Abstract:
A projection-type image display apparatus includes an enlarging projection optical unit which is configured to project an image displayed on an image display element enlargedly upon a display portion, a display controller portion which is configured to move a position of the image within a display surface of the image display element. The enlarging projection optical unit has a lens group for projecting the image enlargedly, wherein the display controller portion moves the image so as to display the image within the display surface of the image display element by projecting a portion selectively fitted to the display portion when displaying on the display portion through the enlarging projection optical unit.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. application Ser. No. 12/704,687, filed Feb. 12, 2010, now U.S. Pat. No. 7,909,472, which is a continuation of U.S. application Ser. No. 12/367,560, filed Feb. 9, 2009, now U.S. Pat. No. 7,670,009, the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to a projection-type image display apparatus for projecting an image on a screen with using an image display element, such as, a liquid crystal panel, etc., and in particular, it relates to a technology of improving an installation (i.e., a degree of freedom of installation) of that apparatus. 
     Various kinds of projection-type image display apparatuses are already known and are applied into various fields of applications, widely, for projecting modulated lights, which are obtained by irradiating lights from a light source upon an image display element, on a display portion, such as, a screen or the like, for example, through so-called an enlarging projection optic system, including a projection lens, etc., while displaying an image on that image display element, such as, a transmission-type liquid crystal panel, etc. 
     Such projection-type image display apparatuses are used, in general, under the condition that the apparatus is installed in the vicinity of the screen or the like. For that reason, to such image display apparatuses, it is requested to shorten that projection distance, while obtaining an enlarged image having a sufficient largeness on the screen at the same time. One of means for achieving this is a wide-angle of the projection lens, and as other means, there are already known an oblique projection method of using a projection lens, having a structure for projecting the image, enlargedly, in a direction inclined to the screen. However, in particular, the oblique projection method of the latter is already disclosed in the following Patent Documents 1 and 2, which will be mentioned below.
     [Patent Document 1] Japanese Patent Laying-Open No. Hei 4-27912 (1992); and   [Patent Document 2] Japanese Patent Laying-Open No. 2006-154720 (2006).   

