Optical system and projector

Abstract

To provide an optical system that can bring a first reflection surface and a second reflection surface close to each other.SOLUTION: An optical system comprises: a first optical element; and a second optical element that is arranged on a reduction side of the first optical element. The first optical element has a first reflection surface with a concave shape. The second optical element has a first transmission surface, a second reflection surface that is arranged on a reduction side of the first transmission surface, and a second transmission surface that is arranged on a reduction side of the second reflection surface. A first optical axis of the first reflection surface is parallel to a second optical axis of the first transmission surface. At least one of the first transmission surface, the second reflection surface, and the second transmission surface has power.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to an optical system and a projector. [Background technology]

[0002] A projection optical system having a projection lens, a first mirror, and a second mirror, in that order from the reduction side to the enlargement side, is described in Patent Document 1. The first mirror is planar, and the second mirror is concave. When the projection optical system is used in a projector, an image display element is placed on the reduction-side image forming surface of the projection optical system. A screen is placed on the enlargement-side image forming surface of the projection optical system. In this document, the projection light that passes through the projection lens from the image display element side and enters the first mirror is a diffuse beam, and the projection light that is reflected by the first mirror and then the second mirror is first concentrated before reaching the screen placed on the enlargement-side image forming surface. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-064816 Summary of the Invention [Problem to be solved by the invention]

[0004] In the projection optical system of Patent Document 1, a large air gap must be secured between the first mirror located on the enlarged side of the projection lens to prevent physical interference with both the projection lens and the second mirror. This makes it difficult to place the first mirror and the second mirror close to each other, resulting in a large projection optical system. [Means for solving the problem]

[0005] In order to solve the above problem, the present invention provides a first optical element and a second optical element arranged on the reduction side of the first optical element, wherein the first optical element has a concave first reflecting surface, and the second optical element has a first transmitting surface, a second reflecting surface arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, wherein a first optical axis of the first reflecting surface is parallel to a second optical axis of the first transmitting surface, and at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power.

[0016] Also, an optical system of the present invention includes a first optical element and a second optical element arranged on the reduction side of the first optical element, wherein the first optical element has a concave first reflecting surface, and the second optical element has a first transmitting surface formed of an aspherical shape, a second reflecting surface also formed of an aspherical shape arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, wherein a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, and at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power, and the first optical element includes a third transmitting surface arranged on the enlargement side of the first reflecting surface and a fourth transmitting surface arranged on the reduction side of the first reflecting surface, wherein the fourth transmitting surface and the first transmitting surface are opposed to each other, and the third optical axis of the third transmitting surface and the fourth optical axis of the fourth transmitting surface coincide with the first optical axis. Further, the optical system of the present invention comprises a first optical element and a second optical element arranged on the reduction side of the first optical element, the first optical element having a concave first reflecting surface, the second optical element having a first transmitting surface formed of an aspherical shape, a second reflecting surface also formed of an aspherical shape arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power, the optical system comprises a refractive optical system arranged on the reduction side of the second optical element, the refractive optical system comprises a plurality of lenses, the plurality of lenses have shapes rotationally symmetrical about a sixth optical axis of the refractive optical system, and the angle formed between the first optical axis and the sixth optical axis is 90° or less.

[0013] Also, the present invention provides an optical system comprising a first optical element, a second optical element arranged on the reduction side of the first optical element, and a refractive optical system arranged on the reduction side of the second optical element, wherein the first optical element has a concave first reflecting surface, and the second optical element has a first transmitting surface formed of an aspherical shape, a second reflecting surface also formed of an aspherical shape arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, wherein a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, and at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power, and the first optical element comprises a third transmitting surface arranged on the enlargement side of the first reflecting surface and a fourth transmitting surface arranged on the reduction side of the first reflecting surface, wherein the fourth transmitting surface and the first transmitting surface are opposed to each other, and the third optical axis of the third transmitting surface and the fourth optical axis of the fourth transmitting surface coincide with the first optical axis. Further, the optical system of the present invention comprises a first optical element, a second optical element arranged on the reduction side of the first optical element, and a refractive optical system arranged on the reduction side of the second optical element, wherein the first optical element has a first reflecting surface having a concave shape, and the second optical element has a first transmitting surface having an aspherical shape, a second reflecting surface having an aspherical shape arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, wherein a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power, and the refractive optical system comprises a plurality of lenses which have shapes rotationally symmetrical about a sixth optical axis of the refractive optical system, and wherein an angle between the first optical axis and the sixth optical axis is 90°.

[0006] Next, a projector of the present invention includes a light modulation element disposed on the reduction-side conjugate plane and modulating light emitted from a light source, and the above-described optical system that projects the light modulated by the light modulation element. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a diagram showing a schematic configuration of a projector including an optical system according to an embodiment of the present invention. [Figure 2] 1 is a ray diagram schematically illustrating the entire optical system of Example 1. FIG. [Figure 3] FIG. 2 is a ray diagram of the optical system of the first embodiment. [Figure 4] FIG. 4 is a diagram showing the MTF on the enlargement side of the optical system of Example 1. [Figure 5] 1 is a spot diagram of the optical system of Example 1. [Figure 6] FIG. 10 is a ray diagram schematically illustrating the entire optical system of Example 2. [Figure 7] FIG. 10 is a ray diagram of the optical system of Example 2. [Figure 8] FIG. 10 is a diagram showing the MTF on the enlargement side of the optical system of Example 2. [Figure 9] 10 is a spot diagram of the optical system of Example 2. [Figure 10] FIG. 10 is a ray diagram schematically illustrating the entire optical system of Example 3. [Figure 11] FIG. 10 is a ray diagram of the optical system of Example 3. [Figure 12] FIG. 10 is a ray diagram of the first optical system of Example 3. [Figure 13] FIG. 10 is a diagram showing the MTF on the enlargement side of the optical system of Example 3. [Figure 14] 10 is a spot diagram of the optical system of Example 3. [Figure 15] FIG. 10 is a ray diagram schematically illustrating the entire optical system of Example 4. [Figure 16] FIG. 10 is a ray diagram of the optical system of Example 4. [Figure 17] FIG. 10 is a ray diagram of the first optical system of Example 4. [Figure 18] FIG. 10 is a diagram showing the MTF on the enlargement side of the optical system of Example 4. [Figure 19] 10 is a spot diagram of the optical system of Example 4. DETAILED DESCRIPTION OF THE INVENTION

[0008] An optical system and a projector according to an embodiment of the invention will be described below with reference to the drawings.

[0009] (projector) 1 is a diagram showing a schematic configuration of a projector equipped with an optical system 3 of the present invention. As shown in Fig. 1, the projector 1 is equipped with an image forming unit 2 that generates a projection image to be projected onto a screen S, an optical system 3 that enlarges the projection image and projects the enlarged image onto the screen S, and a control unit 4 that controls the operation of the image forming unit 2.

[0010] (Image forming unit and control unit) The image forming unit 2 includes a light source 10, a first integrator lens 11, a second integrator lens 12, a polarization conversion element 13, and a superimposing lens 14. The light source 10 is, for example, an ultra-high pressure mercury lamp, a solid-state light source, or the like. The first integrator lens 11 and the second integrator lens 12 each have a plurality of lens elements arranged in an array. The first integrator lens 11 splits the light beam from the light source 10 into a plurality of beams. Each lens element of the first integrator lens 11 focuses the light beam from the light source 10 near each lens element of the second integrator lens 12.

[0011] Polarization conversion element 13 converts the light from second integrator lens 12 into predetermined linearly polarized light. Superimposing lens 14 superimposes the images of each lens element of first integrator lens 11 via second integrator lens 12 onto the display areas of liquid crystal panels 18R, 18G, and 18B, which will be described later.

[0012] The image forming unit 2 also includes a first dichroic mirror 15, a reflecting mirror 16, a field lens 17R, and a liquid crystal panel 18R. The first dichroic mirror 15 reflects R light, which is a portion of the light incident from the superimposing lens 14, and transmits G light and B light, which are also portions of the light incident from the superimposing lens 14. The R light reflected by the first dichroic mirror 15 passes through the reflecting mirror 16 and the field lens 17R and is incident on the liquid crystal panel 18R. The liquid crystal panel 18R is a light modulation element. The liquid crystal panel 18R modulates the R light in accordance with an image signal to form a red projection image.

[0013] The image forming unit 2 further includes a second dichroic mirror 21, a field lens 17G, and a liquid crystal panel 18G. The second dichroic mirror 21 reflects G light, which is a portion of the light from the first dichroic mirror 15, and transmits B light, which is a portion of the light from the first dichroic mirror 15. The G light reflected by the second dichroic mirror 21 passes through the field lens 17G and enters the liquid crystal panel 18G. The liquid crystal panel 18G is a light modulation element. The liquid crystal panel 18G forms a green projection image by modulating the G light in accordance with an image signal.

