JP2008242025A - Projection optical system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a high-performance compact projection optical system capable of zooming or focusing peculiar to a non-axial optical system, where the characteristic of the non-axial optical system is utilized, without causing image skip in oblique projection by the non-axial optical system, and a projection type image display device. <P>SOLUTION: The projection optical system PO enlarging and projecting an image on a display element surface SG onto a screen surface SL has rotationally asymmetric first and second curved surface mirrors M1 and M2 eccentrically arranged in such a manner that an angle formed by the screen surface SL and an axial principal ray incident on the screen surface SL is not perpendicular. The projection optical system PO changes the focal length of the entire system by parallel displacement and rotational displacement of at least one optical element group including the first and the second curved surface mirrors M1 and M2 for the purpose of zooming or focusing. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a projection optical system. For example, the present invention is mounted on an image projection apparatus having a display element such as a liquid crystal display element or a digital micromirror device, and enlarges and projects an image on the display element surface on a screen surface. The present invention relates to a projection optical system, and a projection optical apparatus (particularly a projection image display apparatus) having the projection optical system.

  As computers that are easy to carry (such as notebook personal computers) have become popular, front-type projectors can be used to enlarge images created on computers during office meetings and presentations. Are becoming widely used. In addition, with the diversification and high definition of video information distribution such as digital broadcasting, image viewing on a large screen has been performed at home using a projector. However, when a conventional projector is used on a large screen, it is difficult to secure a sufficient projection space in a medium / small conference room or home. That is, unless a sufficient projection space can be secured, it is difficult to project a large screen image with a conventional projector.

  As a method for achieving a large screen while reducing the required projection space, a projection device is used to introduce an optical path of an imaging light beam used for imaging a projected image by introducing a reflecting surface in the projection optical system. A configuration of folding in is known. If an eccentric reflecting surface is used as the reflecting surface and a so-called non-axial optical system is arranged, the effect of folding the optical path can be further improved. Also known is a configuration in which the distance from the projection optical system to the screen is shortened by increasing the incident angle of the light beam incident on the screen surface.

  When using a projector within a limited space, if the projection optical system has a zooming function, the projection magnification can be changed while the position of the projector or screen is almost fixed. It is very convenient to zoom in and out. Patent Documents 1 to 3 propose using a non-axial optical system as a projection optical system having such a zooming function. In addition, the focusing function is essential in the projection optical system in order to enable focusing when the screen moves and to enable focusing corresponding to the screen position that changes with each use. Patent Documents 4 and 5 propose using a non-axis optical system as a projection optical system having such a focusing function.

The projection optical system proposed in Patent Documents 1 and 2 has a configuration of a non-axis optical system, but performs zooming by changing the focal length of the entire system by translating the coaxial part. is there. The projection optical system proposed in Patent Document 3 performs zooming by changing the focal length of the entire system by translating a mirror. The projection optical systems proposed in Patent Documents 4 and 5 perform focusing by changing the focal length of the entire system by translating non-axially arranged mirrors.
JP 2004-295107 A JP-A-2005-121722 JP 2005-189768 A JP 2005-106900 A JP 2006-184775 A

  As described above, if the optical path is folded using a non-axis optical system, the projection optical system can be made smaller. However, since the axial ray does not become one straight line, it is necessary to consider that it is a non-axial optical system when the focal length is changed by moving the optical element for zooming or focusing. For example, if the portion having power in the non-axis optical system is simply translated, the focal length of the entire projection optical system changes, but the light beam emitted to the screen surface moves greatly. As a result, the center of the screen moves during zooming, and the phenomenon of image distortion appears. For example, the projection optical system proposed in Patent Document 5 is configured to perform focusing by moving a mirror in parallel, but a method for making the axial image point position substantially constant during focusing is disclosed. Therefore, it is difficult to achieve focusing with a substantially constant axial position.

  In the projection optical systems proposed in Patent Documents 1 and 2, zooming is performed by changing the position of the coaxial optical system portion of the non-axial optical system. This zooming method has the advantage that the injection position on the shaft does not shift. However, since the movement of the non-axially arranged portion is not accompanied, it cannot be said that the variable magnification of the non-axial optical system is sufficiently realized. Also, in the case of an oblique projection optical system in which one or both of the object plane and the image plane are tilted, if the focal length of the coaxial portion is uniformly changed regardless of the direction (for example, the vertical and horizontal directions of the screen), the anamorphic in a certain focal length area. The relationship of magnification will be broken. Therefore, the relationship between the design image plane (that is, the design image plane corresponding to the screen surface) and the primary image point (that is, the focus position corresponding to the paraxial image point in the coaxial optical system) is greatly shifted. Thus, an anamorphic magnification relationship is maintained. However, according to this method, the performance is deteriorated due to the effect of defocus at a portion where the primary image point is greatly deviated from the designed image plane, so that a high-performance projection optical system can be realized. Can not.

  In the projection optical system proposed in Patent Document 3, the non-axis-arranged mirror is configured to move in parallel during zooming. In the projection optical system proposed in Patent Document 4, the non-axis-arranged mirror is focused. Sometimes it is configured to translate. In terms of moving the non-axis mirror, both are zooming methods suitable for non-axis optical systems. However, in this method, the axial chief ray incident on the component part of the non-axis mirror to be moved and the axial chief ray emitted from the component part of the non-axis mirror to be moved are designed in parallel. The restriction condition is necessary. Further, since the movement is performed in a direction parallel to the axial principal ray, individual focal lengths cannot be freely changed depending on the direction (for example, the vertical and horizontal directions of the screen). As a result, as in Patent Documents 1 and 2, the anamorphic magnification relationship is broken in a certain focal length region. Therefore, the relationship between the designed image plane and the primary image point is largely shifted to maintain the anamorphic magnification relationship. However, according to this method, the performance is deteriorated due to the effect of defocus at a portion where the primary image point is greatly deviated from the designed image plane, so that a high-performance projection optical system can be realized. Can not.

  The present invention has been made in view of such a situation, and an object thereof is a non-axis optical system that takes advantage of the characteristics of the non-axis optical system without causing image distortion in oblique projection by the non-axis optical system. It is an object of the present invention to provide a high-performance and compact projection optical system that enables unique zooming and focusing, and a projection-type image display device using the same.

  In order to achieve the above object, a projection optical system according to a first aspect of the present invention is a projection optical system for enlarging and projecting an image of a display element surface onto a screen surface, and is an axial principal ray incident on the screen surface and the screen surface. And a rotationally asymmetric reflecting mirror arranged eccentrically, and the focal length of the entire system is changed by translation and rotation of at least one optical element group including the reflecting mirror. It is characterized by.

A projection optical system according to a second invention is characterized in that, in the first invention, the following conditional expression (1) is satisfied.
30 <| θimg | <70… (1)
However,
θimg: Angle (°) between the screen normal of the screen surface and the axial principal ray incident on the screen surface,
It is.

  The projection optical system according to a third aspect of the present invention is the projection optical system according to the first or second aspect of the present invention, in which the enlargement magnification is increased while maintaining the positions of the display element surface and the screen surface substantially constant by changing the focal length of the entire system. It is a zoom optical system to be changed.

The projection optical system according to a fourth aspect of the present invention is the following conditional expression (2) in the third aspect of the present invention, in changing the magnification from the smallest absolute value to an arbitrary magnification by changing the focal length of the entire system. It is characterized by satisfying.
0.2 <| θzmov / Zz | <5.0 (2)
However,
θzmov: rotation angle (°) of the optical element group including the reflection mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is.

The projection optical system according to a fifth aspect of the present invention is the following conditional expression in the third or fourth aspect of the present invention, in changing the magnification from the smallest absolute value to an arbitrary magnification by changing the focal length of the entire system. It is characterized by satisfying (3).
0.01 <| Szmov / (Zz × fz1) | <5.0 (3)
However,
Szmov: distance of translation of the optical element group including the reflecting mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is.

The projection optical system according to a sixth aspect of the present invention is the projection optical system according to any one of the third to fifth aspects, wherein the following conditional expression (4) and (5) is satisfied.
-50 <(Sz1st_ximg-Szx_design) / fzx <20 (4)
-50 <(Sz1st_yimg-Szy_design) / fzy <20 (5)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sz1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Szx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane.
fzx: focal length of the entire system in the x direction,
Sz1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Szy_design: The distance measured along the base ray from the rear principal point position in the y direction to the design image plane.
fzy: focal length of the entire system in the y direction,
It is.

  A projection optical system according to a seventh invention is the projection optical system according to any one of the third to sixth inventions, wherein the zoom optical system has different screen surfaces depending on the parallel movement and the rotational movement of an optical element having a rotationally asymmetric optical surface. It has a focusing function for focusing on a position.

  A projection optical system according to an eighth aspect of the invention is characterized in that, in the first or second aspect of the invention, a focusing function is provided for focusing on different screen surface positions by changing the focal length of the entire system.

A projection optical system according to a ninth invention is the following conditional expression (8) in focusing from the closest projection state closest to the screen surface to an arbitrary focus projection state due to a change in focal length of the entire system in the eighth invention. It is characterized by satisfying 6).
0.2 <| θfmov / Zfoc | <8.0 (6)
However,
θfmov: rotation angle (°) of the optical element group including the reflection mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is.

A projection optical system according to a tenth aspect of the invention is the following in the eighth or ninth aspect, in focusing from the closest projection state closest to the screen surface to an arbitrary focus projection state due to a change in the focal length of the entire system. Conditional expression (7) is satisfied.
0.05 <| Sfmov / (Zfoc × ff1) | <7.0 (7)
However,
Sfmov: distance of translation of the optical element group including the reflecting mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is.

