Patent Publication Number: US-10761415-B2

Title: Projection optical system and projector apparatus

Description:
CROSS-REFERENCES 
     This application is a divisional of U.S. application Ser. No. 14/400,820, filed Nov. 13, 2014, which is a 371 National Stage of PCT/JP2013/007653, filed Dec. 26, 2013, which applications are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a projection optical system of a projector apparatus. 
     BACKGROUND ART 
     Japanese Laid-Open Patent Publication No. 2004-258620 (hereinafter “Document 1”) discloses the realization of a projection optical system which, in addition to using an image forming optical system including a reflective surface to increase the size on the screen of projected images while reducing the projection space outside a projector apparatus, is capable of correcting chromatic aberration and also an image projecting apparatus that uses such projection optical system. To do so, Document 1 discloses that a first and second optical system are disposed in that order from a light valve on the projection side of the light valve, the first optical system includes at least one refractive optical system and has positive refractive power, the second optical system includes at least one reflective surface with refractive power and has positive refractive power, an image formed by the light valve is formed into an intermediate image on the light path of the first and second optical systems, and the intermediate image is enlarged further and projected onto a screen. 
     DISCLOSURE OF THE INVENTION 
     In a variety of applications such as presentations and schools and education, there is demand for a projection lens system that projects images that are sharp and wide angle. 
     A first aspect of the present invention is a projection optical system that projects from a first image plane on a reducing side onto a second image plane on an enlargement side. The projection optical system includes: a first refractive optical system that forms a first intermediate image on the enlargement side using light incident from the reducing side; a second refractive optical system that forms the first image on the reducing side into a second intermediate image on the enlargement side; and a first reflective optical system including a first reflective surface with positive refractive power that is positioned on the enlargement side of the second intermediate image, wherein the second refractive optical system includes a first focus lens group that moves when focusing is carried out, and the first focus lens group includes at least one lens included in the second refractive optical system. 
     In this projection optical system, the first refractive optical system forms a first intermediate image, the second refractive optical system forms the first intermediate image into a second intermediate image on the enlargement side, and the second intermediate image is enlarged and reflected by the first reflected surface. It is not easy to provide a system with a design where the aberration produced when the second intermediate image is enlarged and reflected is corrected at the first reflective surface. But, in this projection optical system, the second refractive optical system can form the second intermediate image so as to curvature of field and the like produced by the first reflective surface are corrected, and the first refractive optical system can form a first intermediate image in which coma aberration and the like produced by the second refractive optical system are corrected. Accordingly, it is easy to project sharp enlarged images. In addition, in this projection optical system, when carrying out focusing, a first focus lens group including at least one lens out of the second refractive optical system is moved. By this focus lens group, it is easy to form a second intermediate image where fluctuations in aberration that accompany changes in the projection distance and the like are corrected and easy to suppress fluctuations in the image formation performance for the projected images. 
     With a projection optical system that is wide-angle and has a short focal length, it is easy to produce a deep depth of field and a deep depth of focus. For this reason, although it is easy to suppress fluctuations in focus near the center of the projected images that accompany changes in the optical distance (projection distance) between the first reflective surface and the second image plane, there is also a tendency for fluctuations in curvature of field to increase in the periphery of the projected images. Accordingly, it is desirable for the first focus lens group to include a first distance correcting lens group that moves when focusing is carried out in response to changes in an optical distance between the first reflective surface and the second image plane. It becomes easy to project sharp enlarged images in which fluctuations in curvature of field that accompany changes in the projection distance are corrected. 
     It is easy to separate image flux for each image angle in the vicinity of the image formation position of the first intermediate image. For this reason, it is desirable for the first distance correcting lens group to include a first lens that is positioned closest to a reducing side of the second refractive optical system. When carrying out focusing, by moving the first lens that is closest to the first intermediate image, it is possible to carry out fine adjustment of focus while suppressing fluctuations in aberration that accompany focusing. Accordingly, it is easy to project sharp, enlarged images in which focus fluctuations that accompany changes in the projection distance are more thoroughly suppressed. 
     It is desirable for the first focus lens group to include a first temperature correcting lens group that moves when focusing is carried out in response to changes in the peripheral temperature of the projection optical system. More sharp enlarged images is projected in which fluctuations in focus due to changes in the refractive indices of lenses that accompany changes in the temperature of the periphery of the projection optical system are corrected. 
     It is desirable for the first refractive optical system to include a second focus lens group that moves when focusing is carried out, and for the second focus lens group to include at least one lens included in the first refractive optical system. When carrying out focusing, by moving the second focus lens group that includes at least one lens out of the first refractive optical system, it is possible to reduce the movement distance of the first focus lens group. This means that it is possible to suppress interference between the first focus lens group and the first intermediate image and possible to carry out focusing by hardly moving the image formation position of the first intermediate image. Accordingly, it is possible to provide a compact projection optical system where it is easy to suppress fluctuations in the image formation performance for projected images. 
     It is desirable for the second focus lens group to include a second distance correcting lens group that moves when focusing is carried out in response to changes in an optical distance between the first reflective surface and the second image plane. It is easy to project a sharp enlarged image where fluctuations in focus that accompany changes in the projection distance over a wide range are suppressed. It is desirable for the second focus lens group to include a second temperature correcting lens group that moves when focusing is carried out in response to changes in the peripheral temperature of the projection optical system. 
     It is desirable for the first reflective surface to not move when focusing is carried out in response to changes in the optical distance between the first reflective surface and the second image plane. By not moving the first reflective surface in response to changes in the projection distance, it is possible to carry out focusing without changing the optical distance between the first image plane and the first reflective surface. This means that it is possible to reduce the influence (tolerance sensitivity) that the mounting tolerance of the first reflective surface has on the image formation performance for the projected images. 
     It is desirable for the first refractive optical system to include a negative lens of meniscus type (negative meniscus lens) whose convex surface is oriented toward the enlargement side, and for the second refractive optical system to include a positive lens of meniscus type (positive meniscus lens) that is positioned closest to a reducing side of the second refractive optical system and whose convex surface is oriented toward the reducing side. By sandwiching the first intermediate image between a convex surface of the negative lens positioned on the reducing side of the first intermediate image and a convex surface of the positive lens positioned on the enlargement side of the first intermediate image, it is possible to suppress the generation of coma aberration and spherical aberration. It is desirable for the negative lens to be position closest to the enlargement side of the first refractive optical system. It is easy to separate image flux for each image angle in the vicinity of the image formation position of the first intermediate image. In addition, by making the convex surface of the negative lens and the convex surface of the positive lens aspherical, it is possible to also effectively correct off-axis aberration including curvature of field, astigmatism, distortion and the like. 
     In this projection optical system, it is desirable for a Petzval sum PTZ 1  of the first refractive optical system, a third-order aberration coefficient DST 1  of distortion of the first refractive optical system, a third-order aberration coefficient TCO 1  of coma aberration of the first refractive optical system, a Petzval sum PTZ 2  of the second refractive optical system, a third-order aberration coefficient DST 2  of distortion of the second refractive optical system, and a third-order aberration coefficient TCO 2  of coma aberration of the second refractive optical system to satisfy Conditions (1) to (3) below.
 
