JP2009122587A - Non-axial variable power projection optical system and projection type image display device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To attain a projection optical system 2 capable of suppressing performance fluctuation in variable power and giving a large variable power ratio with compact constitution. <P>SOLUTION: The projection optical system 2 has at least three reflection surfaces in a non-axial arrangement, and is constituted in such power arrangement as a negative group G1 and a positive group G2 from an enlargement side. By such constitution, the effective range of an optical system nearer to a reduction side than the negative group G1 is made small, and the projection optical system 2 is compact. By changing the power at least of the negative group G1 when varying power of an entire system, Petzval of the entire system can be changed, and fluctuation of an image surface at each variable power position can be suppressed. By changing the power of the negative group G1 so as to perform the variable power, the large variable power is attained by a small moving amount of an optical element when changing the power without causing image skipping. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a non-axis variable magnification projection optical system and a projection type image display apparatus having the projection optical system.

  Front-type projectors are used to enlarge and display images created on computers during meetings and presentations in offices as computers that are easy to carry, such as notebook personal computers, have become popular. Is 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, since a conventional projector requires a large projection space, it is difficult to use it on a large screen in a space where a sufficient projection space such as a small conference room or a home cannot be secured.

  Therefore, as a method for achieving a large screen while reducing the required projection space, a reflecting surface is introduced into the projection optical system to project the optical path of the imaging light beam that forms the projected image. A configuration for folding into an apparatus is known. At this time, by adopting a so-called non-axial optical system using a decentered reflecting surface as the reflecting surface, the effect of folding the optical path can be further increased. Furthermore, a so-called oblique projection optical system configuration is also known 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.

  In addition, in order to reduce the weight of the optical system and reduce deterioration due to chromatic aberration, an optical system composed only of a mirror and an optical system using many mirrors have been proposed. Furthermore, when using within a limited space, if there is a so-called zoom optical system (variable magnification optical system) that changes the projection magnification while the position of the projector or screen is substantially fixed, Reduction can be performed immediately, which is very convenient.

  Several non-axis projection optical systems capable of zooming using an optical system consisting only of mirrors or an optical system using many mirrors have been proposed. For example, Patent Documents 1 and 2 disclose a non-axial projection optical system that can change magnification by using an optical system that uses many mirrors. The optical system of Patent Document 1 has a configuration of a non-axis optical system, but zooming is performed by changing the focal length of the entire system by translating a coaxial optical element that constitutes a part of the optical system. ing. On the other hand, the optical system of Patent Document 2 performs zooming by translating a non-axially arranged mirror to change the focal length of the entire system.

JP-A-2005-121722 JP 2005-189768 A

  By the way, the non-axis optical system can be configured to be small by folding the optical path, but since the axial ray does not become one straight line, the focal length is changed by moving the optical system for zooming. In this case, it is necessary to consider that the optical system is a non-axis optical system. For example, simply moving the non-axial optical system with power changes the overall focal length, but the center of the screen moves during zooming due to the large movement of the light beam emitted to the screen. As a result, a so-called image jump phenomenon occurs. Therefore, in a non-axis optical system, a zooming method that avoids such a phenomenon of image jumping is necessary.

  In this regard, in the non-axial optical system of Patent Document 1, the magnification is changed by moving the optical element of the coaxial system, so that the emission position on the axis does not shift. However, in this zooming method, since the power of the optical element to be moved does not change before and after zooming, it is difficult to correct Petzval for the entire system during zooming. That is, the imaging performance varies due to zooming.

  On the other hand, in the optical system of Patent Document 2, in order to avoid image distortion, an axial principal ray incident on one moving non-axis-arranged mirror and an axis emitted from the other moving non-axis-arranged mirror Since each mirror moves so that it is parallel to the chief ray, the individual power of each moving mirror does not change. For this reason, as described above, the imaging performance fluctuates due to zooming.

  In addition, as in Patent Documents 1 and 2, in the configuration in which the power of the optical element that moves at the time of zooming does not change, in order to increase the zooming ratio, the movement distance of the optical element must be ensured and the compactness is compact. An optical system cannot be realized.

  The present invention has been made to solve the above-described problems, and its purpose is to reduce performance fluctuations in zooming and to obtain a large zooming ratio with a compact configuration. An object of the present invention is to provide an axial variable magnification projection optical system and a projection type image display apparatus including the projection optical system.

  The non-axis variable magnification projection optical system of the present invention is a non-axis variable magnification projection optical system that has a rotationally asymmetric reflective surface arranged eccentrically and projects an image of a display element surface on a projection surface in an enlarged manner. A group having at least three reflecting surfaces, a group having a negative power having at least one reflecting surface from the enlarged side, and a group having a positive power having at least one reflecting surface. And at least the power of the negative group is changed at the time of zooming of the entire system, and zooming is performed while the positions of the display element surface and the projection surface are substantially constant.

In the non-axis variable magnification projection optical system of the present invention, when the state where the magnification on the magnification side is the smallest is wide and the state where the magnification on the magnification side is the largest is tele, It is desirable that the following conditional expression (1) is satisfied in at least one of the short side direction and the long side direction of the element. That is,
0.2 <| (Zφm_refl−1) / (Zφall−1) | <3.0 (1)
However,
Zφm_refl: ratio of tele power to wide power in the negative group Zφall: ratio of tele power to wide power in the entire system.

  In the non-axis variable magnification projection optical system of the present invention, it is desirable to change at least the power of the negative group by moving the negative group reflecting surface and the other reflecting surfaces along different tracks that are not parallel to each other.

  In the non-axis variable magnification projection optical system of the present invention, it is desirable that the axial principal ray is incident from an oblique direction other than the vertical direction with respect to the projection surface.

It is desirable that the non-axis variable magnification projection optical system of the present invention satisfies the following conditional expression (2). That is,
20 ° <| θ | <70 ° (2)
However,
θ: An angle formed between the normal line of the projection surface and the axial principal ray incident on the projection surface.

The non-axis variable magnification projection optical system of the present invention desirably satisfies the following conditional expression (3) in zooming from wide to telephoto. That is,
| ΔSimg / (β × (1 / 2NA ₀ )) | <2.0 (3)
However,
β: projection magnification ΔSimg: between the paraxial image point and the actual center position of the projection surface at the projection magnification β
Distance measured along the axial principal ray NA ₀ : NA on the reduction side of the entire system
It is.

It is desirable that the non-axis variable magnification projection optical system of the present invention satisfies the following conditional expression (4). That is,
0.05 <| fall_W / f1_W | <1.5 (4)
However,
fall_W: wide focal length of the entire system f1_W: wide focal length of the negative group.

  A projection type image display apparatus according to the present invention is a projection type image display apparatus having a display element for displaying a two-dimensional image and a projection optical system for enlarging and projecting an image of the display element surface onto a projection surface. The projection optical system is configured by the non-axis variable magnification projection optical system of the present invention described above.

  According to the present invention, since the optical path can be folded by at least three non-axially arranged reflecting surfaces, a compact projection optical system can be realized. In addition, since the power is arranged in the negative group and the positive group from the enlargement side, the effective range of the optical system on the reduction side (display element side) can be made smaller than that in the negative group. Can be realized.

  Also, the Petzval of the entire system can be changed by changing the power of at least the negative group at the time of zooming of the entire system. As a result, it is possible to suppress fluctuations in the image plane at each zoom position. Further, as compared with the configuration in which the optical element (for example, the reflecting surface) constituting the negative group is moved in parallel and zooming is performed, large zooming can be performed with a small movement amount of the optical element without causing image distortion. it can. That is, a large zoom ratio can be obtained even with a compact configuration.

  In addition, since the magnification is changed while the positions of the display element surface and the projection surface are substantially constant, the axial best focus position can be substantially constant at any magnification, and a high-performance image can be obtained. .

  Embodiments of the present invention will be described below with reference to the drawings. For convenience of explanation below, the zoom state with the smallest enlargement magnification on the enlargement side (screen side) is set to wide (W), and the magnification change state with the largest enlargement magnification on the enlargement side is set to tele (T). The variable power state when the magnification is intermediate between wide and tele is defined as middle (M).

(1. Overall configuration)
1 to 6 are sectional views showing the configuration of the projection type image display apparatus according to the first embodiment. More specifically, FIG. 1 is a cross-sectional view showing the overall configuration of the projection type image display apparatus in the wide zooming state, and FIG. 2 shows the projection optical system 2 of the projection type image display apparatus in the zooming state. It is sectional drawing expanded and shown. FIG. 3 is a cross-sectional view showing the overall configuration of the projection type image display apparatus in the middle zooming state, and FIG. 4 is an enlarged cross-sectional view showing the projection optical system 2 in the zooming state. 5 is a cross-sectional view showing the overall configuration of the projection-type image display apparatus in a tele zooming state, and FIG. 6 is an enlarged cross-sectional view of the projection optical system 2 in the zooming state.

  FIG. 7 shows the projection optical system 2 according to Embodiment 1 in an enlarged manner by superimposing the zoom in the wide, middle, and tele zoom states, and shows the movement trajectory of each optical element from wide to tele. It is explanatory drawing. In FIG. 7, the solid black arrow indicates the direction in which each optical element moves from wide to tele, and the white arrow indicates the direction in which each optical element rotates from wide to tele. Note that the manner of illustration is the same in other drawings.