     BRIEF SUMMARY OF THE INVENTION 
     By the way the projection-type image display apparatuses are also widen in the fields of applications thereof, accompanying with an enlargement of the image projected, and in particular, they are often used for the purpose of presenting image information to a large number of human beings, such as, in a class room of a school, or a meeting room of a company, etc., and in such case, there are many situations that the position installing the apparatus should be changed, for example, depending on an arm (i.e., the right-hand or the left-hand) of a presenter holding an indicator stick and the position where she/he is standing. 
     However, with the projection-type image display apparatuses of the conventional arts mentioned above, because of various kinds of aberrations, such as, a trapezoidal distortion, etc, which are generated in the oblique projection method, accompanying the change of position where that apparatus is installed, for that reason, a large amount of time is necessary to obtain a preferable image, again, and there is pointed out an inferior usability of that apparatus. 
     Then, according to the present invention, for dissolving a problem in the conventional arts mentioned above, it is an object to provide a projection-type image display apparatus, not generating the trapezoidal distortion and/or the various kinds of aberrations on the display screen, in spite of change of the installation position, and for that reason, for enabling an easy change of the installation position of the apparatus (i.e., increasing a degree of freedom of the installation position), thereby being superior in the usability thereof. 
     For accomplishing the object mentioned above, according to the present invention, firstly there is provided a projection-type image display apparatus, comprising: an image display element, which is configured to display an image to be projected onto a display portion; a light source unit, which is configured to irradiate light upon said image display element; an enlarged projection optical unit, which is configured to project the lights from said light source unit onto said display portion, enlargedly; and a display controller portion, which is configured to move position of the image displayed on said image display element within a display surface of said element, wherein said enlarged projection optical unit, further comprising: a projection lens, which is configured to project the image of said image display element, enlargedly; a group of lenses, which are disposed on a same optical axis, sequentially from a side of said image display element and include at least one (1) piece of a lens having a freely curved surface; and a reflection mirror having a reflection surface made up with a freely curved surface, which is disposed between said group of lenses and said display portion, wherein said image display element has a display surface larger than said display portion, when a whole body thereof is projected on said display portion, through said enlarged projection optical unit, to be displayed by projection thereof, said display controller portion brings the image on the display surface of said image display element to be movable, within the display surface of said image display element, so as to project a portion fitting to said display portion, selectively, to be displayed, when projecting it through said enlarged projection optical unit upon said display portion, to be displayed, and thereby enabling an installation position of said projection-type image display apparatus to be movable with respect to said display portion. 
     Also, according to the present invention, within the projection-type image display apparatus, as described in the above, it is preferable that said projection-type image display apparatus is fixed in a vertical direction thereof while movable in a horizontal direction thereof, with respect to said display portion, and further that said image display element has the display surface larger than said display portion in the horizontal direction thereof, when it projects the whole body thereof through said enlarged projection optical unit upon said display portion. In addition thereto, according to the present invention, within the projection-type image display apparatus, as described in the above, it is preferable that said image display element is constructed with a liquid crystal display element of WXGA enable type, while on the other hand, said display portion is a surface of an aspect ration 4:3, and further that a movement mechanism is attached to said apparatus, so as to bring it to be movable in a horizontal direction. 
     Thus, according to the present invention mentioned above, there can be achieved a superior effect of providing a projection-type image display apparatus, not generating the trapezoidal distortion and/or the various kinds of aberrations on the display screen, in spite of change of the installation position, and for that reason, for enabling an easy change of the installation position of the apparatus, thereby being superior in the usability thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       Those and other objects, features and advantages of the present invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings wherein: 
         FIGS. 1A and 1B  are views for explaining the principle of increasing a degree of freedom of the installation position of a projection-type image display apparatus, according to the present invention; 
         FIGS. 2A and 2B  are also views for explaining the principle of increasing a degree of freedom of the installation position of the projection-type image display apparatus, according to the present invention, similar to  FIGS. 1A and 1B  mentioned above; 
         FIGS. 3A and 3B  are views for showing the entire structures of an optic system and the detailed structures including lens compositions thereof, within the projection-type image display apparatus, according to an embodiment of the present invention; 
         FIG. 4  is a block diagram for showing the entire structures of the projection-type image display apparatus, according to the embodiment of the present invention mentioned above; 
         FIGS. 5A to 5C  are views for explaining a relationship between an image display element and a screen, upon a surface of which the image is projected, within the projection-type image display apparatus mentioned above; 
         FIGS. 6A and 6B  are views for showing an external configuration and for explaining an example of a form of use of the projection-type image display apparatus mentioned above; and 
         FIG. 7  is a view for explaining other form of user of the projection-type image display apparatus mentioned above. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments according to the present invention will be fully explained by referring to the attached drawings. However, in the explanation given below, the same reference numerals are given to elements, each having common function, and with those that were explained once, the explanation thereof will be omitted, appropriately, for the purpose of avoiding duplication thereof. 
     However, being applied as a projection-type image display apparatus in the embodiments, which will be shown hereinafter and will be shown the structures thereof, is a display apparatus being able to display a color image, being modulated through a plural number of transmission-type liquid display panels (i.e., three (3) pieces for R, G and B), on a screen as a display portion, for example, without generation of the trapezoidal distortion and/or the various kinds aberrations, with using a lens having a freely-curved surface and also a reflection mirror having a freely-curved surface, as well, as an optic system (i.e., an enlarged projection optic system) for an enlarged projection thereof, as is shown in Japanese Patent Application No. 2006-166434 (U.S. patent application Ser. No. 11/763,465 filed on Jun. 15, 2007: EP Application No. 07252401.0), which was proposed by the same inventors and already filed. 
     Also, from experiments and trials conducted by the present inventors, variously, with applying the enlarged projection optic system distinctive in such the projection-type image display apparatus, in particular, in case when obtaining an enlarged projection image focusing on the screen, for the purpose of enlarging an angle of field in the vertical direction thereof, it is necessary to satisfy a condition in a projection lens of an oblique projection type for obtaining a sufficiently large image with a short projection distance, i.e., the Shaimple condition, and there is a certain limit. However, on the other hand, it is understood that enlargement of the angle of field in the horizontal direction can be secured up to a sufficient largeness, with relative ease. 