|PTZ1|&lt;|PTZ2|  (1)
 
|DST1|&lt;|DST2|  (2)
 
−0.5&lt;|TCO1|−|TCO2|&lt;0.5  (3)
 
     In this projection optical system, according to Condition (1), the second refractive optical system has a larger correction effect for curvature of field than the first refractive optical system, according to Condition (2), the second refractive optical system has a larger correction effect for distortion than the first refractive optical system, and according to Condition (3), the correction effect for coma aberration is substantially equal for the first refractive optical system and the second refractive optical system. This means that it is possible to reduce the correction load of the second refractive optical system. Accordingly, it is possible to simplify the configuration of the second refractive optical system and to make the second refractive optical system compact. 
     In addition, it is desirable for a curvature of field FC 1  of the first intermediate image and a curvature of field FC 2  of the second intermediate image to satisfy Conditions (4) and (5) below.
 
0&lt;FC1×FC2  (4)
 
0.03&lt;|FC1|  (5)
 
     In this projection optical system, it is desirable for principal ray emitted from the first intermediate image to be oriented toward an optical axis of the second refractive optical system. 
     Another aspect of the present invention is a projector apparatus including: the projection optical system described above; and a light modulator that forms an image at the first image plane. 
     Yet another aspect of the present invention is a projector system including: a projection optical system that projects from a first image plane on a reducing side to a second image plane on an enlargement side; and a focusing mechanism that carries out focusing of the projection optical system. The projection optical system of the projector system includes: a first refractive optical system that forms a first intermediate image on the enlargement side using light incident from the reducing side; a second refractive optical system that forms the first image on the reducing side into a second intermediate image on the enlargement side; and a first reflective optical system including a first reflective surface with positive refractive power that is positioned on the enlargement side of the second intermediate image, and the focusing mechanism includes a mechanism that moves at least one lens included in the second refractive optical system. 
     Yet another aspect of the present invention is a method of carrying out focusing of a projection optical system that projects from a first image plane on a reducing side to a second image plane on an enlargement side. The projection optical system includes: a first refractive optical system that forms a first intermediate image on the enlargement side using light incident from the reducing side; a second refractive optical system that forms the first image on the reducing side into a second intermediate image on the enlargement side; and a first reflective optical system including a first reflective surface with positive refractive power that is positioned on the enlargement side of the second intermediate image, and the method includes moving at least one lens included in the second refractive optical system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing the overall configuration of a projector apparatus that uses a projection optical system according to the present invention. 
         FIG. 2  is a diagram showing the overall configuration of the projection optical system according to a first embodiment. 
         FIG. 3  is a light ray diagram of the projection optical system according to the first embodiment. 
         FIG. 4  is a diagram showing lens data of the projection optical system according to the first embodiment. 
         FIG. 5  is a diagram showing various values of the projection optical system according to the first embodiment, with ( a ) showing the distances between lenses at the first and the second projection positions, ( b ) showing fundamental data, and ( c ) showing aspherical surface data. 
         FIG. 6  is a coma aberration graph at the first projection position of the projection optical system according to the first embodiment. 
         FIG. 7  is a coma aberration graph at the second projection position of the projection optical system according to the first embodiment. 
         FIG. 8  is a distortion graph at the first projection position of the projection optical system according to the first embodiment. 
         FIG. 9  is a distortion graph at the second projection position of the projection optical system according to the first embodiment. 
         FIG. 10  is a diagram showing the overall configuration of a projection optical system according to a second embodiment. 
         FIG. 11  is a light ray diagram of the projection optical system according to the second embodiment. 
         FIG. 12  is a diagram showing lens data of the projection optical system according to the second embodiment. 
         FIG. 13  is a diagram showing various values of the projection optical system according to the second embodiment, with ( a ) showing the distances between lenses at the first and the second projection positions, ( b ) showing fundamental data, and ( c ) showing aspherical surface data. 
         FIG. 14  is a coma aberration graph at the first projection position of the projection optical system according to the second embodiment. 
         FIG. 15  is a coma aberration graph at the second projection position of the projection optical system according to the second embodiment. 
         FIG. 16  is a distortion graph at the first projection position of the projection optical system according to the second embodiment. 
         FIG. 17  is a distortion graph at the second projection position of the projection optical system according to the second embodiment. 
         FIG. 18  is a light ray diagram of a projection optical system according to a third embodiment. 
         FIG. 19  is a light ray diagram of a projection optical system according to a fourth embodiment. 
         FIG. 20  is a light ray diagram of a projection optical system according to a fifth embodiment. 
     
    
    