  FIG. 8 shows the projection optical system 2 of the projection-type image display apparatus according to Embodiment 2 in an enlarged manner by superimposing them in the wide, middle, and telephoto variable states, and from the wide to the telephoto of each optical element. It is explanatory drawing which shows the movement locus | trajectory. Similarly, FIGS. 9 to 11 show the projection optical systems 2 of the projection type image display apparatuses according to Embodiments 3 to 5 in an enlarged manner by superimposing them in the wide, middle and tele zooming states, respectively. It is explanatory drawing which shows the movement locus | trajectory from wide to tele of each optical element.

  Each of the projection type image display apparatuses according to the first to fifth embodiments includes a display element 1, a cover glass CG, and a projection optical system 2. The display element 1 is a light modulation element that displays a two-dimensional image, and can be composed of, for example, an LCD or DMD (Digital Micromirror Device; manufactured by Texas Instruments, USA). The cover glass CG is disposed in close contact with the display surface (also referred to as object surface or display element surface) of the display element 1.

  The projection optical system 2 is a variable magnification projection optical system that projects an enlarged image of the display surface of the display element 1 onto a screen SC (also referred to as an image surface) that is a projection surface. The projection optical system 2 of Embodiments 1 to 3 and 5 has five mirrors M1 to M5 from the display element 1 side, and the projection optical system 2 of Embodiment 4 is from the display element 1 side. Three mirrors M1 to M3 are provided.

  The mirrors M1 to M5 (M1 to M3) sequentially reflect the light from the display element 1 transmitted through the cover glass CG and guide it to the screen SC, and the reflection surface is a rotationally asymmetric reflection surface. The mirrors M1 to M5 (M1 to M3) are eccentrically arranged such that the axial principal ray is incident on the screen SC from an oblique direction other than the vertical direction (normal direction). The axial principal ray is a light ray that is emitted from the center of the display surface of the display element 1, passes through the center of the stop, and travels toward the screen center of the screen SC, and is also called a base ray.

  As described above, in each of the first to fifth embodiments, the projection optical system 2 has a so-called oblique projection optical system configuration in which the axial principal ray is obliquely incident on the screen SC. 2 can be made thin, and even with such a thin projection optical system 2, an image of the display surface of the display element 1 can be projected onto a large screen SC.

  In the first, third, and fifth embodiments, the axial principal ray from the mirror M3 to the mirror M4 is the axial principal ray from the display element 1 to the mirror M1, and the axial principal ray from the mirror M1 to the mirror M2. Intersects with both. In the second embodiment, the axial principal ray from the mirror M2 to the mirror M3 intersects with both the axial principal ray from the display element 1 to the mirror M1 and the axial principal ray from the mirror M4 to the mirror M5. is doing. On the other hand, in Embodiment 4, the axial principal ray from the mirror M3 toward the screen SC intersects with both the axial principal ray from the display element 1 to the mirror M1 and the axial principal ray from the mirror M1 to the mirror M2. is doing.

(2. Details of the projection optical system)
Next, further details of the projection optical system 2 of the first to fifth embodiments will be described.

  As described above, the projection optical system 2 has at least three rotationally asymmetric reflecting surfaces arranged eccentrically. Further, the projection optical system 2 includes, from the magnification side, a group having a negative power having at least one reflection surface and a group having a positive power having at least one reflection surface. At the time of zooming of the system, zooming is performed by changing the power of at least the negative group, and zooming is performed while the positions of the display element surface and the projection surface are substantially constant.

(2-1. About at least three reflective surfaces)
Since the projection optical system 2 has at least three rotationally asymmetric reflecting surfaces arranged eccentrically (for example, three surfaces of mirrors M1 to M3), the projection optical system 2 becomes a non-axis optical system, Since the optical path is folded by at least three reflecting surfaces, the volumetric compact projection optical system 2 can be realized. In other words, in the case of a coaxial system, the optical system has the same length as the optical path length, but by using a reflecting surface in the non-axial optical system, even if the optical path length is the same as the coaxial system, the length and volume are reduced. It becomes possible to greatly reduce the size, and a compact projection optical system 2 can be realized.

  In addition, the aberration generated in the non-axis optical system can be corrected by at least three reflecting surfaces. In other words, two reflective surfaces (for example, a surface having a positive power and a surface having a negative power) are corrected to cancel each other's aberrations in the same manner as in the coaxial system, and the remaining one surface is reflected. The surface can correct an aberration (for example, decentered astigmatism) caused by the tilt of the decentered optical element surface, which is seen in the non-axis optical system. In particular, in the case of a projection system, a large amount of decentered astigmatism occurs, so that a high-performance projection optical system 2 can be realized by using at least three reflecting surfaces.

  Furthermore, since a reflecting surface is used, it is not necessary to consider correction of chromatic aberration as in the case of using a refracting surface. Therefore, there is no need to combine optical elements having different dispersions as in the refraction system, and the projection optical system 2 can be configured with a smaller number of reflecting surfaces. Therefore, it can be said that the projection optical system 2 can also be configured compactly in this respect.

(2-2. About power arrangement of negative group and positive group from the enlargement side)
The projection optical system 2 has, from the magnification side, a group having negative power (hereinafter referred to as negative group G1) and a group having positive power (hereinafter referred to as positive group G2). More specifically, in the first to third and fifth embodiments, the mirrors M1, M2, and M3 of the projection optical system 2 constitute the positive group G2, and the mirrors M4 and M5 constitute the negative group G1. In the fourth embodiment, the mirrors M1 and M2 of the projection optical system 2 constitute the positive group G2, and the mirror M3 constitutes the negative group G1. In particular, among the mirrors M1 to M5 included in the projection optical system 2, the reflective surface (mirror M5 or mirror M3) arranged closest to the screen SC has a negative power.

  Thus, when the negative group G1 and the positive group G2 are arranged from the enlargement side, the effective range of the projection optical system 2 on the reduction side (display element 1 side) can be made smaller than the negative group G1. Thereby, the image of the display surface of the display element 1 can be greatly enlarged and projected onto the screen SC while realizing the compact projection optical system 2.

  If there is a positive power group on the reduction side, a negative group and a positive group are arranged on the enlargement side, and the projection optical system 2 is a so-called retrofocus type optical system. In this configuration, a back focus (distance between the display element 1 and the projection optical system 2) can be secured to some extent. Therefore, for example, even when an optical element such as a color combining prism is arranged on the display element 1 side, the optical element can be easily arranged.

(2-3. About magnification change by power change of negative group)
The projection optical system 2 is configured to change the magnification by changing at least the power of the negative group G1 when changing the magnification of the entire system. That is, at the time of zooming of the entire system, only the power of the negative group G1 may change, or both the power of the negative group G1 and the power of the positive group G2 may change. Such zooming is performed, for example, by using at least one reflecting surface constituting the negative group G1 and another reflecting surface out of the at least three reflecting surfaces arranged eccentrically, with different trajectories that are not parallel to each other. It can be realized by moving it. By adopting such a scaling method, the projection optical system 2 can be designed so that the two reflecting surfaces move in a direction other than parallel, so that the degree of freedom in design increases, and the projection optical system 2 is A compact configuration is possible.

  In addition, in such a zooming method, not only the distance between the two reflecting surfaces but also the power of each reflecting surface changes, so that a large amount of change can be made with a small amount of movement of each reflecting surface without causing image distortion. Can be doubled. That is, a large zoom ratio can be obtained even with a compact configuration. In particular, by changing the power of the negative group G1 itself, which is a strong group, even if the amount of change in the interval between the negative group G1 and the positive group G2 is reduced, the power change contributes to zooming and is greatly increased. Can be scaled. That is, the method of changing the power of the negative group G1 at the time of zooming is advantageous for a compact configuration because the movement interval of each group at the time of zooming is small.

  Also, by changing the power of at least the negative group G1 (by changing the power of at least two reflecting surfaces), it is possible to change the Petzval of the entire system, and the fluctuation of the image plane at each zoom position. Can be suppressed. In addition, by changing the power of each reflecting surface, it is possible to realize an optical system with less fluctuations such as spherical aberration and astigmatism due to zooming of the entire system. Furthermore, since the interval between the pupil and the negative group G1 changes during zooming, an optical system with small distortion fluctuations can be realized by changing the power of the negative group G1 in accordance with the change in the interval. From the above points, it can be said that the performance fluctuation in zooming can be suppressed by changing the power of at least the negative group G1 during zooming.

  The zoom ratio mentioned above refers to the ratio (ft / fw) between the longest focal length (ft) and the shortest focal length (fw) in the projection optical system 2. Here, the projection optical system 2 of each of the first to fifth embodiments is a non-axis optical system, but the focal length in the non-axis optical system is considered as follows.