A projection optical system according to an eleventh aspect of the present invention is the projection optical system according to any one of the eighth to tenth aspects of the present invention, wherein the following conditional expressions (8) and (8) It is characterized by satisfying 9).
-50 <(Sf1st_ximg-Sfx_design) / ffx <20 (8)
-50 <(Sf1st_yimg-Sfy_design) / ffy <20 (9)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sf1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Sfx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane,
ffx: focal length of the entire system in the x direction,
Sf1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Sfy_design: The distance measured along the base ray from the back principal point position in the y direction to the design image plane,
ffy: focal length of the entire system in the y direction
It is.

  A projection optical system according to a twelfth aspect of the present invention is a projection optical system for enlarging and projecting an image on the display element surface onto the screen surface, and the angle formed by the screen surface and the axial principal ray incident on the screen surface is not vertical. The rotationally asymmetric reflecting mirror arranged eccentrically, and for use in any one of a state of projecting to a screen position and a state of projecting to a screen position different from the state. It is characterized by having a configuration capable of parallel movement and rotational movement of at least one optical element group.

  A projection optical system according to a thirteenth aspect of the present invention is a projection optical system for enlarging and projecting an image on the display element surface onto the screen surface, and the angle formed between the screen surface and the axial principal ray incident on the screen surface is not vertical. A rotationally asymmetric reflecting mirror arranged eccentrically, and at least one including the reflecting mirror for use in one of a certain projection magnification state and another projection magnification state different from that state The optical element group has a configuration capable of parallel movement and rotational movement.

  A projection type image display apparatus according to a fourteenth aspect of the invention is a projection type image display apparatus comprising: a display element that forms a two-dimensional image; and a projection optical system that enlarges and projects an image of the display element surface on a screen surface. The projection optical system is a projection optical system according to any one of the first to thirteenth inventions.

  According to the present invention, since the focal length of the entire system changes due to the parallel movement and the rotation movement of at least one optical element group including the rotationally asymmetric reflection mirror arranged eccentrically, the performance of the projection optical system can be improved. While achieving compactness, zooming and focusing unique to the non-axis optical system can be performed by taking advantage of the features of the non-axis optical system without causing image distortion in oblique projection by the non-axis optical system.

  Embodiments of a projection optical system according to the present invention will be described below with reference to the drawings. The projection optical system according to the present invention is a projection optical system that enlarges and projects an image of the display element surface on the screen surface, and the angle formed between the screen surface and the axial principal ray incident on the screen surface is not vertical, It has a rotationally asymmetric reflecting mirror arranged eccentrically, and changes the focal length of the entire system by translation and rotation of at least one optical element group including the reflecting mirror. The angle between the screen surface and the axial principal ray incident on the screen surface is not vertical, so a so-called oblique projection optical system configuration is adopted. Can be shortened. In addition, because the optical path is bent using a rotationally asymmetric reflecting mirror with an eccentric arrangement, the projection space is reduced and the screen is enlarged, while being much more compact than a coaxial optical system. A projection optical system can be realized.

  Furthermore, since the focal length of the projection optical system is changed by the parallel movement and the rotation movement of at least one optical element group including the rotationally asymmetric reflecting mirror arranged eccentrically, the occurrence of image distortion occurs. This makes it possible to perform zooming and focusing unique to non-axis optical systems that take advantage of the features of non-axis optical systems. There are two main reasons why the rotational movement of the optical element group is required to change the focal length of the projection optical system. The first reason is that the focal length of the entire system can be changed without changing the position and direction of the axial principal ray toward the screen by the rotational movement of the reflecting mirror which is a non-axis optical element. The second reason is that the power change of the reflection mirror itself, which is a non-axis optical element, can also contribute to the change of the focal length of the entire system. These reasons will be specifically described with reference to FIGS.

  First, the first reason will be described (FIGS. 18 to 21). In order to simplify the explanation, it is assumed that the projection optical system is plane symmetric, and the axial principal ray passes through the plane of symmetry. Further, the direction perpendicular to the symmetry plane is defined as the X direction, and the direction perpendicular thereto (that is, the direction parallel to the symmetry plane) is defined as the Y direction. 18 to 21, M1 and M2 are two curved mirrors arranged eccentrically, SL is a screen surface, and LA is an axial principal ray toward the screen surface SL. It is assumed that the mirrors M1 and M2 move for zooming or focusing, and the focal length of the entire system changes from the focal length state I before the movement to the focal length state II after the movement. 18 to 21, the broken line indicates the arrangement of the mirrors M1 and M2 in the focal length state I, and the thick solid line indicates the arrangement of the mirrors M1 and M2 in the focal length state II. A one-dot chain line indicates a surface normal at the intersection of the axial principal ray LA and the mirrors M1 and M2.

  18 and 19 show optical path changes when the two mirrors M1 and M2 are simply translated. In FIG. 18, the two mirrors M1, M2 are simultaneously translated in the same direction, and in FIG. 19, the two mirrors M1, M2 are translated in different directions by different amounts. In both cases, the focal length state I and the focal length state II differ in the position and direction of the axial principal ray LA emitted from the mirror M2. Therefore, the center of the image plane moves on the screen surface SL due to zooming or focusing, and a so-called image jump phenomenon appears.

  FIG. 20 shows the optical path change when the two mirrors M1 and M2 are only translated independently so that the position and direction of the axial principal ray emitted from the mirror M2 do not change. In this case, the power of each surface (an amount defined by the reciprocal of the focal length) does not change, and only the change in the inter-surface distance changes the focal length of the projection optical system. As will be described later, in the method of changing the focal length in the case of a non-axis optical system, unlike the case of a coaxial optical system, not only the change in the inter-surface distance but also the change in the power of the surface itself is a projection optical system. It is possible to contribute to the change of the focal length. By doing so, the merit of a non-axis optical system can be utilized. Also, in non-axis optical systems, the focal length of the eccentrically arranged optical element (or optical surface) varies depending on the direction, so when the distance between certain planes is changed, the amount of change in the focal length of the entire system varies depending on the direction. . Since the projection optical system is a finite system, the change in magnification differs depending on the direction (for example, the X direction and the Y direction). Therefore, it is difficult to change the magnification while keeping the anamorphic ratio substantially constant. In particular, in the case of an oblique projection optical system in which the object surface and the image surface are inclined, the influence of the inclination of the object surface and the image surface reaches the magnification.

  In the above zooming, a method of controlling the magnification by a method of separating the primary imaging position and the design image plane position in the X direction and the Y direction in order to make the anamorphic ratio of the magnification constant. It has been known. However, in the case of a high-performance projection optical system in which aberrations are almost corrected, the primary focus position has the best focus position. Therefore, if the magnification is adjusted by shifting the design image plane position from the best focus position, Image performance is lowered.

  FIG. 21 shows an optical path change when the focal length of the entire system is changed by adding a rotational movement to the movement of the mirrors M1 and M2. In this case, by performing parallel movement and rotational movement of the eccentrically arranged mirrors M1 and M2, the power and the surface interval of each surface are changed while the axial principal ray LA toward the screen is kept constant. This changes the focal length of the entire system, so that the projection magnification can be changed to a desired value. If this method is adopted, the degree of freedom of zooming increases, so zooming that changes the focal length of the entire system while maintaining high performance becomes possible.

Next, the second reason will be described (FIGS. 22 and 23). Here, the power of the non-axis mirror is considered to be representative of the power of one non-axis optical surface. As shown in FIG. 22, a case where the refraction system is configured by the non-axial optical surface Sr is considered, but in the case of the reflection system, it can be considered as a special case in the same manner as the refraction system. An axial principal ray from the center of the object through the stop center to the center of the design image plane is defined as a base ray LB, a refractive index of the medium before the base ray LB is incident on the optical surface Sr is n, and the refraction of the medium after the incidence is made. Let nd be the rate. The incident angle of the base ray LB to the optical surface Sr is θs, and the emission angle of the base ray LB from the optical surface Sr is θsd. Further, the local curvature in the X direction at the intersection Os between the base ray LB and the optical surface Sr is C11, and the local curvature in the Y direction is C22. Also, {n · cos (θs) −nd · cos (θsd)} = S. The powers φX and φY in the X and Y directions at the intersection Os between the base ray LB and the optical surface Sr are expressed by the following equations (Fr1) and (Fr2).
φX = -S · C11 (Fr1)
φY = −S · C22 / {cos (θs) · cos (θsd)} (Fr2)

  In the case of a reflection system, in the calculation of S, if n = nd and θs = −θsd, then S = 2 cos (θs). Furthermore, the denominator of φY is the square of cos (θs). The values of θs and θsd can be changed by the parallel movement and the rotational movement of the optical surface Sr, and the intersection Os between the base ray LB and the optical surface Sr is changed, so that the local curvatures C11 in the X and Y directions are changed. , C22 can be changed. Thereby, the power at the optical surface Sr can be freely changed.