     DETAIL DESCRIPTION 
       FIG. 1  shows the overall configuration of a projector apparatus that uses a projection optical system according to the present invention. A projector (projector apparatus)  6  includes a light modulator (light valve)  7 , an illumination optical system  8  that illuminates the light valve  7  with illumination light to be modulated, and a projection system  150  that projects an image formed by the light valve  7  onto a screen  9 . The projection system  150  includes a projection optical system  1  that enlarges and projects the images formed by the light valve  7  whose image plane is a first image plane on the reducing side, by the projecting light  90  onto a screen  9  that is a second image plane on the enlargement side, and a focusing mechanism (focusing unit)  80  that carries out focusing of the projection optical system  1 . 
     The light valve  7  may be a device capable of forming an image such as an LCD (liquid crystal display panel), a digital mirror device (DMD) or an organic EL display, and may be a single panel-type device or a device that uses a method where images of different colors are individually formed. Note that the light valve  7  may be a reflective LCD or a transmissive LCD, and if the light valve  7  is a transmissive-type, the illumination optical system  8  is disposed on the opposite side of the light valve  7  in the direction of a first optical axis  100  of the projection optical system  1 . A typical light valve  7  is a single panel-type video projector that uses a DMD, and the illumination optical system  8  includes a white light source, such as a halogen lamp, and a rotating color splitting filter (color wheel) in the form of a disc, with the DMD  7  forming images in the three colors red, green, and blue according to time division. Note that in  FIG. 1 , the DMD  7  shows the first plane set on the DMD. The screen  9  may be a wall surface, a white board, or the like, the projector  6  may be a front projector, or a rear projector that includes a screen. 
     The projection optical system  1  projects from the DMD  7  that is a first image plane on the reducing side onto the screen  9  that is the second image plane on the enlargement side. The projection optical system  1  includes a first refractive optical system  10  that includes a plurality of lenses and forms a first intermediate image  51  on the enlargement side using light that is incident from the reducing side, a second refractive optical system  20  that includes a plurality of lenses and forms the first intermediate image  51  on the reducing side into a second intermediate image  52  on the enlargement side, and a first reflective optical system  30  that includes a first reflective surface  31   a  that has positive refractive power and is positioned on the enlargement side of the second intermediate image  52 . 
     The focusing unit  80  that carries out focusing of the projection optical system  1  includes a distance detecting unit  81  that detects the optical distance (projecting distance) between the first reflective surface  31   a  and the screen  9  and a temperature detection unit  82  that detects the peripheral temperature of the projection optical system  1 . The focusing unit  80  may include a first mechanism that moves at least one lens and/or reflective surface included in the first refractive optical system  10 , the second refractive optical system  20 , and the first reflective optical system  30 , in response to changes in the projecting distance detected by the distance detecting unit  81 . The focusing unit  80  may also include a second mechanism that moves at least one lens and/or reflective surface included in the first refractive optical system  10 , the second refractive optical system  20 , and the first reflective optical system  30  in response to changes in the peripheral temperature detected by the temperature detection unit  82 . 
     In this projection optical system  1 , the first intermediate image  51 , the second intermediate image  52 , and the image formed by the first reflective surface  31   a  are respectively formed on opposite sides of the optical axis  100  that is common to the first refractive optical system  10  and the second refractive optical system  20 . That is, the projection optical system  1  is designed so that light ray (principal ray)  90  that connects the center of the screen  9  and the center of the DMD  7  crosses the optical axis  100  three times. The light rays  90  crosses the optical axis  100  twice between the DMD  7  and the first reflective surface  31   a . That is, the DMD  7  and the first reflective surface  31   a  can be disposed in the same direction with respect to the optical axis  100 , that is, the same direction (a first direction  101   a  (the downward direction in  FIG. 1 )) with respect to a first plane  101  that includes the optical axis  100 . Both of the illumination optical system  8  that illuminates the DMD  7  and the first reflective surface  31   a  can dispose the first direction (downward)  101   a  to the first plane  101  and commonly utilize a space to the first plane  101 . Accordingly, the height (thickness) of the projector  6  including the projection optical system  1  and the illumination optical system  8  can be reduced. 
       FIG. 2  shows the projection optical system  1  according to a first embodiment.  FIG. 3  shows a light ray diagram of the projection optical system  1 . This projection optical system  1  is a fixed focus (single focus)-type projection optical system that is non-telecentric on the incident (reducing) side and does not carry out zooming. The projection optical system  1  includes, in order from the side of the DMD  7  on the reducing side, the first refractive optical system  10  that includes six lenses L 1  to L 6 , the second refractive optical system  20  that includes five lenses L 7  to L 11 , and the first reflective optical system  30  that includes a single mirror (concave mirror)  31  equipped with the first reflective surface  31   a . In the projection optical system  1 , the image formed on the light valve  7  that is the first image plane is enlarged and projected by the first refractive optical system  10 , the second refractive optical system  20 , and the first reflective optical system  30  onto the screen  9  that is the second image plane. Note that the first refractive mirror (mirror surface) for bending the optical axis  100  at an appropriate position or positions. 
     The first refractive optical system  10  is a lens system that as a whole has positive refractive power and is composed of a positive lens L 1  that is biconvex, a cemented lens (balsam lens, doublet) LB 1  where two lenses are stuck together, a positive lens L 4  that is biconvex, a positive lens L 5  that is biconvex, and a negative meniscus lens L 6  whose convex surface S 11  is oriented toward the enlargement side, disposed in that order from the DMD  7  side. The cemented lens LB 1  is composed of a positive lens L 2  that is biconvex and a negative lens L 3  that is biconcave disposed in that order from the DMD  7  side. The convex surface S 3  on the DMD  7  side (reducing side) of the positive lens L 2  is an aspherical surface. In addition, both surfaces of the negative lens L 6 , that is, the concave surface S 10  on the DMD  7  side and the convex surface S 11  on the mirror  31  side (enlargement side), are aspherical surfaces. The DMD  7  is disposed on the reducing side of the first refractive optical system  10  with a cover glass CG in between. The first refractive optical system  10  forms an image on the light valve  7 , which is the first image plane, into the first intermediate image  51  in a space  41  between the first refractive optical system  10  and the second refractive optical system  20 . 
     The second refractive optical system  20  is a lens system that as a whole has positive refractive power and is composed of a positive meniscus lens L 7  whose convex surface S 12  is oriented toward the reducing side, a positive lens L 8  that is biconvex, a positive meniscus lens L 9  whose convex surface S 16  is oriented toward the reducing side, and a cemented lens LB 2  where two lenses are stuck together, disposed in that order from the DMD  7  side. The cemented lens LB 2  is composed of a negative meniscus lens L 10  whose convex surface S 18  is oriented toward the reducing side and a positive lens L 11  that is biconvex. Both surfaces of the positive lens L 7 , that is, the convex surface S 12  on the DMD  7  side and the concave surface S 13  on the mirror  31  side, are aspherical surfaces. The second refractive optical system  20  forms the first intermediate image  51  as the second intermediate image  52  in a space  42  between the second refractive optical system  20  and the first reflective surface  31   a.    
     The first reflective optical system  30  is a mirror system that as a whole has positive refractive power and is composed of the mirror (concave mirror)  31  that has the first reflective surface (mirror surface)  31   a . The first reflective surface  31   a  of the mirror  31  is an aspherical surface. By projecting the second intermediate image  52  onto the screen  9  that is the second image plane, the first reflective optical system  30  enlarges and projects the image on the DMD  7  onto the screen  9 . Note that although lens surfaces and mirror surfaces (reflective surfaces) included in the projection optical system  1  are spherical or aspherical surfaces with rotational symmetry, such surfaces may be surfaces that do not exhibit rotational symmetry, for example, free-formed curved surfaces. This also applies to the embodiments described below. 
     In this projection optical system  1 , the first intermediate image  51  and the second intermediate image  52  are formed (inverted) on opposite sides of the optical axis  100 . This means that light flux that reaches the second intermediate image  52  from the first intermediate image  51  becomes concentrated in the periphery of the optical axis  100  as the light propagates toward the enlargement side. Accordingly, it is possible to reduce the lens diameters on the enlargement side of the second refractive optical system  20  relative to the lens diameters on the reducing side. This means that it is possible to make the second refractive optical system  20  compact. In addition, since it is possible to make the lens diameters on the enlargement side of the second refractive optical system  20  smaller, it is possible to suppress interference between the second refractive optical system  20  and light flux (projecting light) reflected by the first reflective surface  31   a . This means that it is easy to reduce the optical distance (distance in air, air gap) between the second refractive optical system  20  and the first reflective surface  31   a  and to make the first reflective surface  31   a  smaller. 
     In the projection optical system  1 , it is preferable for the second lens from the enlargement side of the second refractive optical system  20  to have positive refractive power. In addition, it is desirable for the third lens from the enlargement side of the second refractive optical system  20  to have positive refractive power. In addition, it is much more desirable for the lens closest to the enlargement side (the final lens) of the second refractive optical system  20  to be a cemented lens where convex surfaces are oriented toward both sides. The projection optical system  1  in the present embodiment satisfies all of the conditions described above, the positive lens L 9  and the positive lens L 8  with positive refractive power are disposed as the second and third lenses from the enlargement side of the second refractive optical system  20 , and a cemented lens LB 2  with the convex surfaces S 18  and S 20  oriented toward both sides is disposed as the final lens on the enlargement side of the second refractive optical system  20 . By this arrangement where a lens with negative refractive power is not disposed immediately before the final lens, the light flux that reaches the second intermediate image  52  converges effectively. Accordingly, it is possible to significantly reduce the lens diameter on the enlargement side of the second refractive optical system  20 . This means that it is possible to suppress interference between the second refractive optical system  20  and the light flux reflected by the first reflective surface  31   a  and it is not necessary to cut the lenses on the enlargement side of the second refractive optical system  20 . Accordingly, it is desirable for the second refractive optical system  20  to be entirely composed of lenses with positive refractive power, including or except for the final lens. It is easy to concentrate light flux that reaches the second intermediate image  52  from the first intermediate image  51  in the periphery of the optical axis  100  and possible to emit projecting light that is closer to the optical axis  100  from the first reflective surface  31   a . Accordingly, it is possible to make effective use up a region close to the optical axis  100  of the first reflective surface  31   a  and to enlarge and project a wide-angle image onto the screen  9  with a large angle of view and a low angle of elevation relative to the optical axis  100 . 
