Projection optical system and projector

Abstract

To provide a projection optical system that can reduce the weight of an end part on an enlargement side.SOLUTION: A projection optical system has a first lens group having a negative power, and a second lens group having a positive power in order from an enlargement side to a reduction side. The first lens group includes a first a lens group having a negative power, a first b lens group located on the reduction side of the first a lens group and having a negative power, and a first c lens group located on the reduction side of the first b lens group and having a positive power. The total number of lenses obtained by adding up the number of lenses in the first a lens group and the number of lenses in the first b lens group is three or less. When the focal distance of the entire lens system is defined as F, back focus air conversion length as BF, and the composite focal distance of the first a lens group and first b lens group as F1ab, all the following conditional expressions (1) and (2) are satisfied. BF / F>5.0 (1) and 0.3<|F / F1ab|<1.0 (2).SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to a projection optical system and a projector.

Background Art

[0002] A projection optical system capable of changing the projection distance is described in Patent Document 1. The projection optical system of Patent Document 1 includes, in order from the magnifying side to the reducing side, a first lens group, a second lens group, a third lens group, a fourth lens group, and a fifth lens group. The first lens group includes, in order from the magnifying side to the reducing side, a first sub-lens group, a second sub-lens group, and a third sub-lens group. The first sub-lens group consists of one lens. The second sub-lens group consists of three lenses. The third sub-lens consists of one lens. When the projection distance is changed, focusing is performed by moving the first sub-lens group, the second sub-lens group, and the third sub-lens group in the optical axis direction.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] When the weight of the end portion on the magnifying side of the projection optical system increases, the center of gravity of the projection optical system moves to the end portion on the magnifying side. Therefore, when the projection optical system is mounted on the housing of the projector, the center of gravity of the projector may move to the side of the end portion on the magnifying side of the projection optical system, disturbing the balance of the projector. In order to avoid or suppress such a situation, in the projection optical system, it is desirable to suppress the total number of lenses of the first sub-lens group and the second sub-lens group located on the magnifying side within the lens group located on the most magnifying side.

Means for Solving the Problems

[0005] In order to solve the above problems, the projection optical system of the present invention has, in order from the magnification side to the reduction side, a first lens group having a negative power and a second lens group having a positive power, the reduction side of the second lens group is telecentric, and the first lens group has a first a lens group having a negative power, a first b lens group having a negative power located on the reduction side of the first a lens group, and a first c lens group having a positive power located on the reduction side of the first b lens group, and the first a lens group consists only of lenses having a negative power, the first b lens group consists only of lenses having a negative power, and among the first a lens group, the first lens located on the most magnification side has an aspherical shape on both surfaces, and the total number of lenses obtained by adding the number of lenses in the first a lens group and the number of lenses in the first b lens group is 3 or less, and the first b lens group and the first c lens group each move in the optical axis direction during focusing, the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, when the combined focal length of the first a lens group and the first b lens group is F1ab, it is characterized by satisfying all of the following conditional expressions (1) and (2). BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) In addition, the projection optical system of the present invention includes, in order from the magnification side to the reduction side, a first lens group having negative power and a second lens group having positive power, and the reduction side from the second lens group is telecentric, and the first lens group includes a first a lens group having negative power, a first b lens group having negative power located on the reduction side of the first a lens group and a first c lens group having positive power located on the reduction side of the first b lens group, and the first a lens group consists only of lenses having negative power, and the first b lens group consists only of lenses having negative power. Among the first a lens groups, the first lens located on the most magnification side has an aspherical shape on both surfaces, and the total number of lenses obtained by adding the number of lenses in the first a lens group and the number of lenses in the first b lens group is 3 or less. The first b lens group and the first c lens group move in the optical axis direction during focusing, Let the focal length of the entire lens system be F, the air-equivalent length of the back focus be BF, and the combined focal length of the first a lens group and the first b lens group be F1ab. Then, all of the following conditional expressions (1) and ( 2) are satisfied, BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) The first a lens group consists of the first lens and a second lens located on the reduction side of the first lens, The first lens is made of resin, The second lens has negative power and is a meniscus lens having a convex shape on the magnification side surface and, The first b lens group consists of a third lens, The third lens has negative power and has a concave shape on the reduction side surface, The power of the magnification side surface of the third lens is smaller than that of the reduction side surface of the third lens, which is characterized by In addition, the projection optical system of the present invention includes, in order from the magnification side to the reduction side, a first lens group having negative power and a second lens group having positive power, and the reduction side from the second lens group is telecentric, and the first lens group includes a first a lens group having negative power, a first b lens group having negative power located on the reduction side of the first a lens group and a first c lens group having positive power located on the reduction side of the first b lens group, and the first a lens group consists only of lenses having negative power, and the first b lens group ​ ​ ​ ​ ​ ​ It consists only of lenses with negative power, and among the first group of lenses (Group 1a), the first lens located on the most magnifying side has an aspherical shape on both sides. The total number of lenses in the first group of lenses (Group 1a) and the second group of lenses (Group 1b) is 3 or less. The second group of lenses (Group 1b) and the third group of lenses (Group 1c) move in the optical axis direction respectively during focusing. Let the focal length of the entire lens system be F, the air-equivalent length of the back focus be BF, and the combined focal length of the first group of lenses (Group 1a) and the second group of lenses (Group 1b) be F1ab. Then, the following conditional expressions (1) and (2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) When the position where the chief ray with the maximum picture angle in the second group of lenses intersects the optical axis is defined as the aperture, the second group of lenses includes a second group of lenses (Group 2a) and a second group of lenses (Group 2b) located on the magnifying side of the aperture. The second group of lenses (Group 2a) is located on the magnifying side of the second group of lenses (Group 2b). The second group of lenses (Group 2a) and the second group of lenses (Group 2b) move in the optical axis direction respectively during zooming. In addition, the projection optical system of the present invention consists of a first group of lenses with negative power and a second group of lenses with positive power in order from the magnifying side to the reducing side. The reducing side from the second group of lenses is telecentric. The first group of lenses consists of a first group of lenses (Group 1a) with negative power, a second group of lenses (Group 1b) with negative power located on the reducing side of the first group of lenses (Group 1a), and a third group of lenses (Group 1c) with positive power located on the reducing side of the second group of lenses (Group 1b). The first group of lenses (Group 1a) consists only of lenses with negative power. The second group of lenses (Group 1b) consists only of lenses with negative power. Among the first group of lenses (Group 1a), the first lens located on the most magnifying side has an aspherical shape on both sides. The total number of lenses in the first group of lenses (Group 1a) and the second group of lenses (Group 1b) is 3 or less. The second group of lenses (Group 1b) and the third group of lenses (Group 1c) move in the optical axis direction respectively during focusing. Let the focal length of the entire lens system be F, the air-equivalent length of the back focus be BF, and the combined focal length of the first group of lenses (Group 1a) and the second group of lenses (Group 1b) be F1ab. Then, the following conditional expressions (1) and (2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ The second lens group does not include a moving group and is fixed. Assuming that the focal length of the first lens group is F1 and the focal length of the second lens group is F2, the following is characterized by satisfying the conditional expression (4). 0.1 < |F1 / F2| < 0.5 (4) In addition, the projection optical system of the present invention comprises, in order from the magnification side to the reduction side, a first lens group having a negative power and a second lens group having a positive power. On the reduction side of the second lens group is telecentric. The first lens group comprises a first a lens group having a negative power, a first b lens group having a negative power located on the reduction side of the first a lens group , and a first c lens group having a positive power located on the reduction side of the first b lens group. The first a lens group consists only of lenses having a negative power. The first b lens group consists only of lenses having a negative power. Among the first a lens group, the first lens located on the most magnification side has an aspherical shape on both surfaces. The total number of lenses obtained by adding the number of lenses in the first a lens group and the number of lenses in the first b lens group is 3 or less. The first b lens group and the first c lens group move in the optical axis direction during focusing, Assuming that the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group and the first b lens group is F1ab, the following conditional expressions (1) and ( 2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) The first a lens group consists of the first lens. The first b lens group consists of a second lens and a third lens located on the reduction side of the second lens. The first lens is made of resin. The second lens has a negative power and is a meniscus lens having a convex shape on the magnification side surface. The third lens has a negative p ower and has a concave shape on the reduction side surface. When the position where the chief ray having the maximum angle of view in the second lens group intersects the optical axis is taken as the aperture stop, the second lens group comprises a second a lens group and a second b lens group located on the magnification side of the aperture stop. The second a lens group is located on the magnification side of the second b lens group. The second a lens group and the second b lens group move in the optical axis direction during zooming . This is the characteristic.

[0006] Next, the projector of the present invention is characterized by comprising a light modulation element that modulates light emitted from a light source, and the projection optical system described above that projects the light modulated by the light modulation element.

Brief Description of the Drawings

[0007]

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Embodiments for Carrying Out the Invention

[0008] Hereinafter, with reference to the drawings, an optical system and a projector according to embodiments of the present invention will be described.

[0009] (Projector) FIG. 1 is a diagram showing a schematic configuration of a projector including the projection optical system 3 of the present invention. As shown in FIG. 1, the projector 1 includes an image forming unit 2 that generates a projection image to be projected onto the screen S, a projection optical system 3 that enlarges the projection image and projects a magnified 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 composed of, for example, an ultra-high pressure mercury lamp, a solid 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 divides the light beam from the light source 10 into a plurality of beams. Each lens element of the first integrator lens 11 condenses the light beam from the light source 10 near each lens element of the second integrator lens 12.

[0011] The polarization conversion element 13 converts the light from the second integrator lens 12 into predetermined linearly polarized light. The superimposing lens 14 superimposes the images of the lens elements of the first integrator lens 11 on the display areas of a liquid crystal panel 18R, a liquid crystal panel 18G, and a liquid crystal panel 18B, which will be described later, via the second integrator lens 12.

[0012] Also, the image forming unit 2 includes a first dichroic mirror 15, a reflection mirror 16, a field lens 17R, and a liquid crystal panel 18R. The first dichroic mirror 15 reflects R light, which is part of the light rays incident from the superimposing lens 14, and transmits G light and B light, which are part of the light rays incident from the superimposing lens 14. The R light reflected by the first dichroic mirror 15 enters the liquid crystal panel 18R via the reflection mirror 16 and the field lens 17R. The liquid crystal panel 18R is a light modulation element. The liquid crystal panel 18R forms a red projection image by modulating the R light according to an image signal.

[0013] Furthermore, the image forming unit 2 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 part of the light rays from the first dichroic mirror 15, and transmits B light, which is part of the light rays from the first dichroic mirror 15. The G light reflected by the second dichroic mirror 21 enters the liquid crystal panel 18G via the field lens 17G. 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 according to an image signal.

[0014] The image forming unit 2 also includes a relay lens 22, a reflection mirror 23, a relay lens 24, a reflection mirror 25, a field lens 17B, a liquid crystal panel 18B, and a cross dichroic prism 19. The B light that has passed through the second dichroic mirror 21 enters the liquid crystal panel 18B after passing through the relay lens 22, the reflection mirror 23, the relay lens 24, the reflection mirror 25, and the field lens 17B. 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 according to the image signal.

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

[0016] The projection optical system 3 enlarges and projects the projection image synthesized by the cross dichroic prism 19 onto the screen S.

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

[0018] The image processing unit 6 converts the image signal input from an external device into an image signal including gradations of each color. The display driving unit 7 operates the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B based on the projection image signals of each color output from the image processing unit 6. Thereby, the image processing unit 6 displays the projection image corresponding to the image signal on the liquid crystal panel 18R, the liquid crystal panel 18G, and the liquid crystal panel 18B.

[0019] (Projection optical system) Next, the projection optical system 3 will be described. FIG. 2 is a ray diagram of the projection optical system 3. In FIG. 2, the liquid crystal panels 18R, 18G, and 18B are represented as the liquid crystal panel 18. As shown in FIG. 2, a screen S is disposed on the conjugate surface on the magnification side of the projection optical system 3. The liquid crystal panel 18 is disposed on the conjugate surface on the reduction side of the projection optical system 3.

[0020] As shown in FIG. 2, the liquid crystal panel 18 disposed on the conjugate surface on the reduction side forms a projection image on one side of the optical axis N of the projection optical system 3. The enlarged image projected onto the screen S by the projection optical system 3 is formed on the other side of the optical axis N.

[0021] Hereinafter, Examples 1 to 5 will be described as configuration examples of the projection optical system 3 mounted on the projector 1.

[0022] (Example 1) FIG. 2 is a ray diagram of the projection optical system 3A of Example 1. As shown in FIG. 2, the projection optical system 3A includes, in order from the magnification side to the reduction side, a first lens group 31 having a negative power and a second lens group 32 having a positive power. The projection optical system 3A also includes a diaphragm 41 disposed inside the second lens group 32. The diaphragm 41 is disposed at a position where the chief ray of the maximum angle of view in the second lens group 32 intersects the optical axis N.

[0023] The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reduction side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reduction side of the first b lens group 34.

[0024] The first a lens group 33 consists of a first lens L1. The first lens L1 has a negative power near the optical axis N. The first lens L1 has a concave shape near the optical axis N and a convex shape at the peripheral portion on the magnification side surface. The first lens L1 has a convex shape near the optical axis N and a concave shape at the peripheral portion on the reduction side surface. The first lens L1 has an aspherical shape on both surfaces.

[0025] The first lens group 34 consists of a second lens L2 and a third lens L3. The second lens L2 and the third lens L3 are arranged in this order from the magnification side to the reduction side. The second lens L2 has a negative power. The second lens L2 is a meniscus lens. The second lens L2 has a convex shape on the magnification side surface and a concave shape on the reduction side surface. The third lens L3 has a negative power. The third lens L3 is a meniscus lens. The third lens L3 has a convex shape on the magnification side surface and a concave shape on the reduction side surface.

