lower side Y 2  of the optical axis N. 
     The second optical system  32  includes the meniscus lens L 16 , which is disposed in the optical axis N of the first optical system  31 , and the mirror M having a concave curved surface, as shown in  FIG. 20 . A surface of the meniscus lens L 16  that is the surface facing the first optical system  31  is recessed in the direction away from the first optical system  31 . The reflection coating layer  36  is provided on a surface of the meniscus lens L 16  that is the surface opposite the first optical system  31 . The mirror M is formed of the reflection coating layer  36 . The mirror M reflects the light rays incident thereon from the first optical system  31  via the meniscus lens L 16  toward the upper side Y 1 . 
     The third optical system  33  is formed of one lens L 17  (second lens) having a meniscus shape. The lens L 17  is disposed at the upper side Y 1  of the optical axis N of the first optical system  31 . The reduction-side surface of the lens L 17  has a concave curved surface recessed toward the enlargement side. The reduction-side surface of the lens L 17  has negative power. The reduction-side surface of the lens L 17  is an aspheric surface. The enlargement-side surface of the lens L 17  is a convex curved surface protruding toward the enlargement side. The enlargement-side surface of the lens L 17  is an aspheric surface. The thickness of the lens L 17  increases with distance from the optical axis N of the first optical system  31  toward the upper side Y 1 . 
     In the projection system  3 E, the area A, where the optical density is maximized in the optical path from the reduction-side image formation plane to the enlargement-side image formation plane, is located between the second optical system  32  and the third optical system  33 . 
     Lens Data 
     Data on the lenses of the projection system  3 E are as follows: The surfaces of the lenses are numbered sequentially from the reduction side toward the enlargement side. Reference characters are given to the lenses and the mirror. Reference character R denotes the radius of curvature of a lens surface or a mirror surface. Reference character D denotes the on-axis distance between surfaces. Reference character C denotes the effective diameter of a lens surface or a mirror surface. Reference characters R, D, and C are each expressed in millimeters. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Reference 
                 Surface 
                   
                   
                   
                 Glass 
                 Refraction/ 
                   
               
               
                 character 
                 number 
                 Shape 
                 R 
                 D 
                 material 
                 reflection 
                 C 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 0.0000 
               
               
                   
                 1 
                 Spherical 
                 Infinity 
                 9.5000 
                   
                 Refraction 
                 11.7000 
               
               
                 19 
                 2 
                 Spherical 
                 Infinity 
                 25.9100 
                 SBSL7 
                 Refraction 
                 13.4739 
               
               
                   
                 3 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 16.6300 
               
               
                 L1 
                 4 
                 Spherical 
                 29.8694 
                 10.1212 
                 507907.7482 
                 Refraction 
                 17.7171 
               
               
                   
                 5 
                 Spherical 
                 −67.4125 
                 0.2000 
                   
                 Refraction 
                 17.4566 
               
               
                 L2 
                 6 
                 Spherical 
                 27.2314 
                 8.9026 
                 480546.8087 
                 Refraction 
                 14.9087 
               
               
                 L3 
                 7 
                 Spherical 
                 −41.0845 
                 1.2000 
                 841641.2724 
                 Refraction 
                 14.0000 
               
               
                   
                 8 
                 Spherical 
                 34.9494 
                 0.2000 
                   
                 Refraction 
                 12.7097 
               
               
                 L4 
                 9 
                 Spherical 
                 20.3128 
                 9.7814 
                 512784.739 
                 Refraction 
                 12.5602 
               
               
                 L5 
                 10 
                 Spherical 
                 −22.5939 
                 1.2000 
                 836218.3898 
                 Refraction 
                 11.9719 
               
               
                   
                 11 
                 Spherical 
                 −445.9411 
                 0.2000 
                   
                 Refraction 
                 11.5039 
               
               
                 L6 
                 12 
                 Aspheric 
                 43.2803 
                 1.2664 
                 680891.3828 
                 Refraction 
                 11.3626 
               
               
                   
                   
                 surface 
               
               
                   
                 13 
                 Aspheric 
                 20.5080 
                 0.2000 
                   
                 Refraction 
                 10.9467 
               
               
                   
                   
                 surface 
               
               
                 L7 
                 14 
                 Spherical 
                 20.3468 
                 5.4927 
                 457217.8557 
                 Refraction 
                 11.0447 
               
               
                   
                 15 
                 Spherical 
                 51.1219 
                 3.7826 
                   
                 Refraction 
                 10.5735 
               
               
                   