Further, consider the combined power of the two non-axial optical surfaces. As shown in FIG. 23, the powers in the X direction and Y direction of the first optical surface are φ1X and φ1Y, respectively, and the powers in the X direction and Y direction of the second optical surface are φ2X and φ2Y, respectively. The incident angle and exit angle for the first optical surface are θ1 and θ1P, respectively, and the incident angle and exit angle for the second optical surface are θ2 and θ2P, respectively. Further, the distance between the rear principal point of the first optical surface and the front principal point of the second optical surface measured along the base ray LB is d2X in the X direction and d2Y in the Y direction. In the case of an optical system that is symmetric with respect to the YZ plane, d2X is equal to the distance measured along the axial principal ray between the intersection points with the principal ray of each optical surface. On the other hand, in the Y direction, the intersection between the optical surface and the principal ray, and the principal point position do not normally match in the case of a refractive system, and match in the case of a reflection surface. Therefore, if the combined power of the two optical surfaces is φ (1 + 2) X in the X direction and φ (1 + 2) Y in the Y direction, the combined powers φ (1 + 2) X and φ (1 + 2) Y are given by Represented by (Fr3) and (Fr4), respectively (n2: refractive index between two surfaces).
φ (1 + 2) X = φ1X + φ2X− (d2X / n2) · φ1X · φ2X (Fr3)
φ (1 + 2) Y = {cos (θ2) / cos (θ2P)} φ1Y + {cos (θ1P) / cos (θ1)} φ2Y− (d2Y / n2) φ1Y · φ2Y (Fr4)

  In the case of a coaxial optical system, only the change in the spacing between optical elements results in a change in power, but in the case of a non-axial optical system, the contribution of the power change on each surface is also effective from the above formulas (Fr3) and (Fr4). It turns out that it is. In particular, it can be seen that the power in the Y direction can be changed by changing the tilt of the surface (that is, the rotation angle). Therefore, it becomes easy to correct the anamorphic ratio of the magnification by rotating the optical surface. In addition, there is no need to make the incident and exiting rays of the axial principal ray parallel for zooming and focusing, which increases design flexibility and maximizes the folding effect of the optical path of non-axial optics. Design is possible. Therefore, a thin optical system can be realized.

  Moreover, compared with the case of a refractive system, even when the curvature of the optical surface to be used is the same, the power can be increased by 2 to 4 times when the reflecting surface is used. Further, when the power is greatly changed, a chromatic aberration is greatly generated in the case of a refractive system, so that an optical element for the correction is required, and the optical system is enlarged. In particular, since correction of non-axisymmetric chromatic aberration is quite complicated, it is desirable to use a reflecting surface in order to greatly change the focal length while maintaining high performance.

  Here, in order to simplify the explanation, the case of YZ plane symmetry is taken as an example, but the idea is the same even when it is not plane symmetry (so-called torsion). However, in the case where there is a twist, if the calculation of diagonalizing by giving the influence of the rotation of the incident surface on the twisted surface by a rotation matrix is performed, 1 is obtained in the direction perpendicular to the incident surface on the optical surface. The next quantity takes an extreme value. The primary amount shifts each surface while taking the form of rotation of the incident surface. Therefore, changing the focal length of the entire system by parallel movement and rotational movement of the optical element group including the non-axis mirror is very effective in changing the magnification of the non-axis oblique projection optical system.

  From the above point of view, in a projection optical system having a rotationally asymmetric reflecting mirror arranged eccentrically, all of the optical elements including the rotationally asymmetric reflecting mirror arranged eccentrically are translated and rotationally moved. It is preferable to change the focal length of the system. With this configuration, it is possible to perform zooming and focusing without occurrence of image jumping in oblique projection by a non-axis optical system while having a high performance and compact configuration. In the projection optical system characterized by the non-axis optical system as described above, conditions desirable for achieving further performance improvement and downsizing, and other effective configurations will be described below. The reference coordinate system in the whole projection optical system is an orthogonal coordinate system (x, y, z), and unless otherwise specified, each direction is taken as follows. The z direction is the screen normal direction of the display element surface. The x direction is a direction perpendicular to the plane formed by the axial principal ray toward the screen and the normal of the screen surface. The y direction is a direction perpendicular to the x direction and the z direction.

In order to obtain the effect of oblique projection, it is desirable to satisfy the following conditional expression (1).
30 <| θimg | <70… (1)
However,
θimg: Angle (°) between the screen normal of the screen surface and the axial principal ray incident on the screen surface,
It is.

  In order to reduce the thickness of the projection optical system, it is effective to tilt the screen surface. If the lower limit of conditional expression (1) is not reached, the oblique projection degree becomes weak and the effect of thinning becomes small. On the contrary, if the upper limit of conditional expression (1) is exceeded, the oblique projection degree becomes too strong, the substantial angle of view of the projection optical system becomes wide, and it becomes difficult to correct distortion and curvature of field.

  The projection optical system according to the present invention is a zoom optical system that changes the magnification while maintaining the positions of the display element surface and the screen surface substantially constant by changing the focal length of the entire system as described above. It is desirable. As described above, a part or all of the non-axis optical element (that is, the rotationally asymmetric reflecting mirror arranged eccentrically or the optical element group including the non-axial optical element) is translated and rotated toward the screen. The focal length of the entire projection optical system can be changed without changing the position and direction of the axial principal ray. When the screen is fixed at a fixed position, even if the projection magnification is changed by changing the focal length of the entire system, the position and direction of the axial principal ray toward the screen does not change, so the image on the axis moves. It does not do (that is, change position).

  For example, consider the case where the screen surface is on the primary image point position. The states before and after the change of the focal length of the entire system are referred to as focal length states I and II, respectively. The angle formed by the screen normal of the display element surface and the axial principal ray emitted from the display element surface is θobj, and the angle formed by the screen normal of the screen surface and the axial principal ray incident on the screen surface Is θimg. According to the method of performing the parallel movement and the rotation movement of the optical element group including the rotationally asymmetric reflecting mirror arranged eccentrically, the angles θobj and θimg are not changed between the focal length state I and the focal length state II. It is possible to change the focal length.

Consider a certain direction, such as the y direction. The focal length in the y direction in the focal length state I is fyI, and the distance measured along the axial principal ray from the display element surface to the front focal point of the entire projection optical system is XyI. Further, the focal length in the y direction in the focal length state II is fyII, and the distance measured along the axial principal ray from the display element surface to the front focal point of the entire projection optical system is XyII. At this time, the projection magnifications βyI and βyII in the y direction in the focal length states I and II are expressed by the following equations (Fr5) and (Fr6), respectively.
βyI = (− 1) × fyI / XyI × (cos (θimg) / cos (θobj)) (Fr5)
βyII = (-1) × fyII / XyII × (cos (θimg) / cos (θobj)) (Fr6)

  As can be seen from the equations (Fr5) and (Fr6), it is possible to change the magnification while keeping the screen constant by changing the focal length of the entire system. When scaling is possible with the screen kept constant, when temporarily enlarging projection or when using the projector in a room with limited space (for example, screen position, projector position, distance between screen and projector, etc.) Can also achieve the desired magnification.

It is desirable that the following conditional expression (2) is satisfied in changing the magnification from the smallest absolute value to an arbitrary magnification by changing the focal length of the entire system.
0.2 <| θzmov / Zz | <5.0 (2)
However,
θzmov: rotation angle (°) of the optical element group including the reflection mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is.

  Conditional expression (2) defines a preferable condition range for the magnitude of the rotation angle of the optical element group to be rotated for zooming. If the rotation angle increases beyond the upper limit of conditional expression (2), the rotation mechanism increases, leading to an increase in the size of the image projection apparatus. Moreover, since the use range of the surface in the optical element group is increased, the effective diameter of the optical element is increased, resulting in an increase in size and cost. Conversely, if the rotation angle becomes too small beyond the lower limit of conditional expression (2), the sensitivity of the change in focal length with respect to the rotation angle increases, so the optical element group including rotationally asymmetric reflection mirrors arranged eccentrically It becomes difficult to produce. In particular, when the change of the axial principal ray due to the angle error becomes large, it is necessary to increase the accuracy of the position control mechanism, and thus the movement mechanism becomes expensive. For example, a sensor is used for position detection, and a rotating mechanism with less backlash is required. If backlash occurs, the axis principal ray position draws a different trajectory when zooming to the enlargement side and zooming to the reduction side. Will be formed. In addition, there is a possibility that chattering may occur by increasing the position control accuracy, and it is necessary to take mechanism measures to prevent this and control measures (by circuit, software, etc.), so the image projection device is very expensive. End up.

It is desirable that the following conditional expression (3) is satisfied in changing the magnification from the smallest absolute value to an arbitrary magnification by changing the focal length of the entire system.
0.01 <| Szmov / (Zz × fz1) | <5.0 (3)
However,
Szmov: distance of translation of the optical element group including the reflecting mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is.

  Conditional expression (3) defines a preferable condition range for the amount of movement of the optical element group to be translated for zooming. If the movement amount exceeds the upper limit of conditional expression (3), a large space is required for movement, and the entire projection optical system cannot be made compact. Conversely, if the amount of movement is too small beyond the lower limit of conditional expression (3), the sensitivity to zooming becomes too high, making it difficult to manufacture optical elements that include rotationally asymmetric reflecting mirrors that are eccentrically arranged. become.

It is more desirable to satisfy the following conditional expression (3a).
0.5 <| Szmov / (Zz × fz1) | <4.0 (3a)
The conditional expression (3a) defines a more preferable condition range based on the above viewpoints, etc., among the condition ranges defined by the conditional expression (3).

It is desirable that the following conditional expressions (4) and (5) are satisfied in an arbitrary focal length state with a variable magnification due to a change in focal length of the entire system.
-50 <(Sz1st_ximg-Szx_design) / fzx <20 (4)
-50 <(Sz1st_yimg-Szy_design) / fzy <20 (5)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sz1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Szx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane.
fzx: focal length of the entire system in the x direction,
Sz1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Szy_design: The distance measured along the base ray from the rear principal point position in the y direction to the design image plane.
fzy: focal length of the entire system in the y direction,
It is.