     Then, according to the present invention, for enabling movement of the installation position of the apparatus and also for increasing the degree of freedom thereof, as will be mentioned in details hereinafter, there is applied the characteristics of the enlarged projection optic system mentioned above. Thus, explaining it in more details thereof, while setting up an original image, which can be obtained without generating the trapezoidal distortion and/or the various kinds of aberrations through that enlarged projection optic system, to be larger than the screen, and then it is so displayed that is can expand in the horizontal direction, in particular, and on the other hand, the image actually displayed on the screen is adjusted on the transmission-type liquid crystal panels, upon surfaces of which the modulated picture of that image are displayed, and thereby displaying it fitting to the size of the screen. 
     Explanation will be given on the principle for increasing the degree of freedom of installation within the projection-type image display apparatus mentioned heretofore, as a gist of the present invention, by referring to  FIGS. 1A ,  1 B and  2 A and  2 B, hereinafter. 
     In  FIG. 1A , as well as, a display portion on surface of which an image is projected, i.e., the screen “S”, there are illustrated an image, which can be originally displayed by that display apparatus, i.e., an image or picture “P” when displaying it by projecting the image display elements or the transmission-type liquid crystal panels, as a whole (hereinafter, it may be also called, an “original image”), and an image “P”, displayed in a part thereof, which is actually displayed on the screen “S” (hereinafter, it may be also called, an “actual image”). And, according to the present invention, as is apparent from  FIG. 1B , on the display screen of the liquid crystal panels, the actual image “P” is moved within a region of the original image “P”, and thereby disposing it to the position fitting to the screen “S”, appropriately. 
     For example, as is shown in  FIG. 2A , when the original image “P” displaying the whole of the liquid crystal panels moves into the right-hand side with respect to the screen “S” (please see an arrow in the figure), due to movement of the projection-type image display apparatus in the installation position thereof, then the smaller actual picture “P” within the region of the original picture “P” is moved to the left-hand side (please see an arrow). On the other hand, as is shown in  FIG. 2B , when the original image “P” displaying the whole of the liquid crystal panels moves into the left-hand side with respect to the screen “S” (please see an arrow in the figure), due to movement of the projection-type image display apparatus in the installation position thereof, then the actual picture “P” is moved to the left-hand side (please see an arrow). With this, also when changing the installation position of the projection-type image display apparatus, in particular, when moving it in the horizontal direction, it is possible to dispose the actual image “P” to the position fitting to the screen “S”, again, with a simple operation, such as, only moving the actual image “P” on the liquid crystal panels, and thereby enabling to maintain a preferable display condition, without generating the trapezoidal distortion and the various kinds of aberrations on the picture displayed on the screen “S”. 
     Embodiment 
     Next, explanation will be given on the details of the projection-type image display apparatus, enabling the movement of the installation position of the apparatus, with the principle explained in the above, thus, securing the degree of freedom of the installation position, by referring to  FIGS. 3A and 3B  and further  FIG. 4 . 
     First of all,  FIGS. 3A and 3B  show an example of structures of the enlarged projection optic system, including the projection lens of the oblique projection method, in the present embodiment, and in particular,  FIG. 3A  of them shows a whole of that, and  FIG. 3B  shows, in particular, the detailed structures of the projection lens. 
     As is shown in  FIG. 3A , the enlarged projection optic system includes, for example, the image display element  2  made of the above-mentioned transmission-type liquid crystal panel (however, in this figure, only one (1) piece of them is shown), a projection lens  1  as a projection optic system, a screen  3 , and a reflection mirror  22  as a return mirror, wherein through this reflection mirror, i.e., the reflection mirror  22 , so-called the oblique projection optic system is constructed. However, an optical axis to be use hereinafter means an optical axis in a local coordinates for each lens. 
     Following to the above, as is shown in  FIG. 3B , the projection lens  1  is built up with a refraction lens system  21  made up with a plural number of lenses, and a reflection mirror  22 , and that refraction lens system  21  is disposed on a side of the image display element  2 , and within an inside of that refraction lens system  21  is provided an eccentric iris, being eccentric with respect to the optical axis thereof. 
     But, the reflection mirror  22  mentioned above is provided for returning the image light from the image display element  2  to the side of the screen  3 , for making the distance between the screen and the apparatus as small as possible, for example, when applying the present embodiment into the projection-type image display apparatus. Of course, this should not be restricted to this. Herein, the reflection mirror  22  is a freely curved surface mirror. 
     By the way, with such oblique projection system as mentioned above, so-called the trapezoidal distortion is generated. Then, with this trapezoidal distortion, as is disclosed in the Patent Document 2 mentioned above, i.e., the patent publication of the patent application, which is proposed by the same inventors and already filed, the reflection mirror  22  is compensated or corrected with using a capacity of aberration compensating of the freely-curved surface mirror building up the reflection mirror  22 . Further, according to the present embodiment, also by means of the freely curved surface lens (will be mentioned later) included in the refraction lens system  21 , the compensation is conducted on the trapezoidal distortion. However, with the projection lens that is disclosed in the Patent Document 2 mentioned above, two (2) pieces of the freely curved surface mirrors are applied, each being superior in the capacity of compensating the trapezoidal distortion and the other aberrations, and the oblique projection angle is still small, i.e., 40 degrees, i.e., it does not reach to that the image display elements are disposed to be oblique to the projection lens. 
     Next, explanation will be give on the detailed numerical embodiment of the projection lens  1  mentioned above, with using tables 1 to 5, which will be given below, as well as, by referring to  FIG. 3B , again. The numerical values of the lens data shown in the tables 1 to 5 below are those of an example, where g an image of a region 13.2×9.9 on a material surface is projected onto a largeness of 1,625.6×1,219.2 on an image surface. 
     Also, the surface numbers of those lenses are shown by references S 0  to S 23 , sequentially, assuming a display surface (i.e., the material surface) of the image display element  2  to S 0 . In more details, a light incident surface of a cross prism  111  (will be mentioned later) disposed next to the display surface (i.e., the material surface) S 0  of the image display element  2  is shown by S 1 , a light emitting surface thereof S 2 , a light incident surface of a first lens building up the refraction lens system  21  disposed next to it by S 3 , and a light emitting surface thereof by S 4 , a surface of the eccentric iris ST 1  by S 11 , . . . , a reflection surface of the reflection mirror  22  by S 22 , and a surface (i.e., an image surface) of the screen  3  by S 23 , respectively. 
     Also, the lens data displays the data of each lens in the local coordinates thereof, sequentially; however for easily understanding of the directions, X-axis, Y-axis and Z-axis, roughly, the local coordinates on an opening iris surface S 11  is shown in  FIG. 3B . 
     Following to the above, in the Table 1 given below, “Rd” shows a radius of curvature of each surface, wherein it is indicated by a positive value when a center of curvature lies on the right-hand side of the surface within the figure, or by a negative value when it is reversed. Also, “TH” is the distance between the surfaces, i.e., it indicates the distance from a summit on that lens surface up to the summit on the next coming lens surface. With a certain lens surface, when the next coming lens surface is located on the right-hand side, then the distance between the surfaces is presented by a positive value, when it on the left-hand side, it is presented by a negative value. Further, surfaces S 5 , S 6 , S 12  and S 13  are rotationally symmetrical aspheric surface, and they are shown with attaching “*” beside the surface number, in the Table 1. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Surface 
                 Rd 
                 TH 
                 nd 
                 νd 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 S0 
                 Infinity 
                 5.977 
                   