[0026] The first lens group 35 consists of a fourth lens L4 and a fifth lens L5. The fourth lens L4 and the fifth lens L5 are arranged in this order from the magnification side to the reduction side. The fourth lens L4 and the fifth lens L5 are a cemented lens L21. The fourth lens L4 has a negative power. The fourth lens L4 is a meniscus lens. The fourth lens L4 has a convex shape on the magnification side surface and a concave shape on the reduction side surface. The fifth lens L5 has a positive power. The fifth lens L5 has a convex shape on both the magnification side and the reduction side surfaces.

[0027] The second lens group 32 includes a second lens group 36 having a negative power, a second lens group 37 having a positive power located on the reduction side of the second lens group 36, a second lens group 38 having a negative power located on the reduction side of the second lens group 37, and a second lens group 39 located on the reduction side of the second lens group 38. A diaphragm 41 is disposed between the second lens group 37 and the second lens group 38.

[0028] The second lens group 36 consists of a sixth lens L6 and a seventh lens L7. The sixth lens L6 and the seventh lens L7 are arranged in this order from the magnification side to the reduction side. The sixth lens L6 and the seventh lens L7 are a cemented lens L22. The sixth lens L6 has a positive power. The sixth lens L6 has a convex shape on both the magnification side and the reduction side surfaces. The seventh lens L7 has a negative power. The seventh lens L7 has a concave shape on both the magnification side and the reduction side surfaces.

[0029] The 2b lens group 37 consists of an eighth lens L8 and a ninth lens L9. The eighth lens L8 and the ninth lens L9 are arranged in this order from the magnification side toward the reduction side. The eighth lens L8 and the ninth lens L9 are a cemented lens L23 that are cemented together. The eighth lens L8 has a negative power. The eighth lens L8 is a meniscus lens. The eighth lens L8 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface. The ninth lens L9 has a positive power. The ninth lens L9 has a convex shape on both the magnification-side and reduction-side surfaces.

[0030] The 2c lens group 38 consists of a tenth lens L10 and an eleventh lens L11. The tenth lens L10 and the eleventh lens L11 are arranged in this order from the magnification side toward the reduction side. The tenth lens L10 and the eleventh lens L11 are a cemented lens L24 that are cemented together. The tenth lens L10 has a negative power. The tenth lens L10 has a concave shape on both the magnification-side and reduction-side surfaces. The eleventh lens L11 has a positive power. The eleventh lens L11 is a meniscus lens. The eleventh lens L11 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface.

[0031] The 2d lens group 39 consists of nine lenses from a twelfth lens L12 to a twentieth lens L20. The twelfth lens L12 to the twentieth lens L20 are arranged in this order from the magnification side toward the reduction side. The twelfth lens L12 has a negative power. The twelfth lens L12 has a concave shape on both the magnification-side and reduction-side surfaces. The twelfth lens L12 has an aspherical shape on both surfaces.

[0032] The thirteenth lens L13 has a positive power. The thirteenth lens L13 has a convex shape on both the magnification-side and reduction-side surfaces. The fourteenth lens L14 has a negative power. The fourteenth lens L14 has a concave shape on both the magnification-side and reduction-side surfaces. The fifteenth lens L15 has a positive power. The fifteenth lens L15 has a convex shape on both the magnification-side and reduction-side surfaces. The thirteenth lens L13, the fourteenth lens L14, and the fifteenth lens L15 are a cemented lens L25 that are cemented together.

[0033] The 16th lens L16 has a negative power. The 16th lens L16 has a concave shape on both the magnifying side and the reducing side. The 17th lens L17 has a positive power. The 17th lens L17 has a convex shape on both the magnifying side and the reducing side. The 16th lens L16 and the 17th lens L17 are a joined lens L26.

[0034] The 18th lens L18 has a negative power. The 18th lens L18 is a meniscus lens. The 18th lens L18 has a convex shape on the magnifying side and a concave shape on the reducing side. The 19th lens L19 has a positive power. The 19th lens L19 has a convex shape on both the magnifying side and the reducing side. The 18th lens L18 and the 19th lens L19 are a joined lens L27.

[0035] The 20th lens L20 has a positive power. The 20th lens L20 has a convex shape on both the magnifying side and the reducing side.

[0036] The 1st lens L1 is made of resin. The 2nd lens L2 to the 20th lens L20 are made of glass.

[0037] In the projection optical system 3A, on the reducing side from the 20th lens L20 of the 2nd lens group 32, it is telecentric. Telecentric means that the central ray of each light beam passing between the 20th lens L20 and the liquid crystal panel 18 arranged on the reducing side conjugate surface is parallel to or substantially parallel to the optical axis. In this specification, telecentric means that the angle formed by the central ray of each light beam and the optical axis N is within ±5°.

[0038] Here, the projection optical system 3A can change the projection distance. When changing the projection distance, the 1b lens group 34 and the 1c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0039] In addition, the projection optical system 3A can vary the magnification of the enlarged image. When varying the magnification of the enlarged image, zooming is performed by moving the second a lens group 36, the second b lens group 37, and the second c lens group 38 in the direction of the optical axis N, respectively. In this example, the magnification of the enlarged image becomes approximately 1.08 times by zooming.

[0040] Let the F number of the projection optical system 3A be FNo, the focal length of the entire system be F, the semi-field angle be ω, the back focus air equivalent value be BF, the focal length of the first b lens group 34 be F1b, the focal length of the first c lens group 35 be F1c, the combined focal length of the first a lens group 33 and the first b lens group 34 be F1ab, the focal length of the second a lens group 36 be F2a, the focal length of the second b lens group 37 be F2b, the focal length of the first lens group 31 be F1, and the focal length of the second lens group 32 be F2. Then, the data of the projection optical system 3A is as follows.

[0041] FNo 1.9 F (wide-angle end to telephoto end) 7.540 mm to 8.140 mm ω (wide-angle end to telephoto end) 60.6° to 58.9° BF 43.138 mm F1b -15.481 mm F1c 60.425 mm F1ab -10.463 mm F2a -63.165 mm F2b 34.515 mm F1 -79.200 mm F2 40.964 mm

[0042] The lens data of the projection optical system 3A is as follows. The surface numbers are assigned in order from the enlarged side to the reduced side. The signs are the signs of the screen, lens, diaphragm, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, diaphragm, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * in the surface numbers are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index of the d line. νd is the Abbe number of the d line. The units of R and D are mm.

[0043] Symbol Surface Number R D nd vd S 0 Infinity Variable Interval 1 L1 1* -31.570 5.000 1.53116 56.04 2* -69.927 Variable Interval 2 L2 3 81.356 3.000 1.83481 42.72 4 22.690 10.537 L3 5 458.537 2.000 1.83481 42.72 6 26.354 Variable Interval 3 L4 7 135.736 1.500 1.72916 54.68 L5 8 27.825 9.500 1.71736 29.52 9 -60.798 Variable Interval 4 L6 10 81.675 7.500 1.80809 22.76 L7 11 -25.447 1.500 1.98612 16.48 12 50.481 Variable Interval 5 L8 13 51.590 1.400 1.77250 49.60 L9 14 24.731 8.500 1.67270 32.10 15 -35.296 Variable Interval 6 41 16 Infinity 1.531 L10 17 -85.133 2.500 1.85150 40.78 L11 18 19.584 4.147 1.86966 20.02 19 173.628 Variable Interval 7 L12 20* -356.258 1.500 1.88202 37.22 21* 48.253 0.100 L13 22 30.697 9.000 1.72825 28.46 L14 23 -25.000 1.500 1.90043 37.37 L15 24 29.537 8.660 1.48749 70.24 25 -27.531 0.100 L16 26 -78.802 1.200 2.00069 25.46 L17 27 57.829 8.600 1.48749 70.24 28 -32.323 0.200 L18 29 106.054 1.200 2.00100 29.13 L19 30 38.114 8.729 1.49700 81.54 31 -62.282 0.200 L20 32 74.967 11.000 1.49700 81.54 33 -35.710 2.000 19 34 Infinity 39.600 1.51680 64.20 35 Infinity 15.068 18 36 Infinity

[0044] Here, the projection optical system 3A of this example can change the projection distance among a reference distance, a short distance shorter than the reference distance, and a long distance longer than the reference distance. When the projection distance is changed, the first b lens group 34 and the first c lens group 35 are respectively moved in the direction of the optical axis N for focusing. Further, the projection optical system 3A of this example can perform zooming by moving the second a lens group 36, the second b lens group 37, and the second c lens group 38 respectively in the direction of the optical axis N. By performing zooming at each projection distance, the angle of view is changed between the wide-angle end and the telephoto end.

[0045] The variable intervals 1, 2, 3, 4, 5, 6, and 7 at each projection distance when focusing and zooming are shown below. The variable interval 1 is the projection distance. The variable interval 2 is the axial upper surface interval between the first lens L1 and the second lens L2. The variable interval 3 is the axial upper surface distance between the third lens L3 and the fourth lens L4. The variable interval 4 is the axial upper surface distance between the fifth lens L5 and the sixth lens L6. The variable interval 5 is the axial upper surface distance between the seventh lens L7 and the eighth lens L8. The variable interval 6 is the axial upper surface distance between the ninth lens L9 and the aperture 41. The variable interval 7 is the axial upper surface distance between the eleventh lens L11 and the twelfth lens L12.

[0046] When the projection distance is long distance, it is as follows.

[0047] Wide-angle end Telephoto end Variable interval 1 10900.000 10900.000 Variable interval 2 25.079 24.082 Variable interval 3 29.441 28.082 Variable interval 4 1.734 3.099 Variable interval 5 5.512 4.791 Variable interval 6 6.804 10.582 Variable interval 7 5.399 3.333

[0048] When the projection distance is the reference distance, it is as follows.

[0049] Wide-angle end Telephoto end Variable interval 1 1450.000 1450.000 Variable interval 2 25.436 24.453 Variable interval 3 29.510 28.154 Variable interval 4 1.308 2.656 Variable interval 5 5.512 4.791 Variable interval 6 6.804 10.582 Variable interval 7 5.399 3.333

[0050] When the projection distance is short, it is as follows.

[0051] Wide-angle end Telephoto end Variable interval 1 1000.000 1000.000 Variable interval 2 25.194 24.609 Variable interval 3 29.540 28.189 Variable interval 4 1.520 2.465 Variable interval 5 5.512 4.791 Variable interval 6 6.804 10.582 Variable interval 7 5.399 3.333

[0052] The projection distance of the projection optical system 3A is 10900.000 mm for the long distance and 1000.000 mm for the short distance. Therefore, the projection distance range of the projection optical system 3A is more than 10 times. The projection distance range is the value obtained by dividing the projection distance at the long distance by the projection distance at the short distance.

[0053] Each aspherical coefficient is as follows.

[0054] Surface number 1 2 Radius of curvature (R) -31.570 -69.927 Conic constant (K) -10.370 -100.000 Cubic coefficient (A) 2.73781E-04 1.98290E-04 Quartic coefficient (A) -2.15742E-06 8.09194E-06 Quintic coefficient (A) 8.79876E-08 -6.74624E-08 Sextic coefficient (A) -4.03014E-09 -2.39594E-09 Septimic coefficient (A) 6.94823E-11 -7.38272E-11 Octic coefficient (A) -1.34611E-12 4.31123E-12 Nonic coefficient (A) 3.83047E-14 -1.56689E-13 Decic coefficient (A) -1.76630E-16 4.09197E-15 Coefficient of 11th order (A) -1.68383E-17 -5.09746E-17 Coefficient of 12th order (A) 3.88736E-19 2.11792E-19 Coefficient of 13th order (A) -3.41429E-21 2.37578E-23 Coefficient of 14th order (A) 1.11872E-23 3.02995E-24

[0055] Surface number 20 21 Radius of curvature (R) -356.258 48.253 Conic constant (K) 0.000 -11.533 Coefficient of 4th order (A) -6.19357E-05 -3.73218E-05 Coefficient of 6th order (A) 2.03376E-07 2.29999E-07 Coefficient of 8th order (A) -3.62824E-10 -7.47999E-10 Coefficient of 10th order (A) -1.28903E-12 1.36328E-12 Coefficient of 12th order (A) 7.52849E-15 -2.42971E-16 Coefficient of 14th order (A) 5.08437E-27 -5.15036E-21 Coefficient of 16th order (A) 1.94873E-30 1.88458E-30

[0056] Here, for the projection optical system 3A in this example, assuming the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first lens group 33 and the first lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. Note that the focal length F in this case is the focal length of the entire lens system at the wide-angle end. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0057] In this example, F 7.540mm BF 43.138mm Therefore, BF / F = 5.721, satisfying the conditional expression (1).

[0058] In this example, F is 7.540 mm F1ab is -10.463 mm Therefore, |F / F1ab| = 0.721, satisfying the conditional expression (2).

[0059] Also, for the projection optical system 3A in this example, assuming the focal length of the second a lens group 36 is F2a and the focal length of the second b lens group 37 is F2b, the following conditional expression (3) is satisfied. 1.0 < |F2a / F2b| < 4.0 (3)

[0060] In this example, F2a is -63.165 mm F2b is 34.515 mm Therefore, |F2a / F2b| = 1.830, satisfying the conditional expression (3).

[0061] Also, for the projection optical system 3A in this example, assuming the focal length of the entire lens system is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, the following conditional expressions (5) and (6) are all satisfied. Note that in this case, the focal length F is the focal length of the entire lens system at the wide-angle end. 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0062] In this example, F is 7.540 mm F1b is -15.481 mm Therefore, |F / F1b| = 0.487, satisfying the conditional expression (5).