     In the projection optical system  1 , the first refractive optical system  10  forms the first intermediate image  51 , the second refractive optical system  20  forms such first intermediate image  51  into the second intermediate image  52  on the enlargement side, and the first reflective surface  31   a  reflects and enlarges the second intermediate image  52 . The second intermediate image  52  is reflected and enlarged at the first reflective surface  31   a , and it is possible to make the image on the DMD  7  extremely wide angle, but the light ray paths that reach the screen  9  from the second intermediate image  52  drastically change, so a large amount of distortion and curvature of field occur. It is not so easy to produce a design where various aberrations such as distortion and curvature of field (keystone distortion) are corrected at the first reflective surface  31   a . Accordingly, in the projection optical system  1 , the first reflective surface  31   a  is assumed to have distortion and curvature of field and the second refractive optical system  20  forms the second intermediate image  52  in which distortion and curvature of field, out of the aberrations produced by the first reflective surface  31   a , are mainly corrected. In addition, the first refractive optical system  10  forms the first intermediate image  51  in which coma aberration to be produced by correction stage of the second refractive optical system  20  and the distortion and curvature of field remaining after correction by the second refractive optical system  20  are pre-corrected. This means that it is possible to provide the projection optical system  1  that is capable of projecting sharp and extremely wide-angle images onto the screen  9 . 
     The second refractive optical system  20  of the projection optical system  1  includes a first focus lens group  61  that moves when focusing (adjusting focus) in response to a change in the environment of projection, such as the projecting distance, peripheral temperature, and peripheral humidity. The first focus lens group  61  according to the present embodiment includes a distance correcting lens group (first distance correcting lens group)  71  that moves when carrying out focusing in response to changes in the optical distance (projecting distance) V 3  between the first reflective surface  31   a  and the screen  9 . The distance correcting lens group  71  is composed of the first lens (positive lens) L 7  positioned closest to the reducing side out of the five lenses L 7  to L 11  included in the second refractive optical system  20 . 
     This projection optical system  1  is a pan focus-type optical system that is ultra-wide angle, whose focal length is extremely short, and has a large depth of field on the first image plane side. This means that the range where the projected image does not appear blurred when the distance between the projection optical system  1  and the screen  9  has changed, or in other words, the depth of focus on the second image plane side is also large. Accordingly, although it is easy for fluctuations in focus near the center of the projected images that accompany changes in the projection distance V 3  to be absorbed in the depth of field, there is also a tendency for fluctuations in aberration (fluctuations in the image plane) to increase in the periphery of the projected images. In this projection optical system  1 , the first lens L 7  that is the distance correcting lens group  71  is moved when focusing is carried out. That is, the first refractive optical system  10  and the first reflective surface  31   a  do not move and the first lens L 7  of the second refractive optical system  20  moves in the direction of the optical axis  100  between the first intermediate image  51  on the reducing side and the second intermediate image  52  on the enlargement side. It is possible to carry out focusing without changing the optical distance between the first intermediate image  51  and the first reflective surface  31   a . Accordingly, it is possible to prevent fluctuations in the image formation position and image formation performance for the first intermediate image  51 . This means that by moving the first lens L 7 , it is easy to form a second intermediate image  52  where fluctuations in distortion and curvature of field that accompany changes in the projection distance V 3  are corrected. Accordingly, it is possible to project, sharp, ultra-wide angle images in which fluctuations in aberration that accompany changes in the projection distance V 3  are corrected. In addition, both surfaces of the first lens L 7 , that is, the convex surface S 12  and the concave surface S 13 , are aspherical surfaces. It is possible to correct aberrations that may fluctuate accompany changes in the projection distance V 3  much more effectively. 
     The first lens L 7  is also the lens that is closest to the first intermediate image  51  out of the second refractive optical system  20 . The projection light  90  disperses in the periphery of the image formation position of the first intermediate image  51 , that is, on the enlargement side of the first intermediate image  51 , which makes it easy to separate the light flux for each image angle. In addition, the first intermediate image  51  is formed so as to be substantially perpendicular to the optical axis  100  so that the image plane becomes slightly tilted to the reducing side as the distance from the optical axis  100  increases. This means that the light rays  90  in the periphery of the first intermediate image  51  are dispersed so that the light flux is not concentrated in a state that is close to telecentric. Accordingly, by disposing the first lens L 7  that carries out focusing at a position that is closest to the first intermediate image  51 , it is possible to carry out fine adjustment of focus without suddenly changing the ray paths when carrying out focusing and suppressing fluctuations in aberration that accompany focusing and also suppressing lateral magnification (image magnification). It is possible to project sharp enlarged images in which focus fluctuations that accompany changes in the projection distance V 3  are more thoroughly suppressed. 
     The focusing unit  80  according to the present embodiment includes a first mechanism that moves the first lens L 7  included in the second refractive optical system  20  in response to changes in the projection distance V 3  detected by the distance detecting unit  81 . When there is a change in the projection distance V 3  from a first projection position P 1  (where the projecting distance V 3 =−550 mm) to a second projection position P 2  (where the projecting distance V 3 =−700 mm), focusing is carried out by the first mechanism moving the first lens L 7  by around 0.64 mm from the reducing side toward the enlargement side, that is from the first intermediate image  51  side toward the second intermediate image  52  side. 
     In addition, the first reflective surface  31   a  does not move when focusing is carried out in response to changes in the projection distance V 3 . If the mirror  31  were moved when focusing is carried out, it would be easy for eccentricity to occur and for the image forming performance to become unbalanced between the near point and the far point. In the projection optical system  1 , by fixing the mirror  31  and moving the first lens L 7  in response to changes in the projection distance V 3 , focusing can be completed within the second refractive optical system  20 . This means that it is possible to reduce the influence that the mounting tolerance (error) of the mirror  31  has on the image formation performance for the projected images. 
     Note that in addition to the distance correcting lens group  71 , the first focus lens group  61  may include a distance correcting lens group that moves when carrying out focusing in response to changes in the projection distance V 3 , and it is preferable for such distance correcting lens group to be composed of four lenses L 8  to L 11 . It is possible to correct fluctuations in curvature of field that accompany changes in the projection distance V 3  even more favorably. The respective distance correcting lens groups may move independently or in concert. 
     Also, the first focus lens group  61  may include a temperature correcting lens group (first temperature correcting lens group) that moves when carrying out focusing in response to changes in the peripheral temperature of the projection optical system  1 , and it is preferable for such temperature correcting lens group to be composed of the five lenses L 7  to L 11 . It is possible to project sharp enlarged images in which fluctuations in focus (fluctuations in back focus) due to changes in the refractive indices of lenses that accompany changes in the temperature of the periphery in which the projection optical system  1  is set up are corrected. 
     The first refractive optical system  10  may also include a second focus lens group that moves when focusing is carried out in response to changes in the projection environment. The second focus lens group may include a number of distance correcting lens groups (second distance correcting lens groups) that move when focusing is carried out in response to changes in the projection distance V 3 , and such number of distance correcting lens groups include groups composed of the four lenses L 1  to L 4  and groups composed of the two lenses L 5  and L 6 . In addition, the second focus lens group may include a temperature correcting lens group (second temperature correcting lens group) that moves when focusing is carried out in response to changes in peripheral temperature and it is preferable for such temperature correcting lens group to be composed of the four lenses L 1  to L 4 . That is, the four lenses L 1  to L 4  that move as the distance correcting lens group may move as a temperature correcting lens group. The respective temperature correcting lens groups may move independently or in concert. 
     In the projection optical system  1 , it is easy to separate the light flux for each image angle before and after the image formation position of the first intermediate image  51 , that is on the reducing side and the enlargement side of the first intermediate image  51 . In the projection optical system  1 , the negative lens L 6  that is aspherical on both surfaces is disposed on the reducing side of the first intermediate image  51  with only an air gap in between, and the first lens L 7  that is aspherical on both surfaces is disposed on the enlargement side of the first intermediate image  51  with only an air gap in between. The first intermediate image  51  is sandwiched by the convex surface S 11  and the convex surface S 12  that are both aspherical. Accordingly, it is possible to suppress the occurrence of spherical aberration and coma aberration and to also effectively correct off-axis aberrations such as curvature of field, astigmatism, and distortion. In addition, the DMD  7  and the first reflective surface  31   a  are disposed in the first direction  101   a  (i.e., the same direction) with respect to the optical axis  100 , and the principal ray  91  from the DMD  7  is bent toward the first reflective surface  31   a  via the first intermediate image  51 . This means that it is easy for the lens diameters of the positive lens L 6  and the first lens L 7  before and after the first intermediate image  51  to increase. Accordingly, by making the negative lens L 6  and the positive lens L 7  out of resin, it is possible to effectively correct various aberrations and to reduce cost. 
     It is possible to design the projection optical system  1  so that the Petzval sum (third-order aberration coefficient of curvature of field) PTZ 1 , the third-order aberration coefficient DST 1  of distortion, and the third-order aberration coefficient TCO 1  of coma aberration of the first refractive optical system  10 , and the Petzval sum PTZ 2 , the third-order aberration coefficient DST 2  of distortion, and the third-order aberration coefficient TCO 2  of coma aberration of the second refractive optical system  20  satisfy the following Conditions (1) to (3).
 
