Patent Publication Number: US-2002001030-A1

Title: Three-dimensional display apparatus and oblique projection optical system

Description:
[0001] This application is based on application No. 2000-156908 filed in Japan, the contents of which are hereby incorporated by reference.  
       BACKGROUND OF THE INVENTION  
       [0002] 1. Field of the Invention  
       [0003] The present invention relates to a three-dimensional display apparatus which has a surface for providing a basic image and a screen surface which is allowed to rotate around a predetermined axis and on which the provided basic image is projected, and also concerns an oblique projection optical system installed therein.  
       [0004] 2. Description of the Background Art  
       [0005] Conventionally, there has been proposed a projection apparatus in which oblique projection optical system is installed so that an image is projected onto a stationary screen placed in a vertical plane obliquely from below so as to be displayed thereon. In such a device, the oblique projection optical system is provided with a decentering lens which focuses the image on the entire surface of the screen.  
       [0006] In recent years, a projection apparatus has been developed in which an image is projected on a screen while the screen is being rotated around a vertical axis so that the image is displayed three-dimensionally by utilizing its after images, and in such an apparatus, the image is projected obliquely from below so as to prevent the projection optical system from disturbing the viewing field. For this reason, the image projected on the screen is susceptible to distortional aberration and focus offset, with the result that the device tends to fail to provide a three-dimensional image with precision.  
       [0007] Here, the conventional oblique projection optical system is only allowed to have a tilt angle of 20° at most. Therefore, when this is applied to the above-mentioned three-dimensional display apparatus, it is difficult to arrange this in a manner so as not to disturb the viewing field.  
       SUMMARY OF THE INVENTION  
       [0008] The present invention is directed to a three-dimensional display apparatus.  
       [0009] In one aspect of the present invention, the three-dimensional display apparatus is provided with: a screen; a rotation mechanism for rotating the screen so as to volume-scan a predetermined space; an image generation section for generating a cross-sectional image of a three-dimensional object to be displayed in response to a rotation of the rotation mechanism and for providing the cross-sectional image; and a projection optical system for correcting distortion and out-of focus on a surface of the screen of the cross-sectional image provided from the image generation section, and for projecting the cross-sectional image to the screen that is rotating. Therefore, the apparatus makes it possible to display a three-dimensional image with high precision.  
       [0010] In another aspect of the present invention, the three-dimensional display apparatus is arranged such that the projection optical system projects the cross-sectional image to the screen from a position that is rotated by the rotation mechanism while maintaining a positional relationship with the screen. Therefore, there are no parts shielding the front side of the screen so that it becomes possible to provide better visibility to the screen.  
       [0011] Moreover, the present invention is also directed to oblique optical system in which a line, which optically connects a center of a short conjugate length focal surface that is a focal surface on a short conjugate length side and a center of a long conjugate length focal surface that is a focal surface on a long conjugate length side, is allowed to have an angle other than vertical with respect to the long conjugate length focal surface.  
       [0012] Therefore, the objective of the present invention is to provide a three-dimensional display apparatus which can display a three-dimensional image with precision and oblique projection optical system that is suitably applied to such a projection apparatus.  
       [0013] These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0014]FIG. 1 is a drawing that schematically shows the appearance of a three-dimensional image display apparatus in accordance with a preferred embodiment;  
     [0015]FIG. 2 is a drawing that shows the structure of an optical system in the three-dimensional image display apparatus;  
     [0016]FIG. 3 is a schematic perspective view that shows one example of a screen and a rotation member;  
     [0017]FIG. 4 is a drawing that shows a size of a cross-sectional image to be projected onto the screen;  
     [0018]FIG. 5 is a drawing that shows the structure of a color filter in accordance with the preferred embodiment;  
     [0019]FIG. 6 is a drawing that schematically shows an image generation surface of a DMD;  
     [0020]FIG. 7 is a drawing that specifically shows an intermediate optical system that is shown in FIG. 2;  
     [0021]FIG. 8 is a drawing that schematically shows the structure of oblique projection optical system together with the DMD and the screen;  
     [0022]FIG. 9 is a drawing that shows a light path of the oblique projection optical system of a first example;  
     [0023]FIG. 10 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the first example;  
     [0024]FIG. 11 is a drawing that shows a light path of the oblique projection optical system of a second example;  
     [0025]FIG. 12 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the second example;  
     [0026]FIG. 13 is a drawing that shows a light path of the oblique projection optical system of a third example;  
     [0027]FIG. 14 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the third example;  
     [0028]FIG. 15 is a drawing that shows a light path of the oblique projection optical system of a fourth example;  
     [0029]FIG. 16 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the fourth example;  
     [0030]FIG. 17 is a drawing that shows a light path of the oblique projection optical system of a fifth example;  
     [0031]FIG. 18 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the fifth example;  
     [0032]FIG. 19 is a drawing that shows a light path of the oblique projection optical system of a sixth example;  
     [0033]FIG. 20 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the sixth example;  
     [0034]FIG. 21 is a drawing that shows a light path of the oblique projection optical system of a seventh example; and  
     [0035]FIG. 22 is a drawing that shows a point spread on the screen surface of the oblique projection optical system of the seventh example. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     [0036] Referring to Figures, the following description will discuss preferred embodiments of the present invention.  
     [0037] &lt;A. Three-dimensional display apparatus&gt; 
     [0038] An explanation will be given of a three-dimensional image display apparatus  100  which is one preferred embodiment of a projection apparatus of the present invention. FIG. 1 is a drawing that schematically shows the appearance of the three-dimensional display apparatus  100 . This three-dimensional image display apparatus  100  is provided with a housing  20  containing an optical system for projecting a cross-sectional image on a screen  38  and a control mechanism for carrying out various kinds of data processing and a cylinder-shaped windshield  20   a  that is installed on the upper side of the housing  20 , and contains a rotating screen therein.  
     [0039] The windshield  20   a  is made of a transparent material such as glass and acrylic resin, and designed so that a cross-sectional image projected on the screen  38  rotating inside thereof is viewed from outside. Moreover, the windshield  20   a  shields the inner space in such a manner that the rotation of the screen  38  is stabilized and the power consumption of the motor used for rotative driving operation is reduced.  
     [0040] On the front face side of the housing  20 , a liquid crystal display (LCD)  21 , an operation switch  22  that is detachably attached thereto and an attaching inlet  23  for a recording medium  4  are placed, and on the side face thereof, a digital input-output terminal  24  is installed. The liquid crystal display  21  is used as a display means for an operation guiding screen used for receiving operational inputs as well as for a two-dimensional image used for an index of a display subject. The digital input-output terminal  24  includes terminals such as an SCSI terminal and an IEEE 1394 . Moreover, speakers  25  used for sound output are placed at four portions on the outer circumferential face of the housing  20 .  
     [0041] Next, an explanation will be given of an optical system for projecting a cross-sectional image on the screen  38  in the three-dimensional display apparatus  100 . FIG. 2 is a drawing that shows a construction including an optical system in the three-dimensional image display apparatus  100 . As illustrated in FIG. 2, this optical system in the three-dimensional image display apparatus  100  is provided with an illuminating optical system  40 , a process and projection optical system  50 , a DMD (digital-micromirror-device)  33 , a TIR prism  44 , a cover glass (not shown) and a color filter  45 . Here, the cover glass is installed on a face of the TIR prism  44  that contacts the color filter  45 , and this is depicted only in an example that will be described later.  