[0014] The image forming unit 2 also includes a relay lens 22, a reflecting mirror 23, a relay lens 24, a reflecting mirror 25, a field lens 17B, a liquid crystal panel 18B, and a cross dichroic prism 19. The B light transmitted through the second dichroic mirror 21 passes through the relay lens 22, the reflecting mirror 23, the relay lens 24, the reflecting mirror 25, and the field lens 17B, and is incident on the liquid crystal panel 18B. The liquid crystal panel 18B is a light modulation element. The liquid crystal panel 18B forms a blue projection image by modulating the B light in accordance with an image signal.

[0015] Liquid crystal panels 18R, 18G, and 18B surround cross dichroic prism 19 on three sides. Cross dichroic prism 19 is a prism for light synthesis, and generates a projection image by synthesizing the light modulated by each of liquid crystal panels 18R, 18G, and 18B.

[0016] The optical system 3 projects the projection image synthesized by the cross dichroic prism 19 onto the screen S in an enlarged scale.

[0017] The control unit 4 includes an image processing unit 6 to which external image signals such as video signals are input, and a display driving unit 7 that drives the liquid crystal panels 18R, 18G, and 18B based on the image signals output from the image processing unit 6.

[0018] Image processing unit 6 converts an image signal input from an external device into an image signal including the gradation of each color. Display drive unit 7 operates liquid crystal panels 18R, 18G, and 18B based on the projection image signals of each color output from image processing unit 6. As a result, image processing unit 6 displays a projection image corresponding to the image signal on liquid crystal panels 18R, 18G, and 18B.

[0019] Example 1 Fig. 2 is a ray diagram schematically illustrating the entire optical system of Example 1. Fig. 3 is a ray diagram of an optical system 3A of Example 1. As shown in Figs. 2 and 3, a liquid crystal panel 18 is disposed on the reduction-side conjugate plane of the optical system 3A.

[0020] For convenience, in the following description, three mutually perpendicular axes are referred to as the X-axis, Y-axis, and Z-axis. The width direction of the screen S, which is the magnification-side conjugate plane, is referred to as the X-axis direction, the vertical direction of the screen S as the Y-axis direction, and the direction perpendicular to the screen S as the Z-axis direction. In the Y-axis direction, the direction above the screen S is referred to as the Y1 direction, and the direction below the screen S as the Y2 direction. In the Z-axis direction, the side where the screen S is located is referred to as the Z1 direction, and the opposite side is referred to as the Z2 direction.

[0021] As shown in FIG. 2, the optical system 3A of this example has, in order from the enlargement side to the reduction side, a first optical system 31 and a second optical system 32. The first optical system 31 is a reflective optical system. The first optical system 31 includes a first optical element 33 and a second optical element 34. The first optical element 33 and the second optical element 34 are arranged in this order from the enlargement side to the reduction side. The optical axis M of the first optical element 33 extends along the Z-axis direction. In other words, the optical axis M of the first optical element 33 is perpendicular to the screen S. The second optical system 32 is a refractive optical system. The optical axis N (sixth optical axis) of the second optical system 32 extends along the Y-axis direction. The screen S is located in the Z1 direction of the optical axis N.

[0022] As shown in FIG. 3, the first optical element 33 has a first reflecting surface 40 facing the Z1 direction. The first reflecting surface 40 has a concave shape recessed in the Z2 direction. The first optical axis of the first reflecting surface 40 is the optical axis M of the first optical element 33. The first reflecting surface 40 has a shape that is rotationally symmetric about the first optical axis. The first reflecting surface 40 has an aspheric shape. Here, the first optical element 33 is designed with the optical axis M as the design axis. In other words, the first optical axis is the designed optical axis of the first reflecting surface 40.

[0023] The second optical element 34 is composed of a single optical element. The second optical element 34 is located in the Z1 direction of the first optical element 33. The second optical element 34 has a first transmitting surface 51, a second reflecting surface 52 located on the reduction side of the first transmitting surface 51, and a second transmitting surface 53 located on the reduction side of the second reflecting surface 52.

[0024] The first transmitting surface 51 faces the first reflecting surface 40 in the Z-axis direction. The first transmitting surface 51 has a convex shape facing the Z2 direction. The second optical axis of the first transmitting surface 51 is approximately parallel to the first optical axis of the first reflecting surface 40. In this example, the second optical axis of the first transmitting surface 51 coincides with the first optical axis of the first reflecting surface 40. In other words, the second optical axis of the first transmitting surface 51 coincides with the optical axis M of the first optical element 33. The first transmitting surface 51 has a shape that is rotationally symmetric about the second optical axis. The first transmitting surface 51 has positive power. The first transmitting surface 51 has an aspherical shape.

[0025] The second reflecting surface 52 is a flat mirror with no power. The second reflecting surface 52 is inclined at 45° with respect to the Y-axis and the Z-axis. The second reflecting surface 52 bends the optical path by 90° between the first transmitting surface 51 and the second transmitting surface 53. The second reflecting surface 52 is formed by providing a reflective coating layer on the outer surface of the second optical element 34 in the Z1 direction.

[0026] The second transmitting surface 53 faces the Y2 direction and faces the lens L15. The angle formed by the optical axis of the second transmitting surface 53 and the second optical axis of the first transmitting surface 51 is 90°. That is, the angle formed by the optical axis of the second transmitting surface 53 and the optical axis M of the first optical element 33 is 90°. The optical axis of the second transmitting surface 53 coincides with the optical axis N of the second optical system 32. The second transmitting surface 53 has a shape that is rotationally symmetrical about the optical axis of the second transmitting surface 53. The second transmitting surface 53 has positive power. The second transmitting surface 53 has an aspherical shape.

[0027] As shown in FIG. 3, the second optical system 32 includes 15 lenses L1 to L15. The lenses L1 to L15 are arranged in this order from the reduction side to the enlargement side. In this example, the lenses L2 and L3 are cemented together to form a first cemented lens L21. The lenses L4 and L5 are cemented together to form a second cemented lens L22. The lenses L11 and L12 are cemented together to form a third cemented lens L23. The lenses L13 and L14 are cemented together to form a fourth cemented lens L24. An aperture O is disposed between the lenses L9 and L10. The lenses L6, L9, and L15 are aspherical lenses having aspherical surfaces on both sides. Each lens in the second optical system 32 has a rotationally symmetric surface centered on the optical axis N.

[0028] As shown in FIG. 3, the liquid crystal panel 18, which is disposed on the reduction-side conjugate plane of the optical system 3A, forms a projected image on the Z2 side of the optical axis N. The angle θ1 formed between the optical axis M of the first optical element 33 and the optical axis N of the second optical system 32 is 90° or less. In this example, the angle θ1 is 90°. Therefore, after passing through the second optical system 32, light from the liquid crystal panel 18 side is bent 90° by the second reflecting surface 52 of the second optical element 34 and heads in the Z2 direction. The light headed in the Z2 direction is bent back in the Z1 and Y1 directions by the first reflecting surface 40 of the first optical element 33 and reaches the screen S.

[0029] 3, the optical system 3A forms an intermediate image 30 between the reduction-side conjugate surface and the magnification-side conjugate surface, the intermediate image 30 being conjugate to the reduction-side conjugate surface and the magnification-side conjugate surface. In this example, the intermediate image 30 is formed between the first reflecting surface 40 of the first optical element 33 and the second transmitting surface 53 of the second optical element 34.

[0030] The lens data for optical system 3A is as follows. Surface numbers are assigned in order from the reduction side to the magnification side. The symbols refer to the liquid crystal panel, dichroic prism, lens, and screen. Data for surface numbers that do not correspond to the liquid crystal panel, dichroic prism, lens, and screen are dummy data. Surfaces with an * next to the surface number are aspheric. R is the radius of curvature. D is the on-axis surface spacing. nd is the refractive index. νd is the Abbe number. Y is the aperture radius. The units for R, D, and Y are mm. The lens data in this example was designed using CODE V by Synopsys.