|PTZ1|&lt;|PTZ2|  (1)
 
|DST1|&lt;|DST2|  (2)
 
−0.5&lt;|TCO1|−|TCO2|0.5  (3)
 
     In the projection optical system  1 , according to Condition (1) the second refractive optical system  20  has a larger correction effect for curvature of field than the first refractive optical system  10 , according to Condition (2) the second refractive optical system  20  has a larger correction effect for distortion than the first refractive optical system  10 , and according to Condition (3), the correction effect for coma aberration is substantially equal for the first refractive optical system  10  and the second refractive optical system  20 . That is, by correcting the majority of the curvature of field and distortion generated by the first reflective surface  31   a  using the second refractive optical system  20  and correcting the curvature of field and distortion remaining after correction by the second refractive optical system  20  using the first refractive optical system  10 , the correction load of the second refractive optical system  20  is reduced. Accordingly, it is possible to simplify the configuration of the second refractive optical system  20  and to make the second refractive optical system  20  compact. As the upper limit of Condition (3), 0.25 is desirable and 0.1 is even more desirable. In addition, as the lower limit of Condition (3), −0.25 is desirable and −0.1 is even more desirable. Coma aberration is cancelled out between the first refractive optical system  10  and the second refractive optical system  20 . 
     This projection optical system  1  can also be designed so that the curvature of field (a value of the curvature of field) FC 1  of the first intermediate image  51  and the curvature of field (a value of the curvature of field) FC 2  of the second intermediate image  52  satisfy Conditions (4) and (5) below.
 