  The focal length in the coaxial optical system is a paraxial amount. That is, the focal length can be obtained by considering the optical axis of the coaxial optical system as a reference ray and calculating the behavior of the ray in the vicinity thereof, that is, the paraxial amount. On the other hand, in a non-axial optical system, there is generally no linear optical axis as in the coaxial optical system, so it is necessary to consider a reference light beam instead of the optical axis of the coaxial optical system. This light beam is a light beam that passes from the center of the object plane to the center of the aperture and reaches the center of the image plane. This is the principal ray of the on-axis ray and the above-described base ray. If this ray (base ray) is considered as a reference ray corresponding to the optical axis of the coaxial system, that is, the optical axis of the non-axis optical system, the paraxial amount of the non-axis optical system is the ray near the base ray. Is equivalent to the behavior of The focal length in the non-axis optical system can be obtained by obtaining such a paraxial amount.

  Hereinafter, at least zooming due to power change of the negative group G1, that is, details of zooming due to movement of the reflecting surface will be described. FIG. 12 is an explanatory diagram schematically showing a configuration in which the optical path from the display element 1 to the screen SC is bent by two mirrors M11 and M21. Here, it is considered that magnification is changed by two mirrors M11 and M21. In addition, in order to make it easy to think, the back (enlarged side) of the mirror M21 is an image plane (screen SC).

  The mirrors M11 and M21 are eccentrically arranged (non-axial arrangement). In the first to third and fifth embodiments, the mirrors M11 and M21 correspond to the mirrors M4 and M5 constituting the negative group G1, and in the fourth embodiment, , Corresponding to the mirror M2 constituting the positive group G2 and the mirror M3 constituting the negative group G1. In addition, here, the number of moving mirrors is two for easy understanding of the description, but the same can be considered when there are three or more moving mirrors. Furthermore, although the case where the axial principal ray incident on the mirror M11 and the axial principal ray emitted from the mirror M21 are not parallel is considered here, the same can be considered even when they are parallel.

The power of the mirror M11 is φ1_1, the power of the mirror M21 is φ2_1, and the interval along the axial principal ray between the two mirrors M11 and M21 is e1_1. Hereinafter, unless otherwise specified, the distance is referred to as an inter-mirror distance. The combined power φall_1 is expressed by the following equation.
φall_1 = φ1_1 + φ2_1 -e1_1 ・ φ1_1 ・ φ2_1

  FIG. 13 is an explanatory diagram schematically showing an optical path when only the mirror M11 is translated to change the magnification. The optical path before the movement of the mirror M11 is indicated by a solid line, and the optical path after the movement is indicated by a broken line. When the mirror M11 is moved parallel to the direction along the axial principal ray incident thereon, the intersection of the mirror M11 and the axial principal ray, the incident angle of the axial principal ray on the mirror M11, the axis from the mirror M11 The emission angle of the upper principal ray does not change. However, the position of the intersection of the mirror M21 and the axial principal ray incident thereon is shifted, and the exit angle of the axial principal ray emitted from the mirror M21 toward the screen SC changes. As a result, the position of the intersection of the axial principal ray and the screen SC shifts, and the center position of the image projected on the screen SC moves (image jump).

Considering the combined power φall_2 at this time, the power of the mirror M11 does not change, and the power of the mirror M21 usually changes from φ2_1 to φ2_2. Further, the distance between the mirrors changes from e1_1 to e1_2. Therefore, the combined power φall_2 is expressed by the following equation.
φall_2 = φ1_1 + φ2_2 −e1_2 ・ φ1_1 ・ φ2_2
Therefore, since the power of the entire system changes, zooming is possible (however, focus is not guaranteed). However, large zooming is not practical because the center position of the image projected on the screen SC is greatly shifted.

  FIG. 14 is an explanatory diagram schematically showing an optical path when both the mirrors M11 and M21 are moved and scaled. The optical path before the movement of the mirrors M11 and M21 is indicated by a solid line, and the optical path after the movement is indicated by a broken line (the same applies to the following drawings). However, in FIG. 14, the mirrors M11 and M21 are moved along different trajectories that are not parallel to each other.

  More specifically, the mirror M11 is moved in parallel to the direction along the axial principal ray incident on the mirror M11, the intersection position of the axial principal ray and the mirror M21, and the incident angle of the axial principal ray on the mirror M21. The mirror M21 is translated so that does not change before and after the movement of the mirror M21. Thus, by moving the mirrors M11 and M21 along different trajectories other than parallel to each other, the position of the intersection of the axial principal ray and the screen SC does not change, and the center position of the image projected on the screen SC does not change. .

Considering the combined power φall_3 at this time, the individual powers of the mirrors M11 and M21 do not change, but the distance between the mirrors changes from e1_1 to e1_3. Therefore, the combined power φall_3 is expressed by the following equation.
φall_3 = φ1_1 + φ2_1 -e1_3 ・ φ1_1 ・ φ2_1
Therefore, since the power of the entire system changes, zooming is possible (however, focus is not guaranteed).

  In this way, by moving the two mirrors M11 and M21 in different directions, the intersection position between the axial principal ray and the screen SC remains substantially constant (that is, the axial principal on the image plane). It is possible to change the magnification (without changing the incident position of the light beam). Therefore, this method can be said to be a zooming method suitable for non-axis optical systems. However, in this zooming method, the change in the distance between the mirrors only contributes to zooming. Therefore, a zooming method suitable for a non-axis optical system will be described below.

  FIG. 15 is an explanatory view schematically showing an optical path when the mirrors M11 and M21 are further rotated when the mirrors M11 and M21 are moved along different trajectories that are not parallel to each other for zooming. That is, in FIG. 15, the mirrors M11 and M21 are moved in different directions that are not parallel to each other by moving and rotating the mirrors M11 and M21 in the direction along the axial principal ray. . By such movement of the mirrors M11 and M21, the incident position and the incident angle of the axial principal ray with respect to the mirrors M11 and M21 change. As a result, the exit angle of the axial principal ray from each of the mirrors M11 and M21 changes, and the surface power at the exit position also changes.

  Therefore, by appropriately moving the mirrors M11 and M21, the incident angle and the incident position of the axial principal ray on the screen SC can be kept the same as before the movement. In the projection system, a slight change in the center position of the image during zooming and a slight change in the incident angle of the axial principal ray with respect to the screen SC are allowed. Therefore, the incident direction of the axial principal ray on the screen SC And the position of the intersection with the screen SC may not be kept exactly the same (so as not to change).

Considering the combined power at this time, since the incident angle and the incident position on the mirrors M11 and M21 change before and after the movement of the mirrors M11 and M21, the power of the mirrors M11 and M21 at that position changes. Specifically, the power of the mirror M11 changes from φ1_1 to φ1_4, and the power of the mirror M21 changes from φ2_1 to φ2_4. Also, the distance between the mirrors changes from e1_1 to e1_4. Therefore, the combined power φall_4 is expressed by the following equation.
φall_4 = φ1_4 + φ2_4 −e1_4 ・ φ1_4 ・ φ2_4
Therefore, since the power of the entire system changes, zooming is possible (however, focus is not guaranteed).

  In the scaling method of FIG. 15, not only the distance between mirrors (usually, the distance between principal points) changes as shown in FIG. 14, but also the power of each surface also changes. Therefore, the amount of movement of the mirrors M11 and M21 Can be made larger even when the distance is the same (even if the change in the distance between the mirrors is the same). Further, it is possible to keep the position of the intersection of the axial principal ray and the screen SC substantially constant by moving the mirrors M11 and M21 as shown in FIG. 14, but it is possible to move the reflecting surface as shown in FIG. Further rotation makes it easier to keep the position of the intersection of the axial principal ray and the screen SC more constant. Further, in the case of a non-axis optical system, it is possible to appropriately correct decentration aberrations by rotating the reflecting surface.

  As described above, in the case of the non-axis projection optical system, in order to change the magnification while keeping the intersection position of the axial principal ray and the screen SC constant or keeping the movement amount of the intersection position small, at least two surfaces are required. It may be desirable to move the reflective surfaces in different directions that are not parallel to each other. Furthermore, it can be said that it is desirable to rotate each reflecting surface in order to change the magnification more effectively.

  As a feature of the non-axis optical system, the power of each surface is not one, but has extreme values in a certain direction perpendicular to each other. Therefore, the magnification and image plane position of the entire system have extreme values in directions perpendicular to each other. Therefore, it is necessary to consider the difference (anamo) of each parameter in each direction and keep them within an allowable range. For this purpose, as described above, it is desirable to change the magnification by moving each surface in different directions and changing the power itself on each surface.

(2-4. Scaling with the object image plane kept substantially constant)
In the projection optical system 2, zooming is performed with the display surface of the display element 1 and the screen SC kept substantially constant, so that the axial aberration is corrected at any magnification (always when zooming). The on-axis best focus position can be made almost constant, and a high-performance image can be obtained. That is, it is possible to obtain a high-performance optical system with small performance fluctuation due to zooming. Hereinafter, this point will be described in detail.

FIG. 16 is an explanatory diagram schematically showing an optical system composed of the display element 1, non-axially arranged two-surface mirrors M11 and M21, and a screen SC, and showing the position coordinates of each surface. is there. For convenience of explanation below, the exit direction of the axial principal ray from the center of the object plane is defined as a direction perpendicular to the display surface, and the direction is defined as the Z direction. Two directions perpendicular to each other on the object plane perpendicular to the Z direction are defined as an X direction and a Y direction, respectively. Here, the direction perpendicular to the paper surface of FIG. 16 is the X direction, and the direction perpendicular to the ZX plane is the Y direction. The coordinates of the center of the object plane are set to (X ₀ , Y ₀ , Z ₀ ).