[0063] In this example, F is 7.540 mm F1c is 60.425 mm Therefore, F / F1c = 0.125, satisfying the conditional expression (6).

[0064] (Function and Effect) The projection optical system 3A in this example has, in order from the magnification side to the reduction side, a first lens group 31 having a negative power and a second lens group 32 having a positive power. On the reduction side of the second lens group 32, it is telecentric. The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reduction side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reduction side of the first b lens group 34. The first a lens group 33 consists of a single first lens L1. The first lens L1 has a negative power near the optical axis N and has an aspherical shape on both surfaces. The first a lens group 33 consists only of lenses having a negative power. The first b lens group 34 consists only of lenses having a negative power. The total number of lens elements of the first a lens group 33 and the first b lens group 34 is 3. The first b lens group 34 and the first c lens group 35 move in the direction of the optical axis N during focusing, respectively.

[0065] In the projection optical system 3A of this example, the total number of lens elements of the first a lens group 33 and the first b lens group 34 is 3. Therefore, it is easy to suppress the weight of the end portion on the magnification side of the projection optical system 3A as compared with the case where the total number of lens elements is 4 or more.

[0066] Further, in the projection optical system 3A of this example, since the first lens L1 disposed on the most magnification side has an aspherical shape on both surfaces, it is easy to correct the distortion aberration generated in the magnified image projected onto the screen S.

[0067] Also, in this example, since the first lens L1 of the first a lens group 33 is made of resin, its weight can be suppressed as compared with the case where the first lens L1 is made of glass.

[0068] Furthermore, for the projection optical system 3A in this example, assuming that the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group 33 and the first b lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0069] Since the projection optical system 3A satisfies the conditional expression (1), the back focus can be ensured. That is, when the value of the conditional expression (1) exceeds the lower limit value, the back focus becomes too short, making it difficult to secure space for placing a color-combining prism or a correction plate of a liquid crystal panel arranged on the reduction side of the projection optical system 3A. Also, when the back focus becomes too short, the distance between the liquid crystal panel and the color-combining prism becomes narrow, so it is likely that the surroundings of the liquid crystal panel and the color-combining prism become hot. Moreover, since the distance between the liquid crystal panel and the color-combining prism becomes narrow, it is difficult to secure space for air-cooling the surroundings of the liquid crystal panel and the color-combining prism.

[0070] Also, since the projection optical system 3A satisfies the conditional expression (2), it is possible to avoid having more than 3 lens elements in the lenses constituting the first a lens group 33 and the first b lens group 34 while ensuring a sufficient back focus.

[0071] That is, when the value of the conditional expression (2) exceeds the lower limit value, the combined focal length F1ab of the first a lens group 33 and the first b lens group 34 becomes too long, so the negative power of the combination of the first a lens group 33 and the first b lens group 34 becomes weak. As a result, it becomes difficult to ensure a sufficiently long back focus. Also, since the overall lens length becomes long, the projection optical system 3A becomes large-sized. When the value of the conditional expression (2) exceeds the upper limit value, the combined focal length F1ab of the first a lens group 33 and the first b lens group 34 becomes too short, so the negative power of the combination of the first a lens group 33 and the first b lens group 34 becomes strong. As a result, in order to correct various aberrations, it is necessary to increase the number of lens elements, so the weight of the front part of the projection optical system 3A increases and the cost becomes higher.

[0072] In this example, the first lens group 33a consists of a first lens L1 made of resin. The first lens group 33b consists of a second lens L2 and a third lens L3 located on the reduction side of the second lens L2. The second lens L2 has a negative power and is a meniscus lens having a convex shape on the magnification side surface. The third lens L3 has a negative power and is a meniscus lens having a concave shape on the reduction side surface. Here, when the first lens L1 is made of resin, the temperature coefficient of refractive index and the coefficient of linear expansion, which change the refractive index with temperature, become larger compared to when the first lens L1 is made of glass. Therefore, the refractive index of the first lens L1 changes due to heat, and the shape is easily distorted. Thus, when the negative power of the first lens L1 is increased, the image quality of the magnified image is easily affected by heat. On the other hand, in this example, the first lens group 33b consists of two negative lenses, and the first lens group 33b compensates for the power of the first lens L1. Thereby, an increase in the negative power of the first lens L1 can be suppressed, and it is possible to suppress the image quality of the magnified image from being easily affected by heat. In the first lens group 33b, since the second lens L2 and the third lens L3 are negative meniscus lenses, the occurrence of spherical aberration and the like during focusing can be suppressed.

[0073] Here, when zooming is performed by moving the lens group in the direction of the optical axis N at a location where the change in the height of the light beam is large, the fluctuations in various aberrations generated by the zooming tend to increase. In contrast, in this example, the second lens group 32 has a diaphragm 41 disposed at a position where the chief ray of the maximum angle of view within the second lens group 32 intersects the optical axis N. The second lens group 32 includes a second a lens group 36 located on the magnifying side of the diaphragm 41 and a second b lens group 37. The second a lens group 36 is located on the magnifying side of the second b lens group 37. The second a lens group 36 and the second b lens group 37 move in the direction of the optical axis N respectively during zooming. Therefore, the generation of various aberrations during zooming can be suppressed. Note that since the diaphragm 41 is set for convenience in defining the F-number, it may be a virtual diaphragm. In the case of a projection optical system, since a light beam of the F-number determined by the illumination system in the front stage of the liquid crystal panel 18 is incident, the diaphragm 41 may be disposed. However, since only the light beam determined by the illumination system passes through the diaphragm, the diaphragm 41 may not be particularly necessary in some cases. The diaphragm 41 can suppress the generation of various aberrations as described above by being disposed. However, the position of the diaphragm 41 is a location where all the light beams converge in the projection optical system, and light that spreads beyond the F-number of the illumination system, such as light wrapping around due to diffraction caused by miniaturization of the pixel size of the liquid crystal panel 18, hits the diaphragm, which may become a heat generation source, causing deformation of the lens surface shape, refractive index fluctuations, etc., and leading to performance degradation. Therefore, there may be cases where it is better not to dispose the diaphragm 41. In that case, a fixed diaphragm disposed at another lens position can suppress the generation of unnecessary light and thus suppress the generation of various aberrations.

[0074] In this example, assuming that the focal length of the second a lens group 36 is F2a and the focal length of the second b lens group 37 is F2b, the following conditional expression (3) is satisfied. 1.0 < |F2a / F2b| < 4.0 (3)

[0075] Since the projection optical system 3A of this example satisfies the conditional expression (3), it is possible to suppress the occurrence of various aberrations while suppressing an increase in the overall lens length. That is, when the value of the conditional expression (3) exceeds the lower limit value, the focal length F2a of the second a lens group 36 becomes too short. In other words, the negative power of the second a lens group 36 becomes too strong. As a result, it becomes difficult to correct the astigmatism at the wide-angle end and the telephoto end in a well-balanced manner. When the value of the conditional expression (3) exceeds the upper limit value, the focal length of the second a lens group 36 becomes too long, or the focal length of the second b lens group 37 becomes too short. When the focal length of the second a lens group 36 becomes too long, the negative power of the second a lens group 36 decreases, so the movement amount of the second a lens group 36 increases. As a result, the overall lens length increases. Further, when the focal length of the second b lens group 37 becomes too short, the positive power of the second b lens group 37 becomes too strong, so spherical aberration and coma aberration are likely to occur, and the contrast of the enlarged image decreases.

[0076] Here, the projection distance range of the projection optical system 3A of this example is 10 times or more. In recent years, in an event venue or the like, multi-projection in which enlarged images projected by a plurality of projectors are connected to form one integrated image may be used. For a projector used in such an event venue, it is desired that the projection distance can be flexibly changed according to the size of the event venue and the like. In response to such a requirement, the projection distance range of the projection optical system 3A of this example is larger than that of a conventional projection optical system having a projection distance range of about 5 times. Therefore, if the projector 1 including the projection optical system 3A is used, the projection distance can be flexibly changed.

[0077] In addition, in multi-projection, even if there is a slight magnification error for each projector, a deviation occurs in adjacent enlarged images, resulting in a sense of incongruity in the integrated image. To address such a problem, the projection optical system 3A in this example can vary the magnification of the enlarged image by zooming. This makes it easier to correct the magnification error for each projector. Also, the projection optical system 3A can suppress the occurrence of various aberrations due to zooming. Therefore, the projector 1 equipped with the projection optical system 3A is suitable for multi-projection applications.

[0078] Also, in this example, assuming the focal length of the entire lens system is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, the following conditional expressions (5) and (6) are all satisfied. 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0079] Since the projection optical system 3A in this example satisfies the conditional expression (5), it is possible to suppress the occurrence of field curvature even when the projection distance range is about 10 times while maintaining sufficient back focus. Also, focus adjustment during focusing is easy.

[0080] That is, when the value of the conditional expression (5) exceeds the lower limit value, the focal length of the first b lens group 34 becomes too long. In other words, the negative power of the first b lens group 34 becomes too weak. As a result, the negative power of the entire first lens group 31 becomes weak, making it difficult to maintain sufficient back focus. When the value of the conditional expression (5) exceeds the upper limit value, the focal length of the first b lens group 34 becomes too short. That is, the negative power of the first b lens group 34 becomes too strong. As a result, the movement amount during focusing becomes too small. Consequently, the focus adjustment becomes difficult due to increased focus adjustment sensitivity, and the amount of field curvature when the projection distance is changed becomes large.

[0081] In addition, since the projection optical system 3A of this example satisfies the conditional expression (6), even if the projection distance range is about 10 times, it is possible to satisfactorily correct various aberrations caused by the change in the projection distance. That is, when the value of the conditional expression (6) exceeds the lower limit value, the positive power of the first c lens group 35 becomes too weak or has a negative power. As a result, it becomes difficult to satisfactorily correct the field curvature due to the variation in the projection distance. When the value of the conditional expression (6) exceeds the upper limit value, since the positive power becomes too strong, it becomes difficult to balance and correct the aberration from the vicinity of the optical axis N to the high image height. Also, since the focus shift near the optical axis N becomes large, it becomes necessary again to adjust the focus position near the optical axis N by the first b lens group 34. As a result, the focusing becomes complicated.

[0082] In this example, the second lens group 32 includes six cemented lenses. Therefore, chromatic aberration can be satisfactorily corrected.

[0083] FIG. 3 is a diagram showing spherical aberration, coma aberration, and distortion at the wide-angle end and the reference distance of the projection optical system 3A. FIG. 4 is a diagram showing spherical aberration, coma aberration, and distortion at the telephoto end and the reference distance of the projection optical system 3A. FIG. 5 is a diagram showing spherical aberration, coma aberration, and distortion at the wide-angle end and the long distance of the projection optical system 3A. FIG. 6 is a diagram showing spherical aberration, coma aberration, and distortion at the telephoto end and the long distance of the projection optical system 3A. FIG. 7 is a diagram showing spherical aberration, coma aberration, and distortion at the wide-angle end and the short distance of the projection optical system 3A. FIG. 8 is a diagram showing spherical aberration, coma aberration, and distortion at the telephoto end and the short distance of the projection optical system 3A. As shown in FIGS. 3 to 8, various aberrations in the magnified image of the projection optical system 3A of this example are suppressed.

[0084] (Example 2) FIG. 9 is a ray diagram of the projection optical system 3B of Example 2. As shown in FIG. 9, the projection optical system 3B includes a first lens group 31 having a negative power and a second lens group 32 having a positive power, in order from the magnifying side to the reducing side. Further, the projection optical system 3B includes a diaphragm 41 disposed inside the second lens group 32. The diaphragm 41 is disposed at a position where the principal ray of the maximum angle of view intersects the optical axis N within the second lens group 32.

[0085] The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reducing side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reducing side of the first b lens group 34.

[0086] The first a lens group 33 consists of a first lens L1 and a second lens L2. The first lens L1 has a negative power near the optical axis N. The first lens L1 has a concave shape near the optical axis N on the magnifying side surface and a convex shape in the peripheral portion. The first lens L1 has a convex shape near the optical axis N on the reducing side surface and a concave shape in the peripheral portion. The first lens L1 has an aspherical shape on both surfaces. The second lens L2 has a negative power. The second lens L2 is a meniscus lens. The second lens L2 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface.

[0087] The first b lens group 34 consists of a third lens L3. The third lens L3 has a negative power. The third lens L3 is a meniscus lens. The third lens L3 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface. The magnifying side surface of the third lens L3 has a smaller power than the reducing side surface of the third lens L3.

[0088] The 1c lens group 35 consists of a fourth lens L4 and a fifth lens L5. The fourth lens L4 and the fifth lens L5 are arranged in this order from the magnification side toward the reduction side. The fourth lens L4 and the fifth lens L5 are a joined lens L21 joined together. The fourth lens L4 has a negative power. The fourth lens L4 is a meniscus lens. The fourth lens L4 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface. The fifth lens L5 has a positive power. The fifth lens L5 has convex shapes on both the magnification-side and reduction-side surfaces.

[0089] The 2nd lens group 32 includes a 2a lens group 36 having a negative power, a 2b lens group 37 having a positive power located on the reduction side of the 2a lens group 36, a 2c lens group 38 having a negative power located on the reduction side of the 2b lens group 37, and a 2d lens group 39 located on the reduction side of the 2c lens group 38. An aperture 41 is disposed between the 2b lens group 37 and the 2c lens group 38.