0&lt;FC1×FC2  (4)
 
0.03&lt;|FC1|  (5)
 
     In the projection optical system  1 , according to Condition (4), the orientations (signs, plus and minus) of the curvature of field of the first intermediate image  51  and the second intermediate image  52  are the same and according to Condition (5), the curvature of field CF 1  of the first intermediate image  51  is larger than a predetermined amount and the curvature of field remaining after correction by the second refractive optical system  20  is corrected by the first refractive optical system  10 . In the present embodiment, according to the first refractive optical system  10  and the second refractive optical system  20 , the first intermediate image  51  and the second intermediate image  52  are respectively formed so that a concave image plane is oriented toward the reducing side (i.e., the image planes are convex on the enlargement side). Alternatively, the first intermediate image  51  and the second intermediate image  52  may be formed so that a convex image plane is oriented toward the reducing side (i.e., the image planes are concave on the enlargement side). 
     In addition, the first refractive optical system  10  forms an image so that the image plane of the first intermediate image  51  is inclined so as to be tilted toward the reducing side as the distance from the optical axis  100  increases. This means that it is possible to use a design where the principal ray  91  emitted from the first intermediate image  51  towards the optical axis  100 , that is, are more downwardly tilted than a telecentric design toward the enlargement side. That is, it is possible to use a design where the ray angle ANG 1  of the principal ray  91  emitted from the first intermediate image  51  satisfy Condition (6) below.
 
ANG1&lt;0  (6)
 
     It is possible to design the projection optical system  1  so that according to Condition (6), the ray angle ANG 1  of the principal ray  91  of the first intermediate image  51  becomes negative in a case where the direction of dispersion (divergence) is positive, or in other words becomes an angle of depression relative to the first axis  111  that is parallel to the optical axis  100 . This means that it is not necessary to raise the power of the second refractive optical system  20 . It is also possible to reduce the lens diameter of the second refractive optical system  20 . 
       FIG. 4  shows lens data of the projection optical system  1 .  FIG. 5  shows various numeric values of the projection optical system  1 . In the lens data, “Ri” represents the radius of curvature (mm) of each lens (i.e., each lens surface) disposed in order from the DMD (light valve)  7  side, “di” represents the distance (mm) between the respective lens surfaces disposed in order from the DMD  7  side, “nd” represents the refractive index (d line) of each lens disposed in order from the DMD  7  side, and “vd” represents the Abbe number (d line) of each lens disposed in order from the DMD  7  side. In  FIG. 4 , “Flat” indicates a flat surface. In  FIG. 5( c ) , “En” represents “10 to the power n” and as one example, “E-05” represents “10 to the power −5”. The same also applies to the following embodiments. 
     As shown in  FIG. 5( a ) , the spatial distance (optical distance, projecting distance) V 3  between the first reflective surface  31   a  and the screen  9  is “−550 mm” at the first projection position P 1  and “−700 mm” at the second projection position P 2 . In the projection optical system  1 , when the projection distance V 3  has changed between the first projection position P 1  and the second projection position P 2 , focusing is carried out by changing the distance in air gap V 1  (d 11 ) between the negative lens L 6  and the positive lens L 7  and the distance in air V 2  ( d   13 ) between the positive lens L 7  and the positive lens L 8 . 
     The convex surface S 3  of the positive lens L 2 , the concave surface S 10  and convex surface S 11  of the negative lens L 6 , and the convex surface S 12  and the concave surface S 13  of the positive lens L 7  and the first reflective surface  31   a  of the mirror  31  are aspherical surfaces. The aspherical surfaces are expressed by the following expression using the coefficients K, A 3 , A 4 , A 6 , A 8 , A 10 , A 12 , and A 14  shown in  FIG. 5( c )  with the direction X as the coordinate in the optical axis  100 , the direction Y as the coordinate in a direction perpendicular to the optical axis  100 , the direction in which light propagates as positive, and R as the paraxial radius of curvature. This is also the case for the embodiments described later.
 
 X =(1 /R ) Y   2 /[1+{1−(1 +K )(1 /R ) 2   Y   2 } 1/2 ]+ A 3 Y   3   +A 4 Y   4   +A 6 Y   6   +A 8 Y   8   +A 10 Y   10   +A 12 Y   12   +A 14 Y   14  
 