  The optical system in FIG. 16 is an optical system that is plane-symmetric with respect to one plane (YZ plane). By making the optical system plane-symmetric, the axial principal ray remains in the YZ plane, and various calculations are simplified as follows. However, even with this setting, there is no essential restriction on a general optical system having no symmetry plane. For example, in the case of torsion, an additional operation of rotating the coordinates may be added. .

First, consider an optical system at a certain magnification (Z1). The powers of the two reflecting surfaces (mirrors M11 and M21) are φ1_Z1 and φ2_Z1, respectively, and the focal lengths are f1_Z1 and f2_Z1, respectively. Furthermore, the distance between the two reflecting surfaces and measured along the axial principal ray is e1_Z1. Also, the coordinates of the intersections of the two reflecting surfaces and the axial principal ray are (X 1 _{—Z 1} , Y 1 _{—Z 1} , Z 1 _{—Z 1} ) and (X 2 _{—Z 1} , Y 2 _{—Z 1} , Z 2 _{—Z 1} ), respectively, and the screen SC and the axial principal ray The coordinates of the intersection point with (X 3 _{—Z 1} , Y 3 _{—Z 1} , Z 3 _{—Z 1} ) are assumed.

Further, the direction cosine in the emission direction of the axial principal ray from the object plane is (L 0 — _{Z 1} , M 0 — _{Z 1} , N 0 — _{Z 1} ), and the direction cosine in the emission direction of the axial principal ray from each reflecting surface is (L _{1_Z1} , _{M1_Z1} , _{N1_Z1} ), ( _{L2_Z1} , _{M2_Z1} , _{N2_Z1} ). Note that the intersection between each reflecting surface and the axial principal ray and the direction cosine in the emission direction of the axial principal ray can be easily calculated by ray tracing.

Further, the combined power of the two reflecting surfaces is φall_Z1, and the combined focal length is f (all_Z1). The _{pre-combination} focus position is (X _{ffp_Z1} , Y _{ffp_Z1} , Z _{ffp_Z1} ), and the post-synthesis focus position is (X _{fbp_Z1} , Y _{fbp_Z1} , Z _{fbp_Z1} ). These two points lie on the axial principal ray or its extension. Then, the composite focal length f (all_Z1) is expressed as follows.
f (all_Z1) = 1 / (φ1_Z1 + φ2_Z1−e1_Z1, φ1_Z1, φ2_Z1)

  Here, since the axial principal ray is considered in the YZ plane symmetric optical system, the X coordinate in all position coordinates is zero.

Next, if the distance from the pre-synthesis focal position to the center position of the object plane is ΔX _Z1 , ΔX _Z1 is expressed by the following equation.
ΔX _Z1 = {(X _{ffp_Z1} −X ₀ ) ² + (Y _{ffp_Z1} −Y ₀ ) ²
+ (Z _{ffp_Z1} −Z ₀ ) ² } ^1/2

On the other hand, if the distance along the axial principal ray from the post-synthesis focal position to the paraxial imaging position is ΔX ′ _Z1 , ΔX ′ _Z1 is expressed by the following equation.
ΔX ′ _Z1 = − {f (all_Z1)} ² / ΔX _Z1

The expression of the axial principal ray incident on the image plane from the mirror M21 is represented by the following expression on the YZ plane.
Y = A _Z1・ Z-B _Z1
However,
A _Z1 = M _{2_Z1} / N _{2_Z1} ,
B _Z1 = (M 2 _{—Z 1} / N 2 _{—Z 1} ) · Z 2 _{—Z 1} −Y 2 _{—Z 1}
It is. The post-synthesis focal point is on this straight line.

Therefore, paraxial image points (X _{UA3 —} Z ₁ , Y _{UA3 —} Z ₁ , Z _{UA3 —} Z ₁ ) in the state of the magnification Z ₁ are expressed as follows.
X _{UA3_Z1} = 0
^{_{Y UA3_Z1 = {- A Z1 3}} · Z fbp_Z1 -A Z1 2 · B Z1 -A Z1 · Z fbp_Z1
+ A _Z1 · ΔX ′ _Z1 · (A _Z1 ² +1) ^1/2 −B _Z1 } / (− A _Z1 ² −1)
Z _{UA3_Z1} = (Y _{UA3_Z1} -B _Z1 ) / A _Z1

The paraxial image point _{(X UA3_Z1, Y UA3_Z1, Z} UA3_Z1) are coordinates on the screen _{SC (X 3_Z1, Y 3_Z1,} Z 3_Z1) and if they match, it comes screen SC on paraxial image point become. However, the actual image plane (screen SC) may be placed at a position shifted from the paraxial image point due to the best defocus position, magnification, and the like. This is the same as the coaxial system. Now, this image plane position is set at the paraxial image point position.

Next, consider an optical system with an enlargement magnification of another magnification (Z2). The powers of the two reflecting surfaces (mirrors M11 and M21) are φ1_Z2 and φ2_Z2, respectively. The distance between the two reflecting surfaces and the distance measured along the axial principal ray is e1_Z2. Further, the direction cosine in the emission direction of the axial principal ray from the mirror M21 is ( _{L2_Z2} , _{M2_Z2} , _{N2_Z2} ), and the intersection of the mirror M21 and the axial principal ray is ( _{X2_Z2} , _{Y2_Z2} , _{Z2_Z2} ). And Further, the _pre- synthesis focal position of the two reflecting surfaces is (X _{ffp_Z2} , Y _{ffp_Z2} , Z _{ffp_Z2} ), the post-synthesis focal position is (X _{fbp_Z2} , Y _{fbp_Z2} , Z _{fbp_Z2} ), and the synthetic focal distance is f (all_Z2). ). In this case, the combined focal length f (all_Z2) is expressed as follows.
f (all_Z2) = 1 / (φ1_Z2 + φ2_Z2-e1_Z2, φ1_Z2, φ2_Z2)

  Since the two reflecting surfaces are non-axial optical systems that move along different trajectories, the power of each surface, the combined power in the optical system that combines the two surfaces, the pre-synthesis focal position, and the post-synthesis focal position are the magnification Z1. It is usually different from the value in.

If the distance from the center position of the object plane to the pre-combination focal position is ΔX _Z2 , ΔX _Z2 is expressed by the following equation.
ΔX _Z2 = {(X _{ffp_Z2} −X ₀ ) ² + (Y _{ffp_Z2} −Y ₀ ) ²
+ (Z _{ffp_Z2} −Z ₀ ) ² } ^1/2

On the other hand, if the distance along the axial principal ray from the post-synthesis focal position to the paraxial imaging position is ΔX ′ _Z2 , ΔX ′ _Z2 is expressed by the following equation.
ΔX ′ _Z2 = − {f (all_Z2)} ² / ΔX _Z2

The expression of the axial principal ray incident on the image plane from the mirror M21 is represented by the following expression on the YZ plane.
Y = A _Z2・ Z-B _Z2
However,
A _Z2 = M _{2_Z2} / N _{2_Z2} ,
B _Z1 = (M 2 _{—Z 2} / N 2 _{—Z 2} ) · Z 2 _{—Z 2} −Y 2 _{—Z 2}
It is.

Therefore, the paraxial image point (X _{UA3 —} Z ₂ , Y _{UA3 —} Z ₂ , Z _{UA3 —} Z ₂ ) at this magnification is expressed as follows.
X _{UA3_Z2} = 0
^{_{Y UA3_Z2 = {- A Z2 3}} · Z fbp_Z2 -A Z2 2 · B Z2 -A Z2 · Z fbp_Z2
+ A _Z2 · ΔX ' _Z2 · (A _Z2 ² +1) ^1/2 -B _Z2 } / (-A _Z2 ² -1)
Z _{UA3_Z2} = (Y _{UA3_Z2} -B _Z2 ) / A _Z2

Therefore, by setting each parameter so that this paraxial image point (X _{UA3_Z2} , Y _{UA3_Z2} , Z _{UA3_Z2} ) is the same as the paraxial image point at the magnification Z1 at other magnifications Z2, the image plane can be changed. A constant variable magnification design is possible. Note that in an actual optical system, the best defocus shifts due to aberrations, so a design that takes into account the amount of variation is necessary.

  One of the features of zooming in a non-axial optical system is that it is not necessary to keep the conjugate length constant unlike a coaxial optical system. In other words, in zooming with a non-axis optical system, the intersection of each reflecting mirror and the axial principal ray so that the paraxial image point position is in the vicinity of the paraxial image point position in another zooming state. The exit direction of the axial principal ray, the focal length and the focal position of the entire system may be set. Therefore, since it is not necessary to keep the conjugate length constant, the degree of freedom of zooming in the non-axis optical system increases.

  Further, the paraxial image point can be shifted within the range of the focus depth on the screen SC side. In the case of a non-axis optical system, an anamorphic magnification is often obtained. However, since the imaging magnification can be changed by shifting the paraxial image point, the anamorphic magnification can be corrected.