     [0042] First, an explanation will be given of the DMD  33 . The DMD  33  and the color filter  45  function as an image generation means for generating a cross-sectional image to be projected onto the screen  38 , and the DMD  33  has a structure in which minute mirrors, each of which is made of a metal piece (for example, aluminum piece) having a rectangular shape one side of which is approximately 16 μm, and serves as a pixel, are affixed on a plane in a scale having several hundred thousands of pieces per chip, and this device is controlled by an electrostatic field function of the output of SRAMs placed right under the respective pixels so that the tilt angle of each mirror is changed within the range of ±10 degrees. Here, the mirror angle is ON/OFF controlled in a binary manner in response to “1” and “0” of the SRAM output, and upon receipt of light from a light source, only light reflected by those mirrors aligned in the ON (OFF) direction is allowed to proceed toward the process and projection optical system  50 , while light reflected by those mirrors aligned in the OFF (ON) direction is directed out of the effective light path, and is not allowed to reach the process and projection optical system  50 . This ON/OFF control of the mirrors generates a cross-sectional image corresponding to the distribution of ON/OFF mirrors, and this image is projected on the screen  38 .  
     [0043] Here, the tilt angle of each mirror is controlled so as to switch the direction of the reflected light, and by adjusting this switching time (the length of reflection time), it is possible to express the density (gradation) of each pixel, and consequently to express 256 gradations for each color.  
     [0044] The DMD  33  of this type has two major advantages; that is, first it has a high efficiency of use of light, and second, it has a high-speed responsivity. In general, this is applied to a video projector, etc., by utilizing its high efficiency of use of light.  
     [0045] In the present preferred embodiment, by utilizing the other major advantage of the DMD  33 , that is, the high-speed responsivity, it is possible to display even a moving image of a display subject by using a volume scanning method utilizing after-image effects.  
     [0046] Since the responsivity of deflection of each mirror is approximately 10 μsec and since the writing operation for image data is carried out in the same manner as the generally-used SRAM, the DMD  33  makes it possible to provide an image at a very high speed, for example, 1 msec or less. Supposing that the speed is 1 msec, in the case when a volume scanning process of 180° at {fraction (1/18)}second (that is, 9 revolutions per second) is carried out so as to achieve after-image effects, the number of cross-sectional images that can be generated is approximately 60. In comparison with a CRT, a liquid crystal display, etc., that is conventionally used as an image generation means for the volume scanning method, the DMD  33  makes it possible to project much more cross-sectional images on the screen  38  per unit time, and consequently to display not only a three-dimensional object having a non-rotation symmetric shape but also a moving image.  
     [0047] Moreover, the other advantage of the DMD  33 , that is, the high efficiency of use of light, devotes to improve the after-image effects by projecting lighter cross-sectional images on the screen  38 , thereby making it possible to display a three-dimensional image with higher quality as compared with the CRT system, etc.  
     [0048] Here, as illustrated in FIG. 2, on the image generation face side of the DMD  33 , a color filter  45  having divided areas for respective color components is placed, and the DVD  33  generates a plurality of cross-sectional images (projection images) corresponding to the respective color components for the areas. On the image generation face side of the DMD  33 , a TIR prism  44 , which directs illuminated light from the illuminating optical system  40  to the minute mirrors through the color filter  45 , and also directs the plurality of cross-sectional images for the respective color components generated by the DMD  33  to the process and projection optical system  50 , is placed.  
     [0049] The illuminating optical system  40  is provided with a white light source  41  and an illuminating lens system  42 , and illuminating light from the white light source 41 is formed into parallel light rays by the illuminating lens system  42 . The illuminating lens system  42  is constituted by a condenser lens  421 , an integrator  422  and a relay lens  423 . The illuminating light from the white light source  41  is converged by the condenser lens  421 , and made incident on the integrator  422 . Then, the illuminating light, which is allowed to have a uniform distribution in quantity of light by the integrator  422 , is formed into parallel light rays by the relay lens  423 , made incident on the TIR prism  44 , and then directed on the DMD  33  through the color filter  45 .  
     [0050] Based upon two-dimensional image data given by a host computer, etc., not shown, the DMD  33  changes the tilt angle of each minute mirror so that only some light components of the illuminating light required for projecting the cross-sectional images are reflected toward the process and projection optical system  50 .  
     [0051] The process and projection optical system  50  is provided with a process and projection lens system  51  and a screen  38 . This process and projection lens system  51  is provided with an intermediate optical system  511 , oblique projection optical system  513  and projection mirrors  36 ,  37  and an image rotation compensating mechanism  34 . Among these, the oblique projection optical system  513  and the projection mirrors  36 ,  37  constitute a rotation optical system  52 , which is placed inside a rotation member  39  that allows the screen  38  to rotate around a rotary axis Z.  
     [0052] The light (cross-sectional image) reflected by the DMD  33  is formed into parallel light rays by the intermediate optical system  511 , and allowed to pass through the image rotation compensating mechanism  34  so as to be subjected to a rotation compensation for the cross-sectional image. The light rays that have been subjected to the rotation compensation in the image rotation compensating mechanism  34  are allowed to pass through the projection mirror  36 , the oblique projection optical system  513  and the projection mirror  37 , and then finally projected onto a main surface (projection surface) of the screen  38 . Therefore, the process and projection optical system  50  and the DMD  33  constitute a projection image generation element which successively generates a plurality of cross-sectional images based upon two-dimensional image data, and successively projects the cross-sectional images on the screen in synchronism with the rotative scanning of the screen  38 .  
     [0053] In this optical system, the projection mirror  36 , the oblique projection optical system  513 , the projection mirror  37  and the screen  38  are fixed onto the rotation member  39 , and these are rotated around the vertical rotary axis Z including the center axis of the screen  38  at an angular velocity of Ω, as the rotation member  39  rotates. In other words, upon rotating the screen  38  so as to carry out the volume scanning, the projection mirror  36 , the oblique projection optical system  513  and projection mirror  37  placed inside the rotation member  39  are rotated integrally with the screen  38 ; therefore, independent of the angle of the screen  38 , the projection of the cross-sectional images is always carried out from the front side.  
     [0054] Here, the rotation angle of the screen  38  is always detected by a position detector  73 .  
     [0055] Thus, the cross-sectional images, generated by the DMD  33 , are projected on the screen  38 . The function of the oblique projection optical system  513  is to allow the light rays to form an appropriate image size before reaching the screen  38 . Moreover, the projection mirror  37  is placed in such a position that it projects the cross-sectional images onto screen  38  from the position obliquely below on the front side thereof (from the inner side of the rotation member  39  in the case of FIG. 2) so as not to disturb the viewing field of the viewer upon observing the three-dimensional image projected onto the screen  38 . Here, the positional order of the oblique projection optical system  513  with respect to the projection mirrors  36  and  37  is not intended to be limited by the present preferred embodiment.  
     [0056] Here, an explanation will be given of the image rotation compensating mechanism  34 . The image rotation compensating mechanism  34 , shown in FIG. 2, is realized by the structure of a so-called image rotator. When the rotation member  39  to which the screen  38  is attached is located with a certain rotation angle, a cross-sectional image projected on the screen  38  is set as a reference image. Supposing that no image rotation compensating mechanism  34  is used, the cross-sectional images being projected are in-plane rotated on the screen  38  as the rotation member  39  rotates, with the result that a cross-sectional image that is projected when the rotation member  39  has rotated 180° is given as an upside-down reversed image with respect to the reference image. The image rotation compensating mechanism  34  is used to prevent this phenomenon.  