                   
               
               
                   
                 S1 
                 Infinity 
                 26.395 
                 1.51680 
                 64.2 
               
               
                   
                 S2 
                 Infinity 
                 9.938 
               
               
                   
                 S3 
                 36.40 
                 6.700 
                 1.84666 
                 23.8 
               
               
                   
                 S4 
                 −172.286 
                 8.870 
               
               
                   
                 S5 * 
                 4710.437 
                 6.000 
                 1.49091 
                 58.0 
               
               
                   
                 S6 * 
                 −1283.473 
                 0.100 
               
               
                   
                 S7 
                 35.918 
                 8.000 
                 1.48749 
                 70.4 
               
               
                   
                 S8 
                 −19.759 
                 2.500 
                 1.84666 
                 23.8 
               
               
                   
                 S9 
                 20.619 
                 5.800 
                 1.48749 
                 70.4 
               
               
                   
                 S10 
                 −48.583 
                 9.000 
               
               
                   
                 S11 
                 Infinity 
                 17.160 
               
               
                   
                 S12 * 
                 −38.217 
                 6.000 
                 1.49091 
                 58.0 
               
               
                   
                 S13 * 
                 −40.281 
                 2.360 
               
               
                   
                 S14 
                 1001.620 
                 7.200 
                 1.80610 
                 33.3 
               
               
                   
                 S15 
                 −42.940 
                 44.228 
               
               
                   
                 S16 
                 −29.908 
                 3.500 
                 1.48749 
                 70.4 
               
               
                   
                 S17 
                 72.760 
                 19.858 
               
               
                   
                 S18 # 
                 Infinity 
                 6.000 
                 1.49091 
                 58.0 
               
               
                   
                 S19 # 
                 Infinity 
                 6.932 
               
               
                   
                 S20 # 
                 Infinity 
                 6.000 
                 1.49091 
                 58.0 
               
               
                   
                 S21 # 
                 Infinity 
                 102.031 
               
               
                   
                 S22 # 
                 Infinity 
                 −888.477 
                 REFL 
               
               
                   
                 S23 
                 Infinity 
                 — 
               
               
                   
                   
               
             
          
         
       
     
     However, the surface configuration of the rotationally symmetrical aspheric surface can be presented by the following equation (Eq. 1), and coefficients on the four (4) aspheric surfaces mentioned above are shown in the following Table 2. 
     
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       
                         cr 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       A 
                       · 
                       
                         r 
                         4 
                       
                     
                     + 
                     
                       B 
                       · 
                       
                         r 
                         6 
                       
                     
                     + 
                     
                       C 
                       · 
                       
                         r 
                         8 
                       
                     
                     + 
                     
                       D 
                       · 
                       
                         r 
                         10 
                       
                     
                     + 
                     
                       E 
                       · 
                       
                         r 
                         12 
                       
                     
                     + 
                     
                       F 
                       · 
                       
                         r 
                         14 
                       
                     
                     + 
                     
                       G 
                       · 
                       
                         r 
                         16 
                       
                     
                     + 
                     
                       H 
                       · 
                       
                         r 
                         18 
                       
                     
                     + 
                     
                       J 
                       · 
                       
                         r 
                         20 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     
       
         
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Surface 
                 Aspheric Surface Coefficients 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 S5 
                 K 
                 76267.9963 
                 C 
                 −4.351E−11 
                 F 
                 −6.488E−18 
                 J 
                 −6.107E−26 
               
               
                   
                 A 
                  −3.65E−05 
                 D 
                 4.0368E−13 
                 G 
                  2.992E−21 
               
               
                   
                 B 
                 −5.477E−09 
                 E 
                 1.5886E−18 
                 H 
                 −4.589E−24 
               
               
                 S6 
                 K 
                 −78271.536 
                 C 
                 −1.557E−11 
                 F 
                 4.9662E−18 
                 J 
                 3.4853E−25 
               
               
                   
                 A 
                 −3.781E−05 
                 D 
                 −2.675E−13 
                 G 
                 −1.676E−20 
               
               
                   
                 B 
                 −9.286E−09 
                 E 
                  −2.14E−17 
                 H 
                 −9.422E−23 
               
               
                 S12 
                 K 
                 0.35333475 
                 C 
                 4.6989E−11 
                 F 
                 1.2748E−18 
                 J 
                 5.3155E−26 
               
               
                   
                 A 
                 −6.576E−07 
                 D 
                 −7.849E−14 
                 G 
                 −4.983E−21 
               
               
                   
                 B 
                 2.5656E−08 
                 E 
                 2.3211E−16 
                 H 
                 −1.857E−23 
               
               
                 S13 
                 K 
                 0.05198949 
                 C 
                 1.2912E−11 
                 F 
                 1.7517E−19 
                 J 
                 7.3476E−27 
               
               
                   
                 A 
                 1.9971E−06 
                 D 
                 1.4302E−14 
                 G 
                 −1.034E−22 
               
               
                   
                 B 
                 1.6908E−08 
                 E 
                  −9.82E−19 
                 H 
                 −4.354E−24 
               
               
                   
               
             
          
         
       
     
     Also, the surfaces from S 18  to S 21  are the respective refraction surfaces of the freely curved surface lenses, and the surface S 22  is a reflection surface of the freely curved surface mirror, being attached with “*” beside the surface number thereof. The configurations of those five (5) pieces of freely curved surfaces can be expressed by the following equation (Eq. 2), and in the following are shown the values of the coefficients C(m,n) for each “m”, “n”, in the Table 3. However, two (2) pieces of the freely curved lenses are for compensating the trapezoidal distortion, which is generated due to the oblique projection, in cooperation with the freely curved mirror of the reflection mirror  22 . 
     