  Let the focal lengths in the x direction and y direction in a certain arbitrary magnification state be fx and fy, respectively. In this state, the distances along the axial principal ray from the front focal point in each direction to the display element surface are denoted by Δx and Δy, respectively. S1st_ximg and S1st_yimg are the distances from the rear principal point position in each direction to the primary image point position in each direction measured along the axial principal ray. In this state, the distance from the rear principal point position in each direction to the design image plane is Sx_design and Sy_design, respectively.

Now, it is assumed that the display element surface and the screen surface are inclined along the YZ section (that is, in a state of being rotated around the x axis). The angle formed by the screen normal of the display element surface and the axial principal ray emitted from the display element surface is θobj, and the angle formed by the screen normal of the screen surface and the axial principal ray incident on the screen surface Is θimg. Further, the exit angle of the axial principal ray from the display element surface is θy, and the incident angle of the axial principal ray on the screen surface is θ′y. At this time, the projection magnifications βx and βy in the x and y directions are expressed by the following equations (Fr7) and (Fr8), respectively.
βx = (fx / Δx) · (Sx_design / S1st_ximg) (Fr7)
βy = (fy / Δy) · (Sy_design / S1st_yimg) · (cosθy / cosθ'y) (Fr8)

  The anamorphic ratio of the projection magnification is expressed by βx / βy. Usually, it is desirable that the anamorphic ratio during zooming is constant. When zooming, the design image plane (that is, the design image plane corresponding to the screen plane) is almost on the primary image plane (that is, the focal position corresponding to the paraxial image plane in the coaxial optical system). In the change of the projection magnification during zooming, the change of the focal length fx and the focal length fy is dominant. However, the tilt of the display element surface and the tilt of the screen surface affect the projection magnification in the y direction. For example, when the focal length in the x direction and the focal length in the y direction are changed by the same amount, the influence of the tilt of the display element surface and the screen surface is applied only in the y direction, and thus the anamorphic ratio is greatly changed. Therefore, in order to perform zooming with a constant anamorphic ratio, it is necessary to shift the position of the design image plane from the position of the primary image plane. That is, the anamorphic ratio can be made constant by changing the position of the primary image plane. However, if the primary image plane position and the design image plane position are greatly deviated, the focus position will be deviated and the performance will deteriorate. Conditional expressions (4) and (5) define an allowable range of deviation between the primary image plane position and the design image plane position. If the designed image plane deviates greatly from the primary image plane position outside the condition range defined by the conditional expressions (4) and (5), the focus is deviated and the performance is deteriorated.

The projection optical system according to the present invention preferably has, as the zoom optical system, a focusing function for focusing on different screen surface positions by parallel movement and rotational movement of an optical element having a rotationally asymmetric optical surface. In general, in an optical system, a magnification relationship represented by the following formula (Fr9) is established. Where ΔX ′ is the distance from the rear focal point to the image plane, ΔX is the distance from the front focal point to the object, and f is the focal length of the optical system.
ΔX ′ = − f ² / ΔX (Fr9)

  In a normal projection system, when the screen position changes, the focus position is adjusted by changing ΔX to change the value of ΔX ′. The above formula (Fr9) indicates that the value of ΔX ′ can be changed by changing the focal length f of the optical system at the same time. As described above, it is possible to change the focal length of the entire non-axis optical system by moving the eccentric non-rotationally symmetric optical element (for example, the reflection mirror). Further, if only the focal length of the entire system is changed, the portion of the coaxial system may be moved. However, it is preferable to use a portion moved by zooming for focusing. This is because if the part moved by zooming is moved and used for focusing, a new moving mechanism is not required for focusing, and the cost can be kept low.

It is desirable that the projection optical system according to the present invention, not limited to the zoom optical system, has a focusing function for focusing on different screen surface positions by changing the focal length of the entire system. Now consider focusing on a ray in the x direction. In a focus projection state (state III) with respect to a certain screen surface position, the focal length of the entire system is fxIII, the distance from the front focus to the display element surface is ΔXxIII, and the distance from the rear focus to the screen surface position is ΔX ′. Let xIII. When there is a primary image point at the screen surface position, the following equation (Fr10) holds.
ΔX′xIII = −fxIII ² / ΔXxIII (Fr10)

Next, in the focus projection state (state IV) when the screen surface position is changed and focused, the focal length of the entire system is fxIV, the distance from the front focus to the display element surface is ΔXxIV, and the rear side The distance from the focal point to the screen surface position is ΔX′xIV. At this time, the following equation (Fr11) is established.
ΔX′xIV = −fxIV ² / ΔXxIV (Fr11)

  Considering that there is a primary image point at the screen surface position even in the state IV, ΔX′xIV is usually set to the screen in order to be in focus even when the screen surface is changed from the state III to the state IV. What is necessary is just to change (DELTA) X'x so that it may become a surface position. However, in the case of a non-axis optical system, this can be realized by changing the focal length fx. That is, focusing can be performed by changing the focal length. Rather than moving the entire optical system to change ΔX′x, moving a part of the non-axial optical element to change the focal length is easier to move in terms of weight. In addition, when the axial principal ray emitted from the display element surface and the axial principal ray incident on the screen surface are not parallel, the center of the image moves when the whole is moved. The phenomenon occurs. As described above, according to the method of translating and rotating a part or all of the non-axial optical element (that is, the rotationally asymmetric reflecting mirror or the optical element group including the eccentrically arranged mirror), the center of the image is obtained. It is possible to change the focal length of the entire system without moving. Furthermore, there is an advantage that it is only necessary to move a part of the optical system without greatly moving the entire projection optical system. Accordingly, it is desirable to perform focusing by changing the focal length of the entire system.

In focusing from the closest projection state closest to the screen surface to an arbitrary focus projection state due to the change in the focal length of the entire system, it is desirable to satisfy the following conditional expression (6).
0.2 <| θfmov / Zfoc | <8.0 (6)
However,
θfmov: rotation angle (°) of the optical element group including the reflection mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is.

  Conditional expression (6) defines a preferable condition range for the magnitude of the rotation angle of the optical element group to be rotated for focusing. If the rotation angle increases beyond the upper limit of conditional expression (6), the rotation mechanism increases and the size of the image projection apparatus increases. Moreover, since the use range of the surface in the optical element group is increased, the effective diameter of the optical element is increased, resulting in an increase in size and cost. Conversely, if the rotation angle becomes too small beyond the lower limit of conditional expression (6), the sensitivity of the change in focal length with respect to the rotation angle increases, so the optical element group including rotationally asymmetric reflection mirrors arranged eccentrically It becomes difficult to produce. In particular, when the change of the axial principal ray due to the angle error becomes large, it is necessary to increase the accuracy of the position control mechanism, and thus the movement mechanism becomes expensive. For example, it is necessary to reduce the positional deviation by using a sensor for position detection. Therefore, the image projection apparatus becomes very expensive.

In focusing from the closest projection state closest to the screen surface to the arbitrary focus projection state due to the change in the focal length of the entire system, it is desirable to satisfy the following conditional expression (7).
0.05 <| Sfmov / (Zfoc × ff1) | <7.0 (7)
However,
Sfmov: distance of translation of the optical element group including the reflecting mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is.

  Conditional expression (7) defines a preferable condition range for the amount of movement of the optical element group to be translated for focusing. If the amount of movement exceeds the upper limit of conditional expression (7), a large space is required for movement, and the entire projection optical system cannot be made compact. Conversely, if the amount of movement is too small beyond the lower limit of conditional expression (7), the sensitivity to focusing becomes too high, making it difficult to manufacture an optical element group including rotationally asymmetric reflecting mirrors arranged eccentrically. Become.

It is more desirable to satisfy the following conditional expression (7a).
0.5 <| Sfmov / (Zfoc × ff1) | <3.0 (7a)
The conditional expression (7a) defines a more preferable condition range based on the above viewpoints, etc., among the condition ranges defined by the conditional expression (7).

It is desirable that the following conditional expressions (8) and (9) are satisfied in an arbitrary focal length state during focusing by changing the focal length of the entire system.
-50 <(Sf1st_ximg-Sfx_design) / ffx <20 (8)
-50 <(Sf1st_yimg-Sfy_design) / ffy <20 (9)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sf1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Sfx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane,
ffx: focal length of the entire system in the x direction,
Sf1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Sfy_design: The distance measured along the base ray from the back principal point position in the y direction to the design image plane,
ffy: focal length of the entire system in the y direction
It is.

  The focal lengths in the x and y directions in a certain focus projection state are assumed to be fx and fy, respectively. In this state, the distances along the axial principal ray from the front focal point in each direction to the display element surface are denoted by Δx and Δy, respectively. S1st_ximg and S1st_yimg are the distances from the rear principal point position in each direction to the primary image point position in each direction measured along the axial principal ray. In this state, the distance from the rear principal point position in each direction to the design image plane is Sx_design and Sy_design, respectively.