[0031] Sign Surface No. RD nd vd Mode Y 18 0 0.00000 9.500000 Refraction 19 1 0.00000 25.910000 1.516330 64.14 Refraction 13.2340 2 0.00000 0.000000 Refraction 15.9410 L1 3 30.00000 9.600000 1.496999 81.55 Refraction 16.8000 4 -65.00000 0.400000 Refraction 16.6040 L2 5 29.00000 7.600000 1.487490 70.24 Refraction 14.7810 L3 6 -78.00000 1.200000 1.805181 25.43 Refraction 13.9320 7 95.00000 0.400000 Refraction 13.1020 L4 8 23.60000 10.500000 1.516330 64.14 Refraction 12.1380 L5 9 -18.30000 1.200000 1.903658 31.32 Refraction 10.5330 10 46.00000 0.964539 Refraction 9.8300 L6 *11 21.71241 1.400000 1.589130 61.15 Refraction 9.8090 *12 13.91712 0.500000 Refraction 9.7310 L7 13 19.66000 4.000000 1.487490 70.24 Refraction 9.8790 14 260.00000 2.500000 Refraction 9.7100 15 0.00000 2.089661 Refraction 9.3700 L8 16 27.70000 4.200000 1.846660 23.78 Refraction 9.8110 17 -78.00000 2.151218 Refraction 9.8000 L9 *18 76.98511 1.800000 1.743198 49.30 Refraction 8.7350 *19 15.61135 3.326970 Refraction 8.3580 O 20 0.00000 1.584940 Refraction 12.0000 L10 21 194.00000 3.200000 1.647689 33.79 Refraction 10.2490 22 -292.00000 13.749192 Refraction 11.0200 L11 23 77.60000 11.000000 1.620041 36.26 Refraction 18.8520 L12 24 -32.00000 2.000000 1.805181 25.43 Refraction 19.2190 25 -152.50000 18.160002 Refraction 20.7470 L13 26 47.40000 17.000000 1.581439 40.75 Refraction 30.0000 L14 27 -196.00000 2.000000 1.805181 25.43 Refraction 29.4690 28 76.00000 11.661272 Refraction 28.5520 L15 *29 30854.59445 2.800000 1.531131 55.75 Refraction 30.6150 *30 34.26687 11.211681 Refraction 29.7720 31 0.00000 10.000000 Refraction 29.8080 34 *32 302.58304 67.000000 1.531131 55.75 Refraction 31.5050 33 0.00000 -2.000000 1.531131 55.75 Reflection 57.9590 *34 -8554.05457 -70.000000 Refraction 61.0680 33 *35 63.34969 501.000000 Reflection 76.0200 36 0.00000 0.000000 Refraction 1450.0980 S 37 0.00000 0.000000 Refraction 1450.0980

[0032] The aspherical coefficients are as follows:

[0033] Face number 11 12 18 19 Conic constant 1.568E+00 -1.3E+00 -1E+00 -8.8E-01 4th order coefficient -3.529091E-04 -2.989935E-04 -1.136128E-04 -8.485042E-05 6th order coefficient 1.857039E-06 2.247788E-06 0 1.263136E-07 8th order coefficient -4.616195E-09 -8.694758E-09 0 4.873501E-11 10th order coefficient 0 1.514578E-11 0 0

[0034] Face number 29 30 32 34 Conic constant 9E+01 0 -2.463741E+02 -5E-01 4th order coefficient 1.94923E-05 -5.224166E-06 -3.402535E-06 2.548342E-07 6th order coefficient -3.426125E-08 -3.962571E-09 5.756798E-10 -8.423093E-12 8th order coefficient 4.318007E-11 -1.23371E-12 -8.070441E-13 6.568096E-15 10th order coefficient -3.081249E-14 1.164683E-14 0 1.660894E-18 12th order coefficient 9.350359E-18 -1.451055E-17 0 -4.287004E-22 14th order coefficient 0 4.754714E-21 0 5.558963E-26

[0035] Face number 35 Conic constant -1E+00 4th order coefficient -1.550607E-07 6th order coefficient 3.752303E-11 8th order coefficient -1.948136E-15 10th order coefficient -5.494016E-19 12th order coefficient 1.640171E-22 14th order coefficient -1.457357E-26

[0036] The ray coordinates at the object plane are:

[0037] Ray number X coordinate Y coordinate 1 0 1.67 2 0 3.67 3 0 5.67 4 0 7.67 5 0 9.67

[0038] In this example, the surface number 33 is an eccentric surface. The parameters of the eccentric surface are as follows:

[0039] Face number 33 Eccentricity type: Decenter and bend Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 0.0000 Parameter α -45.0000

[0040] (Action and effect) In the optical system 3A of this example, the first optical element 33, which is arranged on the most enlargement side, has a concave first reflecting surface 40. The second optical element 34, which is arranged on the reduction side of the first optical element 33, has a first transmitting surface 51, a second reflecting surface 52 arranged on the reduction side of the first transmitting surface 51, and a second transmitting surface 53 arranged on the reduction side of the second reflecting surface 52. The first optical axis of the first reflecting surface 40 coincides with the second optical axis of the first transmitting surface 51. The first transmitting surface 51 and the second transmitting surface 53 have positive power.

[0041] According to this example, the second optical element 34, which includes the first transmitting surface 51 that projects the projection light toward the first optical element 33, has power. This allows the spread and direction of the light traveling from the first transmitting surface 51 toward the first reflecting surface 40 to be controlled, thereby shortening the air gap between the first optical element 33 and the second optical element 34. This makes it easy to control the projection light at the first reflecting surface 40 of the first optical element 33. This makes it possible to project an enlarged image, with aberrations well corrected, onto the screen S. Furthermore, since the air gap between the first optical element 33 and the second optical element 34 can be shortened, the optical system can be made smaller.

[0042] In this example, the angle θ1 between the optical axis M of the first optical element 33 and the optical axis N of the second optical system 32 is 90° or less. This allows the optical elements arranged on the enlargement side of the second optical element 34 to be arranged parallel to the enlargement-side image-forming surface or in a direction away from the enlargement-side image-forming surface. This prevents the optical elements arranged on the enlargement side of the second optical element 34 from interfering with the enlargement-side image-forming surface. This makes it possible to install the optical system in a position close to the screen S.

[0043] Furthermore, in this example, an intermediate image 30 that is conjugate with the reduction-side conjugate surface and the magnification-side conjugate surface is formed between the first reflecting surface 40 of the first optical element 33 and the second transmitting surface 53 of the second optical element 34. This positions the second optical element 34, which has power, in the vicinity of the intermediate image 30. Therefore, it is possible to suppress the occurrence of chromatic aberration and the like in the intermediate image.

[0044] In this example, the second optical system 32 disposed on the reduction side of the second optical element 34 is a refractive optical system. The refractive optical system includes a plurality of lenses, each of which has a rotationally symmetric surface centered on the optical axis N. This makes it easy to manufacture the second optical system 32.

[0045] Fig. 4 is a diagram showing the MTF on the enlargement side of the optical system 3A. The horizontal axis of Fig. 4 represents spatial frequency, and the vertical axis represents contrast reproduction ratio. As shown in Fig. 4, the optical system 3A of this example has high resolution.

[0046] Fig. 5 is a spot diagram of the optical system 3 A. As shown in Fig. 5, in this example, the spot variation is suppressed.

[0047] Example 2 Fig. 6 is a ray diagram schematically illustrating the entire optical system of Example 2. Fig. 7 is a ray diagram for optical system 3B of Example 2. As shown in Figs. 6 and 7, a liquid crystal panel 18 is disposed on the reduction-side conjugate plane of optical system 3B.

[0048] For convenience, in the following description, three mutually perpendicular axes are referred to as the X-axis, Y-axis, and Z-axis. The width direction of the screen S, which is the magnification-side conjugate plane, is referred to as the X-axis direction, the vertical direction of the screen S as the Y-axis direction, and the direction perpendicular to the screen S as the Z-axis direction. In the Y-axis direction, the direction above the screen S is referred to as the Y1 direction, and the direction below the screen S as the Y2 direction. In the Z-axis direction, the side where the screen S is located is referred to as the Z1 direction, and the opposite side is referred to as the Z2 direction.

[0049] As shown in FIG. 6, the optical system 3B of this example has, in order from the enlargement side to the reduction side, a first optical system 31 and a second optical system 32. The first optical system 31 is a reflective optical system. The first optical system 31 includes a first optical element 33 and a second optical element 34. The first optical element 33 and the second optical element 34 are arranged in this order from the enlargement side to the reduction side. The optical axis M of the first optical element 33 extends along the Z-axis direction. That is, the optical axis M of the first optical element 33 is perpendicular to the screen S. The second optical system 32 is a refractive optical system. The optical axis N (sixth optical axis) of the second optical system 32 extends along the Y-axis direction. The screen S is located in the Z1 direction of the optical axis N.

[0050] As shown in FIG. 7, the first optical element 33 has a first reflecting surface 40 facing the Z1 direction. The first reflecting surface 40 has a concave shape recessed in the Z2 direction. The first optical axis of the first reflecting surface 40 is the optical axis M of the first optical element 33. The first reflecting surface 40 has a shape that is rotationally symmetric about the first optical axis. The first reflecting surface 40 has an aspheric shape. Here, the first optical element 33 is designed with the optical axis M as the design axis. In other words, the first optical axis is the designed optical axis of the first reflecting surface 40.

[0051] The second optical element 34 is composed of a single optical element. The second optical element 34 is located in the Z1 direction of the first optical element 33. The second optical element 34 has a first transmitting surface 51, a second reflecting surface 52 located on the reduction side of the first transmitting surface 51, and a second transmitting surface 53 located on the reduction side of the second reflecting surface 52.

[0052] The first transmitting surface 51 faces the first reflecting surface 40 in the Z-axis direction. The first transmitting surface 51 has a convex shape facing the Z2 direction. The second optical axis of the first transmitting surface 51 is approximately parallel to the first optical axis of the first reflecting surface 40. In this example, the second optical axis of the first transmitting surface 51 coincides with the first optical axis of the first reflecting surface 40. In other words, the second optical axis of the first transmitting surface 51 coincides with the optical axis M of the first optical element 33. The first transmitting surface 51 has a shape that is rotationally symmetric about the second optical axis. The first transmitting surface 51 has positive power. The first transmitting surface 51 has an aspherical shape.