[0090] The 2a lens group 36 consists of a sixth lens L6 and a seventh lens L7. The sixth lens L6 and the seventh lens L7 are arranged in this order from the magnification side toward the reduction side. The sixth lens L6 and the seventh lens L7 are a joined lens L22 joined together. The sixth lens L6 has a positive power. The sixth lens L6 has convex shapes on both the magnification-side and reduction-side surfaces. The seventh lens L7 has a negative power. The seventh lens L7 has concave shapes on both the magnification-side and reduction-side surfaces.

[0091] The 2b lens group 37 is composed of an eighth lens L8. The eighth lens L8 has a positive power. The eighth lens L8 has convex shapes on both the magnification-side and reduction-side surfaces.

[0092] The 2c lens group 38 consists of a ninth lens L9 and a tenth lens L10. The ninth lens L9 and the tenth lens L10 are arranged in this order from the magnification side toward the reduction side. The ninth lens L9 and the tenth lens L10 are a cemented lens L23 that are cemented together. The ninth lens L9 has a negative power. The ninth lens L9 has a concave shape on both the magnification-side and reduction-side surfaces. The tenth lens L10 has a positive power. The tenth lens L10 is a meniscus lens. The tenth lens L10 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface.

[0093] The 2d lens group 39 consists of nine lenses, an eleventh lens L11 to a nineteenth lens L19. The eleventh lens L11 to the nineteenth lens L19 are arranged in this order from the magnification side toward the reduction side. The eleventh lens L11 has a negative power. The eleventh lens L11 has a concave shape on both the magnification-side and reduction-side surfaces. The eleventh lens L11 has an aspherical shape on both surfaces.

[0094] The twelfth lens L12 has a positive power. The twelfth lens L12 has a convex shape on both the magnification-side and reduction-side surfaces. The thirteenth lens L13 has a negative power. The thirteenth lens L13 has a concave shape on both the magnification-side and reduction-side surfaces. The fourteenth lens L14 has a positive power. The fourteenth lens L14 has a convex shape on both the magnification-side and reduction-side surfaces. The twelfth lens L12, the thirteenth lens L13, and the fourteenth lens L14 are a cemented lens L24 that are cemented together.

[0095] The fifteenth lens L15 has a negative power. The fifteenth lens L15 has a concave shape on both the magnification-side and reduction-side surfaces. The sixteenth lens L16 has a positive power. The sixteenth lens L16 has a convex shape on both the magnification-side and reduction-side surfaces. The fifteenth lens L15 and the sixteenth lens L16 are a cemented lens L25 that are cemented together.

[0096] The 17th lens L17 has a negative power. The 17th lens L17 is a meniscus lens. The 17th lens L17 has a convex shape on the magnifying side and a concave shape on the reducing side. The 18th lens L18 has a positive power. The 18th lens L18 has a convex shape on both the magnifying side and the reducing side. The 17th lens L17 and the 18th lens L18 are a cemented lens L26.

[0097] The 19th lens L19 has a positive power. The 19th lens L19 has a convex shape on both the magnifying side and the reducing side.

[0098] The 1st lens L1 is made of resin. The 2nd lens L2 to the 19th lens L19 are made of glass.

[0099] In the projection optical system 3B, the reducing side of the 19th lens L19 of the 2nd lens group 32 is telecentric.

[0100] Here, the projection optical system 3B can change the projection distance. When changing the projection distance, the 1b lens group 34 and the 1c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0101] Also, the projection optical system 3B can change the magnification of the magnified image. When changing the magnification of the magnified image, the 2a lens group 36, the 2b lens group 37, and the 2c lens group 38 are each moved in the direction of the optical axis N for zooming. In this example, by zooming, the magnified image becomes about 1.1 times.

[0102] Let the F number of the projection optical system 3B be FNo, the focal length of the entire system be F, the semi-field angle be ω, the back focus air equivalent value be BF, the focal length of the 1b lens group 34 be F1b, the focal length of the 1c lens group 35 be F1c, the combined focal length of the 1a lens group 33 and the 1b lens group 34 be F1ab, the focal length of the 2a lens group 36 be F2a, the focal length of the 2b lens group 37 be F2b, the focal length of the 1st lens group 31 be F1, and the focal length of the 2nd lens group 32 be F2. Then, the data of the projection optical system 3B is as follows.

[0103] F No. 1.9 F (wide-angle end to telephoto end) 7.540 mm to 8.290 mm ω (wide-angle end to telephoto end) 60.7° to 58.4° BF 43.091 mm F1b -32.013 mm F1c 84.863 mm F1ab -10.015 mm F2a -86.522 mm F2b 37.299 mm F1 -22.634 mm F2 47.802 mm

[0104] The lens data of the projection optical system 3B is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, aperture, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, aperture, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical surfaces. R is the radius of curvature. D is the axial distance between surfaces. nd is the refractive index of the d-line. νd is the Abbe number of the d-line. The units of R and D are mm.

[0105] Sign Surface number R D nd vd S 0 Infinity Variable interval 1 L1 1* -31.575 5.000 1.53116 56.04 2 * -71.341 23.233 L2 3 91.093 3.000 1.83481 42.72 4 25.642 Variable interval 2 L3 5 864.103 2.000 1.83481 42.72 6 26.021 Variable interval 3 L4 7 270.672 1.600 1.75500 52.32 L5 8 20.860 9.500 1.72825 28.46 9 -71.441 Variable interval 4 L6 10 100.984 8.400 1.80809 22.76 L7 11 -23.648 1.500 1.98612 16.48 12 78.872 Variable interval 5 L8 13 90.148 8.500 1.67270 32.10 14 -33.750 Variable interval 6 41 15 Infinity 0.629 L9 16 -117.596 1.200 1.90043 37.37 L10 17 21.441 4.313 1.86966 20.02 18 310.198 Variable interval 7 L11 19* Infinity 2.000 1.58913 61.15 20* 33.580 0.100 L12 21 28.329 9.109 1.72825 28.46 L13 22 -25.000 2.000 1.90043 37.37 L14 23 26.544 9.231 1.48749 70.24 24 -31.269 0.100 L15 25 -152.343 1.200 2.00069 25.46 L16 26 41.801 8.600 1.48749 70.24 27 -36.006 0.200 L17 28 87.217 1.200 2.00100 29.13 L18 29 37.711 8.261 1.49700 81.54 30 -80.531 0.200 L19 31 74.700 11.000 1.49700 81.54 32 -34.857 2.000 19 33 Infinity 39.600 1.51680 64.20 34 Infinity 15.412 18 35 Infinity

[0106] Here, the projection optical system 3B in this example can change the projection distance among a reference distance, a short distance shorter than the reference distance, and a long distance longer than the reference distance. When the projection distance is changed, the first b lens group 34 and the first c lens group 35 are each moved in the direction of the optical axis N to perform focusing. Also, the projection optical system 3B in this example can perform zooming by moving the second a lens group 36, the second b lens group 37, and the second c lens group 38 in the direction of the optical axis N, respectively. By performing zooming at each projection distance, the angle of view is changed between the wide-angle end and the telephoto end.

[0107] The variable intervals 1, 2, 3, 4, 5, 6, and 7 at each projection distance when focusing and zooming are shown below. The variable interval 1 is the projection distance. The variable interval 2 is the on-axis distance between the second lens L2 and the third lens L3. The variable interval 3 is the on-axis distance between the third lens L3 and the fourth lens L4. The variable interval 4 is the on-axis distance between the fifth lens L5 and the sixth lens L6. The variable interval 5 is the on-axis distance between the seventh lens L7 and the eighth lens L8. The variable interval 6 is the on-axis distance between the eighth lens L8 and the aperture 41. The variable interval 7 is the on-axis distance between the tenth lens L10 and the eleventh lens L11.

[0108] When the projection distance is the long distance, it is as follows.

[0109] Wide-angle end Telephoto end Variable interval 1 10900.000 10900.000 Variable interval 2 17.061 14.000 Variable interval 3 22.218 22.351 Variable interval 4 1.811 2.483 Variable interval 5 3.716 3.068 Variable interval 6 12.000 16.983 Variable interval 7 4.529 2.450

[0110] When the projection distance is the reference distance, it is as follows.

[0111] Wide-angle end Telephoto end Variable interval 1 1450.000 1450.000 Variable interval 2 17.394 14.648 Variable interval 3 22.491 22.459 Variable interval 4 1.205 1.727 Variable interval 5 3.716 3.068 Variable interval 6 12.000 16.983 Variable interval 7 4.529 2.450

[0112] When the projection distance is the short distance, it is as follows.

[0113] Wide-angle end Telephoto end Variable interval 1 1000.000 1000.000 Variable interval 2 17.608 14.950 Variable interval 3 22.540 22.512 Variable interval 4 0.942 1.372 Variable interval 5 3.716 3.068 Variable interval 6 12.000 16.983 Variable interval 7 4.529 2.450

[0114] The projection distance of the projection optical system 3B in this example is 10900.000 mm for the long distance and 1000.000 mm for the short distance. Therefore, the projection distance range of the projection optical system 3B is more than 10 times.

[0115] Each aspherical coefficient is as follows.

[0116] Surface number 1 2 Radius of curvature (R) -31.575 -71.341 Conic constant (K) -10.576 -100.000 Cubic coefficient (A) 2.62422E-04 2.03518E-04 Coefficient of the 4th order (A) -2.02997E-06 7.52369E-06 Coefficient of the 5th order (A) 9.01284E-08 -5.92772E-08 Coefficient of the 6th order (A) -4.06408E-09 -2.39437E-09 Coefficient of the 7th order (A) 6.82185E-11 -7.40732E-11 Coefficient of the 8th order (A) -1.31834E-12 4.30787E-12 Coefficient of the 9th order (A) 3.81371E-14 -1.56730E-13 Coefficient of the 10th order (A) -1.74852E-16 4.09200E-15 Coefficient of the 11th order (A) -1.68475E-17 -5.09492E-17 Coefficient of the 12th order (A) 3.88227E-19 2.11899E-19 Coefficient of the 13th order (A) -3.41524E-21 2.93682E-23 Coefficient of the 14th order (A) 1.12637E-23 2.88167E-24

[0117] Face number 19 20 Radius of curvature (R) Infinity 33.580 Conic constant (K) 0.000 -12.934 Coefficient of the 4th order (A) -8.91805E-05 -3.83441E-05 Coefficient of the 6th order (A) 3.87821E-07 2.88935E-07 Coefficient of the 8th order (A) -1.13227E-09 -1.06878E-09 Coefficient of the 10th order (A) 1.07229E-13 2.08521E-12 Coefficient of the 12th order (A) 7.40469E-15 -1.03343E-15 Coefficient of the 14th order (A) 5.04824E-27 -5.15036E-21 Coefficient of the 16th order (A) 1.95009E-30 1.89620E-30

[0118] Here, for the projection optical system 3B in this example, assuming the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group 33 and the first b lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. Note that the focal length F in this case is the focal length of the entire lens system at the wide-angle end. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0119] In this example, F 7.540mm BF 43.091mm Therefore, BF / F = 5.715, satisfying the conditional expression (1).

[0120] In this example, F 7.540mm F1ab -10.015mm Therefore, |F / F1ab| = 0.753, satisfying the conditional expression (2).

[0121] Also, for the projection optical system 3B in this example, assuming the focal length of the second a lens group 36 is F2a and the focal length of the second b lens group 37 is F2b, the following conditional expression (3) is satisfied. 1.0 < |F2a / F2b| < 4.0 (3)

[0122] In this example, F2a -86.522mm F2b 37.299mm Therefore, |F2a / F2b| = 2.320, satisfying the conditional expression (3).

[0123] Also, for the projection optical system 3B in this example, assuming the focal length of the entire lens system is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, the following conditional expressions (5) and (6) are all satisfied. Note that the focal length F in this case is the focal length of the entire lens system at the wide-angle end. 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0124] In this example, F is 7.540 mm F1b is -32.013 mm Therefore, |F / F1b| = 0.236, which satisfies the conditional expression (5).

[0125] In this example, F is 7.540 mm F1c is 84.863 mm Therefore, F / F1c = 0.089, which satisfies the conditional expression (6).

[0126] (Function and effect) In the projection optical system 3B of this example, the first lens group 33a consists of a first lens L1 made of resin and a second lens L2 located on the reduction side of the first lens L1. The second lens L2 is a meniscus lens having a negative power and a convex shape on the enlargement side surface. The first lens group 34b consists of a third lens L3. The third lens L3 has a negative power and a concave shape on the reduction side surface. More specifically, the third lens L3 is a meniscus lens having a negative power and a concave shape on the reduction side surface. The power of the enlargement side surface of the third lens L3 is smaller than that of the reduction side surface of the third lens L3.

[0127] In the projection optical system 3B of this example, the total number of lenses of the first lens group 33a and the first lens group 34b is 3. Therefore, it is easy to suppress the weight of the end portion on the enlargement side of the projection optical system 3B.

[0128] Further, in this example, since the first lens L1 of the first a lens group 33 is made of resin, its weight can be suppressed as compared with the case where the first lens L1 is made of glass. Here, when the first lens L1 is made of resin, the temperature coefficient of refractive index and the coefficient of linear expansion, for which the refractive index changes with temperature, become larger as compared with the case where the first lens L1 is made of glass. Therefore, while the refractive index of the first lens L1 changes due to heat, its shape is liable to be distorted. Thus, when the negative power of the first lens L1 is increased, the image quality of the magnified image is liable to be affected by heat. On the other hand, in this example, the first a lens group 33 is composed of two lenses, i.e., the first lens L1 and the second lens L2. Therefore, the power of the first a lens group 33 can be borne by the two lenses, i.e., the first lens L1 and the second lens L2. Thus, while suppressing an increase in the negative power of the first lens L1, the negative power of the first a lens group 33 can be increased, so that it is possible to suppress the image quality of the magnified image from being liable to be affected by heat.