Now, it is assumed that the display element surface and the screen surface are inclined along the YZ section (that is, in a state of being rotated around the x axis). The angle formed by the screen normal of the display element surface and the axial principal ray emitted from the display element surface is θobj, and the angle formed by the screen normal of the screen surface and the axial principal ray incident on the screen surface Is θimg. Further, the exit angle of the axial principal ray from the display element surface is θy, and the incident angle of the axial principal ray on the screen surface is θ′y. At this time, the projection magnifications βx and βy in the x and y directions are expressed by the following equations (Fr7) and (Fr8), respectively.
βx = (fx / Δx) · (Sx_design / S1st_ximg) (Fr7)
βy = (fy / Δy) · (Sy_design / S1st_yimg) · (cosθy / cosθ'y) (Fr8)

  The anamorphic ratio of the projection magnification is expressed by βx / βy. Usually, it is desirable that the anamorphic ratio during focusing be constant. When the design image plane (that is, the design image plane corresponding to the screen plane) is on the primary image plane (that is, the focal position corresponding to the paraxial image plane in the coaxial optical system) during focusing. In the change in the focusing projection magnification, the change in the focal length fx and the focal length fy is dominant. However, the tilt of the display element surface and the tilt of the screen surface affect the projection magnification in the y direction. For example, when the focal length in the x direction and the focal length in the y direction are changed by the same amount, the influence of the tilt of the display element surface and the screen surface is applied only in the y direction, and thus the anamorphic ratio is greatly changed. Therefore, in order to perform focusing with a constant anamorphic ratio, it is necessary to shift the position of the design image plane from the position of the primary image plane. That is, the anamorphic ratio can be made constant by changing the position of the primary image plane. However, if the primary image plane position and the design image plane position are greatly deviated, the focus position will be deviated and the performance will deteriorate. Conditional expressions (8) and (9) define an allowable range of deviation between the primary image plane position and the design image plane position. If the condition range defined by the conditional expressions (8) and (9) is not satisfied and the design image plane is greatly deviated from the primary image plane position, the focus is shifted and the performance is deteriorated.

  As described above, it is possible to focus on different screen positions by translating and rotating a rotationally asymmetric reflecting mirror, and to zoom for use at different projection magnifications. It is. From these facts, the projection optical system according to the present invention can be used as a single-focus projection optical system separately for two or more screen positions, and separately at a projection magnification of two or more. Obviously, it can be used as a focal point projection optical system.

  For example, when a projection optical system with specifications for enlarging and projecting on two different screen positions is required, or when a projection optical system with two different projection magnifications is required, two projection optical systems are usually required. . However, if the projection optical system according to the present invention is used, two projection optical systems are unnecessary, and one projection optical system is sufficient. In order to satisfy these specifications, at least one optical element group including at least one rotationally asymmetric reflecting mirror arranged eccentrically may be translated and rotated. By performing such adjustment, it is possible to deal with image projection apparatuses having different specifications with one projection optical system. Therefore, the cost can be significantly reduced. In addition, the parallel movement and rotational movement of the optical element group can be used when finely adjusting the actual image projection apparatus individually.

  Therefore, the reflection mirror has a rotationally asymmetric reflection mirror arranged eccentrically, and is used in any one of a state of projecting to a screen position and a state of projecting to a screen position different from the state. By having a configuration in which at least one optical element group including can be translated and rotated, it is possible to correspond to the specifications for enlarging and projecting to at least two screen positions or to perform fine adjustment thereof. Further, it has a rotationally asymmetric reflecting mirror arranged eccentrically, and includes at least one reflecting mirror to be used in any one of a certain projection magnification state and another projection magnification state different from the state. By having a configuration in which the two optical element groups can be translated and rotated, it is possible to correspond to the specifications for enlarging and projecting at least two projection magnifications, and to perform fine adjustment thereof.

  Next, a specific optical configuration of the projection optical system according to the present invention will be described using the first to fourth embodiments as examples. 1 to 4 show the optical configuration (optical arrangement, projection light path, etc.) of the entire projection light path from the display element surface SG to the screen surface SL in the first to fourth embodiments, and the screen length of the display element surface SG. Each is shown by an optical cross section (short side cross section) when viewed along the side direction. Moreover, the principal part (from the display element surface SG to the 2nd curved mirror M2) of the optical structure shown in FIGS. 1-4 is expanded and shown in FIGS. 5-8, respectively. FIG. 1A shows the optical arrangement at the wide-angle end in zooming and the closest projection state in focusing, and FIG. 1B shows the optical arrangement at the telephoto end in zooming and the closest projection state in focusing. Yes. FIG. 2 shows an optical arrangement at the wide-angle end in zooming and the closest projection state in focusing. FIGS. 3 and 4 show an optical arrangement in the closest projection state in focusing. 1 to 8, the screen normal direction of the display element surface SG is the z direction, and the direction perpendicular to the plane formed by the axial principal ray toward the screen and the normal of the screen surface is the x direction, perpendicular to them. In the Cartesian coordinate system (x, y, z) in which any direction is the y direction, the optical configurations of the first to fourth embodiments are shown in the yz section. In each embodiment, the x direction coincides with the screen short side direction of the display element surface SG, and the y direction coincides with the screen long side direction of the display element surface SG.

  The projection optical system PO of the first and second embodiments is a zoom optical system having a focusing function and a zooming function, and sequentially from the reduction side (display element surface SG side) to the enlargement side (screen surface SL side). A refractive optical system LG composed of a plurality of i-th lenses Li (i = 1, 2, 3,...), A first curved mirror M1, a second curved mirror M2, and a plane mirror MF. It is made up. Also, an intermediate image is formed in the space between the first curved mirror M1 and the second curved mirror M2, and the angle formed between the screen surface SL and the axial principal ray incident on the screen surface SL is not vertical, so-called. The configuration is such that oblique enlargement projection is performed.

  The projection optical system PO of the third and fourth embodiments is an optical system having a focusing function, and in order from the reduction side (display element surface SG side) to the enlargement side (screen surface SL side) The optical system LG includes a refractive optical system LG including a lens Li (i = 1, 2, 3,...), A first curved mirror M1, and a second curved mirror M2. Also, an intermediate image is formed in the space between the first curved mirror M1 and the second curved mirror M2, and the angle formed between the screen surface SL and the axial principal ray incident on the screen surface SL is not vertical, so-called. The configuration is such that oblique enlargement projection is performed.

  In the first to fourth embodiments, the first curved mirror M1 and the second curved mirror M2 are rotationally asymmetric reflecting mirrors that are eccentrically arranged, and the shape of the reflecting surface is a free-form surface. The projection optical system PO is plane-symmetric with respect to the yz plane. The reflection surface shapes of the first and second curved mirrors M1 and M2 are plane symmetric, and the plane of symmetry is the yz plane. The projection optical system PO of the first to fourth embodiments has a focusing function for focusing on different screen surface positions by changing the focal length of the entire system. Further, the projection optical system PO according to the first and second embodiments can perform zooming to change the magnification while maintaining the positions of the display element surface and the screen surface substantially constant by changing the focal length of the entire system. It has a function. When at least one of focusing and zooming is performed, at least the first and second curved mirrors M1 and M2 are configured to perform translation and rotation, respectively, in order to change the focal length of the entire system. .

  In the first embodiment, in zooming, the first to fourth lenses L1 to L4 and the fifth to seventh lenses L5 to L7 perform parallel movement, respectively, and the eighth lens L8 and the first curved mirror. M1 and the second curved mirror M2 perform parallel movement and rotational movement, respectively. In focusing, the eighth lens L8 performs translation and rotation. In the second embodiment, in zooming, the first to fourth lenses L1 to L4 and the fifth to seventh lenses L5 to L7 perform parallel movement, respectively, and the eighth lens L8 and the first curved mirror. M1 and the second curved mirror M2 perform parallel movement and rotational movement, respectively. In focusing, the first curved mirror M1 and the second curved mirror M2 perform parallel movement and rotational movement, respectively. In the third embodiment, in focusing, the fifth lens L5 performs parallel movement, and the second curved mirror M2 performs parallel movement and rotational movement. In the fourth embodiment, the first curved mirror M1 performs parallel movement and rotational movement during focusing.

  As described above, in the first to fourth embodiments, the focal length of the entire system changes due to the parallel movement and the rotational movement of at least the first curved mirror M1 or the second curved mirror M2. Zooming and focusing can be performed without causing image distortion in oblique projection by a non-axis optical system while achieving reduction in size and size. The first and second curved mirrors M1 and M2 are optical element groups including rotationally asymmetric reflecting mirrors that are eccentrically arranged, and the focal length of the entire system is changed by the parallel movement and rotational movement of each optical element group. However, as can be seen from each embodiment, when changing the focal length of the entire system, the optical element group (lens group or the like) other than the first and second curved mirrors M1 and M2 may be moved. . That is, it is sufficient if at least one optical element group including a rotationally asymmetric reflecting mirror arranged eccentrically is one of the moving groups, and the focal length of the entire system is changed by at least the parallel movement and the rotational movement.

  In the projection optical system PO of each embodiment, a reflecting surface composed of the first and second curved mirrors M1, M2 and the plane mirror MF is disposed between the display element surface SG and the screen surface SL. As in each embodiment, it is desirable to have one or two reflecting surfaces between the display element surface and the screen surface. By bending the optical path at the reflecting surface, the projection optical system can be made compact. If the number of reflecting surfaces is increased, the projection optical system can be made more compact. Therefore, it is desirable that the projection optical system has two or more reflecting surfaces. By having two or more reflecting surfaces, the projection optical system can be bent in a direction substantially parallel to the screen surface. As a result, the size of the projection optical system can be reduced in the depth direction of the screen, and the projection space of the projection optical system can be reduced. It is also possible to reduce the size of the projection optical system in the height direction of the screen by adding a reflecting surface in the projection optical system to bend the optical path.

  It is desirable that all reflecting surfaces have power. By giving power to the reflecting surface, it is possible to correct the aberration on the reflecting surface, and it is possible to correct the aberration of the entire projection optical system. Therefore, it is possible to obtain higher optical performance by giving power to all the reflecting surfaces.