  In addition, since the depth of focus on the screen SC side is wide, it is possible to shift the paraxial image point within that range to increase the magnification or to correct decentration aberrations, thereby realizing a high-performance optical system. be able to. That is, the degree of freedom by shifting the paraxial image point position can be used for high magnification and aberration correction, and a high-performance optical system can be realized.

(3. Various conditional expressions)
Next, various conditional expressions applicable to the first to fifth embodiments will be described.

(3-1. About the power change of the reflecting surface at the time of zooming)
The projection optical system 2 of each of the first to fifth embodiments has at least one of the short side direction (Y direction) and the long side direction (X direction) of the display surface of the display element 1 in zooming from wide to tele. It is desirable to satisfy the following conditional expression (1) for the direction. That is,
0.2 <| (Zφm_refl−1) / (Zφall−1) | <3.0 (1)
However,
Zφm_refl: Ratio of tele power to wide power in the negative group G1 Zφall: Ratio of tele power to wide power in the entire system. That is, when the power in the wide zooming state of the negative group G1 is φreflm_W and the power in the tele zooming state is φreflm_T,
Zφm_refl = φreflm_T / φreflm_W
It is. In addition, when the power in the wide zooming state of the entire system is φall_W and the power in the tele zooming state is φall_T,
Zφall = φall_T / φall_W
It is.

  As described above, the zooming method suitable for the non-axis optical system including a plurality of reflecting surfaces not only changes the interval between the reflecting surfaces (main point interval) during zooming, The power of each reflecting surface is changed by rotation or a combination thereof, and at least the power of the negative group G1 is changed. Conditional expression (1) defines the ratio of changing the power of the negative group G1 when the projection optical system 2 is zoomed.

  That is, if the upper limit of conditional expression (1) is exceeded, the power change of the negative group G1 becomes too large with respect to the power change of the entire system when zooming from wide to tele, and the negative group G1 (reflection surface) ) Becomes large, and it becomes difficult to ensure performance. On the other hand, if the lower limit of conditional expression (1) is not reached, the power change of the negative group G1 becomes too small with respect to the power change of the entire system at the time of zooming from wide to telephoto, which is more suitable for non-axis optical systems It becomes difficult to perform zooming. That is, the effect of the non-axis optical system that obtains a large zoom ratio with a compact configuration is reduced.

  Therefore, by satisfying conditional expression (1), it is possible to obtain a large zoom ratio with a compact configuration while ensuring performance by suppressing aberration fluctuations in the negative group G1.

(3-2. Projection angle)
As described above, the projection optical systems 2 of the first to fifth embodiments are oblique projection optical systems in which the axial principal ray is incident obliquely on the screen SC. At this time, it is desirable that the projection optical system 2 satisfies the following conditional expression (2). That is,
20 ° <| θ | <70 ° (2)
However,
θ: The normal of the screen SC and the axial principal ray incident on the screen SC
Angle to make (°)
It is.

  To increase the magnification, it is advantageous that θ is large. However, as the incident angle of the axial principal ray on the screen SC increases, the influence of decentration aberration increases. In addition, a trapezoidal distortion called keystone distortion becomes large. Conditional expression (2) defines an appropriate range of the oblique projection angle in consideration of aberrations that occur during zooming.

  That is, when the lower limit of conditional expression (2) is not reached, the oblique projection degree is weakened, and the above-described effect of increasing the zoom ratio with a compact configuration is reduced. On the other hand, if the upper limit of conditional expression (2) is exceeded, decentration aberrations cannot be corrected or the keystone distortion becomes large, and the image on the screen SC is distorted and becomes impractical. Therefore, by satisfying conditional expression (2), it is possible to improve the imaging performance while reliably obtaining the effect of increasing the zoom ratio with a compact configuration.

(3-3. Ensuring resolution)
It is desirable that the projection optical systems 2 of Embodiments 1 to 5 satisfy the following conditional expression (3) in zooming from wide to tele. That is,
| ΔSimg / (β × (1 / 2NA ₀ )) | <2.0 (3)
However,
β: Projection magnification ΔSimg: Between the paraxial image point and the actual center position of the screen SC at the projection magnification β
Distance measured along the axial principal ray (mm)
NA ₀ : NA (numerical aperture) on the reduction side (display element 1 side) of the entire system
It is.

  It is desirable that the paraxial image point and the center position of the image projected on the screen SC coincide with each other because the variation of the axial best focus position due to zooming is small. There is a change in the best focus position on the axis. At this time, if the conditional expression (3) is deviated, the axial best focus position greatly fluctuates due to zooming, and the necessary resolving power cannot be secured. In other words, by satisfying conditional expression (3), the axial best focus position can be prevented from fluctuating due to zooming, and the necessary resolving power can be ensured. If the deviation of the on-axis best focus position is within the depth on the screen SC side, there is no problem in practical use. Therefore, the paraxial image point may be within the depth.

(3-4. Range of power change in the negative group)
It is desirable that the projection optical systems 2 of Embodiments 1 to 5 satisfy the following conditional expression (4) in zooming from wide to tele. That is,
0.05 <| fall_W / f1_W | <1.5 (4)
However,
fall_W: Focal length in wide of the entire system (mm)
f1_W: Wide focal length of negative group G1 (mm)
It is.

  Conditional expression (4) defines an appropriate range of power change of the negative group G1 at the time of zooming. That is, if the lower limit of conditional expression (4) is not reached, the power of the negative group G1 becomes too strong with respect to the power of the entire system, and negative distortion and trapezoidal distortion become strong and cannot be corrected by the positive group G2. . On the contrary, if the upper limit of conditional expression (4) is exceeded, the power of the negative group G1 becomes too weak with respect to the power of the entire system, and it becomes difficult to achieve compactness and secure back focus. Therefore, by satisfying conditional expression (4), it is possible to achieve compactness and secure back focus while correcting aberrations.

(4. Other)
In the projection optical systems 2 of the first to fifth embodiments, the optical path between the display surface of the display element 1 and the screen SC has three or five reflecting surfaces. In order to achieve higher specifications, it may have four or six or more reflecting surfaces. These reflection surfaces may be arranged so that the trajectories of the axial principal rays intersect at least once.

  Moreover, it is desirable that each reflecting surface of the projection optical system 2 has power. In this case, it is possible to give aberration to the projection optical system 2 and correct the aberration of the entire optical system. Furthermore, the projection optical system 2 may have a refractive lens.

  Further, it is desirable that each reflecting surface of the projection optical system 2 has a free-form surface shape. With a free-form surface, the degree of freedom in designing the surface shape is increased. Further, by using the free-form surface shape, it is possible to satisfactorily correct aberrations such as image plane tilt due to decentering and astigmatism.

  Moreover, it is desirable that the free curved surface of each reflecting surface is plane-symmetric, that is, configured to have one plane of symmetry. A free-form surface having a symmetric surface has an advantage of low difficulty in manufacturing and evaluation.

(5. About Example)
Hereinafter, examples of the projection type image display apparatuses according to the first to fifth embodiments will be described more specifically with reference to construction data and the like as Examples 1 to 5. Examples 1 to 5 are numerical examples corresponding to the first to fifth embodiments. The optical configuration diagrams and optical path diagrams (FIGS. 1 to 11) of the first to fifth embodiments correspond to the numerical examples. This also applies to the first to fifth embodiments.

  In the construction data shown below, Si (i = 0, 1, 2, 3,...) Represents S0 as the display surface of the display element 1 on the reduction side, and indicates the i-th surface counted from now on. Yes. Incidentally, FIG. 17 schematically shows the correspondence between the surface of each optical element and the surface number, for example, in the projection type image display apparatus of the first embodiment. On the other hand, ri (i = 0, 1, 2, 3,...) Indicates the radius of curvature (mm) of the surface Si, and di (i = 0, 1, 2, 3,...) The axial upper surface distance (mm) between Si and the surface S (i + 1) is shown. Ni (i = 0, 1, 2, 3,...) And νi (i = 0, 1, 2, 3,...) Are refractive indexes with respect to the d-line of the optical material located at the axial upper surface distance di. (Nd) and Abbe number (νd) are shown.

  The data of each surface is shown based on a right-handed orthogonal coordinate system (X, Y, Z) with the Si surface as a coordinate reference. That is, a ray emitted from the center of the object (the center of the display surface (S0 surface) of the display element 1), passing through the center of the stop (for example, on the S6 surface) and going to the center of the image surface (center of the screen SC). An axial principal ray (base ray) is used, and an intersection of the axial principal ray and the Si surface is an origin (0, 0, 0). The direction in which the axial principal ray travels from the object center to the Si surface is defined as the Z direction, and the direction is defined as positive. Further, the direction perpendicular to the paper surface of FIG. At this time, the direction from the front side to the back side of the paper surface is positive, and the counterclockwise direction toward the paper surface is the positive direction of X rotation. On the other hand, a direction that forms a right-handed system with the X direction and the Z direction is a positive direction of the Y direction (a direction parallel to the paper surface). Therefore, the short side direction of the display surface of the display element 1 is the Y direction, and the long side direction is the X direction.