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       
                         cr 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         m 
                       
                       ⁢ 
                       
                         · 
                         
                           
                             ∑ 
                             n 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 C 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     m 
                                     , 
                                     n 
                                   
                                   ) 
                                 
                               
                               · 
                               
                                 x 
                                 m 
                               
                               · 
                               
                                 y 
                                 n 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     
       
         
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Surface 
                 Freely Curved Surface Coefficients 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 S18 
                 K 
                 0 
                 C(4, 1) 
                 2.74E−06 
                 C(2, 5) 
                 −9.44E−09 
                 C(4, 5) 
                 1.74E−11 
               
               
                   
                 C(0, 1) 
                 0.77728116 
                 C(2, 3) 
                 3.86E−06 
                 C(0, 7) 
                 −7.23E−10 
                 C(2, 7) 
                 4.61E−12 
               
               
                   
                 C(2, 0) 
                 −0.0237261 
                 C(0, 5) 
                 3.28E−06 
                 C(8, 0) 
                 2.78E−10 
                 C(0, 9) 
                 −9.63E−13 
               
               
                   
                 C(0, 2) 
                 −0.011193 
                 C(6, 0) 
                 −6.21E−08 
                 C(6, 2) 
                 7.46E−11 
                 C(10, 0) 
                 −2.93E−13 
               
               
                   
                 C(2, 1) 
                 −0.0009319 
                 C(4, 2) 
                 5.72E−08 
                 C(4, 4) 
                 2.14E−10 
                 C(8, 2) 
                 −3.53E−13 
               
               
                   
                 C(0, 3) 
                 −0.0013365 
                 C(2, 4) 
                 −9.29E−08 
                 C(2, 6) 
                 −8.31E−11 
                 C(6, 4) 
                 −9.12E−14 
               
               
                   
                 C(4, 0) 
                  8.592E−06 
                 C(0, 6) 
                 2.16E−08 
                 C(0, 8) 
                 5.95E−11 
                 C(4, 6) 
                 3.04E−13 
               
               
                   
                 C(2, 2) 
                 7.2254E−05 
                 C(6, 1) 
                 −6.35E−09 
                 C(8, 1) 
                 4.34E−12 
                 C(2, 8) 
                 6.40E−14 
               
               
                   
                 C(0, 4) 
                 3.3648E−05 
                 C(4, 3) 
                 −3.10E−09 
                 C(6, 3) 
                 7.31E−12 
                 C(0, 10) 
                 −1.11E−13 
               
               
                 S19 
                 K 
                 0 
                 C(4, 1) 
                 9.64E−07 
                 C(2, 5) 
                 1.90E−09 
                 C(4, 5) 
                 9.12E−12 
               
               
                   
                 C(0, 1) 
                 0.78854159 
                 C(2, 3) 
                 2.85E−07 
                 C(0, 7) 
                 7.20E−10 
                 C(2, 7) 
                 1.82E−12 
               
               
                   
                 C(2, 0) 
                 −0.0216438 
                 C(0, 5) 
                 1.75E−06 
                 C(8, 0) 
                 1.45E−10 
                 C(0, 9) 
                 −2.48E−12 
               
               
                   
                 C(0, 2) 
                 −0.012203 
                 C(6, 0) 
                 −4.13E−08 
                 C(6, 2) 
                 2.25E−10 
                 C(10, 0) 
                 −1.25E−13 
               
               
                   
                 C(2, 1) 
                 −0.0005154 
                 C(4, 2) 
                 −2.39E−08 
                 C(4, 4) 
                 4.12E−10 
                 C(8, 2) 
                 −3.19E−13 
               
               
                   
                 C(0, 3) 
                 −0.0010429 
                 C(2, 4) 
                 −1.68E−07 
                 C(2, 6) 
                 3.16E−10 
                 C(6, 4) 
                 −1.41E−13 
               
               
                   
                 C(4, 0) 
                 3.7301E−06 
                 C(0, 6) 
                 −3.52E−08 
                 C(0, 8) 
                 7.10E−11 
                 C(4, 6) 
                 4.54E−14 
               
               
                   
                 C(2, 2) 
                 7.7564E−05 
                 C(6, 1) 
                 −1.88E−09 
                 C(8, 1) 
                 3.04E−13 
                 C(2, 8) 
                 −1.09E−13 
               
               
                   
                 C(0, 4) 
                 4.9708E−05 
                 C(4, 3) 
                 3.47E−09 
                 C(6, 3) 
                 3.70E−12 
                 C(0, 10) 
                 −1.04E−13 
               
               
                 S20 
                 K 
                 0 
                 C(4, 1) 
                 −9.35E−07 
                 C(2, 5) 
                 2.47E−09 
                 C(4, 5) 
                 −1.19E−12 
               
               
                   
                 C(0, 1) 
                 0.22293143 
                 C(2, 3) 
                 −1.67E−06 
                 C(0, 7) 
                 −3.56E−10 
                 C(2, 7) 
                 −7.50E−13 
               
               
                   
                 C(2, 0) 
                 0.03205384 
                 C(0, 5) 
                 −1.29E−06 
                 C(8, 0) 
                 2.45E−12 
                 C(0, 9) 
                 8.53E−13 
               
               
                   
                 C(0, 2) 
                 0.01991488 
                 C(6, 0) 
                 4.12E−09 
                 C(6, 2) 
                 1.76E−12 
                 C(10, 0) 
                 −1.95E−15 
               
               
                   
                 C(2, 1) 
                 0.00104417 
                 C(4, 2) 
                 −6.91E−09 
                 C(4, 4) 
                 −5.48E−12 
                 C(8, 2) 
                 −4.34E−15 
               
               
                   
                 C(0, 3) 
                 0.0004342 
                 C(2, 4) 
                 9.00E−09 
                 C(2, 6) 
                 4.84E−11 
                 C(6, 4) 
                 −1.07E−14 
               
               
                   
                 C(4, 0) 
                 −1.696E−05 
                 C(0, 6) 
                 −2.31E−08 
                 C(0, 8) 
                 5.54E−12 
                 C(4, 6) 
                 −1.34E−14 
               