     [0057] The image rotation compensating mechanism  34 , shown in FIG. 2, uses an image rotator constituted by a plurality of mirrors combined therein. When the image rotator is rotated around the light axis, it has such a function that, in response to an incident image, a released image is allowed to rotate with an angular velocity twice as fast as the angular velocity of the image rotator. Therefore, by rotating the image rotor at an angular velocity of ½of that of the rotation member  39  to which the screen  38  is attached, it becomes possible to always project an erecting cross-sectional image independent of the rotation of the screen.  
     [0058] Here, with respect to the image rotation compensating mechanism, besides the image rotator, a Dove (type) prism may be used with the same effects. Moreover, instead of using the image rotation compensating mechanism  34  used here, the cross-sectional image to be generated on the surface of the DMD  33  may be formed as an image rotating around the light axis in accordance with the rotation angle of the screen  38  so that the rotation of the projected image may be cancelled.  
     [0059] In other words, the two-dimensional image data for generating the cross-sectional image may be corrected at a stage before being given to the DMD  33  in such a manner that the resulting cross-sectional image generated on the surface of the DMD  33  is formed as an erecting image (or an inverted image) at the start of the volume scanning, and with the rotation of the screen  38 , it rotates to form an inverted image (or an erecting image) upon completion of the volume scanning.  
     [0060]FIG. 3 is a schematic perspective view that shows one example of the screen  38  and the rotation member  39 . As illustrated in FIG. 3, the rotation member  39  has a disc shape, and the rotary shaft of a motor  74  serving as a rotative driving element is made in contact with the side face thereof so that it is driven to rotate. Here, a motor may be directly connected to the center axis of the rotation member  39 , or this may be driven by an element of gears and belts.  
     [0061] As illustrated in FIG. 3, when the screen  38  is located with a rotation angle θ1, a cross-sectional image P 1  (generated by the DMD  33 ) of the display subject corresponding to θ1 is projected onto the screen  38  through the projection mirror  36 , the oblique projection optical system  513  and the projection mirror  37  shown in FIG. 2. After a lapse of an instantaneous time, the screen  38  is rotated, and when the rotation angle becomes θ2, a cross-sectional image P 2  (generated by the DMD  33 ) of the display subject corresponding to θ2 is projected onto the screen  38  through the projection mirror  36 , the oblique projection optical system  513  and the projection mirror  37  shown in FIG. 2.  
     [0062] The projection mirror  36 , the oblique projection optical system  513  and the projection mirror  37  are commonly rotated with a fixed positional relationship with respect to the screen  38 ; thus, a cross-sectional image is always projected onto the screen  38  independent of the rotation thereof. Here, at the time when the rotation member  39  has been rotated 180° (or 360°), the same cross-sectional image as the starting image appears, thereby completing one volume scanning operation. When the above-mentioned processes are carried out with a sufficiently high speed of the rotation member  39  so as to cause the after-image effect, and when the number of the cross-sectional images to be projected is sufficiently increased, the viewer is allowed to observe a three-dimensional image of the display subject as an envelop of the cross-sectional images.  
     [0063] Next, an explanation will be given of the size (resolution) of the cross-sectional image. FIG. 4 is a drawing that shows a size of the cross-sectional image to be projected onto the screen  38 . The cross-sectional image has a size of 256 pixels (horizontal direction)×256 pixels (vertical direction), and is projected symmetrically with respect to the rotation axis of the screen  38 . In other words, the size consists of 128 pixels on each of the right and left sides in the circumferential direction with the rotation axis located in the center. The cross-sectional image thus projected is commonly rotated with a fixed relationship with respect to the screen  38  so that independent of the rotation of the screen  38 , the size of the projected cross-sectional image is constant. Here, the size of the cross-sectional image shown in FIG. 4 is simply given as one example; and this may be set to a desired size depending on the number of minute mirrors installed on the DMD  33  to be used.  
     [0064] &lt;B. Construction for color display&gt; 
     [0065] An explanation will be given of a construction for carrying out a color display in the present preferred embodiment. A color filter  45  is divided into a plurality of areas so that each of the areas is allowed to transmit any one of color components of, for example, R(red), G(green) and B(blue). The divisions into the three color components of R, G and B make it possible to color-display the cross-sectional images on the screen  38 .  
     [0066] In order to provide a color display, the following methods are proposed: as conventionally used, with respect to illuminating light to be applied to the DMD, R component, G component and B component are generated in a time-divided manner; and three DMDs are prepared and in each of the DMDs, a cross-sectional image corresponding to each of R component, G component and B component is generated. However, in the former method, since three cross-sectional images corresponding to R, G and B are projected so as to form one color cross-sectional image, a display time of three times as long is required. Moreover, in the latter method, the three DMDs are required with the result that the costs become high.  
     [0067] The present preferred embodiment provides a construction in which one DMD  33  is divided into plurality of areas corresponding to R, G and B so that a projection time for one color image can be shortened and a color display is available at low costs.  
     [0068]FIG. 5 shows the structure of a color filter  45  in accordance with the present preferred embodiment. In the present preferred embodiment, the color filter  45  as shown in FIG. 5 is used. As illustrated in FIG. 5, the color filter  45  is divided into three areas, that is, a filter portion  45   a  for transmitting light of R component, a filter portion  45   b  for transmitting light of G component and a filter portion  45   c  for transmitting light of B component. The divisions of the color filter  45  into respective areas corresponding to the number of color components can be easily achieved at low costs. Further, as illustrated in FIG. 5, the color filter  45 , thus divided into the respective areas, is placed on the image generating surface side of the DMD  33 .  
     [0069]FIG. 6 is a drawing that schematically shows the image generating surface of the DMD  33 . By placing the color filter shown in FIG. 5 on the DMD  33 , the image generating surface of the DMD  33  is divided into three areas  33   a ,  33   b  and  33   c . The area  33   a  is an area for receiving light of R component through the color filter  45 , the area  33   b  is an area for receiving light of G component, and the area  33   c  is an area for receiving light of B component. In other words, in the present preferred embodiment, not defining color components for the respective pixels, areas corresponding to respective color components are defined as a two-dimensional continuous array of pixels as shown in FIG. 6.  
     [0070] Then, in the case when, as shown in FIG. 4, a cross-sectional image of 256 pixels×256 pixels is projected onto the screen  38 , as illustrated in FIG. 6, a generation of a cross-sectional image corresponding to each of the color components is carried out on an image generation portion of 256 pixels×256 pixels that is located virtually in the center of each of the areas  33   a ,  33   b  and  33   c  on the DMD  33 . Here, in the case when the DMD  33  is provided with a great number of pixels (the number of minute mirrors), distances between the image generation portion of the area  33   a  and the image generation portion of the area  33   b  as well as between the image generation portion of the area  33   b  and the image generation portion of the area  33   c  are set to be sufficiently wider; therefore, it is possible to easily carry out a job for placing the color filters  45  onto the DMD  33 . In other words, in the case when the image generation portions of the respective areas  33   a  to  33   c  are not adjacent to each other, even when the installation position at the time of placing the color filters  45  is slightly offset, the offset will not cause light of another color component to enter the image generation portion; therefore, it is possible to generate a cross-sectional image of each of the color components without causing any problem.  