[0053] The second reflecting surface 52 is a mirror having a non-planar shape. Here, the non-planar shape includes an aspherical shape and a free-form shape. In this example, the second reflecting surface 52 has an aspherical shape. The second reflecting surface 52 is inclined at 45° with respect to the Y-axis and the Z-axis. The second reflecting surface 52 bends the optical path by 90° between the first transmitting surface 51 and the second transmitting surface 53. The second reflecting surface 52 is formed by providing a reflective coating layer on the outer surface of the second optical element 34 in the Z1 direction.

[0054] The second transmitting surface 53 faces the Y2 direction and faces the lens L15. The angle formed by the optical axis of the second transmitting surface 53 and the second optical axis of the first transmitting surface 51 is 90°. That is, the angle formed by the optical axis of the second transmitting surface 53 and the optical axis M of the first optical element 33 is 90°. The optical axis of the second transmitting surface 53 coincides with the optical axis N of the second optical system 32. The second transmitting surface 53 has a shape that is rotationally symmetrical about the optical axis of the second transmitting surface 53. The second transmitting surface 53 has positive power. The second transmitting surface 53 has an aspherical shape.

[0055] As shown in FIG. 7, the second optical system 32 includes 15 lenses L1 to L15. The lenses L1 to L15 are arranged in this order from the reduction side to the enlargement side. In this example, the lenses L2 and L3 are cemented together to form a first cemented lens L21. The lenses L4 and L5 are cemented together to form a second cemented lens L22. The lenses L11 and L12 are cemented together to form a third cemented lens L23. The lenses L13 and L14 are cemented together to form a fourth cemented lens L24. An aperture O is disposed between the lenses L9 and L10. The lenses L6, L9, and L15 are aspherical lenses having aspherical surfaces on both sides. Each lens in the second optical system 32 has a rotationally symmetric surface centered on the optical axis N.

[0056] As shown in FIG. 7, the liquid crystal panel 18, which is disposed on the reduction-side conjugate plane of the optical system 3B, forms a projected image on the Z2 side of the optical axis N. The angle θ1 formed between the optical axis M of the first optical element 33 and the optical axis N of the second optical system 32 is 90° or less. In this example, the angle θ1 is 90°. Therefore, after passing through the second optical system 32, light from the liquid crystal panel 18 side is bent 90° by the second reflecting surface 52 of the second optical element 34 and heads in the Z2 direction. The light headed in the Z2 direction is bent back in the Z1 and Y1 directions by the first reflecting surface 40 of the first optical element 33 and reaches the screen S.

[0057] 7, the optical system 3B forms an intermediate image 30 between the reduction-side conjugate surface and the magnification-side conjugate surface, the intermediate image 30 being conjugate to the reduction-side conjugate surface and the magnification-side conjugate surface. In this example, the intermediate image 30 is formed between the first reflecting surface 40 of the first optical element 33 and the second transmitting surface 53 of the second optical element 34.

[0058] The lens data for optical system 3B is as follows. Surface numbers are assigned in order from the reduction side to the magnification side. The symbols refer to the liquid crystal panel, dichroic prism, lens, and screen. Data for surface numbers that do not correspond to the liquid crystal panel, dichroic prism, lens, and screen are dummy data. Surfaces with an * next to the surface number are aspheric. R is the radius of curvature. D is the on-axis surface spacing. nd is the refractive index. νd is the Abbe number. Y is the aperture radius. The units of R, D, and Y are mm. The lens data in this example was designed using CODE V by Synopsys.

[0059] Sign Surface No. RD nd vd Mode Y 18 0 0.00000 9.500000 Refraction 19 1 0.00000 25.910000 1.516330 64.14 Refraction 13.2340 2 0.00000 0.000000 Refraction 15.6340 L1 3 30.00000 9.600000 1.496999 81.55 Refraction 16.8000 4 -65.00000 0.400000 Refraction 16.6020 L2 5 29.00000 7.600000 1.487490 70.24 Refraction 14.7630 L3 6 -78.00000 1.200000 1.805181 25.43 Refraction 13.8940 7 95.00000 0.400000 Refraction 13.0200 L4 8 23.60000 10.500000 1.516330 64.14 Refraction 11.9960 L5 9 -18.30000 1.200000 1.903658 31.32 Refraction 10.3230 10 46.00000 0.964539 Refraction 9.7120 L6 *11 21.71241 1.400000 1.589130 61.15 Refraction 9.7010 *12 13.91712 0.500000 Refraction 9.6570 L7 13 19.66000 4.000000 1.487490 70.24 Refraction 9.8250 14 260.00000 2.500000 Refraction 9.6710 15 0.00000 2.089661 Refraction 9.3700 L8 16 27.70000 4.200000 1.846660 23.78 Refraction 9.8110 17 -78.00000 2.151218 Refraction 9.8000 L9 *18 77.68045 1.800000 1.743198 49.30 Refraction 8.7360 *19 15.64096 3.326970 Refraction 8.3600 O 20 0.00000 1.584940 Refraction 12.0000 L10 21 194.00000 3.200000 1.647689 33.79 Refraction 10.1370 22 -292.00000 13.749192 Refraction 10.8660 L11 23 77.60000 11.000000 1.620041 36.26 Refraction 17.8780 L12 24 -32.00000 2.000000 1.805181 25.43 Refraction 18.3410 25 -152.50000 18.160002 Refraction 19.6460 L13 26 47.40000 17.000000 1.581439 40.75 Refraction 30.0000 L14 27 -196.00000 2.000000 1.805181 25.43 Refraction 26.1240 28 76.00000 11.661272 Refraction 25.5120 L15 *29 4309.39295 2.800000 1.531131 55.75 Refraction 27.4050 *30 34.15409 11.211681 Refraction 26.8130 31 0.00000 10.000000 Refraction 27.2800 34 *32 313.53737 67.000000 1.531131 55.75 Refraction 29.2980 *33 -103885.77749 -2.000000 1.531131 55.75 Reflection 55.6670 *34 19040.67849 -70.000000 Refraction 56.3870 33 *35 63.27787 501.000000 Reflection 73.4220 36 0.00000 0.000000 Refraction 1209.1380 S 37 0.00000 0.000000 Refraction 1209.1380

[0060] The aspherical coefficients are as follows:

[0061] Face number 11 12 18 19 Conic constant 1.568E+00 -1.3E+00 -1E+00 -8.8E-01 4th order coefficient -3.529091E-04 -2.989935E-04 -1.132643E-04 -8.464936E-05 6th order coefficient 1.857039E-06 2.247788E-06 0 1.292515E-07 8th order coefficient -4.616195E-09 -8.694758E-09 0 3.109839E-11 10th order coefficient 0 1.514578E-11 0 0

[0062] Face number 29 30 32 Conic constant 9E+01 0 -3.054475E+02 4th order coefficient 1.946184E-05 -5.220573E-06 -3.393991E-06 6th order coefficient -3.421317E-08 -3.911385E-09 6.733864E-10 8th order coefficient 4.344816E-11 -1.18385E-12 -9.366763E-13 10th order coefficient -3.071711E-14 1.189918E-14 0 12th order coefficient 9.210641E-18 -1.44075E-17 0 14th order coefficient 0 4.539799E-21 0

[0063] Face number 33 34 35 Conic constant 6.8E+05 -5E-01 -1E+00 4th order coefficient 7.865978E-06 2.707534E-07 -1.582381E-07 6th order coefficient -3.645436E-07 -9.732092E-12 3.754637E-11 8th order coefficient 3.761944E-07 5.614726E-15 -1.909969E-15 10th order coefficient -3.846650E-07 1.622204E-18 -5.570042E-19 12th order coefficient 0 -3.79798E-22 1.578769E-22 14th order coefficient 0 4.501296E-26 -1.341184E-26

[0064] The ray coordinates at the object plane are:

[0065] Ray number X coordinate Y coordinate 1 0 1.67 2 0 3.67 3 0 5.67 4 0 7.67 5 0 9.67

[0066] In this example, the surface number 33 is an eccentric surface. The parameters of the eccentric surface are as follows:

[0067] Face number 33 Eccentricity type: Decenter and bend Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 0.0000 Parameter α -45.0000

[0068] (Action and effect) The optical system 3B of this example can achieve the same effects as the optical system 3A of Example 1. Furthermore, in this example, the second reflecting surface 52 has a non-planar shape. That is, the second reflecting surface 52 is an aspherical surface or a free-form surface. Specifically, the second reflecting surface 52 has an aspherical shape. Therefore, it is easier to correct various aberrations in the intermediate image 30.

[0069] Fig. 8 is a diagram showing the MTF on the enlargement side of the optical system 3B. The horizontal axis of Fig. 8 represents the spatial frequency, and the vertical axis represents the contrast reproduction ratio. As shown in Fig. 8, the optical system 3B of this example has high resolution.