  The reflecting surface having power preferably has a free-form surface shape. The free-form surface has a merit that since the degree of freedom in design is high, the degree of freedom in setting the light deflection direction is high. Further, by using a free-form surface shape, it is possible to satisfactorily correct aberrations such as image plane tilt and astigmatism. Furthermore, it is desirable that the free-form surface used for the reflecting surface has one plane of symmetry. A free-form surface having a symmetric surface has an advantage of low difficulty in manufacturing and evaluation.

  It is desirable to install the reflecting surface at a position closest to the screen surface in the projection optical system. A space necessary for projecting an image can be made compact by installing a reflecting surface near the screen surface and bending the optical path. In addition, since the light beams having different angles of view incident on the reflection surface are separated, a high aberration correction effect can be obtained by disposing a reflection surface having a free-form surface.

  The base of the mirror including the free-form surface and the refractive lens are preferably made of a plastic material. By using plastic as a constituent material of an optical element (mirror, lens, etc.) including a free-form surface, it is possible to achieve cost reduction of the optical element. For example, an eighth lens L8 of Examples 3 and 4 to be described later is a glass lens having an anamorphic aspheric surface, but it can be replaced with a plastic lens.

  The projection optical system PO of each embodiment has a refractive optical system LG composed of a refractive optical element having power. As in each embodiment, it is desirable that the projection optical system has at least one refractive optical element having power. By using a refracting optical element having power, it is possible to correct aberrations that cannot be corrected only by the reflecting surface, such as chromatic aberration generated in the color synthesis prism. The characteristic configuration of the present invention is not limited to being applied to a projection optical system having a refracting optical element, but can also exhibit the same effect when applied to a projection optical system having only a mirror.

  As the refracting surface, it is desirable to use surfaces having different powers in the x-axis direction and the y-axis direction (that is, anamorphic aspheric surfaces). By using refracting surfaces having different powers in the x-axis direction and the y-axis direction, it is possible to correct asymmetric aberrations in the x-axis direction and the y-axis direction. Refractive surfaces having different powers in the x-axis direction and the y-axis direction are preferably used as surfaces close to the screen surface. However, since the luminous fluxes at the respective angles of view are separated on the surface closest to the screen surface, it is desirable to arrange a reflecting surface having a free-form surface in order to obtain a high aberration correction effect.

  During zooming, it is preferable to move the non-rotationally symmetric reflecting surfaces arranged eccentrically on the two surfaces because aberration variations due to zooming can be corrected well. Further, at the time of focusing, it is preferable to move the non-rotationally symmetric reflecting surface in which one or two surfaces are eccentrically arranged because aberration fluctuations due to focusing can be corrected well. In addition, it is preferable to move the optical element having a non-rotationally symmetric transmission surface arranged eccentrically on two surfaces because aberration variations due to focusing can be favorably corrected. Further, during focusing, it is preferable to move a total of two optical elements, one reflective optical element and one refractive optical element, because aberration fluctuations due to focusing can be favorably corrected. Of course, it is also possible to perform focusing using only a reflective optical element or a refractive optical element.

  It is desirable to form an intermediate image once in the projection optical system and then form the intermediate image on the screen surface with a reflecting surface. By giving aberration to the intermediate image so as to cancel out the distortion generated by the optical element located on the screen surface side of the intermediate image, it is possible to obtain a good optical performance on the screen surface even though it is a wide-angle projection optical system. Is possible. Moreover, since the size of the reflecting surface can be reduced by forming the intermediate image, the manufacturing of the reflecting surface is facilitated.

  The reflecting surface closest to the screen surface is preferably a concave surface. By using the concave reflecting surface as the reflecting surface closest to the screen surface, an intermediate image can be formed by the power of the concave reflecting surface. Therefore, it is possible to correct aberrations of the entire projection optical system such as distortion and inclination of the image plane using the aberration of the intermediate image. When the reflective surface closest to the screen surface is a convex reflective surface, a positive power optical element is required in addition to the convex mirror in order to form an intermediate image once formed on the screen surface. For this reason, it is difficult to reduce the size of the configuration in which the intermediate image is formed. Therefore, when the reflective surface closest to the screen surface is a convex reflective surface and an intermediate image is not formed, it is desirable to add a free-form refractive optical element or reflective optical element for aberration correction.

  The first to fourth embodiments are projection optical systems PO for an image projection apparatus that project an enlarged display image on a screen surface SL. Accordingly, the display element surface SG corresponds to an image forming surface on which a two-dimensional image is formed by modulation of light intensity or the like, and the screen surface SL corresponds to the projected image surface. In each embodiment, a digital micromirror device is assumed as a display element. However, the display element is not limited to this, and other non-light-emitting / reflective type (or a suitable type) for the projection optical system PO of each embodiment (or A transmission type display element (for example, a liquid crystal display element) may be used. When a digital micromirror device is used as a display element, when the display element surface SG is illuminated with an illumination optical system, the light incident on the display element surface SG is in an ON / OFF state (for example, an inclination state of ± 12 °). It is spatially modulated by being reflected by each micromirror. At that time, only the light reflected by the micromirrors in the ON state enters the projection optical system PO and is projected onto the screen surface SL.

  As can be seen from the above description, each of the above-described embodiments and each example described later includes the following configurations of the projection optical system and the image projection apparatus. According to this configuration, as described above, it is possible to perform zooming and focusing without causing image distortion in oblique projection by a non-axis optical system while achieving high performance and compactness of the projection optical system.

  (T1) A projection optical system for enlarging and projecting an image of the display element surface onto the screen surface, and the angle formed between the screen surface and the axial principal ray incident on the screen surface is not vertical, but is rotated eccentrically A projection having an asymmetric reflection mirror, wherein at least one optical element group including the reflection mirror is used as a moving group, and the focal length of the entire system is changed by at least parallel movement and rotational movement of the optical element group. Optical system.

  (T2) The projection optical system according to (T1), wherein the conditional expression (1) is satisfied.

  (T3) The above (T1) or (T1), wherein the zoom optical system changes the magnification while maintaining the positions of the display element surface and the screen surface substantially constant by changing the focal length of the entire system. The projection optical system according to (T2).

  (T4) In changing magnification from the smallest absolute value to an arbitrary magnification by changing the focal length of the entire system, at least one of the conditional expressions (2), (3), (3a) is The projection optical system according to (T3) above, characterized in that:

  (T5) Projection optics according to the above (T3) or (T4), wherein the conditional expressions (4) and (5) are satisfied in an arbitrary focal length state at a variable magnification due to a change in focal length of the entire system system.

  (T6) The zoom optical system has a focusing function for focusing on different screen surface positions by parallel movement and rotational movement of an optical element having a rotationally asymmetric optical surface. The projection optical system according to any one of the above.

  (T7) The projection optical system according to (T1) or (T2) above, wherein the projection optical system has a focusing function for focusing on different screen surface positions by changing the focal length of the entire system.

  (T8) At least one of the conditional expressions (6), (7), and (7a) in focusing from the closest projection state closest to the screen surface to an arbitrary focus projection state due to the change in the focal length of the entire system The projection optical system described in (T7) above, wherein:

  (T9) The projection optical system according to (T7) or (T8), wherein the conditional expressions (8) and (9) are satisfied in an arbitrary focal length state in focusing by a change in focal length of the entire system .

  (T10) A projection optical system for enlarging and projecting an image of a display element surface on a screen surface, and the angle formed between the screen surface and the axial principal ray incident on the screen surface is not vertical, but is rotated eccentrically At least one optical element group having an asymmetric reflection mirror and including the reflection mirror for use in any one of a state of projecting to a screen position and a state of projecting to a screen position different from the state A projection optical system characterized by having a configuration capable of parallel movement and rotational movement.

  (T11) A projection optical system for enlarging and projecting an image of a display element surface on a screen surface, and the angle formed by the screen surface and the axial principal ray incident on the screen surface is not vertical, but is rotated eccentrically A translational movement of at least one optical element group including the reflection mirror for use in any one of a certain projection magnification state and another projection magnification state different from that state, having an asymmetric reflection mirror; A projection optical system having a configuration capable of rotational movement.

  (U1) An image projection apparatus comprising: a display element that forms a two-dimensional image; and a projection optical system that magnifies and projects an image of the display element surface onto a screen surface, wherein the projection optical system is the above ( An image projection apparatus, which is the projection optical system according to any one of T1) to (T11).

  (U2) comprising a display element for forming a two-dimensional image and a projection optical system for enlarging and projecting the image of the display element surface onto the screen surface, and comprising the screen surface and an axial principal ray incident on the screen surface An image projection apparatus having a non-vertical angle, wherein the projection optical system includes a rotationally asymmetric reflecting mirror arranged eccentrically, and at least one optical element group including the reflecting mirror is used as a moving group, An image projection apparatus characterized in that the focal length of the entire system is changed by parallel movement and rotational movement of an optical element group.

  Hereinafter, the projection optical system and the like embodying the present invention will be described more specifically with reference to construction data and the like. Examples 1 to 4 listed here are numerical examples corresponding to the first to fourth embodiments, respectively, and are optical path diagrams representing the optical configurations of the first to fourth embodiments (FIG. 1). 4 to 4) show the optical arrangement, projection optical path, and the like of the corresponding first to fourth embodiments.