                 16 
                 Spherical 
                 Infinity 
                 0.7848 
                   
                 Refraction 
                 10.3442 
               
               
                 L8 
                 17 
                 Spherical 
                 32.8048 
                 5.5105 
                 846613.2379 
                 Refraction 
                 11.6466 
               
               
                   
                 18 
                 Spherical 
                 −50.5221 
                 1.2407 
                   
                 Refraction 
                 11.7007 
               
               
                 L9 
                 19 
                 Aspheric 
                 86.0385 
                 1.2128 
                 793362.4698 
                 Refraction 
                 11.3524 
               
               
                   
                   
                 surface 
               
               
                   
                 20 
                 Aspheric 
                 21.2155 
                 18.1704 
                   
                 Refraction 
                 11.5237 
               
               
                   
                   
                 surface 
               
               
                   
                 21 
                 Spherical 
                 Infinity 
                 13.4313 
                   
                 Refraction 
                 17.0204 
               
               
                 L10 
                 22 
                 Spherical 
                 −1615.9383 
                 4.8741 
                 609228.3456 
                 Refraction 
                 21.6521 
               
               
                   
                 23 
                 Spherical 
                 −82.2654 
                 10.9859 
                   
                 Refraction 
                 22.0804 
               
               
                 L11 
                 24 
                 Spherical 
                 54.4549 
                 18.2441 
                 614134.343 
                 Refraction 
                 26.6000 
               
               
                 L12 
                 25 
                 Spherical 
                 −42.3381 
                 1.2007 
                 846663.2378 
                 Refraction 
                 26.4607 
               
               
                   
                 26 
                 Spherical 
                 343.3072 
                 10.3212 
                   
                 Refraction 
                 26.9555 
               
               
                 L13 
                 27 
                 Spherical 
                 −51.5322 
                 10.9749 
                 632600.3261 
                 Refraction 
                 27.1806 
               
               
                 L14 
                 28 
                 Spherical 
                 −31.5200 
                 1.2716 
                 846663.2378 
                 Refraction 
                 27.8268 
               
               
                   
                 29 
                 Spherical 
                 −42.0428 
                 0.2009 
                   
                 Refraction 
                 30.1604 
               
               
                 L15 
                 30 
                 Aspheric 
                 −316.6043 
                 7.3099 
                 □Z-E48R□ 
                 Refraction 
                 30.8006 
               
               
                   
                   
                 surface 
               
               
                   
                 31 
                 Aspheric 
                 41.0756 
                 8.8391 
                   
                 Refraction 
                 30.9558 
               
               
                   
                   
                 surface 
               
               
                   
                 32 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 30.4576 
               
               
                   
                 33 
                 Spherical 
                 Infinity 
                 61.6812 
                   
                 Refraction 
                 30.4576 
               
               
                 L16 
                 34 
                 Aspheric 
                 −44.4514 
                 2.7888 
                 □Z-E48R□ 
                 Refraction 
                 33.6082 
               
               
                   
                   
                 surface 
               
               
                 M 
                 35 
                 Aspheric 
                 −36.0879 
                 −2.7888 
                 □Z-E48R□ 
                 Reflection 
                 36.5870 
               
               
                   
                   
                 surface 
               
               
                 L16 
                 36 
                 Aspheric 
                 −44.4514 
                 0.0000 
                   
                 Refraction 
                 32.7646 
               
               
                   
                   
                 surface 
               
               
                   
                 37 
                 Spherical 
                 Infinity 
                 −61.6812 
                   
                 Refraction 
                 67.4665 
               
               
                 L17 
                 38 
                 Aspheric 
                 35.2091 
                 −1.2025 
                 □Z-E48R□ 
                 Refraction 
                 35.7627 
               
               
                   
                   
                 surface 
               
               
                   
                 39 
                 Aspheric 
                 184.3284 
                 0.0000 
                   
                 Refraction 
                 59.9902 
               
               
                   
                   
                 surface 
               
               
                   
                 40 
                 Spherical 
                 Infinity 
                 −224.4195 
                   
                 Refraction 
                 218.5843 
               
               
                   
                 41 
                 Spherical 
                 Infinity 
                 0.0000 
                   
                 Refraction 
                 1488.5872 
               
               
                   
               
            
           
         
       
     
     The aspheric constants of each of the aspheric surfaces are listed below. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
             
            
               
                 Surface number 
                 S12 
                 S13 
                 S19 
                 S20 
               
               
                   
               
               
                 Radius of 
                 43.28029149 
                 20.50803314 
                 86.03847258 
                 21.21553721 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 1.568 
                 −1.3 
                 −1 
                 −0.88 
               
               
                 (K) 
               