[0070] Fig. 9 is a spot diagram of the optical system 3B. As shown in Fig. 9, in this example, the variation in the spots is suppressed.

[0071] Example 3 Fig. 10 is a ray diagram schematically showing the entire optical system of Example 3. Fig. 11 is a ray diagram for optical system 3C of Example 3. Fig. 12 is a ray diagram for the first optical system of Example 3. As shown in Figs. 10 and 11, a liquid crystal panel 18 is disposed on the reduction-side conjugate surface of optical system 3.

[0072] For convenience, in the following description, three mutually perpendicular axes are referred to as the X-axis, Y-axis, and Z-axis. The width direction of the screen S, which is the magnification-side conjugate plane, is referred to as the X-axis direction, the vertical direction of the screen S as the Y-axis direction, and the direction perpendicular to the screen S as the Z-axis direction. In the Y-axis direction, the direction above the screen S is referred to as the Y1 direction, and the direction below the screen S as the Y2 direction. In the Z-axis direction, the side where the screen S is located is referred to as the Z1 direction, and the opposite side is referred to as the Z2 direction.

[0073] As shown in FIG. 10, the optical system 3C of this example has, in order from the enlargement side to the reduction side, a first optical system 31 and a second optical system 32. The first optical system 31 is a reflective optical system. The first optical system 31 includes a first optical element 33 and a second optical element 34. The first optical element 33 and the second optical element 34 are arranged in this order from the enlargement side to the reduction side. The optical axis M of the first optical element 33 extends along the Z-axis direction. That is, the optical axis M of the first optical element 33 is perpendicular to the screen S. The second optical system 32 is a refractive optical system. The optical axis N (sixth optical axis) of the second optical system 32 extends along the Y-axis direction. The screen S is located in the Z1 direction of the optical axis N.

[0074] 11, the first optical element 33 is composed of a single optical element. The first optical element 33 is located in the Z2 direction of the second optical element 34. The first optical element 33 has a third transmitting surface 41, a first reflecting surface 42 located on the reduction side of the third transmitting surface 41, and a fourth transmitting surface 43 located on the reduction side of the first reflecting surface 42.

[0075] The third transmitting surface 41 has a convex surface shape facing the Y1 direction. A third optical axis of the third transmitting surface 41 coincides with the optical axis M of the first optical system 31. The third transmitting surface 41 has a shape that is rotationally symmetric about the third optical axis of the third transmitting surface 41. The third transmitting surface 41 has positive power.

[0076] The first reflecting surface 42 is located in the Y2 direction of the third transmitting surface 41. The first reflecting surface 42 has a concave shape recessed in the Z2 direction. A first optical axis of the first reflecting surface 42 coincides with the optical axis M of the first optical system 31. The first reflecting surface 42 has a shape that is rotationally symmetrical about the first optical axis of the first reflecting surface 42. The first reflecting surface 42 has positive power. The first reflecting surface 42 has an aspheric shape. The first reflecting surface 42 is formed by providing a reflective coating layer on the outer surface of the first optical element 33 in the Z2 direction.

[0077] A fourth optical axis of the fourth transmitting surface 43 coincides with the optical axis M of the first optical system 31. The fourth transmitting surface 43 has a shape that is rotationally symmetric about the fourth optical axis of the fourth transmitting surface 43. The fourth transmitting surface 43 has positive power. The fourth transmitting surface 43 has an aspherical shape.

[0078] Here, the first optical element 33 is designed with the optical axis M as its design axis. That is, the third optical axis is the designed optical axis of the third transmitting surface 41. The first optical axis is the designed optical axis of the first reflecting surface 42. The fourth optical axis is the designed optical axis of the fourth transmitting surface 43.

[0079] The second optical element 34 is composed of a single optical element. The second optical element 34 is located in the Z1 direction of the first optical element 33. The second optical element 34 has a first transmitting surface 51, a second reflecting surface 52 located on the reduction side of the first transmitting surface 51, and a second transmitting surface 53 located on the reduction side of the second reflecting surface 52.

[0080] The first transmitting surface 51 faces the fourth transmitting surface 43 in the Z-axis direction. The first transmitting surface 51 has a convex shape facing the Z2 direction. The second optical axis of the first transmitting surface 51 is approximately parallel to the first optical axis of the first reflecting surface 42. In this example, the second optical axis of the first transmitting surface 51 coincides with the first optical axis of the first reflecting surface 42. In other words, the second optical axis of the first transmitting surface 51 coincides with the optical axis M of the first optical element 33. The first transmitting surface 51 has a shape that is rotationally symmetric about the second optical axis. The first transmitting surface 51 has positive power. The first transmitting surface 51 has an aspherical shape.

[0081] The second reflecting surface 52 is a flat mirror with no power. The second reflecting surface 52 is inclined at 45° with respect to the Y-axis and the Z-axis. The second reflecting surface 52 bends the optical path by 90° between the first transmitting surface 51 and the second transmitting surface 53. The second reflecting surface 52 is formed by providing a reflective coating layer on the outer surface of the second optical element 34 in the Z1 direction.

[0082] The second transmitting surface 53 faces the Y2 direction and faces the lens L15. The angle formed by the optical axis of the second transmitting surface 53 and the second optical axis of the first transmitting surface 51 is 90°. That is, the angle formed by the optical axis of the second transmitting surface 53 and the optical axis M of the first optical element 33 is 90°. The optical axis of the second transmitting surface 53 coincides with the optical axis N of the second optical system 32. The second transmitting surface 53 has a shape that is rotationally symmetrical about the optical axis of the second transmitting surface 53. The second transmitting surface 53 has positive power. The second transmitting surface 53 has an aspherical shape.

[0083] As shown in Fig. 11, the second optical system 32 includes 12 lenses L1 to L12. The lenses L1 to L12 are arranged in this order from the reduction side to the enlargement side. The lenses L2, L7, and L12 are aspherical lenses with aspherical shapes on both sides. Each lens in the first optical system 31 has a rotationally symmetric surface centered on the optical axis N.

[0084] 11, the liquid crystal panel 18, which is disposed on the reduction-side conjugate plane of the optical system 3C, forms a projected image on the Z2 side of the optical axis N. The angle θ1 formed between the optical axis M of the first optical element 33 and the optical axis N of the second optical system 32 is 90° or less. In this example, the angle θ1 is 90°. Therefore, after passing through the second optical system 32, light from the liquid crystal panel 18 side is bent 90° by the second reflecting surface 52 of the second optical element 34 and heads in the Z2 direction. The light headed in the Z2 direction is bent back in the Z1 and Y1 directions by the first reflecting surface 42 of the first optical element 33 and reaches the screen S.

[0085] 11, the optical system 3C forms an intermediate image 30 between the reduction-side conjugate surface and the magnification-side conjugate surface, the intermediate image 30 being conjugate to the reduction-side conjugate surface and the magnification-side conjugate surface. In this example, the intermediate image 30 is formed between the first reflecting surface 42 of the first optical element 33 and the second transmitting surface 53 of the second optical element 34.

[0086] 12, the light traveling between the third transmitting surface 41 and the first reflecting surface 42 includes peripheral light L that is inclined in a direction away from the screen S, which is the magnification-side conjugate surface, as it approaches the third transmitting surface 41. Between the third transmitting surface 41 and the screen S, the peripheral light L is inclined in a direction approaching the screen S as it moves away from the third transmitting surface 41. In addition, an imaginary line Q connecting a maximum effective point P of the peripheral light L on the third transmitting surface 41 and the center of curvature of the third transmitting surface 41 intersects with the optical axis M (third optical axis) at an angle θ2 of 90° or more.

[0087] The lens data for optical system 3C is as follows. Surface numbers are assigned in order from the reduction side to the magnification side. The symbols refer to the LCD panel, dichroic prism, lens, and screen. Data for surface numbers that do not correspond to the LCD panel, dichroic prism, lens, and screen are dummy data. Surfaces with an * next to the surface number are aspheric. R is the radius of curvature. D is the on-axis surface spacing. nd is the refractive index. νd is the Abbe number. Y is the aperture radius. The units for R, D, and Y are mm. The lens data in this example was designed using Synopsys' CODE V.