               
                   
                 C(2, 2) 
                 −1.633E−05 
                 C(6, 1) 
                 1.63E−10 
                 C(8, 1) 
                 −1.56E−14 
                 C(2, 8) 
                 −2.64E−14 
               
               
                   
                 C(0, 4) 
                 −2.687E−05 
                 C(4, 3) 
                 6.15E−10 
                 C(6, 3) 
                 −6.25E−14 
                 C(0, 10) 
                 1.47E−14 
               
               
                 S21 
                 K 
                 0 
                 C(4, 1) 
                 −1.36E−06 
                 C(2, 5) 
                 2.59E−09 
                 C(4, 5) 
                 −9.87E−13 
               
               
                   
                 C(0, 1) 
                 0.21505056 
                 C(2, 3) 
                 −2.06E−06 
                 C(0, 7) 
                 1.96E−10 
                 C(2, 7) 
                 −6.75E−13 
               
               
                   
                 C(2, 0) 
                 0.03681255 
                 C(0, 5) 
                 −1.28E−06 
                 C(8, 0) 
                 2.06E−12 
                 C(0, 9) 
                 4.03E−13 
               
               
                   
                 C(0, 2) 
                 0.02059904 
                 C(6, 0) 
                 7.16E−09 
                 C(6, 2) 
                 4.46E−12 
                 C(10, 0) 
                 −2.22E−15 
               
               
                   
                 C(2, 1) 
                 0.00115712 
                 C(4, 2) 
                 −4.08E−09 
                 C(4, 4) 
                 1.52E−11 
                 C(8, 2) 
                 −3.08E−15 
               
               
                   
                 C(0, 3) 
                 0.00031471 
                 C(2, 4) 
                 8.85E−09 
                 C(2, 6) 
                 4.61E−11 
                 C(6, 4) 
                 −1.23E−14 
               
               
                   
                 C(4, 0) 
                 −2.255E−05 
                 C(0, 6) 
                 −1.31E−08 
                 C(0, 8) 
                 1.13E−11 
                 C(4, 6) 
                 −1.38E−14 
               
               
                   
                 C(2, 2) 
                 −2.824E−05 
                 C(6, 1) 
                 5.16E−10 
                 C(8, 1) 
                 −1.24E−13 
                 C(2, 8) 
                 −2.08E−14 
               
               
                   
                 C(0, 4) 
                 −3.402E−05 
                 C(4, 3) 
                 1.32E−09 
                 C(6, 3) 
                 −1.52E−13 
                 C(0, 10) 
                 4.81E−15 
               
               
                 S22 
                 K 
                 0 
                 C(4, 1) 
                 −9.57E−09 
                 C(2, 5) 
                 −9.95E−13 
                 C(4, 5) 
                 −3.43E−17 
               
               
                   
                 C(0, 1) 
                 −0.0417768 
                 C(2, 3) 
                 6.23E−09 
                 C(0, 7) 
                 3.38E−13 
                 C(2, 7) 
                 −2.20E−16 
               
               
                   
                 C(2, 0) 
                 0.00360484 
                 C(0, 5) 
                 2.84E−09 
                 C(8, 0) 
                 −2.59E−15 
                 C(0, 9) 
                 9.64E−17 
               
               
                   
                 C(0, 2) 
                 0.00061986 
                 C(6, 0) 
                 2.61E−11 
                 C(6, 2) 
                 3.13E−14 
                 C(10, 0) 
                 2.90E−20 
               
               
                   
                 C(2, 1) 
                 5.9071E−05 
                 C(4, 2) 
                 −2.00E−10 
                 C(4, 4) 
                 −9.77E−15 
                 C(8, 2) 
                 −4.97E−19 
               
               
                   
                 C(0, 3) 
                 1.6888E−05 
                 C(2, 4) 
                 2.64E−12 
                 C(2, 6) 
                 −2.15E−14 
                 C(6, 4) 
                 2.04E−18 
               
               
                   
                 C(4, 0) 
                 −2.322E−07 
                 C(0, 6) 
                 2.00E−11 
                 C(0, 8) 
                 8.14E−15 
                 C(4, 6) 
                 −2.90E−19 
               
               
                   
                 C(2, 2) 
                 7.5974E−07 
                 C(6, 1) 
                 1.25E−12 
                 C(8, 1) 
                 −6.62E−17 
                 C(2, 8) 
                 −8.62E−19 
               
               
                   
                 C(0, 4) 
                 2.7513E−07 
                 C(4, 3) 
                 −2.09E−12 
                 C(6, 3) 
                 4.00E−16 
                 C(0, 10) 
                 4.21E−19 
               
               
                   
               
             
          
         
       
     
     However, in the Table 3 given above, a title and a value of the coefficient are aligned left to right by a set of framework, wherein the right-hand side is the value, the left-hand side indicates the title, and two (2) sets of numerical values divided by comma in a bracket indicate the values of “m” and “n” shown in the equation (Eq. 2). 
     Following to the above, the condition of inclination or eccentricity of the local coordinates on each surface is shown in the following Table 4, in the present embodiment. However, herein, the inclination of the surface is presented by an inclination angle with respect to a main surface of the lens before, and the to eccentricity is presented by an eccentric amount with respect to the optical axis of the lens before. In this Table 4, “ADE” is amplitude of the inclination within the surface parallel with the cross-section in the figure, and direction of the inclination is positive rotating in the clockwise direction within the cross-section of  FIG. 3B , with a unit of degree. Also, “YDE” is amplitude of the eccentricity, and the eccentricity is set up in the direction perpendicular to the optical axis within the cross-section of the figure, wherein the eccentricity to a lower side is positive in the cross-section shown in  FIG. 3B , with a unit of degree. However, herein, the lens data are displayed, sequentially, upon basis of each of the local coordinates, however the local coordinates on the opening iris surface S 11  is shown in  FIG. 3B , representatively, for easy understanding of the X-axis, Y-axis and Z-axis, roughly. 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Surface 
                 ADE (°) 
                 YDE (mm) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 S3 
                 2.602 
                 −1.289 
               