               
                 Fourth-order 
                 −1.58537E−04  
                 −1.17452E−04  
                 −7.01987E−05  
                 −4.77470E−05  
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 9.55101E−07 
                 1.02304E−06 
                 3.87255E−08 
                 5.99956E−08 
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 −3.05979E−09  
                 −3.81639E−09  
                 −2.71036E−10  
                 −1.71069E−10  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 4.81421E−12 
                 6.84466E−12 
               
               
                 coefficient (D) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface number 
                 S30 
                 S31 
                 S34 
                 S35 
               
               
                   
               
               
                 Radius of 
                 −316.6043306 
                 41.07563553 
                 −44.45142177 
                 −36.08791139 
               
               
                 curvature in 
               
               
                 axis-Y direction 
               
               
                 Conic constant 
                 90 
                 0 
                 0.582889825 
                 −1 
               
               
                 (K) 
               
               
                 Fourth-order 
                 1.51233E−05 
                 −1.22055E−05  
                 −3.29891E−06 
                 1.11825E−06 
               
               
                 coefficient (A) 
               
               
                 Sixth-order 
                 −1.67413E−08  
                 1.54800E−08 
                  4.58126E−09 
                 −1.21257E−09  
               
               
                 coefficient (B) 
               
               
                 Eighth-order 
                 1.48808E−11 
                 −2.22732E−11  
                 −5.29526E−12 
                 −1.25146E−12  
               
               
                 coefficient (C) 
               
               
                 Tenth-order 
                 −1.25723E−14  
                 6.54334E−15 
                  5.28622E−15 
                 3.40742E−15 
               
               
                 coefficient (D) 
               
               
                 Twelfth-order 
                 5.84164E−18 
                 5.29981E−18 
                 −1.32591E−18 
                 −2.54861E−18  
               
               
                 coefficient (E) 
               
               
                 Fourteenth-order 
                 −1.11131E−21  
                 −3.14911E−21  
                 −5.28881E−22 
                 6.04186E−22 
               
               
                 coefficient (F) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface number 
                 S36 
                 S38 
                 S39 
               
               
                   
                   
               
               
                   
                 Radius of 
                 −44.45142177 
                 35.20906928 
                 184.3283787 
               
               
                   
                 curvature in 
               
               
                   
                 axis-Y direction 
               
               
                   
                 Conic constant 
                 0.582889825 
                 −0.064848482 
                 7.605219081 
               
               
                   
                 (K) 
               
               
                   
                 Fourth-order 
                 −3.29891E−06 
                 −6.47726E−07  
                 1.50866E−06 
               
               
                   
                 coefficient (A) 
               
               
                   
                 Sixth-order 
                  4.58126E−09 
                 1.15778E−09 
                 −2.51376E−10  
               
               
                   
                 coefficient (B) 
               
               
                   
                 Eighth-order 
                 −5.29526E−12 
                 7.21849E−13 
                 3.07333E−14 
               
               
                   
                 coefficient (C) 
               
               
                   
                   
               
            
           
         
       
     
     The maximum object height, the brightness, the mirror radius, the final lens radius, the lens overall length, and TR of the projection system  3 E are as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Maximum object height 
                 11.7 
               
               
                   
                 NA 
                 0.3125 
               
               
                   
                 Mirror radius 
                 36.6 
               
               
                   
                 Final lens radius 
                 60.0 
               
               
                   
                 Overall lens length 
                 257 
               
               
                   
                 TR (0.59□WXGA) 
                 0.138 
               
               
                   
                   
               
            
           
         
       
     
     Effects and Advantages 
     The projection system  3 E according to the present example can provide the same effects and advantages as those provided by the projection system  3 D described above. In the present example, the thickness of the meniscus lens L 16  of the second optical system  32  does not decrease with distance from the optical axis N in the axis-Y direction. The refractive power of the second optical system  32  is therefore smaller than that of the projection system  3 D. The size of the mirror M therefore increases as compared with that in the projection system  3 D. 
     The third optical system  33  may further include a lens at the enlargement side of the lens L 17 . 
       FIG. 21  shows the enlargement-side MTF of the projection system  3 E. The projection system  3 E according to the present example provides high resolution, as shown in  FIG. 21 . 
     In each of the examples described above, the first optical system  31  forms an intermediate image once, and the present disclosure is also applicable to a first optical system  31  that forms an intermediate image multiple times. Further, in the examples described above, the lens disposed in a position closest to the enlargement side in the first optical system  31  and the lens disposed in a position closest to the reduction side in the third optical system  33  each have an aspheric surface, and the lenses may each be formed of spherical surfaces.