       FIG. 6  shows a coma aberration graph at the first projection position P 1  of the projection optical system  1 .  FIG. 7  shows a coma aberration graph at the second projection position P 2  of the projection optical system  1 .  FIG. 8  shows a distortion graph at the first projection position P 1  of the projection optical system  1 .  FIG. 9  shows a distortion graph at the second projection position P 2  of the projection optical system  1 . As shown in  FIGS. 6 to 9 , all of the aberrations are favorably corrected and it is possible to project sharp enlarged images. Note that coma aberration is shown for a wavelength of 620 nm (dotted line), a wavelength of 550 nm (solid line), and a wavelength of 460 nm (dot-dash line). 
       FIG. 10  shows a projection optical system  2  according to a second embodiment.  FIG. 11  is a ray diagram of the projection optical system  2 . The projection optical system  2  is a fixed focus (single focus)-type projection optical system that is telecentric on the incident side (reducing side) and does not carrying out zooming. The projection optical system  2  includes the first refractive optical system  10  that includes twelve lenses L 1  to L 12 , the second refractive optical system  20  that includes six lenses L 13  to L 18 , and the first reflective optical system  30  that includes a single mirror (concave mirror)  31  with the first reflective surface  31   a , disposed in that order from the DMD  7  side on the reducing side. In the projection optical system  2  also, images formed on the DMD  7  that is the first image plane are enlarged and projected onto the screen  9  that is the second image plane by the first refractive optical system  10 , the second refractive optical system  20 , and the first reflective optical system  30 . Note that component elements that are the same as the embodiment described above have been assigned the same numerals and description thereof is omitted. 
     The first refractive optical system  10  is a lens system that as a whole has positive refractive power and is composed of a positive meniscus lens L 1  whose convex surface S 2  is oriented toward the enlargement side, a positive meniscus lens L 2  whose convex surface S 3  is oriented toward the reducing side, a cemented lens (balsam lens, triplet) LB 1  where three lenses are stuck together, a cemented lens LB 2  where two lenses are stuck together, a positive meniscus lens L 8  whose convex surface S 13  is oriented toward the enlargement side, a positive lens L 9  that is biconvex, a negative meniscus lens L 10  whose convex surface S 17  is oriented toward the enlargement side, and a cemented lens LB 3  where two lenses are stuck together, disposed in that order from the DMD  7  side. The cemented lens LB 1  is composed of a negative meniscus lens L 3  whose convex surface S 5  is oriented toward the reducing side, a positive lens L 4  that is biconvex, and a negative meniscus lens L 5  whose convex surface S 8  is oriented toward the enlargement side, disposed in that order from the DMD  7  side. The cemented lens LB 2  is composed of a negative lens L 6  that is biconcave and a positive lens L 7  that is biconvex disposed in that order from the DMD  7  side. The cemented lens LB 3  is composed of a negative lens L 11  that is biconcave and a positive lens L 12  that is biconvex disposed in that order from the DMD  7  side. The DMD  7  is disposed on the reducing side of the first refractive optical system  10  with a prism (TIR prism) Pr and the cover glass CG, which are disposed in that order from the enlargement side, in between. Both surfaces of the negative lens L 10 , that is, the concave surface S 16  on the DMD  7  side and the convex surface S 17  on the mirror  31  side, are aspherical surfaces. A stop St is disposed on the mirror  31  side of the cemented lens LB 2 , that is, in the space between the cemented lens LB 2  and the positive lens L 8 . 
     The second refractive optical system  20  is a lens system that as a whole has positive refractive power and is composed of a positive meniscus lens L 13  whose convex surface S 21  is oriented toward the reducing side, a positive meniscus lens L 14  whose convex surface S 24  is oriented toward the enlargement side, a positive meniscus lens L 15  whose convex surface S 26  is oriented toward the enlargement side, a positive meniscus lens L 16  whose convex surface S 28  is oriented toward the enlargement side, and a cemented lens LB 4  where two lenses are stuck together, disposed in that order from the DMD  7  side. The cemented lens LB 4  is composed of a negative meniscus lens L 17  whose convex surface S 29  is oriented toward the reducing side and a positive lens L 18  that is biconvex. Both surfaces of the positive lens L 13 , that is, the convex surface S 21  on the DMD  7  side and the concave surface S 22  on the mirror  31  side, are aspherical surfaces. 
     The second refractive optical system  20  of the projection optical system  2  includes a first focus lens group  61  that moves when carrying out focusing (focus adjustment) in response to changes in the environment conditions at the projection. The first focus lens group  61  in the present embodiment includes a distance correcting lens group (first distance correcting lens group)  71  that moves when carrying out focusing in response to changes in the optical distance (projecting distance) V 5  between the first reflective surface  31   a  and the screen  9 . The distance correcting lens group  71  is composed of a first lens (positive lens) L 13  that is disposed closest to the reducing side out of the six lenses L 13  to L 18  included in the second refractive optical system  20 . 
     In the projection optical system  2 , the positive lens L 16  and the positive lens L 15  that have positive refractive power are disposed as the second and third lenses from the enlargement side of the second refractive optical system  20  and the cemented lens LB 4  where convex surfaces S 29  and S 31  are oriented on both sides is disposed as the lens (final lens) that is closest to the enlargement side of the second refractive optical system  20 . It is possible to cause the light flux that reaches the second intermediate image  52  to effectively converge without disposing a lens with negative refractive power immediately before the final lens. Accordingly, it is possible to significantly reduce the lens diameter on the enlargement side of the second refractive optical system  20 . This means that it is possible to suppress interference between the second refractive optical system  20  and the light flux reflected by the first reflective surface  31   a  and it is not necessary to cut the lenses on the enlargement side of the second refractive optical system  20 . Accordingly, it is desirable for the second refractive optical system  20  to be entirely composed of lenses with positive refractive power, including or except for the final lens. 
     In the projection optical system  2 , when carrying out focusing, the first lens L 13  that is the distance correcting lens group  71  and closest to the first intermediate image  51  out of the second refractive optical system  20  is moved. It is possible to carry out fine adjustment of focus while suppressing fluctuations in aberration that accompany focusing. It is possible to project sharp, enlarged images in which fluctuations in curvature of field that accompany changes in the projection distance V 5  are corrected. 
     The focusing unit  80  according to the present embodiment includes a first mechanism that moves the first lens L 13  included in the second refractive optical system  20  in response to changes in the projection distance V 5  detected by the distance detecting unit  81 . For this reason, when there is a change in the projection distance V 5  from the first projection position P 1  (where the projection distance V 5 =−469 mm) to the second projection position P 2  (where the projection distance V 5 =−1449 mm), focusing is carried out by the first mechanism moving the first lens L 13  by around 1.77 mm from the reducing side toward the enlargement side. 
     The first refractive optical system  10  of the projection optical system  2  includes a second focus lens group  62  that moves when carrying out focusing in response to changes in the projection environment. The second focus lens group  62  according to the present embodiment includes a distance correcting lens group (second distance correcting lens group)  72  that moves in response to changes in the projection distance V 5 . The distance correcting lens group  72  is composed of the seven lenses L 2  to L 8  included in the first refractive optical system  10 . 