               
                   
                 S22 
                 26.495 
                 −17.365 
               
               
                   
                 S23 
                 −50.000 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     In the inclinations and the eccentricities shown in the Table 4 given above, the surface S 3  defines an eccentricity/falling amount thereof upon basis of the surface S 2 , and in the similar manner, the surface S 22  defines the eccentricity/falling amount thereof upon basis of the surface S 21 . 
     By the way, in case where the lens surface is a transparent surface, it is possible to build up an optic system by defining the eccentricity/falling amounts, sequentially, upon basis of the lens surface before. However, in case where the lens surface is the reflection surface, if inclining the reflection surface by θ degree, then a ray of light (i.e., the next optical axis) is inclined by 2θ degree. Moreover, since the surface S 22  is the freely curved surface mirror, which can have an inclination on the surface thereof even on the optical axis, and further thereto, since the eccentricity amount thereof is already determined, a shift is generated between the local optical shaft, which is determined after the surface S 22  and the actual ray of light. Then, a dummy surface (not shown in the figure) defining the local optical axis after reflection upon the surface S 22  is set at the position of the surface S 22  inclining by +59.8 degrees upon basis of the surface S 21 . This angle is shifted from 52.99 degrees, two (2) times large as the inclination of the surface S 22 , 26.49 degrees; however, this reason is, as was explained in the above, due to an influence of the freely curved surface mirror, which is eccentric. 
     And, the surface S 23  (the screen surface) is disposed to incline by −50 degrees with respect to the optical axis of this dummy surface. However, also upon the surface S 23  (the screen surface), there is a difference between the positions of the optical axis and the actual ray of light, and this results into an inclination of −55.6 degrees, with respect to the projection axis of the projection lens, which was defined previously, as is shown in  FIGS. 1A and 1B . 
     Further, the following Table 5 shows changes of the distance between the moving lens surfaces, for the lenses moving responding to change of the projection distance. The values in the columns corresponding to “Sc1”, “Sc2” and “Sc3” on the Table 3 indicate lens intervals between corresponding to the screen positions, at which the screen size comes to 80 inches, 100 inches and 60 inches, respectively. 
     
       
         
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
             
             
               
                   
                   
               
               
                   
                 TH 
               
             
          
           
               
                   
                 Surface 
                 Sc1 
                 Sc2 
                 Sc3 
               
               
                   
                   
               
             
          
           
               
                   
                 S15 
                 44.228 
                 44.192 
                 44.300 
               
               
                   
                 S17 
                 19.858 
                 19.525 
                 20.401 
               
               
                   
                 S19 
                 6.932 
                 6.192 
                 8.083 
               
               
                   
                 S21 
                 102.031 
                 102.771 
                 100.880 
               
               
                   
                 S22 
                 −888.477 
                 −1124.755 
                 −652.884 
               
               
                   
                   
               
             
          
         
       