[0088] Sign Surface No. RD nd vd Mode Y 18 0 0.00000 22.000000 Refraction 19 1 0.00000 37.300000 1.516800 64.17 Refraction 18.4130 2 0.00000 0.409841 Refraction 22.0000 L1 3 -590.67796 10.000000 1.601496 58.49 Refraction 22.0000 4 -42.72242 3.000000 Refraction 22.4270 L2 *5 -31.66863 2.000000 2.001100 28.26 Refraction 21.9910 *6 -61.15100 0.500000 Refraction 23.5070 L3 7 144.21520 2.000000 2.001000 29.13 Refraction 25.6220 8 122.54476 0.500000 Refraction 25.8240 L4 9 90.65158 7.654132 1.505040 72.69 Refraction 26.5750 10 654.66116 0.500000 Refraction 27.2070 L5 11 112.22630 2.000000 1.879323 36.94 Refraction 28.0900 12 76.00335 1.535871 Refraction 28.1060 L6 13 92.61405 20.000000 1.480772 78.39 Refraction 28.3600 14 -46.55932 80.000000 Refraction 29.1400 O 15 0.00000 78.806011 Refraction 17.0000 L7 *16 68.28008 7.570544 1.509398 56.47 Refraction 40.0000 *17 94.93422 71.132325 Refraction 34.5630 L8 18 -1518.99365 19.999983 2.002500 19.32 Refraction 43.9240 19 -155.81886 17.456943 Refraction 45.2540 L9 20 71.47955 30.000000 1.529865 45.90 Refraction 40.9460 21 -121.50056 1.883188 Refraction 37.5510 L10 22 -101.70642 2.000000 2.002700 19.32 Refraction 36.5880 23 82.52373 31.678777 Refraction 34.9860 L11 24 -105.69324 4.989296 1.437001 95.10 Refraction 39.9880 25 -89.28078 17.118289 Refraction 40.9730 L12 *26 -23.55002 8.000000 1.509398 56.47 Refraction 48.0000 *27 -165.75191 43.658778 Refraction 47.5050 34 *28 -100.00000 72.000000 1.509398 56.47 Refraction 57.2550 29 0.00000 -15.000000 1.509398 56.47 Reflection 81.6940 *30 2014.46301 -3.472339 Refraction 63.3480 33 *31 -138.80012 -64.000000 1.509398 56.47 Refraction 62.0000 *32 33.36242 0.000000 1.509398 56.47 Reflection 69.4220 33 -80.00000 0.000000 Refraction 41.5690 34 0.00000 0.000000 Refraction 1773.6130 S 35 0.00000 0.000000 Refraction 1773.6130

[0089] The aspherical coefficients are as follows:

[0090] Face number 5 6 16 17 Conic constant -1E+00 -1E+00 -1E+00 -1E+00 4th order coefficient 3.694405E-06 7.654845E-06 2.143317E-06 2.748365E-06 6th order coefficient -8.028217E-09 -6.949011E-09 1.366512E-09 1.549676E-09 8th order coefficient 6.506012E-12 8.188262E-12 -1.450751E-13 1.723083E-13 10th order coefficient -1.527956E-15 -2.860017E-15 1.382604E-16 1.058483E-16

[0091] Face number 26 27 28 30 Conic constant -1.133807E+00 -5.958633E+01 -1.074643E+01 -1.115037E+43 4th order coefficient 4.559836E-06 -4.700304E-06 2.368596E-06 -2.160545E-06 6th order coefficient -3.539447E-09 1.031617E-09 -7.978636E-10 1.808458E-09 8th order coefficient 1.671317E-12 -2.69451E-13 1.397035E-13 -3.726332E-13 10th order coefficient -2.300276E-16 5.580673E-17 -9.252121E-18 2.502569E-17

[0092] Face number 31 32 Conic constant -4.86632E+01 -1.098222E+00 4th order coefficient -2.274983E-06 -1.57618E-06 6th order coefficient 7.397958E-10 1.305372E-10 8th order coefficient 8.793892E-15 2.869818E-14 10th order coefficient -1.526278E-18 -3.836358E-18

[0093] The ray coordinates at the object plane are:

[0094] Ray number X coordinate Y coordinate 1 0 -1.38 2 0 -4.83 3 0 -8.28 4 0 -11.73 5 0 -15.18

[0095] In this example, the surface numbers 29, 33, and 34 are decentered surfaces. The parameters of the decentered surfaces are as follows:

[0096] Face number 29 Eccentricity type: Decenter and bend Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 0.0000 Parameter α 45.0000

[0097] Face number 33 Eccentricity Type Global Coordinates Global Reference Plane 32 Parameter X 0.0000 Parameter Y -80.0000 Parameter Z 44.6790 Parameter α -90.0000

[0098] Face number 34 Eccentricity Type Global Coordinates Global Reference Plane 32 Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 201.0000 Parameter α 0.0000

[0099] (Action and effect) The optical system 3C of this example can achieve the same effects as the optical system 3A of Example 1. In addition, in this example, the first optical element 33 has a third transmitting surface 41 located on the enlargement side of the first reflecting surface 42 and a fourth transmitting surface 43 located on the reduction side of the first reflecting surface 42. Therefore, light emitted from the first transmitting surface 51 of the second optical element 34 passes through the fourth transmitting surface 43 of the first optical element 33, the first reflecting surface 42, and the third transmitting surface 41, in this order, before reaching the screen S. This allows the projection light to be controlled before it is incident on the first reflecting surface 42, thereby suppressing field curvature aberration in the intermediate image 30 formed on the reduction side of the first reflecting surface 42. Furthermore, since field curvature aberration can be corrected in the intermediate image 30, the burden on the reduction-side optical system that cancels the amount of curvature can be reduced. This allows the overall optical system to be made smaller.

[0100] In this example, the third transmitting surface 41 has a convex shape that is rotationally symmetric about the third optical axis. In the optical system 3C of this example, light passing between the third transmitting surface 41 and the first reflecting surface 42 contains peripheral light L that inclines toward the third transmitting surface 41 in a direction away from the screen S, which is the magnification-side conjugate surface. Furthermore, when a virtual line Q is defined connecting the maximum effective point P of the peripheral light L on the third transmitting surface 41 and the center of curvature of the third transmitting surface 41, the virtual line Q intersects with the third optical axis at an angle θ2 of 90° or more. Therefore, when light incident on the first optical element 33 from the reduction-side fourth transmitting surface 43 is turned back by the first reflecting surface 42 toward the third transmitting surface 41, the peripheral light L of the light travels away from the screen S and reaches a region of the third transmitting surface 41 that does not directly face the screen S. If the peripheral light L does not reach the screen S, the periphery of the magnified image projected onto the screen S becomes dark. In contrast, in this example, the third transmitting surface 41 has power. As a result, the peripheral light L is inclined between the third transmitting surface 41 and the screen S in a direction approaching the screen S as it moves away from the third transmitting surface 41. In other words, the peripheral light L, which is turned by the first reflecting surface 42 and then travels within the first optical element 33 in a direction away from the screen S, travels toward the screen S via the third transmitting surface 41. This makes it possible to ensure the amount of light around the enlarged image projected onto the screen S.

[0101] In this example, the third optical axis of the third transmitting surface 41 and the fourth optical axis of the fourth transmitting surface coincide with the first optical axis. In this way, the first optical element 33 can be manufactured easily.

[0102] In this example, the first reflecting surface 42 and the fourth transmitting surface 43 have aspherical shapes, which makes it easier to correct various aberrations.

[0103] Fig. 13 is a diagram showing the MTF on the enlargement side of optical system 3C. The horizontal axis of Fig. 13 represents spatial frequency, and the vertical axis represents contrast reproduction ratio. As shown in Fig. 13, optical system 3C of this example has high resolution.

[0104] Fig. 14 is a spot diagram of the optical system 3 C. As shown in Fig. 14, in this example, the variation in the spots is suppressed.

[0105] Example 4 Fig. 15 is a ray diagram schematically showing the entire optical system of Example 4. Fig. 16 is a ray diagram of the optical system 3D of Example 4. Fig. 17 is a ray diagram of the first optical system of Example 4. As shown in Figs. 15 and 16, a liquid crystal panel 18 is disposed on the reduction-side conjugate plane of the optical system 3.

[0106] For convenience, in the following description, three mutually perpendicular axes are referred to as the X-axis, Y-axis, and Z-axis. The width direction of the screen S, which is the magnification-side conjugate plane, is referred to as the X-axis direction, the vertical direction of the screen S as the Y-axis direction, and the direction perpendicular to the screen S as the Z-axis direction. In the Y-axis direction, the direction above the screen S is referred to as the Y1 direction, and the direction below the screen S as the Y2 direction. In the Z-axis direction, the side where the screen S is located is referred to as the Z1 direction, and the opposite side is referred to as the Z2 direction.

[0107] As shown in FIG. 15, the optical system 3D of this example has, in order from the enlargement side to the reduction side, a first optical system 31 and a second optical system 32. The first optical system 31 is a reflective optical system. The first optical system 31 includes a correcting lens 35, a first optical element 33, and a second optical element 34. The correcting lens 35, the first optical element 33, and the second optical element 34 are arranged in this order from the enlargement side to the reduction side. The optical axis M of the first optical element 33 extends along the Z-axis direction. In other words, the optical axis M of the first optical element 33 is perpendicular to the screen S. The second optical system 32 is a refractive optical system. The optical axis N (sixth optical axis) of the second optical system 32 extends along the Y-axis direction. The screen S is located in the Z1 direction of the optical axis N.