[0129] Further, since the negative power of the first a lens group 33 can be increased, the first b lens group 34 can be composed of a single lens. As a result, the first b lens group 34 becomes lighter and is easier to move during focusing. Further, the power of the magnifying side surface of the third lens L3 is smaller than that of the reducing side surface of the third lens L3. Therefore, in the third lens L3, it is possible to suppress the aberration generated on the magnifying side surface. As a result, it is possible to suppress the occurrence of astigmatism and the like during focusing.

[0130] In this example, the second lens group 32 includes five cemented lenses. Therefore, chromatic aberration can be corrected well.

[0131] Since the projection optical system 3B in this example satisfies the conditional expressions (1) to (3), (5), and (6), the same effects as those of the projection optical system 3A in the first embodiment can be obtained. FIG. 10 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and the reference distance of the projection optical system 3B. FIG. 11 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and the reference distance of the projection optical system 3B. FIG. 12 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and the long distance of the projection optical system 3B. FIG. 13 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and the long distance of the projection optical system 3B. FIG. 14 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and the short distance of the projection optical system 3B. FIG. 15 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and the short distance of the projection optical system 3B. As shown in FIGS. 10 to 15, various aberrations in the enlarged image of the projection optical system 3B in this example are suppressed.

[0132] (Example 3) FIG. 16 is a ray diagram of the projection optical system 3C of Example 3. As shown in FIG. 16, the projection optical system 3C includes a first lens group 31 having a negative power and a second lens group 32 having a positive power, in order from the enlargement side to the reduction side. Further, the projection optical system 3C includes a diaphragm 41 disposed inside the second lens group 32. The diaphragm 41 is disposed at a position where the chief ray of the maximum angle of view intersects the optical axis N within the second lens group 32.

[0133] The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reduction side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reduction side of the first b lens group 34.

[0134] The first lens group 33 consists of a first lens L1 and a second lens L2. The first lens L1 has a negative power near the optical axis N. The first lens L1 has a concave shape near the optical axis N on the magnifying side surface and a convex shape in the peripheral portion. The first lens L1 has a convex shape near the optical axis N on the reducing side surface and a concave shape in the peripheral portion. The first lens L1 has an aspherical shape on both surfaces. The second lens L2 has a negative power. The second lens L2 is a meniscus lens. The second lens L2 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface.

[0135] The first lens group 34 consists of a third lens L3. The third lens L3 has a negative power. The third lens L3 is a meniscus lens. The third lens L3 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface. The magnifying side surface of the third lens L3 has a smaller power than the reducing side surface of the third lens L3.

[0136] The first lens group 35 consists of a fourth lens L4 and a fifth lens L5. The fourth lens L4 and the fifth lens L5 are arranged in this order from the magnifying side to the reducing side. The fourth lens L4 and the fifth lens L5 are a cemented lens L21. The fourth lens L4 has a negative power. The fourth lens L4 has a concave shape on both the magnifying side and reducing side surfaces. The fifth lens L5 has a positive power. The fifth lens L5 has a convex shape on both the magnifying side and reducing side surfaces.

[0137] The second lens group 32 includes a second lens group 36 having a negative power, a second lens group 37 having a positive power located on the reducing side of the second lens group 36, a second lens group 38 having a negative power located on the reducing side of the second lens group 37, and a second lens group 39 located on the reducing side of the second lens group 38. A diaphragm 41 is arranged between the second lens group 37 and the second lens group 38.

[0138] The 2a lens group 36 consists of a sixth lens L6 and a seventh lens L7. The sixth lens L6 and the seventh lens L7 are arranged in this order from the magnification side toward the reduction side. The sixth lens L6 and the seventh lens L7 are a cemented lens L22 that are cemented together. The sixth lens L6 has a positive power. The sixth lens L6 has a convex shape on both the magnification side and the reduction side surfaces. The seventh lens L7 has a negative power. The seventh lens L7 has a concave shape on both the magnification side and the reduction side surfaces.

[0139] The 2b lens group 37 consists of an eighth lens L8 and a ninth lens L9. The eighth lens L8 and the ninth lens L9 are arranged in this order from the magnification side toward the reduction side. The eighth lens L8 and the ninth lens L9 are a cemented lens L23 that are cemented together. The eighth lens L8 has a negative power. The eighth lens L8 is a meniscus lens. The eighth lens L8 has a convex shape on the magnification side surface and a concave shape on the reduction side surface. The ninth lens L9 has a positive power. The ninth lens L9 has a convex shape on both the magnification side and the reduction side surfaces.

[0140] The 2c lens group 38 consists of a tenth lens L10 and an eleventh lens L11. The tenth lens L10 and the eleventh lens L11 are arranged in this order from the magnification side toward the reduction side. The tenth lens L10 and the eleventh lens L11 are a cemented lens L24 that are cemented together. The tenth lens L10 has a positive power. The tenth lens L10 is a meniscus lens. The tenth lens L10 has a concave shape on the magnification side surface and a convex shape on the reduction side surface. The eleventh lens L11 has a negative power. The eleventh lens L11 has a concave shape on both the magnification side and the reduction side surfaces.

[0141] The 2d lens group 39 consists of nine lenses from a twelfth lens L12 to a twentieth lens L20. The twelfth lens L12 to the twentieth lens L20 are arranged in this order from the magnification side toward the reduction side. The twelfth lens L12 has a negative power. The twelfth lens L12 has a concave shape on both the magnification side and the reduction side surfaces. The twelfth lens L12 has an aspherical shape on both surfaces.

[0142] The 13th lens L13 has a positive power. The 13th lens L13 has convex shapes on the magnifying side and the reducing side surfaces. The 14th lens L14 has a negative power. The 14th lens L14 has concave shapes on the magnifying side and the reducing side surfaces. The 15th lens L15 has a positive power. The 15th lens L15 has convex shapes on the magnifying side and the reducing side surfaces. The 13th lens L13, the 14th lens L14, and the 15th lens L15 are a cemented lens L25.

[0143] The 16th lens L16 has a negative power. The 16th lens L16 has concave shapes on the magnifying side and the reducing side surfaces. The 17th lens L17 has a positive power. The 17th lens L17 has convex shapes on the magnifying side and the reducing side surfaces. The 16th lens L16 and the 17th lens L17 are a cemented lens L26.

[0144] The 18th lens L18 has a negative power. The 18th lens L18 is a meniscus lens. The 18th lens L18 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface. The 19th lens L19 has a positive power. The 19th lens L19 has convex shapes on the magnifying side and the reducing side surfaces. The 18th lens L18 and the 19th lens L19 are a cemented lens L27.

[0145] The 20th lens L20 has a positive power. The 20th lens L20 has convex shapes on the magnifying side and the reducing side surfaces.

[0146] The 1st lens L1 is made of resin. The 2nd lens L2 to the 20th lens L20 are made of glass.

[0147] In the projection optical system 3C, the side closer to the reduction side than the 20th lens L20 of the 2nd lens group 32 is telecentric.

[0148] Here, the projection optical system 3C can change the projection distance. When changing the projection distance, the 1b lens group 34 and the 1c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0149] Let the F number of the projection optical system 3C be FNo, the focal length of the entire system be F, the semi-field angle be ω, the back focus air equivalent value be BF, the focal length of the first b lens group 34 be F1b, the focal length of the first c lens group 35 be F1c, the combined focal length of the first a lens group 33 and the first b lens group 34 be F1ab, the focal length of the second a lens group 36 be F2a, the focal length of the second b lens group 37 be F2b, the focal length of the first lens group 31 be F1, and the focal length of the second lens group 32 be F2. Then, the data of the projection optical system 3C is as follows.

[0150] FNo 1.9 F (wide-angle end to telephoto end) 7.540 mm to 7.920 mm ω (wide-angle end to telephoto end) 60.7° to 59.6° BF 43.138 mm F1b -26.039 mm F1c 104.187 mm F1ab -14.785 mm F2a -86.000 mm F2b 34.141 mm F1 -21.864 mm F2 50.259 mm

[0151] The lens data of the projection optical system 3C is as follows. The surface numbers are assigned in order from the magnification side to the reduction side. The signs are the signs of the screen, lens, aperture, dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, aperture, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * in the surface numbers are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index of the d line. νd is the Abbe number of the d line. The units of R and D are mm.

[0152] Sign Surface number R D nd vd S 0 Infinity Variable interval 1 L1 1* -31.925 5.000 1.53116 56.04 2 * -69.616 20.969 L2 3 53.658 3.000 1.90043 37.37 4 26.168 Variable interval 2 L3 5 333.950 2.000 1.90043 37.37 6 21.961 Variable interval 3 L4 7 -91.514 2.000 1.72916 54.68 L5 8 25.283 9.000 1.76182 26.52 9 -49.528 Variable interval 4 L6 10 49.923 8.000 1.76182 26.52 L7 11 -24.583 1.837 1.98612 16.48 12 50.502 Variable interval 5 L8 13 78.023 1.200 1.73400 51.47 L9 14 33.567 9.000 1.69895 30.13 15 -32.065 Variable interval 6 41 16 Infinity 2.000 L10 17 -145.677 3.736 1.86966 20.02 L11 18 -22.645 1.200 1.90043 37.37 19 124.744 Variable interval 7 L12 20* Infinity 2.000 1.58913 61.15 21* 36.202 0.100 L13 22 26.378 10.904 1.74077 27.79 L14 23 -17.927 2.000 1.90043 37.37 L15 24 28.086 9.258 1.48749 70.24 25 -25.601 0.100 L16 26 -63.030 1.200 2.00069 25.46 L17 27 40.834 8.600 1.48749 70.24 28 -33.235 0.100 L18 29 71.777 1.200 2.00100 29.13 L19 30 35.238 8.789 1.49700 81.54 31 -71.773 0.100 L20 32 69.781 11.000 1.49700 81.54 33 -35.788 2.000 19 34 Infinity 39.600 1.51680 64.20 35 Infinity 15.065 18 36 Infinity

[0153] Here, the projection optical system 3C of this example can change the projection distance among a reference distance, a short distance shorter than the reference distance, and a long distance longer than the reference distance. When the projection distance is changed, the first b lens group 34 and the first c lens group 35 are each moved in the direction of the optical axis N to perform focusing. Further, the projection optical system 3C of this example can perform zooming by moving the second a lens group 36, the second b lens group 37, and the second c lens group 38 in the direction of the optical axis N, respectively. By performing zooming at each projection distance, the angle of view is changed between the wide-angle end and the telephoto end.

[0154] The relationships of the variable intervals 1, 2, 3, 4, 5, 6, and 7 at each projection distance when focusing and zooming are shown below. The variable interval 1 is the projection distance. The variable interval 2 is the on-axis distance between the second lens L2 and the third lens L3. The variable interval 3 is the on-axis distance between the third lens L3 and the fourth lens L4. The variable interval 4 is the on-axis distance between the fifth lens L5 and the sixth lens L6. The variable interval 5 is the on-axis distance between the seventh lens L7 and the eighth lens L8. The variable interval 6 is the on-axis distance between the ninth lens L9 and the aperture 41. The variable interval 7 is the on-axis distance between the eleventh lens L11 and the twelfth lens L12.

[0155] When the projection distance is long distance, it is as follows.

[0156] Wide-angle end Telephoto end Variable interval 1 10900.000 10900.000 Variable interval 2 14.722 14.000 Variable interval 3 25.883 25.166 Variable interval 4 1.676 2.476 Variable interval 5 3.695 3.481 Variable interval 6 8.039 10.604 Variable interval 7 5.068 3.356

[0157] When the projection distance is the reference distance, it is as follows.

[0158] Wide-angle end Telephoto end Variable interval 1 1450.000 1450.000 Variable interval 2 15.209 14.452 Variable interval 3 26.054 25.335 Variable interval 4 1.018 1.855 Variable interval 5 3.695 3.481 Variable interval 6 8.039 10.604 Variable interval 7 5.068 3.356

[0159] When the projection distance is short distance, it is as follows.

[0160] Wide-angle end Telephoto end Variable interval 1 1000.000 1000.000 Variable interval 2 15.473 14.738 Variable interval 3 26.138 25.427 Variable interval 4 0.670 1.477 Variable interval 5 3.695 3.481 Variable interval 6 8.039 10.604 Variable interval 7 5.068 3.356

[0161] The projection distance of the projection optical system 3C in this example is 10900.000 mm for the long distance and 1000.000 mm for the short distance. Therefore, the projection distance range of the projection optical system 3C is more than 10 times.

[0162] Each aspherical coefficient is as follows.

[0163] Surface number 1 2 Radius of curvature (R) -31.925 -69.616 Conic constant (K) -10.280 -100.000 Cubic coefficient (A) 2.56214E-04 1.72672E-04 Quartic coefficient (A) -1.65047E-06 8.07117E-06 Quintic coefficient (A) 8.61548E-08 -4.31471E-08 Sextic coefficient (A) -3.95031E-09 -2.54588E-09 Septimic coefficient (A) 6.48932E-11 -7.82864E-11 Octic coefficient (A) -1.34188E-12 4.27445E-12 Nonic coefficient (A) 3.90508E-14 -1.56545E-13 Decic coefficient (A) -1.69162E-16 4.10349E-15 Undecic coefficient (A) -1.69107E-17 -5.07510E-17 Dodecic coefficient (A) 3.86354E-19 2.14054E-19 Tridecic coefficient (A) -3.42934E-21 2.32114E-23 Tetradecic coefficient (A) 1.16276E-23 1.82729E-24

[0164] Surface number 20 21 Radius of curvature (R) Infinity 36.202 Conic constant (K) 0.000 -11.142 Coefficient of the 4th order (A) -6.39966E-05 -2.44004E-05 Coefficient of the 6th order (A) 1.96912E-07 1.74843E-07 Coefficient of the 8th order (A) -8.43534E-12 -4.82077E-10 Coefficient of the 10th order (A) -2.66355E-12 1.36551E-12 Coefficient of the 12th order (A) 6.77398E-15 -6.43950E-15 Coefficient of the 14th order (A) 5.00647E-27 3.55555E-27 Coefficient of the 16th order (A) 1.95468E-30 1.91126E-30

[0165] Here, for the projection optical system 3C in this example, assuming the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group 33 and the first b lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. Note that in this case, the focal length F is the focal length of the entire lens system at the wide-angle end. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0166] In this example, F 7.540mm BF 43.138mm Therefore, BF / F = 5.721, satisfying the conditional expression (1).