  In particular, for an eccentrically arranged surface, the coordinate (mm) of the surface vertex of each surface is expressed as a surface vertex position (X, Y, Z) with the S3 surface as a coordinate reference, and the surface vertex of that surface is the center. The inclination of the surface (X rotation, Y rotation, Z rotation) is represented by the rotation angle (°) around the axis in each of the X, Y, and Z directions. The positive direction of each rotation angle is as follows: X rotation and Y rotation are counterclockwise with respect to the positive directions of the X and Y axes, and Z rotation is relative to the positive direction of the Z axis. The direction is clockwise. A surface indicated as FFS represents a free-form surface.

  Further, the coordinate data at the time of zooming is shown only for the surface that moves at the time of zooming. POS indicates a zooming position (zoom position) of any one of wide (W), middle (M), and tele (T).

A surface Si composed of a free-form surface is defined by the following equation 1 using a local orthogonal coordinate system (x, y, z) having the surface vertex as an origin. In the polynomial free-form surface data shown below, the coefficient of the term not described is 0, and for all data, E−n = × 10 ⁻ⁿ .

However,
z: Amount of displacement in the z-axis direction at the 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 / radius of curvature)
k: conic coefficient Cj: polynomial free-form surface coefficient. Further, the second term (free-form surface term) of Equation 1 can be expanded as shown in Equation 2 below.

Example 1
<Each side data>
Surface vertex coordinates Rotation angle Surface number Surface characteristics ri di Ni νi Coordinate standard XYZX rotation 0 Object surface (display element) ∞
1 plane ∞ 3 51.7 64.2
2 plane ∞ 20
3 Reference surface (dummy surface) ∞ 0
4 Mirror (FFS) ∞ S3 0 0 80.00 14.870
5 Mirror (FFS) ∞ S3 0 -61.61 7.21 11.102
6 Mirror (FFS) stop ∞ S3 0 -62.20 76.33 -40.062
7 Mirror (FFS) ∞ S3 0 144.82 -56.14 -36.422
8 Mirror (FFS) ∞ S3 0 44.02 133.75 24.484
9 Image plane (screen) ∞ S3 0 1011.91 -348.14 -26.221

<Coordinate data during zooming>
Surface vertex coordinates Rotation angle Surface number Coordinate reference Scaling position XYZX rotation Y rotation Z rotation 4 S3 W 0 0 80.00 14.870 0 0
4 S3 M 0 0 80.00 14.530 0 0
4 S3 T 0 0 80.00 14.269 0 0
5 S3 W 0 -61.61 7.21 11.102 0 0
5 S3 M 0 -61.66 5.92 10.737 0 0
5 S3 T 0 -61.71 5.29 10.437 0 0
6 S3 W 0 -62.20 76.33 -40.062 0 0
6 S3 M 0 -60.12 70.99 -39.375 0 0
6 S3 T 0 -57.78 65.68 -38.134 0 0
7 S3 W 0 144.82 -56.14 -36.422 0 0
7 S3 M 0 140.14 -64.78 -36.458 0 0
7 S3 T 0 133.44 -77.26 -36.408 0 0
8 S3 W 0 44.02 133.75 24.484 0 0
8 S3 M 0 31.90 161.52 22.528 0 0
8 S3 T 0 10.92 182.04 19.669 0 0

<Polynomial free-form surface>
Coefficient \ Surface number 4 5 6 7 8
C3 4.7521E-02 1.3645E-01 -1.8970E-03 -5.7200E-02 2.4851E-01
C4 -3.3611E-03 -2.5994E-03 -1.5367E-03 -2.4742E-03 2.5827E-03
C6 -1.6018E-03 6.4937E-04 -4.1332E-04 -1.2098E-03 1.0226E-02
C8 4.2994E-07 1.6010E-05 6.5623E-06 -9.9758E-06 3.4314E-05
C10 -3.1168E-06 2.1413E-06 2.4140E-06 8.0786E-06 -2.3877E-05
C11 -4.5705E-08 -6.7401E-08 1.1071E-08 -1.9256E-07 -7.3698E-08
C13 -3.9503E-08 -1.7619E-07 -4.2116E-08 -1.5239E-07 1.6831E-07
C15 -9.5005E-09 2.6124E-08 -1.5782E-08 -1.5551E-07 7.9980E-07
C17 -9.8291E-12 -1.1634E-10 -4.6007E-11 -3.0065E-10 -3.1287E-09
C19 -3.5585E-10 2.1417E-09 3.7337E-10 -1.5807E-09 -1.0820E-08
C21 -2.4521E-10 -6.0355E-10 2.7646E-11 1.3809E-09 6.7199E-09
C22 -1.6706E-12 -7.1400E-12 -1.4557E-12 1.8479E-11 4.5107E-12
C24 1.9635E-12 1.1890E-11 2.6807E-12 -4.6440E-11 3.3594E-11
C26 -3.1218E-12 -1.6600E-11 -1.3612E-11 -9.0564E-11 3.6665E-11
C28 7.7113E-12 3.2933E-12 3.8671E-12 -1.3660E-11 -1.0790E-10

(Example 2)
<Each side data>
Surface vertex coordinates Rotation angle Surface number Surface characteristics ri di Ni νi Coordinate standard XYZX rotation 0 Object surface (display element) ∞
1 plane ∞ 3 51.7 64.2
2 plane ∞ 17
3 Reference surface (dummy surface) ∞
4 Mirror (FFS) ∞ S3 0 0 80.00 26.537
5 Mirror (FFS) ∞ S3 0 -55.20 78.68 70.129
6 Mirror (FFS) stop ∞ S3 0 74.21 24.78 54.393
7 Mirror (FFS) ∞ S3 0 56.12 -65.24 36.780
8 Mirror (FFS) ∞ S3 0 26.83 84.16 -42.550
9 Image plane (screen) ∞ S3 0 1227.42 -291.46 -29.101

<Coordinate data during zooming>
Surface vertex coordinates Rotation angle Surface number Coordinate reference Scaling position XYZX rotation Y rotation Z rotation 4 S3 W 0 0 80.00 26.537 0 0
4 S3 M 0 0 80.00 25.444 0 0
4 S3 T 0 0 80.00 24.470 0 0
5 S3 W 0 -55.20 78.68 70.129 0 0
5 S3 M 0 -49.06 66.41 63.768 0 0
5 S3 T 0 -42.23 56.14 58.028 0 0
6 S3 W 0 74.21 24.78 54.393 0 0
6 S3 M 0 79.46 33.79 52.320 0 0
6 S3 T 0 83.09 42.31 50.554 0 0
7 S3 W 0 56.12 -65.24 36.780 0 0
7 S3 M 0 62.79 -69.54 36.889 0 0
7 S3 T 0 66.82 -74.21 37.415 0 0
8 S3 W 0 26.83 84.16 -42.550 0 0
8 S3 M 0 33.11 101.63 -43.141 0 0
8 S3 T 0 38.81 115.95 -43.382 0 0

<Polynomial free-form surface>
Coefficient \ Surface number 4 5 6 7 8
C3 -2.4136E-03 -2.7313E-01 -2.2619E-02 6.4890E-01 -1.5561E-01
C4 -1.0723E-03 2.6369E-03 2.1806E-03 -2.0156E-03 3.2141E-03
C6 -1.8835E-04 2.6066E-03 6.0406E-04 -1.6661E-03 4.5667E-03
C8 -7.7499E-06 -4.6725E-06 1.1126E-05 -1.1860E-05 -5.0804E-05
C10 -1.1958E-06 -4.3937E-06 2.4035E-06 -4.9552E-05 -7.2283E-05
C11 2.6554E-08 2.8133E-08 1.9174E-07 -2.2211E-07 -1.0825E-07
C13 -3.0435E-08 4.8123E-08 2.1601E-08 -9.3741E-07 5.1945E-07
C15 -3.3697E-10 2.6610E-08 -2.0174E-09 -7.9809E-07 1.1186E-06
C17 2.1533E-10 -1.8903E-10 1.9839E-09 7.1412E-09 4.6773E-09
C19 1.3120E-11 -2.0484E-10 -3.9280E-11 -5.9219E-09 -7.4011E-09
C21 1.6409E-11 -9.9706E-11 -3.1327E-11 3.5405E-09 -1.7037E-08
C22 1.0179E-12 1.0764E-12 3.9050E-11 7.5952E-11 6.5562E-12
C24 -1.1536E-12 1.9297E-12 4.2244E-12 3.0382E-10 -1.0646E-10
C26 3.5913E-13 1.3944E-12 -1.3252E-11 -7.3609E-11 1.8088E-10
C28 -8.3738E-13 3.3999E-13 -1.2329E-12 6.9196E-10 1.4164E-10
C30 -2.8747E-13
C32 1.5020E-12
C34 -2.3733E-12
C36 -7.0530E-13
C37 -3.3628E-16
C39 3.4888E-15
C41 -7.7638E-15
C43 4.3159E-15
C45 1.0986E-14