  Tables 1 to 27 show construction data of Examples 1 to 4. In the basic optical configurations shown in Table 1, Table 7, Table 13, and Table 19, the basic arrangement is the wide angle end and closest projection state in Examples 1 and 2, and the closest projection state in Examples 3 and 4. ), A system including a display element surface SG on the reduction side (S0: an image display surface of the display element and corresponding to an object surface) to a screen surface SL on the enlargement side (corresponding to an image surface). Si (surface number: i = 0, 1, 2, 3,...) Is the i-th surface counted from the reduction side, and ri (i = 0, 1, 2, 3,...) Is a surface. It is a curvature radius (mm) of Si. Also, di (i = 0, 1, 2, 3,...) Is the axial upper surface distance between the surface Si and the surface Si + 1 (mm, but in the case of the eccentric surface interval, as eccentric data or eccentricity Ni (i = 0, 1, 2, 3,...), Νi (i = 0, 1, 2, 3,...) The refractive index (Nd) and Abbe number (νd) for the d-line of the optical material positioned are shown.

  The eccentric surface is indicated by A in the corresponding column * of the surface Si, and the eccentric data is shown in Table 2, Table 8, Table 14, and Table 20. The eccentricity data is expressed based on a right-handed orthogonal coordinate system (X, Y, Z). In the orthogonal coordinate system (X, Y, Z), the center position of the surface Si as a coordinate reference is set to the origin (0, 0,0) plane vertex coordinates (X, Y, Z) = {parallel eccentric position in the X-axis direction (mm), parallel eccentric position in the Y-axis direction (mm), parallel eccentric position in the Z-axis direction (mm) } Represents the position of the parallel decentered surface, and represents the inclination (°) of the surface by the rotation angle (X rotation, Y rotation, Z rotation) around each axis around the surface vertex of the surface. In addition, when the surface Si as the coordinate reference is the display element surface S0, the screen normal direction of the display element surface S0 is the z direction, the screen short side direction of the display element surface S0 is the y direction, and the display element surface S0 An orthogonal coordinate system (x, y, z) having the long side direction of the screen as the x direction is an orthogonal coordinate system (X, Y, Z) of the plane Si as a coordinate reference, and each optical path diagram (FIGS. 1 to 8). ), The X-axis direction is a direction perpendicular to the paper surface (the back surface direction of the paper surface is positive, and the counterclockwise rotation toward the paper surface is X rotation positive), and the Y-axis direction is the X-axis and Z-axis. The direction is a right-handed system (parallel to the page).

  The surface moved by zooming is indicated by adding B to the corresponding column * of the surface Si, and zoom data thereof are shown in Tables 3 and 9 (the focus projection state is the closest projection state, and the zoom position POS is Wide angle end W, middle (intermediate focal length state) M and telephoto end T.) The zoom data is expressed on the basis of the axial top surface distance di and the right-handed orthogonal coordinate system (X, Y, Z). In the orthogonal coordinate system (X, Y, Z), the center position of the surface Si as a coordinate reference is expressed. Coordinates of surface vertex (X, Y, Z) with {0, 0, 0) as the origin (= X axis direction translation position (mm), Y axis direction translation position (mm), Z axis direction parallel The movement position (mm)} represents the position of the translated surface, and the inclination of the surface (°) at a rotation angle (X rotation, Y rotation, Z rotation) about each axis around the surface vertex of the surface. Represents. In addition, when the surface Si as the coordinate reference is the display element surface S0, the screen normal direction of the display element surface S0 is the z direction, the screen short side direction of the display element surface S0 is the y direction, and the display element surface S0 An orthogonal coordinate system (x, y, z) having the long side direction of the screen as the x direction is an orthogonal coordinate system (X, Y, Z) of the plane Si as a coordinate reference, and each optical path diagram (FIGS. 1 to 8). ), The X-axis direction is a direction perpendicular to the paper surface (the back surface direction of the paper surface is positive, and the counterclockwise rotation toward the paper surface is X rotation positive), and the Y-axis direction is the X-axis and Z-axis. The direction is a right-handed system (parallel to the page).

  The surface moved by focusing is indicated by adding C to the corresponding column * of the surface Si, and the zoom data is shown in Tables 4, 10, 15, and 21 (from the closest projection state to the long-distance projection state). The zoom position POS is at the wide-angle end W, the middle (intermediate focal length state) M, and the telephoto end T). The focus data is expressed on the basis of the axial upper surface distance di and the right-handed orthogonal coordinate system (X, Y, Z). In the orthogonal coordinate system (X, Y, Z), the center position of the surface S0 as the coordinate reference is expressed. Coordinates of surface vertex (X, Y, Z) with {0, 0, 0) as the origin (= X axis direction translation position (mm), Y axis direction translation position (mm), Z axis direction parallel The movement position (mm)} represents the position of the translated surface, and the inclination of the surface (°) at a rotation angle (X rotation, Y rotation, Z rotation) about each axis around the surface vertex of the surface. Represents. However, description of data that does not change due to focusing is omitted. In the orthogonal coordinate system (X, Y, Z) of the display element surface S0 as the coordinate reference, the screen normal direction of the display element surface S0 is the Z direction, and the screen short side direction of the display element surface S0 is the Y direction. The screen long side direction of the element surface S0 is the X direction, and in each optical path diagram (FIGS. 1 to 8), the X-axis direction is a direction perpendicular to the paper surface (the back surface direction of the paper surface is positive, and it faces the paper surface). The Y-axis direction is the direction (parallel to the paper surface) that forms the right-handed system by the X-axis and the Z-axis.

A surface Si composed of a rotationally symmetric aspheric surface is indicated by A in the corresponding column # of the surface Si. A surface Si composed of a rotationally symmetric aspherical surface is defined by the following expression (AS) using a local orthogonal coordinate system (x, y, z) having the surface vertex as an origin. Table 5, Table 11, Table 16, and Table 22 show the aspheric surface data of each example. However, the coefficient of the term without description is 0, and E−n = × 10 ⁻ⁿ for all data.
z = (c · h ² ) / [1 + √ {1− (1 + K) · c ² · h ² }] + A · h ⁴ + B · h ⁶ + C · h ⁸ + D · h ¹⁰ + E · h ¹² + F · h ¹⁴ + G · h ¹⁶ + H · h ¹⁸ + J · h ²⁰ (AS)
However, in the formula (AS)
z: amount of displacement in the z-axis direction at the position of height h (based on the surface vertex),
h: height in the direction perpendicular to the z-axis (h ² = x ² + y ² ),
c: curvature at the surface vertex (= 1 / ri),
K: cone coefficient,
A, ..., J: aspheric coefficient,
It is.

For the surface Si composed of an anamorphic aspheric surface, B is shown in the corresponding column # of the surface Si. A surface Si composed of an anamorphic aspheric surface is defined by the following equation (BS) using a local orthogonal coordinate system (x, y, z) having the surface vertex as an origin. Tables 17 and 23 show the anamorphic aspheric data of Examples 3 and 4. However, the coefficient of the term without description is 0, and E−n = × 10 ⁻ⁿ for all data.
z = (CUX · x ² + CUY · y ² ) / [1 + √ {1− (1 + KX) · CUX ² · x ² − (1 + KY) · CUY ² · y ² }] + AR · {(1−AP) · x ² + (1 + AP) · y ² } ² + BR · {(1−BP) · x ² + (1 + BP) · y ² } ³ + CR · {(1−CP) · x ² + (1 + CP) · y ² } ⁴ + DR · {(1−DP) · x ² + (1 + DP) · y ² } ⁵ (BS)
However, in the formula (BS)
x, y: Cartesian coordinates in a plane perpendicular to the z axis,
z: the amount of displacement in the z-axis direction at the coordinates (x, y) (based on the surface vertex),
CUX: curvature in the x-axis direction at the surface vertex,
CUY: curvature in the y-axis direction at the surface vertex,
KX: cone coefficient in the x-axis direction,
KY: the cone coefficient in the y-axis direction,
AR, BR, CR, DR: rotationally symmetric components of fourth, sixth, eighth, and tenth order deformation coefficients from a cone,
AP, BP, CP, DP: non-rotation symmetric components of fourth, sixth, eighth, and tenth order deformation coefficients from a cone,
It is.

For the surface Si composed of a free-form surface, C is shown in the corresponding column # of the surface Si. A surface Si composed of a free-form surface is defined by the following equation (CS) using a local orthogonal coordinate system (x, y, z) having the surface vertex as an origin. Table 6, Table 12, Table 18, and Table 24 show the polynomial free-form surface data of each example. However, the coefficient of the term without description is 0, and E−n = × 10 ⁻ⁿ for all data.

…(CS)

… (CS)

However, in the formula (CS)
z: amount of displacement in the z-axis direction at the position of height h (based on the surface vertex),
h: height in the direction perpendicular to the z-axis (h ² = x ² + y ² ),
c: paraxial curvature (= 1 / ri),
k: cone coefficient,
C _j : polynomial free-form surface coefficient,
The free-form surface term is expressed by the following formula (CF).

…(CF)

… (CF)

  Table 25 shows the amount of translation ΔS (mm) and the movement direction φ (°) and the rotational movement of the optical element group that moves integrally during zooming and the optical element group that moves integrally during focusing. The rotation angle θ (°) is shown. As shown in FIG. 24 (A), the movement direction φ of the parallel movement is positive in the counterclockwise direction with respect to the z axis, and the rotation angle θ of the rotational movement is positive in the counterclockwise direction as shown in FIG. 24 (B). And Further, focusing is performed from the closest projection state to the far-distance projection state (in the case of zoom optical system, the zoom position is the telephoto end T), and zooming is performed from the wide-angle end W to the telephoto end T in the closest projection state. Done.

  Table 26 shows the projection magnification of the entire system (the average value of the projection magnification βx in the screen long side direction and the projection magnification βy in the screen short side direction), and Table 27 shows the effective area of the display element surface SG (object surface S0). The size (mm), NA (numerical aperture) and aperture radius (mm) on the display element side are shown. Tables 28 to 32 show the correspondence data of the conditional expressions for each example.