     [0071] In other words, in the present preferred embodiment, an image generation element, constituted by the DMD  33  and the color filters  45 , is provided with a plurality of areas that are respectively defined as a two-dimensional continuous array of pixels by dividing an integrally formed pixel array surface, and a plurality of cross-sectional images corresponding to respectively different color components are simultaneously generated at the respective areas; thus, it is possible to generate the cross-sectional images corresponding to the respective color components required for providing colors to a three-dimensional image to be projected onto the screen  38 . Therefore, it becomes possible to carry out a color display by using a simple structure comparatively with ease at low costs. Moreover, in the case when the respective color components are the three color components of R, G and B, since three times as many cross-sectional images as the case for providing a color display in a time-divided manner are projected, it is possible to provide a projected three-dimensional image with high precision. Furthermore, in the case when the color display is carried out in a time divided manner, a driving section, etc., for rotating a rotary color filter is required; in contrast, in the arrangement as described in the present preferred embodiment, the DMD  33  is divided into a plurality of areas, and cross-sectional images corresponding to the respective color components are simultaneously generated at the respective areas. Since this arrangement eliminates the necessity of installing any specific driving section, etc., for carrying out a color display, it becomes possible to miniaturize the construction for carrying out a color display.  
     [0072] Next, an explanation will be given of the intermediate optical system  511 . FIG. 7 is a drawing that shows the intermediate optical system  511  shown in FIG. 2 in detail. In the case when cross-sectional images are generated for the respective components of R, G and B in the different areas as described above, these cross-sectional images need to be composed into one image during a process in which they are projected onto the screen  38 . Through this process, one color image is formed.  
     [0073] For this reason, the intermediate optical system  511  is provided with telecentric optical systems  511   a  on both sides, light path length adjusting devices  511   b ,  511   c , dichroic mirrors  511   d ,  511   e  and mirrors  511   f ,  511   g , and the cross-sectional images corresponding to the respective color components generated in the areas  33   a  to  33   c  of FIG. 6 are composed onto one light path.  
     [0074] Respective light rays (cross-sectional images) of R component, G component and B component, which have been generated on the respective areas of the DMD  33 , are allowed to pass through the TIR prism  44 , and formed into parallel light rays by the telecentric optical systems  511   a  on both sides. Then, the light rays of respective components of R, G and B (cross-sectional images), formed into the parallel light rays, form respectively different three light paths. For example, as illustrated in FIG. 7, the light ray of R component is allowed to pass above the light ray of G component, and the light ray of B component is allowed to pass below the light ray of G component; thus, three parallel light rays are formed.  
     [0075] Then, the light ray of R component, which has been formed into parallel light, is made incident on the light path length adjusting device  511   b , where this is subjected to a compensating process for a light-path difference caused between it and the cross-sectional image of G component, and this is then entirely reflected by the mirror  511   f , and composed by the dichroic mirror  511   d  with the light ray of G component passing through it.  
     [0076] Moreover, the light ray of B component, which has been formed into parallel light, is also made incident on the light path length adjusting device  511   c , where this is subjected to a compensating process for a light-path difference caused between it and the cross-sectional image of G component, and this is then entirely reflected by the mirror  511   g , and composed by the dichroic mirror  511   e  with the light rays of R component and G component.  
     [0077] As illustrated in FIG. 2, the composed light derived from the light rays of the respective color components is projected onto the screen  38  through the image rotation compensating mechanism  34 , the projection mirror  36 , the oblique projection optical system  513  and the projection mirror  37 .  
     [0078] In this manner, even in the case when cross-sectional images corresponding to the respective components of R, G and B are generated in the different areas on the DMD  33 , these cross-sectional images are composed into one image during a process in which they are projected onto the screen  38 ; thus, it is possible to properly project one color-displayed cross-sectional image on the screen  38 .  
     [0079] &lt;C. Oblique Projection Optical System&gt; 
     [0080]FIG. 8 is a drawing that shows the schematic structure of the oblique projection optical system together with the DMD  33  and the screen  38 . Here, in FIG. 8, the detailed lens structures of the respective lens systems are simply given as examples; and they are not necessarily the same as the detailed structures of respective examples which will be described below. Moreover, in FIG. 8, the projection mirror  37  is omitted, and this Figure shows a short conjugate length focal surface FS serving as a conjugate face with the display surface, in which the display surface of the DMD  33  is relayed by the projection mirror  36 , the image rotation compensating mechanism  34 , the intermediate optical system  511 , the TIR prism  44 , etc. Therefore, the following description given with respect to the short conjugate length focal surface FS is also equivalent to the display surface of the DMD  33 .  
     [0081] The oblique projection optical system  513  has an arrangement in which the line optically connecting the center of the short conjugate length focal surface and the center of the long conjugate length focal surface (screen surface) is allowed to have any angle except for vertical with respect to the long conjugate length focal surface, and is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133  that are aligned in this order from the short conjugate length focal surface FS, and each lens system contains a plurality of single lenses. Moreover, the third group lens system  5133  is allowed to face the screen face (long conjugate length focal surface) with a predetermined angle through the projection mirror.  
     [0082] Here, the respective lens systems have the following schematic structures (see FIG. 9, FIG. 11, FIG. 13, FIG. 15, FIG. 17, FIG. 19 and FIG. 21).  
     [0083] The first group lens system  5131 , which contains a beam regulator such as diaphragms, has a telecentric structure.  
     [0084] Moreover, the second group lens system  5132  is set to have a great tilt decentration and a parallel decentration with respect to the first group lens system  5131 . Here, the tilt decentration refers to a state in which the angle made by the main axis of the lens group with respect to the short conjugate length focus surface FS is any angle except for 0°, and the parallel decentration refers to a state in which the principal ray is set to pass through a position other than the main axis of the lens group. More specifically, with respect to the tilt decentration, a decentering angle of not less than 10° is provided. Here, the decentering angle around the X-axis of the second group lens system  5132  with respect to the first group lens system  5131  is preferably set in the range of −20 to 30°.  
     [0085] Furthermore, the third group lens system  5133  is set to have a great tilt decentration and a parallel decentration with respect to the second group lens system  5132 . More specifically, with respect to the tilt decentration, a decentering angle of not less than 10° is provided. Here, the decentering angle around the X-axis of the third group lens system  5133  with respect to the second group lens system  5132  is preferably set in the range of 30 to 40°.  
     [0086] Here, the screen  38  is placed on the rear side of the third group lens system  5133 , and the angle between the normal of the screen  38  and the principal ray in the center of an image is set in the range of 35° to 40°, and even with such an angle, the oblique projection optical system allows the entire surface of the screen to be in focus and reduces the distortion aberration to approximately ±10%. In other words, in order to provide such properties, the first group lens system  5131 , the second group lens system  5132  and the third group lens system  5133  are off-centered from each other as described above.  
     [0087] Here, in conventional devices, the angle between the normal to the screen  38  and the principal ray of the center of an image is less than 35°, and no conventional devices set the angle to not less than 35°. In the respective examples which will be described below, this angle is set in the range of 38° to 40°.  
     [0088] Moreover, the angle between the normal of the display surface of the DMD  33  or the short conjugate length focal surface FS that is a conjugate face in which its surface is relayed by coaxial systems and the principal ray of the center of an image is set to ±1° , which forms a telecentric system.  
     [0089] Moreover, the tilt decentration of the first group lens system  5131  with respect to the short conjugate length focal surface (FS) (equivalent to the display surface) is set within 1° and the parallel decentration in the Y-axis direction is set within 2 mm.  
     [0090] In order to apply oblique projection to the screen  38 , it is necessary to solve problems of out-of-focus and distortion. Although these problems can be solved by making the optical systems partially decentered, it is difficult to process each single lens so as to provide it with decentration.  
     [0091] Therefore, in the present oblique projection optical system, the lens system is divided into three groups of the first group lens system  5131  to the third group lens system  5133 , as described above, and in each lens system, neither single lens nor group lenses are decentered. Instead, the relative positions of the three lens systems are decentered from each other.  