[0167] In this example, F 7.540mm F1ab -14.785mm Therefore, |F / F1ab| = 0.510, satisfying the conditional expression (2).

[0168] Also, for the projection optical system 3C in this example, assuming the focal length of the second a lens group 36 is F2a and the focal length of the second b lens group 37 is F2b, the following conditional expression (3) is satisfied. 1.0 < |F2a / F2b| < 4.0 (3)

[0169] In this example, F2a -86.000 mm F2b 34.141 mm Therefore, |F2a / F2b| = 2.519, satisfying the conditional expression (3).

[0170] Also, for the projection optical system 3C in this example, assuming the focal length of the entire lens system is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, the following conditional expressions (5) and (6) are all satisfied. Note that the focal length F in this case is the focal length of the entire lens system at the wide-angle end. 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0171] In this example, F 7.540 mm F1b -26.039 mm Therefore, |F / F1b| = 0.290, satisfying the conditional expression (5).

[0172] In this example, F 7.540 mm F1c 104.187 mm Therefore, F / F1c = 0.072, satisfying the conditional expression (6).

[0173] (Function and effect) For the projection optical system 3C in this example, the total number of lens elements of the first lens element number of the first a lens group 33 and the second lens element number of the first b lens group 34 is 3. Therefore, it is easy to suppress the weight of the end portion on the magnification side of the projection optical system 3C.

[0174] In addition, in the projection optical system 3C of this example, since the first lens L1 of the first lens group 33a is made of resin, its weight can be suppressed as compared with the case where the first lens L1 is made of glass. Here, when the first lens L1 is made of resin, the temperature coefficient of refractive index and the coefficient of linear expansion, for which the refractive index changes with temperature, become larger as compared with the case where the first lens L1 is made of glass. Therefore, the refractive index of the first lens L1 changes due to heat, and its shape is likely to be distorted. Thus, when the negative power of the first lens L1 is increased, the image quality of the magnified image is likely to be affected by heat. On the other hand, in this example, the first lens group 33a consists of two lenses, the first lens L1 and the second lens L2. Therefore, the power of the first lens group 33a can be borne by the two lenses, the first lens L1 and the second lens L2. Thus, while suppressing an increase in the negative power of the first lens L1, the negative power of the first lens group 33a can be increased, so that it is possible to suppress the image quality of the magnified image from being easily affected by heat.

[0175] In addition, since the negative power of the first lens group 33a can be increased, the first lens group 34 can be composed of a single lens. As a result, the first lens group 34 becomes lighter and is easier to move during focusing. Further, the power of the magnifying-side surface of the third lens L3 is smaller than that of the reducing-side surface of the third lens L3. Therefore, in the third lens L3, it is possible to suppress the aberration generated on the magnifying-side surface. As a result, it is possible to suppress the occurrence of astigmatism and the like during focusing.

[0176] Since the projection optical system 3C of this example satisfies the conditional expressions (1) to (3), (5), and (6), the same operational effects as those of the projection optical system 3A of the first embodiment can be obtained. In this example, the second lens group 32 includes six cemented lenses. Therefore, chromatic aberration can be corrected satisfactorily.

[0177] FIG. 17 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and the reference distance of the projection optical system 3C. FIG. 18 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and the reference distance of the projection optical system 3C. FIG. 19 is a diagram showing spherical aberration, astigmatism, and distortion. FIG. 19 shows the spherical aberration, astigmatism, and distortion of the projection optical system 3C at the wide-angle end and at a long distance. FIG. 20 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and at a long distance of the projection optical system 3C. 2 0 FIG. 21 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and at a long distance of the projection optical system 3C. FIG. 22 is a diagram showing spherical aberration, astigmatism, and distortion at the wide-angle end and at a short distance of the projection optical system 3C. FIG. 23 is a diagram showing spherical aberration, astigmatism, and distortion at the telephoto end and at a short distance of the projection optical system 3C. As shown in FIGS. 17 to 22, in the projection optical system 3C of this example, various aberrations in the enlarged image are suppressed.

[0178] (Embodiment 4)

[0179] FIG. 24 is a ray diagram of the projection optical system 3D of Embodiment 4. As shown in FIG. 24, the projection optical system 3D includes a first lens group 31 having a negative power and a second lens group 32 having a positive power, in order from the enlargement side to the reduction side. Further, the projection optical system 3D includes a diaphragm 41 disposed inside the second lens group 32. The diaphragm 41 is disposed at a position where the chief ray of the maximum angle of view intersects the optical axis N within the second lens group 32.

[0180] The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reduction side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reduction side of the first b lens group 34.

[0180] The first a lens group 33 consists of a first lens L1. The first lens L1 has a negative power near the optical axis N. The first lens L1 has a concave shape near the optical axis N on the enlargement-side surface and a convex shape at the peripheral portion. The first lens L1 has a convex shape near the optical axis N on the reduction-side surface and a concave shape at the peripheral portion. The first lens L1 has an aspherical shape on both surfaces.

[0181] The first lens group 34 consists of a second lens L2 and a third lens L3. The second lens L2 and the third lens L3 are arranged in this order from the magnification side toward the reduction side. The second lens L2 has a negative power. The second lens L2 is a meniscus lens. The second lens L2 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface. The third lens L3 has a negative power. The third lens L3 is a meniscus lens. The third lens L3 has a convex shape on the magnification-side surface and a concave shape on the reduction-side surface.

[0182] The first lens group 35 consists of a fourth lens L4 and a fifth lens L5. The fourth lens L4 and the fifth lens L5 are arranged in this order from the magnification side toward the reduction side. The fourth lens L4 and the fifth lens L5 are a cemented lens L21. The fourth lens L4 has a negative power. The fourth lens L4 has a concave shape on both the magnification-side and reduction-side surfaces. The fifth lens L5 has a positive power. The fifth lens L5 has a convex shape on both the magnification-side and reduction-side surfaces.

[0183] The second lens group 32 consists of 14 lenses from a sixth lens L6 to a nineteenth lens L19. The sixth lens L6 to the nineteenth lens L19 are arranged in this order from the magnification side toward the reduction side. The second lens group 32 is fixed. An aperture 41 is arranged between the eighth lens L8 and the ninth lens L9.

[0184] The sixth lens L6 has a positive power. The sixth lens L6 is a meniscus lens. The sixth lens L6 has a concave shape on the magnification-side surface and a convex shape on the reduction-side surface. The seventh lens L7 has a negative power. The seventh lens L7 is a meniscus lens. The seventh lens L7 has a concave shape on the magnification-side surface and a convex shape on the reduction-side surface. The sixth lens L6 and the seventh lens L7 are a cemented lens L22.

[0185] The eighth lens L8 has a positive power. The eighth lens L8 has a convex shape on both the magnification-side and reduction-side surfaces.

[0186] The ninth lens L9 has a negative power. The ninth lens L9 has a concave shape on both the magnifying side and the reducing side surfaces. The tenth lens L10 has a positive power. The tenth lens L10 has a convex shape on both the magnifying side and the reducing side surfaces. The ninth lens L9 and the tenth lens L10 are a joined lens L23.

[0187] The eleventh lens L11 has a negative power. The eleventh lens L11 has a concave shape on both the magnifying side and the reducing side surfaces. The eleventh lens L11 has an aspherical shape on both surfaces.

[0188] The twelfth lens L12 has a positive power. The twelfth lens L12 has a convex shape on both the magnifying side and the reducing side surfaces. The thirteenth lens L13 has a negative power. The thirteenth lens L13 has a concave shape on both the magnifying side and the reducing side surfaces. The fourteenth lens L14 has a positive power. The fourteenth lens L14 has a convex shape on both the magnifying side and the reducing side surfaces. The first lens L1 has a positive power. The first lens L1 2 The first lens L1 2 The first lens L1 3 The first lens L1 3 and the fourteenth lens L14 are a joined lens L24.

[0189] The fifteenth lens L15 has a negative power. The fifteenth lens L15 has a concave shape on both the magnifying side and the reducing side surfaces. The sixteenth lens L16 has a positive power. The sixteenth lens L16 has a convex shape on both the magnifying side and the reducing side surfaces. The fifteenth lens L15 and the sixteenth lens L16 are a joined lens L25.

[0190] The 17th lens L17 has a negative power. The 17th lens L17 is a meniscus lens. The 17th lens L17 has a convex shape on the magnifying side and a concave shape on the reducing side. The 18th lens L18 has a positive power. The 18th lens L18 has a convex shape on both the magnifying side and the reducing side. The 17th lens L17 and the 18th lens L18 are a combined lens L26 joined together.

[0191] The 19th lens L19 has a positive power. The 19th lens L19 has a convex shape on both the magnifying side and the reducing side.

[0192] The 1st lens L1 is made of resin. The 2nd lens L2 to the 19th lens L19 are made of glass.

[0193] In the projection optical system 3D, the reducing side from the 19th lens L19 of the 2nd lens group 32 is telecentric.

[0194] Here, the projection optical system 3D can change the projection distance. When changing the projection distance, the 1b lens group 34 and the 1c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0195] Let the F-number of the projection optical system 3D be FNo, the focal length of the entire system be F, the semi-field angle be ω, the back focus air equivalent value be BF, the focal length of the 1b lens group 34 be F1b, the focal length of the 1c lens group 35 be F1c, the combined focal length of the 1a lens group 33 and the 1b lens group 34 be F1ab, the focal length of the 1st lens group 31 be F1, and the focal length of the 2nd lens group 32 be F2. Then, the data of the projection optical system 3D is as follows.

[0196] FNo 1.9 F 7.540mm ω 60.7° BF 43.156mm F1b -20.429mm F1c 837.410mm F1ab -14.785mm F1 -17.355mm F2 40.190 mm

[0197] The lens data of the projection optical system 3D is as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, aperture dichroic prism, and liquid crystal panel. The data of the surface numbers that do not correspond to the screen, lens, aperture, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with * are aspherical surfaces. R is the radius of curvature. D is the axial surface interval. nd is the refractive index of the d-line. νd is the Abbe number of the d-line. The units of R and D are mm.

[0198] Sign Surface number R D nd vd S 0 Infinity Variable interval 1 L1 1* -34.584 5.000 1.53116 56.04 2* -68.772 Variable interval 2 L2 3 55.271 2.500 1.83481 42.72 4 26.388 8.742 L3 5 64.368 2.000 1.83481 42.72 6 19.757 Variable interval 3 L4 7 -56.430 1.500 1.72916 54.68 L5 8 25.000 12.000 1.69895 30.05 9 -51.078 Variable interval 4 L6 10 -118.104 9.000 1.80809 22.76 L7 11 -19.044 1.500 1.98612 16.48 12 -203.334 4.044 L8 13 243.448 6.345 1.69895 30.13 14 -33.370 16.326 41 15 Infinity 0.894 L9 16 -57.994 2.000 1.90043 37.37 L10 17 19.841 10.464 1.86966 20.02 18 -75.115 0.100 L11 19* 330.026 2.000 1.58913 61.15 20* 29.237 0.500 L12 21 25.613 7.782 1.72825 28.46 L13 22 -25.000 1.500 1.90043 37.37 L14 23 24.710 8.825 1.48749 70.24 24 -29.949 0.100 L15 25 -52.380 1.200 2.00069 25.46 L16 26 44.272 8.600 1.48749 70.24 27 -27.918 0.200 L17 28 74.624 1.200 2.00100 29.13 L18 29 34.572 8.901 1.49700 81.54 30 -56.314 0.200 L19 31 66.262 11.000 1.49700 81.54 32 -36.354 2.000 19 33 Infinity 39.600 1.51680 64.20 34 Infinity 15.084 18 35 Infinity

[0199] Here, the projection optical system 3D in this example can vary the projection distance among a reference distance, a short distance shorter than the reference distance, and a long distance longer than the reference distance. When the projection distance is varied, the first b lens group 34 and the first c lens group 35 are each moved in the direction of the optical axis N to perform focusing.

[0200] The relationships of variable interval 1, variable interval 2, variable interval 3, and variable interval 4 at each projection distance when focusing are shown below. Variable interval 1 is the projection distance. Variable interval 2 is the axial upper surface interval between the first lens L1 and the second lens L2. Variable interval 3 is the axial upper surface distance between the third lens L3 and the fourth lens L4. Variable interval 4 is the axial upper surface distance between the fifth lens L5 and the sixth lens L6.

[0201] Long distance, reference distance, short distance Variable interval 1 10900.000 1450.000 1000.000 Variable interval 2 17.102 17.456 17.491 Variable interval 3 12.818 14.177 14.512 Variable interval 4 4.088 2.375 2.005

[0202] The projection distance of the projection optical system 3D in this example is 10900.000 mm for the long distance and 1000.000 mm for the short distance. Therefore, the projection distance range of the projection optical system 3D is more than 10 times.

[0203] Each aspherical coefficient is as follows.