  The optical performance of each example is shown by spot diagrams (FIGS. 9 to 17). 9 is a spot diagram in the wide-angle end W of the first embodiment, in the closest projection state, FIG. 10 is a middle M in the first embodiment, a spot diagram in the closest projection state, and FIG. 11 is a telephoto end T in the first embodiment. FIG. 12 is a spot diagram in the closest projection state, and FIG. 12 is a spot diagram in the wide angle end W, long distance projection state of the first embodiment. 13 is a spot diagram in the middle M of the first embodiment, in the long-distance projection state, FIG. 14 is a telephoto end T in the first embodiment, a spot diagram in the long-distance projection state, and FIG. 15 is a wide-angle end W in the second embodiment. FIG. 16 is a spot diagram in the closest projection state of the third embodiment, and FIG. 17 is a spot diagram in the closest projection state of the fourth embodiment. Each spot diagram shows the imaging characteristics (mm) on the screen surface SL for three wavelengths, C-line (wavelength 656.3 nm), d-line (wavelength 587.6 nm) and g-line (wavelength 435.8 nm). The field position of each spot indicates coordinates (x, y) on the display element surface SG (object surface S0).

The optical path figure which shows the optical structure to the screen surface of 1st Embodiment (Example 1). The optical path figure which shows the optical structure to the screen surface of 2nd Embodiment (Example 2). The optical path figure which shows the optical structure to the screen surface of 3rd Embodiment (Example 3). The optical path figure which shows the optical structure to the screen surface of 4th Embodiment (Example 4). The optical path figure which shows the optical structure to the 2nd curved-surface mirror of 1st Embodiment (Example 1). The optical path figure which shows the optical structure to the 2nd curved surface mirror of 2nd Embodiment (Example 2). The optical path figure which shows the optical structure to the 2nd curved surface mirror of 3rd Embodiment (Example 3). The optical path figure which shows the optical structure to the 2nd curved surface mirror of 4th Embodiment (Example 4). FIG. 2 is a spot diagram of the first embodiment at a wide angle end and a closest projection state. FIG. FIG. 2 is a spot diagram in the middle and closest projection state of Example 1. FIG. 2 is a spot diagram in the telephoto end and closest projection state of Embodiment 1. FIG. 2 is a spot diagram in the wide-angle end and long-distance projection state according to the first embodiment. 2 is a spot diagram in the middle, long-distance projection state of Example 1. FIG. FIG. 2 is a spot diagram in the telephoto end and long-distance projection state of Embodiment 1. FIG. FIG. 7 is a spot diagram in the wide-angle end and closest projection state of Example 2. FIG. FIG. 6 is a spot diagram in the closest projection state according to the third embodiment. FIG. 7 is a spot diagram in the closest projection state according to the fourth embodiment. The schematic diagram for demonstrating the optical path change at the time of parallel-translating two mirrors to the same direction simultaneously. The schematic diagram for demonstrating the optical path change at the time of translating two mirrors by different amount in a different direction. The schematic diagram for demonstrating the optical path change at the time of shifting only two mirrors independently so that the position and direction of the axial principal ray which inject | emits may not change. The schematic diagram for demonstrating the optical path change at the time of adding rotation to mirror movement and changing the focal distance of the whole system. The schematic diagram for demonstrating the power change in one non-axial optical surface. The schematic diagram for demonstrating the power change in two non-axis optical surfaces. The schematic diagram for demonstrating the direction of the parallel movement of a reflective mirror, and a rotational movement.

Explanation of symbols

SG Display element surface SL Screen surface PO Projection optical system (zoom optical system)
M1 first curved mirror (reflection mirror, optical element group)
M2 Second curved mirror (reflection mirror, optical element group)
MF plane mirror LG refractive optical system L1-L8 1st-8th lens ST stop

Claims (14)

  A projection optical system for enlarging and projecting an image of a display element surface on a screen surface, where the angle formed by the screen surface and an axial principal ray incident on the screen surface is not vertical, but is a rotationally asymmetric reflection arranged eccentrically A projection optical system comprising a mirror, wherein the focal length of the entire system is changed by translation and rotation of at least one optical element group including the reflection mirror. The projection optical system according to claim 1, wherein the following conditional expression (1) is satisfied:
30 <| θimg | <70… (1)
However,
θimg: Angle (°) between the screen normal of the screen surface and the axial principal ray incident on the screen surface,
It is.   3. A projection optical system according to claim 1, wherein the zoom optical system changes the magnification while maintaining the positions of the display element surface and the screen surface substantially constant by changing the focal length of the entire system. Optical system. 4. The projection optical system according to claim 3, wherein the following conditional expression (2) is satisfied in zooming from an enlargement magnification having the smallest absolute value to an arbitrary enlargement magnification due to a change in focal length of the entire system:
0.2 <| θzmov / Zz | <5.0 (2)
However,
θzmov: rotation angle (°) of the optical element group including the reflection mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is. 5. The projection optical system according to claim 3, wherein the following conditional expression (3) is satisfied in zooming from an enlargement magnification having the smallest absolute value to an arbitrary enlargement magnification due to a change in focal length of the entire system: ;
0.01 <| Szmov / (Zz × fz1) | <5.0 (3)
However,
Szmov: distance of translation of the optical element group including the reflecting mirror,
Zz = fz1 / fz2,
fz1: the focal length of the entire system when the absolute value of the magnification is the smallest,
fz2: focal length of the entire system after zooming,
It is. The projection according to any one of claims 3 to 5, wherein the following conditional expressions (4) and (5) are satisfied in an arbitrary focal length state at a variable magnification due to a change in focal length of the entire system: Optical system;
-50 <(Sz1st_ximg-Szx_design) / fzx <20 (4)
-50 <(Sz1st_yimg-Szy_design) / fzy <20 (5)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sz1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Szx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane.
fzx: focal length of the entire system in the x direction,
Sz1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Szy_design: The distance measured along the base ray from the rear principal point position in the y direction to the design image plane.
fzy: focal length of the entire system in the y direction,
It is.   The zoom optical system has a focusing function for focusing on different screen surface positions by parallel movement and rotational movement of an optical element having a rotationally asymmetric optical surface. The projection optical system described in 1.   3. The projection optical system according to claim 1, further comprising a focusing function for focusing on different screen surface positions by changing a focal length of the entire system. 9. The projection optical system according to claim 8, wherein the following conditional expression (6) is satisfied in focusing from the closest projection state closest to the screen surface to an arbitrary focus projection state due to a change in focal length of the entire system: ;
0.2 <| θfmov / Zfoc | <8.0 (6)
However,
θfmov: rotation angle (°) of the optical element group including the reflection mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is. 10. The projection according to claim 8, wherein the following conditional expression (7) is satisfied in focusing from a closest projection state closest to the screen surface to an arbitrary focus projection state due to a change in focal length of the entire system: Optical system;
0.05 <| Sfmov / (Zfoc × ff1) | <7.0 (7)
However,
Sfmov: distance of translation of the optical element group including the reflecting mirror,
Zfoc = ff1 / ff2,
ff1: Focal length of the entire system in the closest projection state,
ff2: focal length of the entire system after focusing,
It is. The projection optics according to any one of claims 8 to 10, wherein the following conditional expressions (8) and (9) are satisfied in an arbitrary focal length state in focusing by a change in focal length of the entire system: system;
-50 <(Sf1st_ximg-Sfx_design) / ffx <20 (8)
-50 <(Sf1st_yimg-Sfy_design) / ffy <20 (9)
However, the axial principal ray from the center of the object to the center of the design image plane through the center of the aperture is used as the base ray, the screen normal direction of the display element surface is the z direction, and the axial principal ray toward the screen and the normal of the screen surface. If the direction perpendicular to the plane formed by x is the x direction and the direction perpendicular to the x direction and the z direction is the y direction,
Sf1st_ximg: distance measured along the base ray from the back principal point position of the x-direction ray to the primary image point position of the x-direction ray,
Sfx_design: Distance measured along the base ray from the back principal point position in the x direction to the design image plane,
ffx: focal length of the entire system in the x direction,
Sf1st_yimg: distance measured along the base ray from the back principal point position of the y-direction ray to the primary image point position of the y-direction ray,
Sfy_design: The distance measured along the base ray from the back principal point position in the y direction to the design image plane,
ffy: focal length of the entire system in the y direction
It is.   A projection optical system for enlarging and projecting an image of a display element surface on a screen surface, in which the angle formed between the screen surface and an axial principal ray incident on the screen surface is not vertical, but rotationally asymmetric reflection arranged eccentrically Translation of at least one optical element group including the reflecting mirror for use in any one of a state having a mirror and projecting to a screen position and a state projecting to a screen position different from the state And a projection optical system characterized by having a configuration capable of rotational movement.   A projection optical system for enlarging and projecting an image of a display element surface on a screen surface, where the angle formed by the screen surface and an axial principal ray incident on the screen surface is not vertical, but is a rotationally asymmetric reflection arranged eccentrically In order to use any one of a certain projection magnification state and another projection magnification state different from that state, the at least one optical element group including the reflection mirror is translated and rotated. A projection optical system having a possible configuration.   A projection-type image display apparatus comprising: a display element that forms a two-dimensional image; and a projection optical system that magnifies and projects an image of the display element surface on a screen surface, wherein the projection optical system includes: 14. A projection type image display apparatus, characterized in that it is a projection optical system according to any one of.

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