     In the projection optical system  2 , when carrying out focusing, aside from the first lens L 13  of the distance correcting lens group  71 , the lenses L 2  to L 8  of the distance correcting lens group  72  are moved. That is, the lenses L 2  to L 8  move along the optical axis  100  between the DMD  7  on the reducing side and the first intermediate image  51  on the enlargement side. This means that by moving the lenses L 2  to L 8 , it is possible to reduce the movement distance of the first lens L 13 . Accordingly, it is possible to suppress interference between the first lens L 13  and the first intermediate image  51  and possible to carry out focusing while hardly moving the image formation position of the first intermediate image  51 . This means that it is possible to project a sharp enlarged image where fluctuations in focus that accompany changes in the projection distance V 5  over a wide range are suppressed. 
     The focusing unit  80  according to the present embodiment includes a first mechanism that moves the lenses L 2  to L 8  included in the first refractive optical system  10  in response to changes in the projecting distance V 5  detected by the distance detecting unit  81 . If the projection distance V 5  changes from the first projection position P 1  (where the projection distance V 5 =−469 mm) to the second projection position P 2  (where the projection distance V 5 =−1449 mm), focusing is carried out by the first mechanism moving the lenses L 2  to L 8  by around 0.96 mm from the reducing side to the enlargement side. 
     Note that in addition to the distance correcting lens group  71 , the first focus lens group  61  may include a distance correcting lens group that moves when focusing is carried out in response to changes in the projection distance V 5  and it is preferable for such distance correcting lens group to be composed of the five lenses L 14  to L 18 . 
     Also, the first focus lens group  61  may include a temperature correcting lens group (first temperature correcting lens group) that moves when focusing is carried out in response to changes in peripheral temperature of the projection optical system  2 , and it is preferable for such temperature correcting lens group to be composed of the six lenses L 13  to L 18 . 
     Also, in addition to the distance correcting lens group  72 , the second focus lens group  62  may include a distance correcting lens group that moves when focusing is carried out in response to changes in the projecting distance V 5  and it is preferable for such distance correcting lens group to be composed of the four lenses L 9  to L 12 . 
     Also, the second focus lens group  62  may include a number of temperature correcting lens groups (second temperature correcting lens groups) that move when focusing is carried out in response to changes in peripheral temperature of the projection optical system  2 , and such number of temperature correcting lens groups include a group composed of the single lens L 1  and a group composed of the twelve lenses L 1  to L 12 . 
       FIG. 12  shows lens data of the projection optical system  2 .  FIG. 13  shows various numeric values of the projection optical system  2 . As shown in  FIG. 13( a ) , the distance in air (optical distance, projection distance) V 5  between the first reflective surface  31   a  and the screen  9  is “−469 mm” at the first projection position P 1  and is “−1449 mm” at the second projection position P 2 . In the projection optical system  2 , when the projecting distance V 5  changes between the first projection position P 1  and the second projection position P 2 , focusing is carried out by changing the distance in air V 1 ( d   2 ) between the positive lens L 1  and the positive lens L 2 , the distance in air V 2 ( d   13 ) between the positive lens L 8  and the positive lens L 9 , the distance in air V 3 ( d   20 ) between the positive lens L 12  and the positive lens L 13 , and the distance in air V 4 ( d   22 ) between the positive lens L 13  and the positive lens L 14 . 
       FIG. 14  shows a coma aberration graph at the first projection position P 1  of the projection optical system  2 .  FIG. 15  shows a coma aberration graph at the second projection position P 2  of the projection optical system  2 .  FIG. 16  shows a distortion graph at the first projection position P 1  of the projection optical system  2 .  FIG. 17  shows a distortion graph at the second projection position P 2  of the projection optical system  2 . As shown in  FIGS. 14 to 17 , all of the aberrations are favorably corrected and it is possible to project sharp enlarged images. Note that coma aberration is shown for a wavelength of 650 nm (dotted line), a wavelength of 550 nm (solid line), and a wavelength of 440 nm (dot-dash line). 
       FIG. 18  shows a projection optical system  3  according to a third embodiment. The projection optical system  3  is a projection optical system of a type where the projection optical system  2  is bent midway in the first refractive optical system  10 . The first refractive optical system  10  of the projection optical system  3  includes a mirror  95  that bends the optical axis  100  at substantially a right angle in a space between the positive lens L 8  and the positive lens L 9 . In the projection optical system  3 , by having the mirror  95  bend the first refractive optical system  10 , it is possible to reduce the overall length of the projection optical system  3 . In addition, by disposing the illumination optical system  8  and the focusing mechanism  80  in a space  99  formed by bending the first refractive optical system  10 , it is possible to miniaturize a projector  6  including the projection optical system  3 , the illumination optical system  8 , and the like. 
       FIG. 19  shows a projection optical system  4  according to a fourth embodiment. This projection optical system  4  is a projection optical system of a type where the projection optical system  2  is bent midway in the second refractive optical system  20 . In addition,  FIG. 20  shows a projection optical system  5  according to a fifth embodiment. The projection optical system  5  is a projection optical system of a type where the projection optical system  2  is bent between the second refractive optical system  20  and the mirror  31 . As shown in  FIGS. 19 and 20 , in the projection optical systems  4  and  5 , since it is possible to miniaturize the second refractive optical system  20  and the mirror  31 , even if the projection direction of the projection light is changed in the periphery of the mirror  31 , it is possible to suppress interference between the projection light reflected by the first reflective surface  31   a  and the second refractive optical system  20 , the mirror  31 , and the like. Such projection optical systems  3  to  5  may be equipped with a plurality of prisms and/or mirror (mirror surfaces) for bending the optical path multiple times at appropriate positions. 
     Note that the present invention is not limited to such embodiments and includes the devices defined by the range of the patent claims. When carrying out focusing in response to changes in the peripheral temperature of the projection optical system, the entire refractive optical systems of the first refractive optical system and the second refractive optical system may be moved, the second refractive optical system and the first reflective optical system may be moved, the entire projection optical systems of the first refractive optical system, the second refractive optical system, and the first reflective optical system may be moved, or only the first reflective optical system may be moved. It is also possible to use the optical system including the first refractive optical system, the second refractive optical system, and the first reflective optical system in a variety of applications including not only projection but also image pickup. Also, the lens surfaces and mirror surfaces (reflective surfaces) included in the projection optical systems may be spherical or aspherical surfaces with rotational symmetry, or such surfaces may be surfaces that do not exhibit rotational symmetry, for example, free-formed curved surfaces. Also, the optical axis of the first refractive optical system and the optical axis of the second refractive optical system may be shared or may be shifted. Also, the projection optical system may be a fixed focus type that does not carry out zooming or may be a variable focus (zoom) type that carries out zooming. Also, at least one lens included in the first refractive optical system and the second refractive optical system and/or the reflective surface included in the first reflective optical system may be off-center with respect to the optical axis. In this case, the optical axes of the respective optical systems include the optical axes of the main optical elements. Also, the optical axis of the first refractive optical system and the optical axis of the second refractive optical system may be shared or may be off-center (shifted). Also, another refractive optical system may be provided on an enlargement side of the first reflective optical system. It is also possible to use anamorphic optical elements for the lenses and/or reflective surfaces included in the projection optical system