[0108] The corrector lens 35 is located in the Y1 direction of the first optical element 33. The fifth optical axis of the corrector lens 35 coincides with the optical axis M of the first optical system 31. The corrector lens 35 has positive power. The corrector lens 35 has a first lens surface 61 facing the enlargement side and a second lens surface 62 facing the reduction side. The first lens surface 61 has a convex shape. The first lens surface 61 has an aspherical shape. The second lens surface 62 has a concave shape. The second lens surface 62 has an aspherical shape. The first lens surface 61 and the second lens surface 62 both have shapes that are rotationally symmetric about the fifth optical axis of the corrector lens 35.

[0109] 16, the first optical element 33 is composed of one optical element. The first optical element 33 is located in the Z2 direction of the second optical element 34. The first optical element 33 has a third transmitting surface 41, a first reflecting surface 42 located on the reduction side of the third transmitting surface 41, and a fourth transmitting surface 43 located on the reduction side of the first reflecting surface 42.

[0110] The third transmitting surface 41 has a convex surface shape facing the Y1 direction. A third optical axis of the third transmitting surface 41 coincides with the optical axis M of the first optical system 31. The third transmitting surface 41 has a shape that is rotationally symmetric about the third optical axis of the third transmitting surface 41. The third transmitting surface 41 has positive power.

[0111] The first reflecting surface 42 is located in the Y2 direction of the third transmitting surface 41. The first reflecting surface 42 has a concave shape recessed in the Z2 direction. A first optical axis of the first reflecting surface 42 coincides with the optical axis M of the first optical system 31. The first reflecting surface 42 has a shape that is rotationally symmetrical about the first optical axis of the first reflecting surface 42. The first reflecting surface 42 has positive power. The first reflecting surface 42 has an aspheric shape. The first reflecting surface 42 is formed by providing a reflective coating layer on the outer surface of the first optical element 33 in the Z2 direction.

[0112] A fourth optical axis of the fourth transmitting surface 43 coincides with the optical axis M of the first optical system 31. The fourth transmitting surface 43 has a shape that is rotationally symmetric about the fourth optical axis of the fourth transmitting surface 43. The fourth transmitting surface 43 has positive power. The fourth transmitting surface 43 has an aspherical shape.

[0113] Here, the first optical element 33 is designed with the optical axis M as its design axis. That is, the third optical axis is the designed optical axis of the third transmitting surface 41. The first optical axis is the designed optical axis of the first reflecting surface 42. The fourth optical axis is the designed optical axis of the fourth transmitting surface 43.

[0114] The second optical element 34 is composed of a single optical element. The second optical element 34 is located in the Z1 direction of the first optical element 33. The second optical element 34 has a first transmitting surface 51, a second reflecting surface 52 located on the reduction side of the first transmitting surface 51, and a second transmitting surface 53 located on the reduction side of the second reflecting surface 52.

[0115] The first transmitting surface 51 faces the fourth transmitting surface 43 in the Z-axis direction. The first transmitting surface 51 has a convex shape facing the Z2 direction. The second optical axis of the first transmitting surface 51 is approximately parallel to the first optical axis of the first reflecting surface 42. In this example, the second optical axis of the first transmitting surface 51 coincides with the first optical axis of the first reflecting surface 42. In other words, the second optical axis of the first transmitting surface 51 coincides with the optical axis M of the first optical element 33. The first transmitting surface 51 has a shape that is rotationally symmetric about the second optical axis. The first transmitting surface 51 has positive power. The first transmitting surface 51 has an aspherical shape.

[0116] The second reflecting surface 52 is a flat mirror with no power. The second reflecting surface 52 is inclined at 45° with respect to the Y-axis and the Z-axis. The second reflecting surface 52 bends the optical path by 90° between the first transmitting surface 51 and the second transmitting surface 53. The second reflecting surface 52 is formed by providing a reflective coating layer on the outer surface of the second optical element 34 in the Z1 direction.

[0117] The second transmitting surface 53 faces the Y2 direction and faces the lens L15. The angle formed by the optical axis of the second transmitting surface 53 and the second optical axis of the first transmitting surface 51 is 90°. That is, the angle formed by the optical axis of the second transmitting surface 53 and the optical axis M of the first optical element 33 is 90°. The optical axis of the second transmitting surface 53 coincides with the optical axis N of the second optical system 32. The second transmitting surface 53 has a shape that is rotationally symmetrical about the optical axis of the second transmitting surface 53. The second transmitting surface 53 has positive power. The second transmitting surface 53 has an aspherical shape.

[0118] As shown in Fig. 16, the second optical system 32 includes 12 lenses L1 to L12. The lenses L1 to L12 are arranged in this order from the reduction side to the enlargement side. The lenses L2, L7, and L12 are aspherical lenses with aspherical shapes on both sides. Each lens in the first optical system 31 has a rotationally symmetric surface centered on the optical axis N.

[0119] 16, the liquid crystal panel 18, which is disposed on the reduction-side conjugate plane of the optical system 3D, forms a projected image on the Z2 side of the optical axis N. The angle θ1 formed between the optical axis M of the first optical element 33 and the optical axis N of the second optical system 32 is 90° or less. In this example, the angle θ1 is 90°. Therefore, after passing through the second optical system 32, light from the liquid crystal panel 18 side is bent 90° by the second reflecting surface 52 of the second optical element 34 and heads in the Z2 direction. The light headed in the Z2 direction is bent back in the Z1 and Y1 directions by the first reflecting surface 42 of the first optical element 33 and reaches the screen S.

[0120] 16, the optical system 3D forms an intermediate image 30 between the reduction-side conjugate surface and the magnification-side conjugate surface, the intermediate image 30 being conjugate to the reduction-side conjugate surface and the magnification-side conjugate surface. In this example, the intermediate image 30 is formed between the first reflecting surface 42 of the first optical element 33 and the second transmitting surface 53 of the second optical element 34.

[0121] 17, light traveling between the third transmitting surface 41 and the first reflecting surface 42 includes peripheral light L that is inclined in a direction away from the screen S, which is the magnification-side conjugate surface, as it approaches the third transmitting surface 41. Between the third transmitting surface 41 and the correcting lens 35, the peripheral light L is inclined in a direction away from the screen S as it moves away from the third transmitting surface 41. Furthermore, between the correcting lens 35 and the screen S, the peripheral light L is inclined in a direction approaching the screen S as it moves away from the correcting lens 35. Furthermore, an imaginary line Q connecting a maximum effective point P of the peripheral light L on the third transmitting surface 41 and the center of curvature of the third transmitting surface 41 intersects with the optical axis M (third optical axis) at an angle θ2 of 90° or more.

[0122] The lens data for the 3D optical system is as follows. Surface numbers are assigned in order from the reduction side to the magnification side. The symbols refer to the LCD panel, dichroic prism, lens, and screen. Data for surface numbers that do not correspond to the LCD panel, dichroic prism, lens, and screen is dummy data. Surfaces with an * next to the surface number are aspheric. R is the radius of curvature. D is the on-axis surface spacing. nd is the refractive index. νd is the Abbe number. Y is the aperture radius. The units for R, D, and Y are mm. The lens data in this example was designed using CODE V from Synopsys.

[0123] Sign Surface No. RD nd vd Mode Y 18 0 0.00000 22.000000 Refraction 19 1 0.00000 37.300000 1.516800 64.17 Refraction 20.3480 2 0.00000 0.762700 Refraction 22.1060 L1 3 157.73710 10.000000 1.994904 27.96 Refraction 22.2740 4 -59.76320 4.440906 Refraction 22.1250 L2 5 -47.37529 10.000000 2.050800 26.94 Refraction 19.2330 6 -103.89113 7.276867 Refraction 19.2740 L3 7 -35.49424 3.259752 1.937229 32.32 Refraction 18.4950 8 -63.50302 3.002572 Refraction 19.5370 L4 9 103.13388 8.732663 1.658725 41.40 Refraction 20.1430 10 -94.40586 0.500000 Refraction 19.9850 L5 11 89.94729 2.000000 2.050800 26.94 Refraction 19.0060 12 37.49030 0.500000 Refraction 18.0290 L6 13 36.86363 20.000000 1.446156 80.88 Refraction 18.1140 14 -69.65825 30.000000 Refraction 17.0000 O 15 0.00000 134.972004 Refraction 14.4000 L7 16 105.41092 13.783413 1.469124 82.22 Refraction 40.0000 17 1094.72746 3.834971 Refraction 39.0280 L8 18 137.23940 11.351333 1.986125 16.48 Refraction 39.2540 19 -228.96975 12.674715 Refraction 38.9460 L9 20 -90.50307 17.528035 1.869148 18.09 Refraction 34.1820 21 -301.24837 8.314561 Refraction 33.5580 L10 22 -97.26184 2.000000 1.986125 16.48 Refraction 32.8700 23 137.98515 2.000000 Refraction 34.1190 L11 24 70.50560 10.000000 1.455365 87.06 Refraction 39.7670 25 157.41492 79.583464 Refraction 39.9520 L12 *26 -27.57550 8.000000 1.509186 56.32 Refraction 48.0000 *27 -47.11522 9.521845 Refraction 51.6580 34 *28 -140.46983 72.000000 1.509186 56.32 Refraction 64.8350 29 0.00000 -15.000000 1.509186 56.32 Reflection 91.6220 *30 230.59254 -3.000000 Refraction 63.7000 33 *31 -54.82491 -64.000000 1.509186 56.32 Refraction 54.3140 *32 20.67261 0.000000 1.509186 56.32 Reflection 51.1060 33 -44.00000 0.000000 Refraction 21.6820 35 *34 -131.10106 20.000000 1.509186 56.32 Refraction 117.8940 *35 -100.00000 0.000000 Refraction 120.9940 36 0.00000 0.000000 Refraction 2186.7700 S 37 0.00000 0.000000 Refraction 2186.7700