     
     In  FIG. 3B  mentioned above, the eccentric iris “ST 1 ” is disposed in the refraction lens system  21  of the projection lens  1 , being eccentric by 1.75 mm, shifting into left-upper direction a little bit, with respect to the optical axis of the refraction lens system  21 . 
     Following to the above, explanation will be given on the entire structures of the projection-type image display apparatus, by referring to  FIG. 4  attached herewith. However, in this  FIG. 4 , a light flux emitting from a light source unit  101 , being cut off the ultraviolet components thereof by means of an UV cut filter  102 , is incident upon a pair of multi-lens arrays  103   a  and  103   b , as an integrator. However, in general, the cut-off of the ultraviolet rays, including the cut-off of the infrared lays, as well, may be also conducted by other optical element(s), but the detailed description thereof will be omitted, since it is not the gist of the present invention. 
     In the multi-lens arrays  103   a  and  103   b  are disposed convex lenses (or, cells) in a two (2) dimensional manner, and a flux of light incident upon the multi-lens array  103   a  forms a light source image on each cell of the multi-lens array  103   b , in the two (2) dimensional manner. With the respective light source images, each focusing respectively, natural lights thereof is converted into a linear polarized light having vibration in a certain direction, by means of a light converter element  104 . This is because, the image display elements  2   a ,  2   b  and  2   c , which will be mentioned later, allow only the linear polarized light having vibration in the certain direction to pass through. The light source images, which are divided in the two (2) dimensional manner by the multi-lens arrays  103   a  and  103   b , are overlaid on the image display surfaces of the image display elements  2   a ,  2   b  and  2   c , by an overlay lens  105  having an overlaying function. However, they are dissolved into three (3) colors, red, green and blue, through a color dissolving optic system lying between the overlay lens  105  and the image display elements  2   a ,  2   b  and  2   c.    
     Next, with the flux of lights, passing through the overlay lens  105  and being deflected with an optical path thereof by a total reflection mirror  106   a , first of all, by means of a first dichroic mirror  107   a , a flux of blue color light passes therethrough, while the red color and the green color lights are reflected thereupon. The flux of blue color light, being deflected upon a total reflection mirror  106   b , is irradiated upon the image display element  2   b  for use of blue color light through a condenser lens  108   b . With the red color and the green color lights, by means of a second dichroic mirror  107   b , the flux of green color light is reflected thereupon, while the red color light passes therethrough. The flux of red color light is deflected upon total reflection mirrors  106   c  and  106   d , to be irradiated on the image display element  2   c  for use of the red color light passing through a condenser lens  108   c . However, since the optical path of the red color light is long in the length thereof than those of the blue color light and the green color light, it is mapped with using relay lenses  109  and  110 . 
     It is so constructed that each light flux, irradiating upon the image display element  2   b  for the blue color light and the image display element  2   a  for the green color light, is color composed or synthesized by the cross prism  111 , to be incident upon the projection lens  1 . And, as an example of those image display elements can be considered, in particular, liquid crystal panels of transmission type (a type of WXGA enable) of wide width (an aspect ratio=16:9) to be applied therein, preferably. 
     And, for example, as is shown in  FIGS. 5A to 5C  attached herewith, the image or picture having the aspect ratio 4:3 (i.e., the actual image) “P” is projected, which is widely used, in general, within the range of the image (i.e., the original picture) “P”, which can be obtained by this wide liquid crystal panel (however, the sizes are coincided in the vertical direction of both). With this fact, since the actual image “P” can be moved in the horizontal direction, freely, within the region of the original image “P” of wide width (the aspect ratio 16:9), it is possible to easily achieve movement/adjustment of the installation position of the projection-type image display apparatus in the horizontal direction, without accompanying the trapezoidal distortion and/or various kinds of aberrations caused due to change of the installation position. 
     Further, display of the actual image “P” within the image display surface of such the wide width liquid crystal panel (i.e., the original image “P”) (in other to words, display controls of three (3) pieces of image display elements  2   a ,  2   b  and  2   c  for use of R, G and B) is conducted, for example, by so-called a liquid crystal controller portion  120 , which is constructed with an control element for forming an image on the liquid crystal panel upon basis of the image signal inputted from an outside of the apparatus. Also, movement of the image after changing the installation position of the apparatus (i.e., the actual image) “P” is executed in accordance with an input for image movement, which is inputted by an operator through a key for use of movement, such as, scroll keys or the like, for example, which is provided in a remote controller, in a part or a separated from that apparatus. Or, alternatively, a sensor for detecting the position of the screen  3  is provided in a part of the projection-type image display apparatus, so that the apparatus itself conducts the display control mentioned above, automatically, upon basis of an output of detection of that sensor. 
     However, though it is omitted in the explanation given in the above, there is disposed a polarizing plate, for cutting off the light rays other than a predetermined polarized light ray, or a phase difference plate, for controlling the vibration direction of the polarized light ray for each color. However, since such the structure does not constitute the gist of the present invention, the detailed explanation thereof will be omitted. 
     Further, explanation will be given, hereinafter, upon the projection-type image display apparatus, the internal details of which are given heretofore, including more detailed form of application thereof, by referring to  FIGS. 6A and 6B  and  FIG. 7 . 
     First of all,  FIG. 6A  shows an outlook of the projection-type image display apparatus  200  mentioned above, wherein the above-mentioned reflection mirror  22  is attached in a part of a main body housing  201  having a roughly box-like shape, so that it can be stored therein by rotating (see an arrow in the figure). Also,  FIG. 6B  shows a form of application wherein that apparatus  200  installed to be movable on a ceiling surface “C” of a class room, for example, turning it upside-down, and an image or picture thereof is projected on a whiteboard or an instructive board. However, in the figure, a reference numeral  210  is a movement mechanism for brining the apparatus to be slidable, such as, a rail or a guide, etc., for example. Below this movement mechanism  210  is fixed that apparatus with turning it upside-down, and therefore the projection-type image display apparatus  200  mentioned above is slidable in the direction of an arrow. However, herein, the instructive board is that for enabling an operation of an application on the board surface, while projecting a screen of a personal computer on the board, and further for enabling take-in of characters and/or figures written on the board. With this, the position of the apparatus can be changed, appropriately, depending on the standing position of a teacher or a pupil. 
     Further,  FIG. 7  attached herewith shows the projection-type image display apparatus, also being unified with the whiteboard or the instructive board, in the structures thereof, thereby building up a projection-type image display system for projecting a large screen on a surface  221 (S) of that whiteboard  220 . However, in this case, it is preferable that the projection-type image display apparatus  200  is attached in a part of a frame body of that whiteboard  220 , in particular, around a central portion of an upper-side frame  222  thereof, also via such the mechanism as was mentioned above (in this example, not shown in the figure, but attaching the movement mechanism on the upper-side frame  221 , in advance, the apparatus  200  is fixed on this with using fixing tools of “L” shape), and thereby brining that apparatus  200  to be movable in the horizontal direction with respect to the surface  221  of the whiteboard  220 . With this, in the similar manner to that of the form of application mentioned above, it is possible to change the installation position of the projector apparatus, appropriately, depending on the standing position of a presenter, etc., and thereby enabling superior display images, without interruption of the projection image. 
     While we have shown and described several embodiments in accordance with our invention, it should be understood that disclosed embodiments are susceptible of changes and modifications without departing from the scope of the invention. Therefore, we do not intend to be bound by the details shown and described herein but intend to cover all such changes and modifications that fall within the ambit of the appended claims.