(Example 3)
<Each side data>
Surface vertex coordinates Rotation angle Surface number Surface characteristics ri di Ni νi Coordinate standard XYZX rotation 0 Object surface (display element) ∞
1 plane ∞ 3 51.7 64.2
2 plane ∞ 20
3 Reference surface (dummy surface) ∞
4 Mirror (FFS) ∞ S3 0 0 80.00 13.906
5 Mirror (FFS) ∞ S3 0 -68.05 13.40 9.690
6 Mirror (FFS) Aperture ∞ S3 0 -91.08 101.06 -44.868
7 Mirror (FFS) ∞ S3 0 111.65 -16.17 -41.339
8 Mirror (FFS) ∞ S3 0 7.95 110.68 23.455
9 Image plane (screen) ∞ S3 0 2008.53 -915.58 -35.454

<Coordinate data during zooming>
Surface vertex coordinates Rotation angle Surface number Coordinate reference Scaling position XYZX rotation Y rotation Z rotation 4 S3 W 0 0 80.00 13.906 0 0
4 S3 M 0 0 80.00 13.020 0 0
4 S3 T 0 0 80.00 12.006 0 0
5 S3 W 0 -68.05 13.40 9.690 0 0
5 S3 M 0 -69.87 5.44 9.855 0 0
5 S3 T 0 -71.16 -3.73 9.839 0 0
6 S3 W 0 -91.08 101.06 -44.868 0 0
6 S3 M 0 -87.76 92.06 -42.238 0 0
6 S3 T 0 -83.64 80.45 -39.585 0 0
7 S3 W 0 111.65 -16.17 -41.339 0 0
7 S3 M 0 111.59 -37.00 -41.599 0 0
7 S3 T 0 110.42 -61.17 -42.186 0 0
8 S3 W 0 7.95 110.68 23.455 0 0
8 S3 M 0 5.51 122.42 17.921 0 0
8 S3 T 0 3.82 116.86 9.821 0 0

<Polynomial free-form surface>
Coefficient \ Surface number 4 5 6 7 8
C3 -8.4484E-03 1.4735E-01 4.4853E-02 -4.3831E-02 4.5793E-01
C4 -3.0809E-03 -2.1051E-03 -1.4859E-03 -2.6174E-03 2.1687E-03
C6 -1.3168E-03 6.9731E-04 -4.5450E-04 -1.4058E-03 1.1097E-02
C8 1.2792E-06 1.1111E-05 4.4181E-06 -1.5366E-05 1.0881E-06
C10 -3.4054E-06 2.7369E-06 5.5556E-07 1.1246E-05 -4.5086E-05
C11 -2.6133E-08 2.0706E-08 1.0888E-08 -1.4411E-07 -7.4258E-08
C13 -2.1406E-08 -5.2268E-08 -2.6288E-08 -1.5226E-08 1.9318E-08
C15 -8.7648E-08 2.5536E-08 -4.1929E-08 -4.1187E-08 2.7562E-07
C17 -7.3423E-13 -1.4209E-09 -1.6054E-10 2.7468E-09 -7.1507E-10
C19 -3.9622E-10 3.4789E-10 1.2663E-11 -3.7335E-09 -4.5061E-09
C21 -1.1857E-09 -7.4744E-10 -2.1818E-10 -3.1082E-09 5.1084E-09
C22 1.1918E-12 5.8791E-11 1.0099E-12 -4.9510E-11 1.1514E-12
C24 1.7837E-12 4.0304E-11 1.1971E-12 -4.0063E-11 1.3734E-11
C26 -8.2486E-13 -1.7588E-12 -2.8239E-12 1.0680E-11 1.5911E-11
C28 2.0136E-12 3.6561E-12 1.4649E-12 2.8193E-11 -5.1038E-11
C30 -9.8489E-12
C32 1.4118E-12
C34 2.2534E-12
C36 3.9384E-13
C37 5.4454E-14
C39 7.1727E-14
C41 -1.2491E-13
C43 -5.4899E-14
C45 -9.4242E-15

Example 4
<Each side data>
Surface vertex coordinates Rotation angle Surface number Surface characteristics ri di Ni νi Coordinate standard XYZX rotation 0 Object surface (display element) ∞
1 plane ∞ 3 51.7 64.2
2 plane ∞ 20
3 Reference surface (dummy surface) ∞
4 Mirror (FFS) stop ∞ S3 0 0 120.00 9.562
5 Mirror (FFS) ∞ S3 0 -113.26 -132.51 2.375
6 Mirror (FFS) ∞ S3 0 -75.42 84.75 -34.327
7 Image plane (screen) ∞ S3 0 1046.81 -667.80 62.536

<Coordinate data during zooming>
Surface vertex coordinates Rotation angle Surface number Coordinate reference Scaling position XYZX rotation Y rotation Z rotation 4 S3 W 0 0 120.00 9.562 0 0
4 S3 M 0 0 120.00 9.631 0 0
4 S3 T 0 0 120.00 9.671 0 0
5 S3 W 0 -113.26 -132.51 2.375 0 0
5 S3 M 0 -78.60 -190.54 -4.636 0 0
5 S3 T 0 -91.69 -211.97 -5.015 0 0
6 S3 W 0 -75.42 84.75 -34.327 0 0
6 S3 M 0 -184.69 129.17 -34.188 0 0
6 S3 T 0 -290.23 129.37 -28.398 0 0

<Polynomial free-form surface>
Coefficient \ Surface number 4 5 6
C3 5.3164E-02 -9.5085E-02 -4.3815E-02
C4 -2.1524E-03 -5.7224E-04 2.5724E-07
C6 -1.1656E-03 6.9268E-04 3.9696E-04
C8 6.1805E-07 2.4422E-06 3.2852E-07
C10 1.7945E-06 4.2108E-07 9.6840E-07
C11 -1.4450E-08 -1.2228E-07 -7.7727E-09
C13 -1.1566E-08 1.6374E-08 3.3214E-08
C15 4.6801E-09 -7.7700E-10 1.1772E-08
C17 7.2719E-10 3.3866E-10 1.1495E-10
C19 -1.3354E-09 -6.7140E-11 3.0139E-11
C21 1.5100E-09 1.4583E-11 -1.0428E-10
C22 3.0581E-11 1.4906E-10 3.2645E-12
C24 1.6042E-10 -6.7829E-11 -1.7542E-11
C26 -1.0586E-09 -1.2102E-11 -5.3182E-12
C28 -6.2167E-11 -9.5679E-13 -4.4514E-13
C30 -4.8430E-12 -1.2928E-12 2.2729E-13
C32 5.0630E-11 4.0517E-13 1.6215E-13
C34 -6.3799E-11 -1.2746E-13 4.6749E-14
C36 -9.1142E-12 1.1481E-14 8.5551E-15
C37 -9.4413E-14 -2.7537E-13 -3.8234E-15
C39 7.1835E-13 -3.5966E-14 -5.6893E-16
C41 -2.5494E-12 4.7818E-14 -4.7424E-16
C43 7.7163E-12 5.6338E-15 -1.2396E-16
C45 2.3363E-14 2.0165E-17 -2.5393E-17
C47 -1.1642E-14 7.3445E-15
C49 1.9630E-13 -2.4050E-16
C51 -4.7603E-13 -5.1295E-16
C53 2.9315E-13 -3.2530E-17
C55 1.1267E-14 -5.1567E-19

(Example 5)
<Each side data>
Surface vertex coordinates Rotation angle Surface number Surface characteristics ri di Ni νi Coordinate standard XYZX rotation 0 Object surface (display element) ∞
1 plane ∞ 3 51.7 64.2
2 plane ∞ 20
3 Reference surface (dummy surface) ∞
4 Mirror (FFS) ∞ S3 0 0 80.00 13.266
5 Mirror (FFS) ∞ S3 0 -36.09 15.08 9.688
6 Mirror (FFS) Aperture ∞ S3 0 -96.60 93.24 -45.703
7 Mirror (FFS) ∞ S3 0 130.86 -32.52 -44.536
8 Mirror (FFS) ∞ S3 0 -45.73 204.60 42.008
9 Image plane (screen) ∞ S3 0 1998.86 -919.04 -25.997

<Coordinate data during zooming>
Surface vertex coordinates Rotation angle Surface number Coordinate reference Scaling position XYZX rotation Y rotation Z rotation 7 S3 W 0 130.86 -32.52 -44.536 0 0
7 S3 M 0 131.44 -32.74 -44.587 0 0
7 S3 T 0 131.85 -32.90 -44.572 0 0
8 S3 W 0 -45.73 204.60 42.008 0 0
8 S3 M 0 -31.23 229.26 40.863 0 0
8 S3 T 0 -17.82 252.12 39.800 0 0