[0204] Surface number 1 2 Radius of curvature (R) -34.584 -68.772 Conic constant (K) -11.401 -100.000 Cubic coefficient (A) 2.34194E-04 1.30494E-04 Quartic coefficient (A) -1.13226E-06 7.91852E-06 Quintic coefficient (A) 8.87260E-08 -5.09293E-08 Sextic coefficient (A) -4.09380E-09 -2.35275E-09 Septimic coefficient (A) 6.74074E-11 -7.44043E-11 Octic coefficient (A) -1.32006E-12 4.30173E-12 Coefficient of the 9th power (A) 3.85785E-14 -1.56644E-13 Coefficient of the 10th power (A) -1.78515E-16 4.09438E-15 Coefficient of the 11th power (A) -1.69184E-17 -5.09345E-17 Coefficient of the 12th power (A) 3.87634E-19 2.11593E-19 Coefficient of the 13th power (A) -3.41106E-21 1.84565E-23 Coefficient of the 14th power (A) 1.16140E-23 2.86559E-24

[0205] Surface number 19 20 Radius of curvature (R) 330.026 29.237 Conic constant (K) 0.000 -11.363 Coefficient of the 4th power (A) -1.01832E-04 -4.16004E-05 Coefficient of the 6th power (A) 4.15400E-07 2.54288E-07 Coefficient of the 8th power (A) -1.02308E-09 -6.07846E-10 Coefficient of the 10th power (A) -1.11338E-12 -9.40986E-14 Coefficient of the 12th power (A) 1.48744E-14 4.12170E-15 Coefficient of the 14th power (A) 5.23764E-27 -5.15036E-21 Coefficient of the 16th power (A) 2.02623E-30 1.96665E-30

[0206] Here, for the projection optical system 3D in this example, assuming the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group 33 and the first b lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0207] In this example, F 7.540mm BF 43.156 mm Therefore, BF / F = 5.724, satisfying the conditional expression (1).

[0208] In this example, F 7.540 mm F1ab -14.785 mm Therefore, |F / F1ab| = 0.510, satisfying the conditional expression (2).

[0209] Also, the projection optical system 3D in this example does not include a moving group. Assuming the focal length of the first lens group 31 is F1 and the focal length of the second lens group 32 is F2, it satisfies the following conditional expression (4). 0.1 < |F1 / F2| < 0.5 (4)

[0210] In this example, F1 -17.355 mm F2 40.190 mm Therefore, |F1 / F2| = 0.432, satisfying the conditional expression (4).

[0211] Also, assuming the focal length of the entire lens system of the projection optical system 3D in this example is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, it satisfies all of the following conditional expressions (5) and (6). 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0212] In this example, F 7.540 mm F1b -20.429 mm Therefore, |F / F1b| = 0.369, satisfying the conditional expression (5).

[0213] In this example, F 7.540 mm F1c 837.410 mm Therefore, F / F1c = 0.009, satisfying the conditional expression (6).

[0214] Effect In the projection optical system 3D of this example, the total number of lenses of the first a lens group 33 and the first b lens group 34 is 3. Therefore, it is easy to suppress the weight of the end portion on the magnification side of the projection optical system 3D.

[0215] Also, in this example, since the first lens L1 of the first a lens group 33 is made of resin, its weight can be suppressed as compared with the case where the first lens L1 is made of glass. Here, when the first lens L1 is made of resin, the temperature coefficient of refractive index and the coefficient of linear expansion, which change the refractive index with temperature, become larger as compared with the case where the first lens L1 is made of glass. Therefore, the refractive index of the first lens L1 changes due to heat, and its shape is easily distorted. Thus, when the negative power of the first lens L1 is increased, the image quality of the magnified image is easily affected by heat. On the other hand, in this example, the first b lens group 34 consists of two negative lenses, and the first b lens group 34 compensates for the power of the first lens L1. Thereby, an increase in the negative power of the first lens L1 can be suppressed, so that it is possible to suppress the image quality of the magnified image from being easily affected by heat. In the first b lens group 34, since the second lens L2 and the third lens L3 are negative meniscus lenses, the occurrence of astigmatism and the like during focusing can be suppressed.

[0216] Also, in the projection optical system 3D of this example, the second lens group 32 is fixed in the direction of the optical axis N. Assuming that the focal length of the first lens group 31 is F1 and the focal length of the second lens group 32 is F2, the following conditional expression (4) is satisfied. 0.1 < |F1 / F2| < 0.5 (4)

[0217] Since the projection optical system 3D of this example satisfies the conditional expression (4), it is possible to sufficiently secure the back focus while suppressing the occurrence of various aberrations. That is, when the value of the conditional expression (4) exceeds the lower limit value, the focal length F1 of the first lens group 31 becomes shorter, and the negative power of the first lens group 31 becomes stronger. In this case, it is easy to secure the back focus, but since the radius of curvature of each lens constituting the first lens group 31 becomes smaller, coma aberration, magnification chromatic aberration, etc. are likely to occur in the region with a high image height of each lens. Also, when the negative power of the first lens group 31 becomes stronger, it is conceivable to increase the number of lens elements and reduce the power of each lens to suppress the occurrence of various aberrations, but since the number of lens elements increases, the cost increases. When the value of the conditional expression (4) exceeds the upper limit value, it becomes difficult to sufficiently secure the back focus.

[0218] Since the projection optical system 3D of this example satisfies the conditional expressions (1), (2), (5), and (6), the same operational effects as those of the projection optical system 3A of the first embodiment can be obtained. Also, in this example, the second lens group 32 includes five cemented lenses. Therefore, chromatic aberration can be corrected well.

[0219] FIG. 24 is a diagram showing spherical aberration, astigmatism, and distortion at the reference distance of the projection optical system 3D. FIG. 25 is a diagram showing spherical aberration, astigmatism, and distortion at a long distance of the projection optical system 3D. FIG. 26 is a diagram showing spherical aberration, astigmatism, and distortion at a short distance of the projection optical system 3D. As shown in FIGS. 24 to 26, various aberrations in the enlarged image of the projection optical system 3D of this example are suppressed.

[0220] (Embodiment 5) FIG. 27 is a ray diagram of the projection optical system 3E of Embodiment 5. As shown in FIG. 27, the projection optical system 3E has, in order from the magnifying side to the reducing side, a first lens group 31 having a negative power and a second lens group 32 having a positive power. Also, the projection optical system 3E includes a diaphragm 41 disposed inside the second lens group 32. The diaphragm 41 is disposed at a position where the chief ray of the maximum picture angle intersects the optical axis N within the second lens group 32.

[0221] The first lens group 31 includes a first a lens group 33 having a negative power, a first b lens group 34 having a negative power located on the reducing side of the first a lens group 33, and a first c lens group 35 having a positive power located on the reducing side of the first b lens group 34.

[0222] The first a lens group 33 consists of a first lens L1 and a second lens L2. The first lens L1 has a negative power near the optical axis N. The first lens L1 has a concave shape near the optical axis N on the magnifying side surface and a convex shape in the peripheral portion. The first lens L1 has a convex shape near the optical axis N on the reducing side surface and a concave shape in the peripheral portion. The first lens L1 has an aspherical shape on both surfaces. The second lens L2 has a negative power. The second lens L2 is a meniscus lens. The second lens L2 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface.

[0223] The first b lens group 34 consists of a third lens L3. The third lens L3 has a negative power. The third lens L3 is a meniscus lens. The third lens L3 has a convex shape on the magnifying side surface and a concave shape on the reducing side surface. The magnifying side surface of the third lens L3 has a smaller power than the reducing side surface of the third lens L3.

[0224] The first c lens group 35 consists of a fourth lens L4 and a fifth lens L5. The fourth lens L4 and the fifth lens L5 are arranged in this order from the magnifying side to the reducing side. The fourth lens L4 and the fifth lens L5 are a joined lens L21 joined together. The fourth lens L4 has a negative power. The fourth lens L4 has a concave shape on both the magnifying side and the reducing side surfaces. The fifth lens L5 has a positive power. The fifth lens L5 has a convex shape on both the magnifying side and the reducing side surfaces.

[0225] The second lens group 32 consists of 13 lenses from the sixth lens L6 to the eighteenth lens L18. The sixth lens L6 to the eighteenth lens L18 are arranged in this order from the magnification side to the reduction side. The second lens group 32 is fixed. An aperture 41 is arranged between the eighth lens L8 and the ninth lens L9.

[0226] The sixth lens L6 has a positive power. The sixth lens L6 has convex shapes on the magnification side and the reduction side surfaces. The seventh lens L7 has a negative power. The seventh lens L7 has concave shapes on the magnification side and the reduction side surfaces. The eighth lens L8 has a positive power. The eighth lens L8 has convex shapes on the magnification side and the reduction side surfaces. The sixth lens L6, the seventh lens L7, and the eighth lens L8 are a cemented lens L22.

[0227] The ninth lens L9 has a negative power. The ninth lens L9 has concave shapes on the magnification side and the reduction side surfaces. The tenth lens L10 has a positive power. The tenth lens L10 has convex shapes on the magnification side and the reduction side surfaces. The ninth lens L9 and the tenth lens L10 are a cemented lens L23.

[0228] The eleventh lens L11 has a negative power. The eleventh lens L11 is a meniscus lens. The eleventh lens L11 has a concave shape on the magnification side surface and a convex shape on the reduction side surface. The eleventh lens L11 has aspherical shapes on both surfaces.

[0229] The twelfth lens L12 has a positive power. The twelfth lens L12 has convex shapes on the magnification side and the reduction side surfaces. The thirteenth lens L13 has a negative power. The thirteenth lens L13 has concave shapes on the magnification side and the reduction side surfaces. The fourteenth lens L14 has a positive power. The fourteenth lens L14 has convex shapes on the magnification side and the reduction side surfaces. The first lens L1 and the first lens L1 2 lens L1 2 and the first lens L1 3 lens L1 3is the joined lens L24.

[0230] The 15th lens L15 has a negative power. The 15th lens L15 has a concave shape on both the magnifying side and the reducing side. The 16th lens L16 has a positive power. The 16th lens L16 has a convex shape on both the magnifying side and the reducing side. The 15th lens L15 and the 16th lens L16 are the joined lens L25.

[0231] The 17th lens L17 has a positive power. The 17th lens L17 is a meniscus lens. The 17th lens L17 has a concave shape on the magnifying side and a convex shape on the reducing side. The 18th lens L18 has a positive power. The 18th lens L18 has a convex shape on both the magnifying side and the reducing side.

[0232] The 1st lens L1 is made of resin. The 2nd lens L2 to the 18th lens L18 are made of glass.

[0233] In the projection optical system 3E, the side closer to the reduction side than the 18th lens L18 of the 2nd lens group 32 is telecentric.

[0234] Here, the projection optical system 3E can change the projection distance. When changing the projection distance, the 1b lens group 34 and the 1c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0235] Let the F-number of the projection optical system 3E be FNo, the focal length of the entire system be F, the semi-field angle be ω, the back focus air equivalent value be BF, the focal length of the 1b lens group 34 be F1b, the focal length of the 1c lens group 35 be F1c, the combined focal length of the 1a lens group 33 and the 1b lens group 34 be F1ab, the focal length of the 1st lens group 31 be F1, and the focal length of the 2nd lens group 32 be F2. Then, the data of the projection optical system 3E is as follows.

[0236] FNo 1.9 F 7.540mm ω 60.7° BF 43.201 mm F1b -20.960 mm F1c 198.610 mm F1ab -9.532 mm F1 -12.266 mm F2 55.827 mm

[0237] The lens data of the projection optical system 3E are as follows. The surface numbers are assigned in order from the magnifying side to the reducing side. The signs are the signs of the screen, lens, aperture, dichroic prism, and liquid crystal panel. The data for surface numbers that do not correspond to the screen, lens, aperture, dichroic prism, and liquid crystal panel are dummy data. The surfaces marked with an asterisk (*) in the surface number are aspherical. R is the radius of curvature. D is the axial surface interval. nd is the refractive index of the d-line. νd is the Abbe number of the d-line. The units of R and D are mm.

[0238] Sign Surface number R D nd vd S 0 Infinity Variable interval 1 L1 1* -29.011 5.000 1.5312 56.04 2* -70.875 17.779 L2 3 48.497 2.200 1.7292 54.68 4 25.386 Variable interval 2 L3 5 242.442 1.800 2.0010 29.13 6 19.366 Variable interval 3 L4 7 -152.549 1.500 1.7292 54.68 L5 8 33.587 6.500 1.7618 26.52 9 -89.211 Variable interval 4 L6 10 49.655 8.081 1.7408 27.79 L7 11 -24.544 1.500 1.9229 20.88 L8 12 62.765 6.200 1.6727 32.10 13 -32.915 14.770 41 14 Infinity 0.894 L9 15 -48.800 1.000 1.9004 37.37 L10 16 14.440 5.384 1.8697 20.02 17 -64.985 1.300 L11 18* -30.756 1.500 1.9515 29.83 19* -60.415 0.200 L12 20 42.102 6.000 1.5163 64.14 L13 21 -25.000 1.500 1.9004 37.37 22 177.303 0.500 L14 23 84.819 6.938 1.4875 70.24 24 -22.790 0.100 L15 25 -53.681 1.200 2.0007 25.46 L16 26 38.030 8.600 1.4875 70.24 27 -31.043 0.200 L17 28 -1132.273 4.603 1.4970 81.54 29 -47.659 0.200 L18 30 113.148 9.400 1.4970 81.54 31 -34.806 2.000 19 32 Infinity 39.600 1.5168 64.20 33 Infinity 15.128 18 34 Infinity

[0239] Here, the projection optical system 3E of this example can change the projection distance among a reference distance, a short distance shorter than the reference distance, and a long distance longer than the reference distance. When the projection distance is changed, the first b lens group 34 and the first c lens group 35 are each moved in the direction of the optical axis N for focusing.