[0124] The aspherical coefficients are as follows:

[0125] Face number 26 27 28 30 Conic constant -7.983351E-01 -7.935454E-01 -5.694192E+01 7.416526E-01 4th order coefficient 1.571127E-06 -2.932391E-06 8.694656E-07 -5.656628E-07 6th order coefficient -5.227067E-10 7.948796E-10 -1.45704E-10 7.550079E-10 8th order coefficient 4.752561E-13 -2.731021E-13 3.119986E-14 -2.009279E-13 10th order coefficient -3.805627E-17 7.607665E-17 -2.61777E-18 1.677154E-17

[0126] Face number 31 32 34 35 Conic constant -1.386817E+02 -1.637304E+00 -4.949426E-01 -4.448864E-01 4th order coefficient -4.815839E-06 -1.617638E-06 2.724492E-08 3.262084E-07 6th order coefficient 5.544913E-10 2.867275E-10 -1.631719E-12 -2.720302E-11 8th order coefficient 5.021641E-13 5.726965E-14 2.587226E-16 1.045415E-15 10th order coefficient -1.123307E-16 -2.044994E-17 -9.382203E-21 -5.756513E-21

[0127] The ray coordinates at the object plane are:

[0128] Ray number X coordinate Y coordinate 1 0 -1.38 2 0 -4.86 3 0 -8.34 4 0 -11.81 5 0 -15.29 6 0 -18.77

[0129] In this example, the surface numbers 29, 33, 34, and 36 are decentered surfaces. The parameters of the decentered surfaces are as follows:

[0130] Face number 29 Eccentricity type: Decenter and bend Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 0.0000 Parameter α 45.0000

[0131] Face number 33 Eccentricity Type Global Coordinates Global Reference Plane 32 Parameter X 0.0000 Parameter Y -44.0000 Parameter Z 24.0000 Parameter α -90.0000

[0132] Face number 34 Eccentricity Type Global Coordinates Global Reference Plane 32 Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 55.0000 Parameter α 0.0000

[0133] Face number 36 Eccentricity Type Global Coordinates Global Reference Plane 32 Parameter X 0.0000 Parameter Y 0.0000 Parameter Z 201.0000 Parameter α 0.0000

[0134] (Action and effect) The optical system 3D of this example can achieve the same effects as the optical system 3C of Example 3. Furthermore, since the optical system 3D of this example includes the correcting lens 35 disposed on the enlargement side of the first optical element 33, the projection light can be controlled at a position close to the screen S. Therefore, the third transmitting surface 41 and the correcting lens 35 can tilt the peripheral light L in a direction approaching the screen S as the peripheral light L moves away from the correcting lens 35. In other words, the lens power for refracting the peripheral light L toward the screen S can be generated by both the third transmitting surface 41 and the correcting lens 35. This allows the lens power of the third transmitting surface 41 to be reduced compared to Example 3, making it easier to process the first optical element 33. Furthermore, since the lens power of the third transmitting surface 41 can be reduced, it is easier to correct various aberrations in the enlarged image.

[0135] Furthermore, in this example, the fifth optical axis of the correcting lens 35 coincides with the first optical axis of the first reflecting surface 42. In other words, the fifth optical axis of the correcting lens 35 coincides with the optical axis M of the first optical element 33. Therefore, the first optical element 33 and the correcting lens 35 can be positioned with high precision.

[0136] Fig. 18 is a diagram showing the MTF on the enlargement side of the optical system 3D. The horizontal axis of Fig. 18 represents spatial frequency, and the vertical axis represents contrast reproduction ratio. As shown in Fig. 18, the optical system 3D of this example has high resolution.

[0137] Fig. 19 is a spot diagram of the optical system 3D. As shown in Fig. 19, in this example, the spot variation is suppressed.

[0138] (Other embodiments) The optical system 3 of this example can be used as an imaging lens. In this case, an imaging element is disposed on the reduction-side image-forming surface of the optical system 3. [Explanation of symbols]

[0139] 1...projector, 2...image forming section, 3, 3A, 3B, 3C, 3D...optical system, 4...control section, 6...image processing section, 7...display driving section, 10...light source, 11...integrator lens, 12...integrator lens, 13...polarization conversion element, 14...superimposing lens, 15...dichroic mirror, 16...reflecting mirror, 17R...field lens, 17G...field lens, 17B...field lens, 18 (18B, 18R, 18G)...liquid crystal panel, 19...cross dichroic prism, 21...dichroic mirror, 22...relay lens, 23...reflecting mirror, 24...relay lens, 25... Reflecting mirror, 30...intermediate image, 31...first optical system, 32...second optical system, 33...first optical element, 34...second optical element, 35...correcting lens, 36...correcting optical element, 37...second relay element, 38...first relay element, 40...first reflecting surface, 41...third transmitting surface, 42...first reflecting surface, 43...fourth transmitting surface, 51...first transmitting surface, 52...second reflecting surface, 53...second transmitting surface, 61...first lens surface, 62...second lens surface, 71...first lens surface, 72...second lens surface, 73...second relay reflecting surface, 74...first relay reflecting surface, L1 to L15...lens, N...optical axis, M...optical axis, P...maximum effective point, Q...virtual line, S...screen.

Claims

1. a first optical element; and a second optical element disposed on the reduction side of the first optical element; a refractive optical system disposed on the reduction side of the second optical element, the first optical element has a first reflecting surface having a concave shape; the second optical element has a first transmitting surface having an aspherical shape, a second reflecting surface having an aspherical shape and arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power; the first optical element includes a third transmitting surface disposed on the enlargement side of the first reflecting surface and a fourth transmitting surface disposed on the reduction side of the first reflecting surface, the fourth transmitting surface and the first transmitting surface face each other, an optical system, wherein a third optical axis of the third transmitting surface and a fourth optical axis of the fourth transmitting surface coincide with the first optical axis;

2. 2. The optical system according to claim 1, wherein an intermediate image conjugate to a reduction-side conjugate surface and a magnification-side conjugate surface is formed between said first reflecting surface and said second transmitting surface.

3. 3. The optical system according to claim 1, further comprising a correction lens disposed on the enlargement side of the first optical element.

4. 4. The optical system according to claim 3, wherein a fifth optical axis of the correcting lens coincides with the first optical axis.

5. the third transmitting surface has a convex shape that is rotationally symmetric about the third optical axis, the light passing between the third transmitting surface and the first reflecting surface includes a peripheral ray that is inclined in a direction away from the magnification-side conjugate surface as it approaches the third transmitting surface, 2. The optical system according to claim 1, wherein when a virtual line connecting a maximum effective point of the peripheral light on the third transmitting surface and a center of curvature of the third transmitting surface is defined, an angle formed by the virtual line and the third optical axis on the fourth transmitting surface side is 90° or more when viewed from the enlargement side of the first optical element.

6. The optical system according to claim 1 , wherein the second reflecting surface has a non-planar shape.

7. The optical system according to claim 1 , further comprising a refractive optical system disposed on a reduction side of the second optical element.

8. the refractive optical system comprises a plurality of lenses; The optical system according to claim 7 , wherein the plurality of lenses have a shape that is rotationally symmetric about a sixth optical axis of the refractive optical system.

9. 9. The optical system according to claim 8, wherein the angle between the first optical axis and the sixth optical axis is 90 degrees.

10. a first optical element; and a second optical element disposed on the reduction side of the first optical element; a refractive optical system disposed on the reduction side of the second optical element, the first optical element has a first reflecting surface having a concave shape; the second optical element has a first transmitting surface having an aspherical shape, a second reflecting surface having an aspherical shape and arranged on the reduction side of the first transmitting surface, and a second transmitting surface arranged on the reduction side of the second reflecting surface, a first optical axis which is a design axis of the first reflecting surface coincides with a second optical axis which is a design axis of the first transmitting surface, at least one of the first transmitting surface, the second reflecting surface, and the second transmitting surface has power; the refractive optical system comprises a plurality of lenses; the plurality of lenses have shapes that are rotationally symmetric about a sixth optical axis of the refractive optical system, An optical system characterized in that the angle formed between the first optical axis and the sixth optical axis is 90°.

11. a light modulation element disposed on the reduction-side conjugate plane and modulating light emitted from the light source; an optical system according to claim 7 , which projects light modulated by the light modulation element; A projector comprising:

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