     [0092] With this arrangement, since each single lens has no decentration in each lens system, the processing of each single lens is carried out comparatively with ease, and it is also possible to provide an optical system in which the problems of out-of-focus and distortion have been solved. Moreover, the lens system closest to the display surface is provided as a telecentric optical system so that a diaphragm or a beam regulating plate having the same effect as the diaphragm is installed in the group. Further, as described above, the decentration angle of the first group lens system  5131  with respect to the short conjugate length focal surface FS (display surface) is set within 1° and the amount of offset in the Y-axis direction is set within 2 mm; thus, it is possible to minimize the effective diameter of each lens on the display side.  
     [0093] As described above, in accordance with the present preferred embodiment, the oblique projection optical system  513 , which corrects distortion aberration and/or focal position on the screen surface, is installed so that it is possible to provide a three-dimensional image display apparatus  100  capable of displaying a three-dimensional image with high precision. Moreover, a position from which a basic image is projected to the screen surface, that is, the position of the projection mirror  37 , is set at a position that is allowed to rotate following the screen  38 , and is apart from the screen surface with a predetermined distance, with at least an angle except for vertical with respect to the screen surface; therefore, there are no parts shielding the front side of the screen  38  so that it becomes possible to provide better visibility to the screen  38 .  
     [0094] Moreover, the oblique projection optical system is provided with a plurality of lenses, and among the lenses, the first group lens system  5131 , the second group lens system  5132  and the third group lens system  5133  are relatively decentered from each other; therefore, in comparison with a case in which decentering lenses are used, the systems can be easily manufactured at low costs.  
     [0095] Moreover, the angle between the normal to the screen surface and the principal ray of the center of an image is set to greater than 35° so that it is possible to properly project an image onto the screen  38  that is tilted greatly.  
     [0096] Moreover, in the first group lens system  5131 , the tilt decentration with respect to the short conjugate length focal surface FS (that is, display surface of the DMD  33 ) is set within 1° and the parallel decentration is set within 2 mm; thus, it is possible to minimize the effective diameter of each lens on the display side.  
     [0097] Furthermore, since the first group lens system  5131  includes the beam regulator so that it is possible to easily form a telecentric optical system on the display surface side.  
     [0098] The following description will discuss examples of the oblique projection optical system having the above-mentioned arrangement. Here, not particularly shown in the following examples, in any of the examples, the angle between the normal to the short conjugate length focal surface FS (that is, the display surface of the DMD  33 ) and the principal ray of the center of an image is precisely set to 0°.  
     FIRST EXAMPLE  
     [0099]FIG. 9 is a drawing that shows a light path in oblique projection optical system  513 A in accordance with a first example. As illustrated in FIG. 9, the oblique projection optical system  513 A is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 9  and a beam regulator S, the second group lens system  5132  is provided with lenses L 10  to L 12 , and the third group lens system  5133  is provided with lenses L 13  to L 17 , respectively.  
     [0100] Moreover, FIG. 10 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 A of the first example. In FIG. 10, supposing that a X-Y coordinates system is defined on the screen surface, the point spread is shown at the respective points in the ranges of −1 ≦−≦1 and −1≦Y≦1, more specifically, at the points of (1.00, −1.00), (1.00, 0.00), (1.00, 1.00), (0.50, −1.00), (0.50, 0.00), (0.50, 1.00), (0.00, −1.00), (0.00, 1.00) and (0.00, 0.00). Here, the numeric value indicated below each of the coordinate values is a coordinate value represented in unit of mm with respect to the origin placed in the center on the display surface. Additionally, even the same X-Y coordinate value has a slight difference when given as a coordinate value on the display surface due to distortion. As illustrated in FIG. 10, in the first example, even though it is oblique projection optical system, a superior point spread is obtained on the entire screen surface.  
     [0101] Tables 1 and 2 show data values in the first example. In Tables 1 and 2, figures on the left side show the respective lens faces from the object side in succession. Moreover, it is supposed that the rotation symmetric axis of each lens is the Z-axis, the longitudinal direction within the face vertical to the Z-axis is defined as the Y-axis and the lateral direction is defined as the X-axis. Here, all numeric values related to lengths are given in unit of mm.  
               TABLE 1                          Distance from the short conjugate length focal surface (display surface)       to the first face apex:       Z = 5.949768 Y = 0.845814 X = 0.0       Decentering angle around the X-axis of the first face with respect to the       short conjugate length focal surface (display surface) = −0.096296°                                     Radius of   Face distance   Refractive               curvature   on axix   index   Dispersion                                              1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   38.221200   1.516800   64.1200        4:   ∞   14.084700        5:   75.33759   5.841056   1.704960   52.7453        6:   −53.92407   2.299234        7:   49.54646   7.243995   1.539525   65.4266        8:   −573.56333   4.517894        9:   −46.48155   4.758539   1.803185   30.5527       10:   −108.81608   3.728823       11:   22.05642   5.997375   1.490024   70.0624       12:   −86.86711   0.999821       13:   −83.66036   3.998264   1.784657   32.6803       14:   39.01111   1.823592       15:   37.21683   4.983036   1.779282   32.1370       16:   15.74168   1.071080       17:   16.43048   5.000000   1.506287   68.3665       18:   31.30497   2.671659       Diaphragm:   ∞                  
 
     [0102]               TABLE 2                          Distance from the diaphragm face to the 20 th  face apex:       Z = 12.661336 Y = 4.735755 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect       to the diaphragm face = −33.848039°                                         20:   −47.67927   7.018549   1.487000   70.4000       21:   −43.10056   18.082829       22:   −13.08732   6.680422   1.504232   66.7197       23:   −63.21998   0.100000       24:   100.91450   10.000000   1.599302   61.4142       25:   −603.33898                         Distance from the 25 th  face apex to the 26 th  face apex:       Z = 22.189491 Y = 31.252037 X = 0.0       Decentering angle around X-axis of the 26 th  face with respect       to the 25 th  face = 38.791046°                                         26:   −65.65142   5.779867   1.487000   70.4000       27:   40.76688   8.176854       28:   −15.20945   2.500000   1.487000   70.4000       29:   −113.18171   17.561662       30:   −34.98483   10.000000   1.797822   31.7222       31:   −31.98704   23.353005       32:   −64.25078   8.210612   1.847000   23.8000       33:   −90.92535   18.000000   1.750000   50.0000       34:   −58.40176                         Distance from the 34 th  face apex to the screen surface:       Z = 1040.715312 Y = −100.0307891       Decentering angle around X-axis of the screen surface with respect       to the 34 th  face =−44.534065°       Diaphragm diameter = 4.359293 Angle between normal to screen       surface and principal ray in the center of an image = 40°                    
     [0103] As shown in Table 1 and Table 2, in the first example, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focus surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 A in the first example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0104] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 10. This indicates that the oblique projection optical system  513 A makes it possible to properly correct the focal positions over the entire screen surface.  
     SECOND EXAMPLE  
     [0105]FIG. 11 is a drawing that shows a light path in oblique projection optical system  513 B in accordance with a second example. As illustrated in FIG. 11, the oblique projection optical system  513 B is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 9  and a beam regulator S, the second group lens system  5132  is provided with lenses L 10  to L 12 , and the third group lens system  5133  is provided with lenses L 13  to L 17 , respectively.  