[0240] The relationships among variable interval 1, variable interval 2, variable interval 3, and variable interval 4 at each projection distance when focusing are shown below. Variable interval 1 is the projection distance. Variable interval 2 is the axial upper surface interval between the second lens L2 and the third lens L3. Variable interval 3 is the axial upper surface distance between the third lens L3 and the fourth lens L4. Variable interval 4 is the axial upper surface distance between the fifth lens L5 and the sixth lens L6.

[0241] Long distance, reference distance, short distance Variable interval 1 10900.000 1450.000 1000.000 Variable interval 2 13.521 13.775 13.789 Variable interval 3 20.844 21.359 21.005 Variable interval 4 2.847 2.112 2.000

[0242] The projection distance of the projection optical system 3E in this example is 10900.000 mm for the long distance and 1000.000 mm for the short distance. Therefore, the projection distance range of the projection optical system 3E is more than 10 times.

[0243] Each aspherical coefficient is as follows.

[0244] Surface number 1 2 Radius of curvature (R) -29.011 -70.875 Conic constant (K) -9.778 -100.000 Cubic coefficient (A) 3.13999E-04 2.70566E-04 Quartic coefficient (A) -2.60295E-06 7.38868E-06 Quintic coefficient (A) 6.22622E-08 -8.18659E-08 Sextic coefficient (A) -3.32841E-09 -2.49448E-09 Septimic coefficient (A) 6.25208E-11 -7.29705E-11 Octic coefficient (A) -1.18690E-12 4.34518E-12 Coefficient of 9th order (A) 3.67034E-14 -1.56396E-13 Coefficient of 10th order (A) -2.01958E-16 4.09740E-15 Coefficient of 11th order (A) -1.67819E-17 -5.09700E-17 Coefficient of 12th order (A) 3.93865E-19 2.11578E-19 Coefficient of 13th order (A) -3.34928E-21 1.11805E-23 Coefficient of 14th order (A) 1.00736E-23 2.56762E-24

[0245] Surface number 18 19 Radius of curvature (R) -30.756 -60.415 Conic constant (K) -16.228 0.000 Coefficient of 4th order (A) 4.67542E-05 1.19021E-04 Coefficient of 6th order (A) -5.58071E-07 -7.83004E-07 Coefficient of 8th order (A) 1.42005E-09 1.86419E-09 Coefficient of 10th order (A) 1.86501E-12 5.52550E-12 Coefficient of 12th order (A) -2.59878E-14 -3.43530E-14 Coefficient of 14th order (A) 2.76945E-17 -1.43094E-17 Coefficient of 16th order (A) 3.10888E-20 -2.04785E-30

[0246] Also, for the projection optical system 3E in this example, assuming the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group 33 and the first b lens group 34 is F1ab, the following conditional expressions (1) and (2) are all satisfied. BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2)

[0247] In this example, F 7.540mm BF is 43.201 mm Therefore, BF / F = 5.730, satisfying the conditional expression (1).

[0248] In this example F is 7.540 mm F1ab is -9.532 mm Therefore, |F / F1ab| = 0.791, satisfying the conditional expression (2).

[0249] Also, for the projection optical system 3E in this example, when the focal length of the first lens group 31 is F1 and the focal length of the second lens group 32 is F2, the following conditional expression (4) is satisfied. 0.1 < |F1 / F2| < 0.5 (4)

[0250] In this example F1 is -12.266 mm F2 is 55.827 mm Therefore, |F1 / F2| = 0.220, satisfying the conditional expression (4).

[0251] Here, for the projection optical system 3E in this example, when the focal length of the entire lens system is F, the focal length of the first b lens group 34 is F1b, and the focal length of the first c lens group 35 is F1c, the following conditional expressions (5) and (6) are all satisfied. 0.2 < |F / F1b| < 0.6 (5) 0.0 < F / F1c < 0.14 (6)

[0252] In this example F is 7.540 mm F1b is -20.960 mm Therefore, |F / F1b| = 0.360, satisfying the conditional expression (5).

[0253] In this example F is 7.540 mm F1c is 198.610 mm Therefore, F / F1c = 0.038, satisfying the conditional expression (6).

[0254] (Effect) In the projection optical system 3E of this example, the total number of lenses of the first a lens group 33 and the first b lens group 34 is three. Therefore, it is easy to suppress the weight of the end portion on the magnification side of the projection optical system 3E.

[0255] Also, in this example, since the first lens L1 of the first a lens group 33 is made of resin, its weight can be suppressed as compared with the case where the first lens L1 is made of glass. Here, when the first lens L1 is made of resin, the temperature coefficient of refractive index and the linear expansion coefficient, in which the refractive index changes with temperature, become larger than those in the case where the first lens L1 is made of glass. Therefore, while the refractive index of the first lens L1 changes due to heat, its shape is likely to be distorted. Thus, when the negative power of the first lens L1 is increased, the image quality of the magnified image is likely to be affected by heat. On the other hand, in this example, the first a lens group 33 is composed of two lenses, the first lens L1 and the second lens L2. Therefore, the power of the first a lens group 33 can be borne by the two lenses, the first lens L1 and the second lens L2. Thus, while suppressing an increase in the negative power of the first lens L1, the negative power of the first a lens group 33 can be increased, so that it is possible to suppress the image quality of the magnified image from being easily affected by heat.

[0256] Also, since the negative power of the first a lens group 33 can be increased, the first b lens group 34 can be a single lens. As a result, the first b lens group 34 becomes lighter and is easier to move during focusing. Also, the power of the magnification-side surface of the third lens L3 is smaller than that of the reduction-side surface of the third lens L3. Therefore, in the third lens L3, it is possible to suppress the aberration generated on the magnification-side surface. As a result, it is possible to suppress the occurrence of astigmatism and the like during focusing.

[0257] Since the projection optical system 3E of this example satisfies the conditional expressions (1), (2), (5), and (6), the same operational effects as those of the projection optical system 3A of Example 1 can be obtained. Further, since the projection optical system 3E of this example satisfies the conditional expression (4), the same operational effects as those of the projection optical system 3D of Example 4 can be obtained. Further, in this example, the second lens group 32 includes four cemented lenses. Therefore, chromatic aberration can be corrected well.

[0258] FIG. 28 is a diagram showing spherical aberration, astigmatism, and distortion at the reference distance of the projection optical system 3E. FIG. 29 is a diagram showing spherical aberration, astigmatism, and distortion at a long distance of the projection optical system 3E. FIG. 30 is a diagram showing spherical aberration, astigmatism, and distortion at a short distance of the projection optical system 3E. As shown in FIGS. 28 to 30, various aberrations in the enlarged image of the projection optical system 3E of this example are suppressed.

Explanation of Signs

[0259] 1... projector, 2... image forming unit, 3, 3A, 3B, 3C, 3D, 3E... projection optical system, 4... control unit, 6... image processing unit, 7... display driving unit, 10... light source, 11... integrator lens, 12... integrator lens, 13... polarization conversion element, 14... superimposing lens, 15... dichroic mirror, 16... reflection 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... reflection mirror, 24... relay lens, 25... reflection mirror, 31... first lens group, 32... second lens group, 33... first a lens group, 34... first b lens group, 35... first c lens group, 36... second a lens group, 37... second b lens group, 38... second c lens group, 39... second c lens group, 41... aperture stop, L1 to L20... lenses, L21 to L27... cemented lenses, N... optical axis, S... screen.

Claims

1. A first lens group having a negative power, a second lens group having a positive power, and a third lens group having a negative power, arranged in order from the enlargement side to the reduction side, and the reduction side of the second lens group is telecentric, the first lens group consists of a first a lens group having a negative power, a first b lens group having a negative power located on the reduction side of the first a lens group, and a first c lens group having a positive power located on the reduction side of the first b lens group, the first a lens group consists only of lenses having a negative power, the first b lens group consists only of lenses having a negative power, among the first a lens group, the first lens located on the most enlargement side has an aspherical shape on both surfaces, the total number of lenses obtained by adding the number of lenses in the first a lens group and the number of lenses in the first b lens group is 3 or less, the first b lens group and the first c lens group move in the optical axis direction respectively during focusing, when the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group and the first b lens group is F1ab, the following conditional expressions (1) and (2) are all satisfied, BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) the first a lens group consists of the first lens and a second lens located on the reduction side of the first lens, the first lens is made of resin, the second lens has a negative power and is a meniscus lens having a convex shape on the enlargement side surface, and the following conditions are satisfied: BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) the first a lens group consists of the first lens and a second lens located on the reduction side of the first lens, the first lens is made of resin, the second lens has a negative power and is a meniscus lens having a convex shape on the enlargement side surface, and the following conditions are satisfied: BF / F > 5.0 (1) The first lens group 1b consists of a third lens, The third lens has a negative power and has a concave shape on the reducing side surface, The power of the enlarging side surface of the third lens is less than that of the reducing side surface of the third lens, and a projection optical system characterized by this.

2. A projection optical system comprising, in order from the enlarging side to the reducing side, a first lens group having a negative power and a second lens group having a positive power, The reducing side of the second lens group is telecentric, The first lens group consists of a first lens group 1a having a negative power, a first lens group 1b having a negative power located on the reducing side of the first lens group 1a, and a first lens group 1c having a positive power located on the reducing side of the first lens group 1b, The first lens group 1a consists only of lenses having a negative power, The first lens group 1b consists only of lenses having a negative power, Among the first lens group 1a, the first lens located on the most enlarging side has an aspherical shape on both surfaces, The total number of lenses obtained by adding the number of lenses in the first lens group 1a and the number of lenses in the first lens group 1b is 3 or less, The first lens group 1b and the first lens group 1c move in the direction of the optical axis during focusing, When the focal length of the entire lens system is F, the air-converted length of the back focus is BF, and the combined focal length of the first lens group 1a and the first lens group 1b is F1ab, the following conditional expressions (1) and (2) are all satisfied, BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) When the position where the chief ray with the maximum picture angle intersects the optical axis within the second lens group is taken as the aperture stop, the second lens group includes a second a lens group and a second b lens group located on the magnification side of the aperture stop, and the second a lens group is located on the magnification side of the second b lens group, and the second a lens group and the second b lens group move in the optical axis direction respectively during zooming, characterizing the projection optical system.

3. The second a lens group has a negative power and is located on the most magnification side of the second lens group, and the second b lens group has a positive power, characterizing the projection optical system according to claim 2.

4. If the focal length of the second a lens group is F2a and the focal length of the second b lens group is F2b, the projection optical system according to claim 3 is characterized by satisfying the following conditional expression (3). 1.0 < |F2a / F2b| < 4.0 (3)

5. In order from the magnification side to the reduction side, it consists of a first lens group having a negative power and a second lens group having a positive power, and the reduction side of the second lens group is telecentric, the first lens group consists of a first a lens group having a negative power, a first b lens group having a negative power located on the reduction side of the first a lens group, and a first c lens group having a positive power located on the reduction side of the first b lens group, the first a lens group consists of only lenses having a negative power, the first b lens group consists of only lenses having a negative power, among the first a lens group, the first lens located on the most magnification side has aspherical shapes on both surfaces, and The total number of lenses obtained by summing the number of lenses in the first a lens group and the number of lenses in the first b lens group is three or less, the first b lens group and the first c lens group each move in the direction of the optical axis during focusing, and assuming that the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group and the first b lens group is F1ab, the following conditional expressions (1) and (2) are all satisfied, BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) The second lens group does not include a moving group and is fixed. Assuming that the focal length of the first lens group is F1 and the focal length of the second lens group is F2, a projection optical system characterized by satisfying the following conditional expression (4). 0.1 < |F1 / F2| < 0.5 (4)

6. A projection optical system comprising, in order from the enlargement side to the reduction side, a first lens group having a negative power and a second lens group having a positive power, and on the reduction side of the second lens group is telecentric, the first lens group includes a first a lens group having a negative power, a first b lens group having a negative power located on the reduction side of the first a lens group, and a first c lens group having a positive power located on the reduction side of the first b lens group, the first a lens group consists only of lenses having a negative power, the first b lens group consists only of lenses having a negative power, among the first a lens group, the first lens located on the most enlargement side has an aspherical shape on both surfaces, and The total number of lenses obtained by adding the number of lenses in the first a lens group and the number of lenses in the first b lens group is 3 or less, the first b lens group and the first c lens group each move in the optical axis direction during focusing, and assuming that the focal length of the entire lens system is F, the air-equivalent length of the back focus is BF, and the combined focal length of the first a lens group and the first b lens group is F1ab, the following conditional expressions (1) and (2) are all satisfied, BF / F > 5.0 (1) 0.3 < |F / F1ab| < 1.0 (2) The first a lens group consists of the first lens, the first b lens group consists of a second lens and a third lens located on the reduced side of the second lens, the first lens is made of resin, the second lens has a negative power and is a meniscus lens having a convex shape on the enlarged side surface, the third lens has a negative power and has a concave shape on the reduced side surface, when the position where the chief ray having the maximum angle of view in the second lens group intersects the optical axis is defined as the aperture stop, the second lens group includes a second a lens group and a second b lens group located on the enlarged side of the aperture stop, the second a lens group is located on the enlarged side of the second b lens group, the second a lens group and the second b lens group each move in the optical axis direction during zooming, and characterized in that it is a projection optical system.

7. The projection optical system according to any one of claims 1 to 6, characterized in that the second lens group includes four cemented lenses.

8. ​ An optical modulation element that modulates light emitted from a light source, and a projection optical system according to any one of claims 1 to 7 that projects the light modulated by the optical modulation element, wherein the projection optical system is provided. A projector characterized by comprising the above.

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