<Polynomial free-form surface>
Coefficient \ Surface number 4 5 6 7 8
C3 -3.4570E-02 2.3005E-01 5.5514E-02 -2.0787E-01 1.0679E + 00
C4 -3.0690E-03 -1.9395E-03 -1.4913E-03 -3.5784E-03 1.7087E-03
C6 -1.5472E-03 7.3132E-04 -4.2310E-04 -1.0666E-03 1.4885E-02
C8 -1.3733E-06 5.0345E-06 3.6225E-06 -1.2428E-05 -9.8586E-06
C10 -5.9551E-06 -2.2015E-06 -1.3955E-06 5.1056E-06 -4.8515E-05
C11 -3.5236E-08 -2.8078E-08 4.1829E-09 -1.8269E-07 1.5327E-09
C13 6.7089E-08 1.6275E-07 4.1332E-08 1.1496E-07 3.4421E-08
C15 -8.2107E-08 -5.2765E-08 -2.7291E-08 -7.4827E-08 1.0783E-07
C17 -2.7629E-10 -9.2716E-10 -1.1604E-11 -1.3505E-09 -8.8420E-10
C19 -1.3168E-11 -9.5118E-11 -6.6666E-10 -2.2190E-09 -4.6102E-10
C21 -1.5692E-09 -8.2164E-10 -5.0644E-10 -8.1550E-10 7.7016E-09
C22 -1.3864E-12 -6.9523E-12 -2.2797E-13 -1.2012E-11 4.5990E-13
C24 3.8917E-12 6.8331E-12 2.0792E-12 6.7876E-11 7.9416E-12
C26 1.7038E-12 9.2395E-12 4.9250E-12 4.6385E-11 -1.3679E-11
C28 -7.5632E-12 -7.1200E-12 2.2690E-12 -2.0896E-11 -2.8588E-11
C30 1.0586E-13 -5.5855E-13
C32 2.5036E-14 3.2090E-13
C34 2.0947E-13 6.9576E-13
C36 -1.1702E-13 -5.8937E-13
C37 4.0946E-15 5.5446E-14
C39 6.7936E-15 -9.6726E-14
C41 5.6167E-15 -1.2932E-13
C43 3.3774E-15 8.8310E-15
C45 -1.1083E-15 1.1284E-14

Table 1 shows the projection magnification of the entire system, and Table 2 shows the effective area size (mm), NA ₀ (reduction side NA), and aperture radius (mm) of the display surface of the display element 1. Yes. The projection magnification and NA ₀ are shown as average values in the X direction and the Y direction. Table 3 shows the configurations of the negative group G1 and the positive group G2 of the projection optical system 2, and the behavior of the surface during zooming (whether it moves). In the first to fourth embodiments, all three or five mirrors are moved to change the magnification. However, in the fifth embodiment, only the two enlargement-side mirrors are moved to change the magnification. Yes. Tables 4 to 7 show the values of the conditional expressions (1) to (4), respectively.

  18 to 32 show spot diagrams obtained in each of the zooming states of wide (W), middle (M), and tele (T) in each of the first to fifth embodiments. Each spot diagram shows imaging characteristics (mm) on the screen SC for three wavelengths of 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 surface (S0 surface) of the display element 1.

  In the above, the projection surface is the screen SC, but the projection surface may be a wall.

  The present invention is particularly applicable to a projection optical system using a display element typified by LCD and DMD, and an optical apparatus having the projection optical system.

It is sectional drawing which shows the whole structure of the projection type image display apparatus in the wide zooming state based on Embodiment 1 of this invention. It is sectional drawing which expands and shows the projection optical system in the wide magnification state of the said projection type image display apparatus. It is sectional drawing which shows the whole structure of the said projection type image display apparatus in the middle magnification state. It is sectional drawing which expands and shows the projection optical system in the zooming state of the middle of the said projection type image display apparatus. It is sectional drawing which shows the whole structure of the said projection type image display apparatus in the zooming state of tele. It is sectional drawing which expands and shows the projection optical system in the zooming state of the middle of the said projection type image display apparatus. It is explanatory drawing which shows the movement locus | trajectory of each optical element while overlapping and expanding and showing the said projection optical system in each magnification state of wide, middle, and tele. The projection optical system of the projection type image display apparatus according to Embodiment 2 of the present invention is shown in an enlarged manner by superposing and enlarging each of the zooming states of wide, middle, and tele, and showing the movement trajectory of each optical element It is. Explanatory drawing which shows the projection optical system of the projection type image display apparatus which concerns on Embodiment 3 of this invention on a zooming state of each of a wide, a middle, and a telephoto magnification, it expands, and shows the movement locus | trajectory of each optical element. It is. Explanatory drawing which shows the projection optical system of the projection type image display apparatus which concerns on Embodiment 4 of this invention on a zooming state of each of a wide, a middle, and a telephoto magnification, it expands, and shows the movement locus | trajectory of each optical element. It is. Explanatory drawing which shows the projection optical system of the projection type image display apparatus which concerns on Embodiment 5 of this invention on a zooming state of each of a wide, a middle, and a telephoto magnification, it expands, and shows the movement locus | trajectory of each optical element. It is. It is explanatory drawing which shows typically the structure which bends the optical path from a display element to a screen with two mirrors. It is explanatory drawing which shows typically an optical path when only the mirror by the side of a display element is moved parallel and is changed in magnification. It is explanatory drawing which shows typically an optical path when both mirrors are moved and scaled. It is explanatory drawing which shows typically an optical path when two mirrors are further rotated when moving by zooming by moving two mirrors along different paths that are not parallel to each other. It is explanatory drawing which shows typically the position coordinate of each surface while showing typically the optical system comprised with a display element, the mirror of 2 surfaces arrange | positioned non-axially, and a screen. In the projection type image display apparatus of Embodiment 1, it is explanatory drawing which shows typically the correspondence of the surface of each optical element, and a surface number. FIG. 3 is an explanatory diagram showing a spot diagram obtained in the wide zoom state of Example 1. FIG. 3 is an explanatory diagram showing a spot diagram obtained in a middle magnification state of Example 1. It is explanatory drawing which shows the spot diagram obtained in the tele magnification state of Example 1. FIG. FIG. 6 is an explanatory diagram showing a spot diagram obtained in a wide variable magnification state of Example 2. It is explanatory drawing which shows the spot diagram obtained in the middle magnification variation state of Example 2. FIG. It is explanatory drawing which shows the spot diagram obtained in the variable magnification state of the tele of Example 2. FIG. 6 is an explanatory diagram showing a spot diagram obtained in a wide zoom state of Example 3. It is explanatory drawing which shows the spot diagram obtained in the middle magnification variation state of Example 3. FIG. It is explanatory drawing which shows the spot diagram obtained in the tele magnification state of Example 3. FIG. 10 is an explanatory diagram showing a spot diagram obtained in the wide variable magnification state of Example 4. It is explanatory drawing which shows the spot diagram obtained in the middle magnification variation state of Example 4. It is explanatory drawing which shows the spot diagram obtained in the variable magnification state of the tele of Example 4. FIG. 10 is an explanatory diagram showing a spot diagram obtained in a wide zoom state of Example 5. It is explanatory drawing which shows the spot diagram obtained in the middle magnification variation state of Example 5. It is explanatory drawing which shows the spot diagram obtained in the tele magnification state of Example 5.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Display element 2 Projection optical system G1 Negative group G2 Positive group M1-M5 Mirror (reflection surface)
SC screen (projection surface)

Claims (8)

A non-axis variable magnification projection optical system having a rotationally asymmetric reflecting surface arranged eccentrically and projecting an image of a display element surface on a projection surface in an enlarged manner,
In addition to having at least three reflecting surfaces, from the enlarged side, there are a negative power group having at least one reflecting surface and a positive power group having at least one reflecting surface. And
A non-axis variable magnification projection optical system characterized in that the power of at least a negative group is changed at the time of zooming of the entire system, and zooming is performed while the positions of the display element surface and the projection surface are substantially constant. When the state with the smallest magnification on the magnification side is wide and the state with the largest magnification on the magnification side is tele,
2. The non-axial change according to claim 1, wherein, in zooming from wide to tele, the following conditional expression (1) is satisfied in at least one of a short side direction and a long side direction of the display element. Double projection optics;
0.2 <| (Zφm_refl−1) / (Zφall−1) | <3.0 (1)
However,
Zφm_refl: ratio of tele power to wide power in the negative group Zφall: ratio of tele power to wide power in the entire system.   3. The non-axis variable magnification projection optical according to claim 1, wherein at least the power of the negative group is changed by moving the reflecting surface of the negative group and another reflecting surface along different trajectories that are not parallel to each other. system.   4. The non-axis variable magnification projection optical system according to claim 1, wherein the axial principal ray is incident from an oblique direction other than the vertical direction with respect to the projection surface. The non-axis variable magnification projection optical system according to claim 4, wherein the following conditional expression (2) is satisfied:
20 ° <| θ | <70 ° (2)
However,
θ: An angle formed between the normal line of the projection surface and the axial principal ray incident on the projection surface. 3. The non-axis variable magnification projection optical system according to claim 2, wherein the following conditional expression (3) is satisfied in zooming from wide to telephoto;
| ΔSimg / (β × (1 / 2NA ₀ )) | <2.0 (3)
However,
β: projection magnification ΔSimg: between the paraxial image point and the actual center position of the projection surface at the projection magnification β
Distance measured along the axial principal ray NA ₀ : NA on the reduction side of the entire system
It is. The non-axial variable magnification projection optical system according to claim 1, wherein the following conditional expression (4) is satisfied:
0.05 <| fall_W / f1_W | <1.5 (4)
However,
fall_W: wide focal length of the entire system f1_W: wide focal length of the negative group. A display element for displaying a two-dimensional image;
A projection type image display device having a projection optical system for enlarging and projecting an image of a display element surface on a projection surface,
8. A projection type image display apparatus, wherein the projection optical system comprises the non-axis variable magnification projection optical system according to claim 1.

Images