     [0106] Moreover, FIG. 12 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 B of the second example. In FIG. 12 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in the Figures, in the second example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0107] Tables 3 and 4 show data values in the second example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 3                          Distance from the short conjugate length focal surface (display surface)       to the first face apex:       Z = 5.949768 Y = −1.308371 X = 0.0       Decentering angle around the X-axis of the first face with respect to the       short conjugate length focal surface (display surface) = −0.583514°                                     Radius of   Face distance   Refractive               curvature   on axix   index   Dispersion                                              1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   38.221200   1.516800   64.1200        4:   ∞   14.084700        5:   73.85458   4.830500   1.705397   49.5496        6:   −54.04729   1.073698        7:   56.47422   5.956284   1.539670   65.4151        8:   −286.53392   4.440318        9:   −45.53007   2.000000   1.791655   33.2054       10:   −95.87581   3.769121       11:   22.26876   5.822063   1.490909   69.9650       12:   −89.96370   1.009653       13:   −90.30883   3.778571   1.780552   31.6632       14:   37.03083   0.945371       15:   35.71668   4.994815   1.767475   30.5619       16:   15.99770   1.103573       17:   17.12999   4.482808   1.516997   67.3489       18:   33.93408   1.500000       Diaphragm:   ∞                  
 
     [0108]               TABLE 4                          Distance from the diaphragm face to the 20 th  face apex:       Z = 12.733428 Y = 5.608071 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect       to the diaphragm face = −32.586912°                                         20:   −39.93170   3.652252   1.487000   70.4000       21:   −38.95472   22.956336       22:   −13.09838   4.000000   1.487000   70.4000       23:   −75.89404   5.648772       24:   89.53553   6.376519   1.487000   70.4000       25:   −407.51200                         Distance from the 25 th  face apex to the 26 th  face apex:       Z = 22.263321 Y = 33.694665 X = 0.0       Decentering angle around X-axis of the 26 th  face with respect       to the 25 th  face = 34.502529°                                         26:   −97.92713   2.000000   1.827195   24.3214       27:   84.31410   4.577575       28:   −27.70310   2.500000   1.487000   70.4000       29:   481.59087   7.515467       30:   −20.81969   6.000000   1.487000   70.4000       31:   −41.68266   45.331090       32:   −67.88034   12.000000   1.798199   31.6367       33:   −56.93636   0.100000       34:   481.86477   13.557868   1.750000   50.0000       35:   −364.60557                         Distance from the 35 th  face apex to the screen surface:       Z = 1056.711449 Y = −97.185953 X = 0.0       Decentering angle around X-axis of the screen surface with respect       to the 35 th  face =−44.165138°       Diaphragm diameter = 4.821992 Angle between normal to screen       surface and principal ray in the center of an image = 40°                    
     [0109] As shown in Table 3 and Table 4, in the second example, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 B in the second example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0110] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 12. This indicates that the oblique projection optical system  513 B makes it possible to properly correct the focal positions over the entire screen surface.  
     THIRD EXAMPLE  
     [0111]FIG. 13 is a drawing that shows a light path in oblique projection optical system  513 C in accordance with a third example. As illustrated in FIG. 13, the oblique projection optical system  513 C is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 9  and a beam regulator S, the second group lens system  5132  is provided with lenses L 10  to L 12 , and the third group lens system  5133  is provided with lenses L 13  to L 17 , respectively.  
     [0112] Moreover, FIG. 14 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 C of the third example. In FIG. 14 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in the Figures, in the third example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0113] Tables 5 and 6 show data values in the third example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 5                          Distance from the short conjugate length focal surface (display surface)       to the first face apex:       Z = 5.949768 Y = −1.122473 X = 0.0       Decentering angle around the X-axis of the first face with respect to the       short conjugate length focal surface (display surface) = −0.567467°                                     Radius of   Face distance   Refractive               curvature   on axix   index   Dispersion                                              1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   38.221200   1.516800   64.1200        4:   ∞   14.084700        5:   74.28003   4.733831   1.707388   51.3674        6:   −53.86271   1.203080        7:   56.93716   5.938692   1.543403   65.1222        8:   −318.59371   4.983707        9:   −46.52361   2.000000   1.778859   35.1952       10:   −92.19303   4.079296       11:   22.50276   5.874315   1.493659   69.6662       12:   −96.92982   0.029414       13:   −96.92982   2.538293   1.773389   32.8665       14:   44.84663   2.012741       15:   40.15791   2.542965   1.754062   32.1014       16:   16.02325   2.075011       17:   16.39374   4.545680   1.530933   66.1275       18:   29.87854   2.000000       Diaphragm:   ∞                  
 
     [0114]               TABLE 6                          Distance from the diaphragm face to the 20 th  face apex:       Z = 14.58785 Y = 6.781019 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect       to the diaphragm face = −32.351118°                                         20:   −47.26686   4.070155   1.487000   70.4000       21:   −46.04827   25.767757       22:   −13.90173   4.000000   1.487000   70.4000       23:   −77.45419   6.844086       24:   108.99735   10.000000   1.487000   70.4000       25:   −270.24506                         Distance from the 25 th  face apex to the 26 th  face apex:       Z = 29.323286 Y = 41.451338 X = 0.0       Decentering angle around X-axis of the 26 th  face with respect       to the 25 th  face = 34.092103°                                         26:   −57.86728   1.700000   1.184700   23.8000       27:   82.82463   5.589318       28:   −23.16223   2.500000   1.487000   70.4000       29:   −86.04849   13.764594       30:   −28.01500   8.000000   1.487000   70.4000       31:   −47.75515   33.928089       32:   −85.78069   15.000000   1.792574   32.9741       33:   −63.09082   0.100000       34:   432.62289   13.000000   1.750000   50.0000       35:   −533.52771   0.000000       36:   ∞                         Distance from the 35 th  face apex to the screen surface:       Z = 1082.747374 Y = −89.8748672 X = 0.0       Decentering angle around X-axis of the screen surface with respect       to the 35 th  face =−43.722341°       Diaphragm diameter = 5.273248 Angle between normal to screen       surface and principal ray in the center of an image = 40°                    
     [0115] As shown in Table 5 and Table 6, in the third example also, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 C in the third example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0116] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 14. This indicates that the oblique projection optical system  513 C makes it possible to properly correct the focal positions over the entire screen surface.  
     FOURTH EXAMPLE  
     [0117]FIG. 15 is a drawing that shows a light path in oblique projection optical system  513 D in accordance with a fourth example. As illustrated in FIG. 15, the oblique projection optical system  513 D is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 9  and a beam regulator S, the second group lens system  5132  is provided with lenses L 10  to L 12 , and the third group lens system  5133  is provided with lenses L 13  to L 17 , respectively.  
     [0118] Moreover, FIG. 16 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 D of the fourth example. In FIG. 16 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in FIG. 16, in the fourth example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0119] Tables 7 and 8 show data values in the fourth example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 7                          Distance from the short conjugate length focal surface (display surface)       to the first face apex:       Z = 5.949768 Y = 0.067101 X = 0.0       Decentering angle around the X-axis of the first face with respect to the       short conjugate length focal surface (display surface) = −0.996571°                                     Radius of   Face distance   Refractive               curvature   on axix   index   Dispersion                                              1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   38.221200   1.516800   64.1200        4:   ∞   14.084700        5:   113.94575   4.333024   1.703335   52.8569        6:   −43.15745   6.012567        7:   81.82446   6.000000   1.536051   65.7055        8:   −69.75852   3.108973        9:   −34.86769   2.000000   1.775946   33.6764       10:   −84.20953   3.690402       11:   23.46113   5.272109   1.490450   70.0154       12:   −87.07677   0.473583       13:   −106.13471   3.589513   1.767016   35.6746       14:   37.45404   1.063644       15:   39.34728   4.889980   1.742340   40.5256       16:   17.40803   1.633282       17:   15.70858   4.853463   1.543687   65.1001       18:   30.07761   1.500000       Diaphragm:   ∞                  
 
     [0120]               TABLE 8                          Distance from the diaphragm face to the 20 th  face apex:       Z = 13.628212 Y = 8.834915 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect       to the diaphragm face = −36.654220°                                         20:   −1000.00000   8.000000   1.651849   32.5172       21:   −1000.00000   22.205981       22:   −11.91452   4.000000   1.517232   67.3273       23:   −93.76220   0.100000       24:   485.28331   11.000000   1.628354   59.3620       25:   −38.14977                         Distance from the 25 th  face apex to the 26 th  face apex:       Z = 16.967477 Y = 29.343573 X = 0.0       Decentering angle around X-axis of the 26 th  face with respect       to the 25 th  face = 42.461399°                                         26:   893.04084   2.000000   1.847000   23.8000       27:   30.62958   13.704967       28:   −30.93346   2.500000   1.847000   23.8000       29:   −107.16827   14.220811       30:   −23.09491   2.500000   1.750000   50.0000       31:   −37.42524   30.556222       32:   −82.24677   15.000000   1.844639   24.0726       33:   −58.67561   0.100000       34:   536.01143   13.000000   1.727982   51.2631       35:   −375.20273                         Distance from the 35 th  face apex to the screen surface:       Z = 1024.755636 Y = −146.8563819 X = 0.0       Decentering angle around X-axis of the screen surface with respect       to the 35 th  face =−46.300866°       Diaphragm diameter = 5.319092 Angle between normal to screen       surface and principal ray in the center of an image = 40°                    
     [0121] As shown in Table 7 and Table 8, in the fourth example also, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 D in the fourth example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0122] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 16. This indicates that the oblique projection optical system  513 D makes it possible to properly correct the focal positions over the entire screen surface.  
     FIFTH EXAMPLE  
     [0123]FIG. 17 is a drawing that shows a light path in oblique projection optical system  513 E in accordance with a fifth example. As illustrated in FIG. 17, the oblique projection optical system  513 E is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 10  and a beam regulator S, the second group lens system  5132  is provided with lenses L 11  to L 14 , and the third group lens system  5133  is provided with lenses L 15  to L 19 , respectively.  
     [0124] Moreover, FIG. 18 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 E of the fifth example. In FIG. 18 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in FIG. 18, in the fifth example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0125] Tables 9 and 10 show data values in the fifth example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 9                          Distance from the short conjugate length focal surface (display surface)       to the first face apex:       Z = 6.000000 Y = 0.529822 X = 0.0       Decentering angle around the X-axis of the first face with respect to the       short conjugate length focal surface (display surface) = −0.35390°                                     Radius of   Face distance   Refractive               curvature   on axix   index   Dispersion                                              1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   25.541600   1.516800   64.1200        4:   ∞   15.373600   1.846660   23.8200        5:   ∞   14.084700        6:   113.44442   3.374433   1.708209   52.5250        7:   −42.34061   0.100000        8:   79.21774   5.907913   1.541902   65.2392        9:   −56.49506   2.592473       10:   −39.72059   2.169390   1.762688   35.0879       11:   −292.89048   0.100000       12:   23.65028   5.051883   1.496005   69.4159       13:   −82.53851   2.499901   1.754040   37.4847       14:   50.69722   2.533144       15:   50.96294   2.490963   1.720437   44.4215       16:   19.29961   2.544468       17:   18.85957   4.990256   1.568492   42.4005       18:   42.34971   1.500000       Diaphragm:   ∞                  
 
     [0126]               TABLE 10                          Distance from the diaphragm face to the 20 th  face apex:       Z = 12.327426 Y = 7.839569 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect       to the diaphragm face = −29.213854°                                         20:   ∞   8.000000   1.847000   23.8000       21:   ∞   25.247334       22:   −14.07095   4.000000   1.487000   70.4000       23:   261.55184   2.229494       24:   205.64301   9.000000   1.487000   70.4000       25:   −51.55262   6.770506       26:   125.44677   9.000000   1.487000   70.4000       27:   −449.47255   24.421910                         Distance from the 27 th  face apex to the 28 th  face apex:       Z = 24.421910 Y = 37.630668 X = 0.0       Decentering angle around X-axis of the 27 th  face with respect       to the 25 th  face = 33.262617°                                         28:   −705.15080   2.000000   1.847000   23.8000       29:   47.33251   42.266891       30:   −41.63109   2.500000   1.750000   50.0000       31:   −1549.46272   14.208903       32:   −27.97234   3.300000   1.738271   50.6556       33:   −45.64841   6.083346       34:   −71.57645   15.000000   1.820990   27.3047       35:   −48.40633   0.100000       36:   496.73527   13.000000   1.750000   50.0000       37:   −273.21549                         Distance from the 37 th  face apex to the screen surface:       Z = 968.6672109 Y = −140.3129543 X = 0.0       Decentering angle around X-axis of the screen surface with respect       to the 37 th  face =−47.041713°       Flat plate for protecting screen:       Thickness = 6.00 Refractive index = 1.49140 Dispersion = 57.82       Diaphragm diameter = 3.880331 Angle between normal to screen       surface and principal ray in the center of an image = 40°                    
     [0127] As shown in Table 9 and Table 10, in the fifth example also, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 E in the fifth example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0128] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 18. This indicates that the oblique projection optical system  513 E makes it possible to properly correct the focal positions over the entire screen surface.  
     SIXTH EXAMPLE  
     [0129]FIG. 19 is a drawing that shows a light path in oblique projection optical system  513 F in accordance with a sixth example. As illustrated in FIG. 19, the oblique projection optical system  513 F is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 10  and a beam regulator S, the second group lens system  5132  is provided with lenses L 11  to L 14 , and the third group lens system  5133  is provided with lenses L 15  to L 19 , respectively.  
     [0130] Moreover, FIG. 20 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 F of the sixth example. In FIG. 20 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined, in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in FIG. 20, in the sixth example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0131] Tables 11 and 12 show data values in the sixth example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 11                          Distance from the short conjugate length focal surface (display surface) to       the first face apex:       Z = 6.000000 Y = 0.729656 X = 0.0       Decentering angle around the X-axis of the first face with respect to       the short conjugate length focal surface (display surface) = 0.021305°                                     Radius of   Face distance   Refractive               curvature   on axis   index   Dispersion                                          1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   25.541600   1.516800   64.1200        4:   ∞   15.373600   1.846660   23.8200        5:   ∞   14.084700        6:   98.03684   3.368332   1.713000   53.9300        7:   −43.12470   0.140716        8:   101.01689   4.489869   1.563840   60.8300        9:   −53.68387   2.369961       10:   −38.43325   2.989132   1.806100   32.2700       11:   −161.15564   0.636991       12:   24.17058   4.495610   1.487490   70.4400       13:   −94.42883   2.452344   1.775510   37.9000       14:   56.30284   2.011187       15:   52.40108   2.451651   1.744000   44.9300       16:   19.61209   2.319062       17:   19.12781   3.931340   1.581440   40.8900       18:   41.63622   1.602280       Diaphragm:   ∞                  
 
     [0132]               TABLE 12                          Distance from the diaphragm face to the 20 th  face apex:       Z = 13.974411 Y = 8.17488 X = 0.0       Decentering angle around X-axis of the 20 th  face with       respect to the diaphragm face = −27.809781°                                 20:   ∞   8.000000   1.846660   23.8200       21:   ∞   27.032571       22:   −14.69214   4.000000   1.487490   70.4400       23:   175.70622   2.269175       24:   161.59147   9.000000   1.487490   70.4400       25:   −53.89157   6.730825       26:   106.50594   9.000000   1.487490   70.4400       27:   −999.99490                 Distance from the 27 th  face apex to the 28 th  face apex:       Z = 26.524091 Y = 36.734257 X = 0.0       Decentering angle around X-axis of the 28 th  face with respect to the       27 th  face = 32.670877°                                         28:   −171.79506   2.000000   1.846660   23.8200       29:   50.39937   37.232271       30:   −43.14722   2.500000   1.772500   49.7700       31:   −7294.92020   12.891325       32:   −26.48702   3.300000   1.620410   60.3400       33:   −51.14594   5.683093       34:   −86.94265   15.000000   1.805180   25.4300       35:   −49.70172   85.393311       36:   839.19597   20.000000   1.775510   37.9000       37:   −623.71943                 Distance from the 37 th  face apex to the screen surface:       Z = 728.7220047 Y = −59.9869675 X = 0.0       Decentering angle around X-axis of the screen surface with       respect to the 37 th  face = 46.750441°       Flat plate for protecting screen: Thickness = 6.00       Refractive index = 1.49140 Dispersion = 57.82       Diaphragm diameter = 5.113682 Angle between normal to screen surface       and principal ray in the center of an image = 40°                    
     [0133] As shown in Table 11 and Table 12, in the sixth example also, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 40°. In this manner, the oblique projection optical system  513 F in the sixth example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0134] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 40°, a superior point spread is obtained on the entire screen surface as shown in FIG. 20. This indicates that the oblique projection optical system  513 F makes it possible to properly correct the focal positions over the entire screen surface.  
     SEVENTH EXAMPLE  
     [0135]FIG. 21 is a drawing that shows a light path in oblique projection optical system  513 G in accordance with a seventh example. As illustrated in FIG. 21, the oblique projection optical system  513 G is provided with a first group lens system  5131 , a second group lens system  5132  and a third group lens system  5133 ; and the first group lens system  5131  is provided with lenses L 1  to L 10  and a beam regulator S, the second group lens system  5132  is provided with lenses L 11  to L 14 , and the third group lens system  5133  is provided with lenses L 15  to L 19 , respectively.  
     [0136] Moreover, FIG. 22 is a drawing that shows a point spread on the screen surface in the case of the oblique projection optical system  513 G of the seventh example. In FIG. 22 also, the X-Y coordinates system on the screen surface is defined and the coordinate system on the display surface is defined, in the same manner as FIG. 10, and the point spread is shown at the respective coordinate points. As shown in FIG. 22, in the seventh example also, although it is oblique projection optical system, a superior point spread is obtained over the entire screen face.  
     [0137] Tables 13 and 14 show data values in the seventh example. The respective numeric values in these Tables and the X-axis, Y-axis and Z-axis are defined in the same manner as the first example.  
               TABLE 13                          Distance from the short conjugate length focal surface (display       surface) to the first face apex:       Z = 6.097202 Y = 0.616367 X = 0.0       Decentering angle around the X-axis of the first face with respect to       the short conjugate length focal surface (display surface) = 0.0°                                     Radius of   Face distance   Refractive               curvature   on axis   index   Dispersion                                          1:   ∞   6.528000   1.516800   64.1200        2:   ∞   9.680300        3:   ∞   25.541600   1.516800   64.1200        4:   ∞   15.373600   1.846660   23.8200        5:   ∞   14.084700        6:   140.87200   3.400000   1.713000   53.9300        7:   −37.16100   1.180000        8:   224.03000   3.200000   1.563840   60.8300        9:   −40.78400   1.470000       10:   −32.42700   2.400000   1.806100   33.2700       11:   −96.11900   0.390000       12:   24.71100   4.400000   1.487490   70.4400       13:   −84.34100   2.500000   1.775510   37.9000       14:   54.74900   2.440000       15:   52.28800   2.500000   1.754500   51.5700       16:   20.45000   3.280000       17:   19.55200   4.300000   1.581440   40.8700       18:   44.09800   3.770000       Diaphragm:   ∞                  
 
     [0138]               TABLE 14                          Distance from the diaphragm face to the 20 th  face apex:       Z = 14.330000 Y = 8.841067 X = 0.0       Decentering angle around X-axis of the 20 th  face with respect to the       diaphragm face = 27.00°                                 20:   ∞   8.000000   1.688930   31.1600       21:   ∞   28.880000       22:   −15.30000   4.000000   1.487490   70.4400       23:   136.41200   2.300000       24:   126.42900   9.000000   1.487490   70.4400       25:   −55.76000   6.650000       26:   88.90300   9.000000   1.487490   70.4400       27:   3050.00000                 Distance from the 27 th  face apex to the 28 th  face apex:       Z = 27.600000 Y = 34.746295 X = 0.0       Decentering angle around X-axis of the 28 th  face with respect to the       27 th  face = 32.126851°                                         28:   −148.15900   2.000000   1.846660   23.8200       29:   35.32500   22.090000       30:   −28.75200   2.630000   1.772500   49.7700       31:   −57.90100   7.070000       32:   −24.51200   3.900000   1.772500   49.7700       33:   −37.46100   67.400000       34:   −98.98400   16.500000   1.846660   23.8200       35:   −82.50000   0.100000       36:   576.64500   19.700000   1.584000   31.0000       37:   −576.64500                 Distance from the 37 th  face apex to the screen surface:       Z = 670.117137 Y = −34.895616 X = 0.0       Decentering angle around X-axis of the screen surface with respect       to the 37 th  face = −42.906623°       Flat plate for protecting screen: Thickness = 6.00       Refractive index = 1.49140 Dispersion = 57.82       Diaphragm diameter = 5.2511605 Angle between normal to screen       surface and principal ray in the center of an image = 38.5°                    
     [0139] As shown in Table 13 and Table 14, in the seventh example also, the second group lens system  5132  has a great tilt decentration to the first group lens system  5131 , and the third group lens system  5133  also has a great tilt decentration to the second group lens system  5132 . Moreover, the decentering angle of the tilt decentration around the X-axis of the first group lens system  5131  is set within ±1° with respect to the short conjugate length focal surface FS (display surface), and the angle between the normal to the screen surface and the principal ray in the center of an image is set to 38.5°. In this manner, the oblique projection optical system  513 G in the seventh example satisfies the aforementioned conditions in the present preferred embodiment.  
     [0140] Moreover, although the angle between the normal to the screen surface and the principal ray in the center of an image has a tilt angle of 38.5°, a superior point spread is obtained on the entire screen surface as shown in FIG. 22. This indicates that the oblique projection optical system  513 G makes it possible to properly correct the focal positions over the entire screen surface.  
     [0141] &lt;D. Modified Example&gt; 
     [0142] In the above-mentioned preferred embodiment, examples of the projection apparatus and oblique projection optical system have been given; however, the present invention is not limited by these.  
     [0143] For example, in the above-mentioned preferred embodiment, the oblique projection optical system is placed between the projection mirror  36  and the projection mirror  37 ; however, this may be placed at any proper place between the DMD  33  and the screen  38 , for example, between the projection mirror  37  and the screen  38 .  
     [0144] Moreover, in the above-mentioned preferred embodiment, the first group lens system  5131  is provided with the beam regulator S; however, a diaphragm having a variable aperture diameter may be installed.  
     [0145] Furthermore, in the above-mentioned preferred embodiment, the distortion aberration and focal position on the screen surface are corrected by the oblique projection optical system; however, the oblique projection optical system may be arranged as an optical system that has functions for correcting only either the distortion aberration or the focal position.  
     [0146] While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous other modifications and variations can be devised without departing from the scope of the invention.