Projection optical system and image projecting apparatus
09625692 ยท 2017-04-18
Assignee
Inventors
Cpc classification
International classification
Abstract
Disclosed is a projection optical system including a first optical system configured to form a first image conjugate to an object and have an optical axis and a second optical system configured to project a second image conjugate to the first image onto a surface to be projected on, wherein the first image satisfies a condition of:
ImTr1.70
wherein Im denotes a length of the first image in a direction of an optical axis of the first optical system, normalized by a focal length of the first optical system, and Tr denotes a throw ratio for the projection optical system.
Claims
1. A projection optical system, comprising: a first optical system configured to form a first image conjugate to an object and have an optical axis; and a second optical system configured to project a second image conjugate to the first image onto a surface to be projected on, the surface extending in a horizontal direction and a vertical direction perpendicular to the horizontal direction, wherein the first image satisfies a condition of:
0.78ImTr0.90,
4.55Im, and
Tr0.18, wherein Im denotes a length of the first image in a direction of an optical axis of the first optical system, normalized by a focal length of the first optical system; and Tr denotes a throw ratio for the projection optical system, wherein a TV distortion in the second image is less than or equal to 3%, wherein the second optical system includes a single mirror with a refractive power, wherein the horizontal direction and the vertical direction are normal to the first optical system, and wherein the throw ratio Tr is a ratio of a projection distance of the projection optical system to a length of the second image in the horizontal direction.
2. The projection optical system as claimed in claim 1, wherein the second optical system includes a reflection surface with a free-form surface shape.
3. An image projecting apparatus comprising: an image forming part configured to form an image; and a projection optical system configured to project the image onto a surface to be projected on, wherein the projection optical system is the projection optical system as claimed in claim 1.
4. A projection optical system, comprising: a first optical system configured to form a first image conjugate to an object and have an optical axis; and a second optical system configured to project a second image conjugate to the first image onto a surface to be projected on, the surface extending in a horizontal direction and a vertical direction perpendicular to the horizontal direction, the second optical system including a single mirror with a reflection surface having a rotationally asymmetric aspheric surface, wherein the first image satisfies a condition of:
0.78ImTr0.90,
4.55Im, and
Tr0.18, wherein Im denotes a length of the first image in a direction of an optical axis of the first optical system, normalized by a focal length of the first optical system; and Tr denotes a throw ratio for the projection optical system, and wherein a TV distortion in the second image is less than or equal to 3%, wherein the horizontal direction and the vertical direction are normal to the first optical system, and wherein the throw ratio Tr is a ratio of a projection distance of the projection optical system to a length of the second image in the horizontal direction.
5. The projection optical system as claimed in claim 4, wherein the reflection surface of the second optical system has a free-form surface shape.
6. The projection optical system as claimed in claim 5, wherein the reflection surface is adjusted for each light beam corresponding to an image point for the first image.
7. The projection optical system as claimed in claim 5, wherein the reflection surface is adjusted to conduct aberration correction for each light beam corresponding to an image point for the first image.
8. An image projecting apparatus comprising: an image forming part configured to form an image; and a projection optical system configured to project the image onto a surface to be projected on, wherein the projection optical system is the projection optical system as claimed in claim 4.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
(54) Next, a mode(s) for implementing the present invention (an embodiment(s) of the present invention) will be described with reference to the accompanying drawing(s).
(55) A first embodiment of the present invention is a projection optical system including a first optical system which forms a first image conjugate to an object and has an optical axis and a second optical system which projects a second image conjugate to the first image onto a surface to be projected on, wherein the first image satisfies a condition of ImTr1.70, wherein Im denotes a length of the first image in a direction of an optical axis of the first optical system which is normalized by a focal length of the first optical system and Tr denotes a throw ratio for the projection optical system.
(56) In a projection optical system according to the first embodiment of the present invention, a first image is conjugate to an object and a second image is conjugate to the first image. Thereby, the second image is conjugate to the object. The second image may be referred to as an image conjugate to an object, and in this case, a first image may be referred to as an intermediate image between the object and the image (second image). In a projection optical system according to the first embodiment of the present invention, each of a first image and a second image may include aberration or not include aberration.
(57) In a projection optical system according to the first embodiment of the present invention, a surface to be projected on is a surface onto which a second image conjugate to a first image is projected. Herein, a surface to be projected on may be, for example, a flat surface or screen.
(58) In a projection optical system according to the first embodiment of the present invention, to project includes to conduct enlargement and projection, to conduct projection at a same magnification, or to conduct reduction and projection, and preferably is to conduct enlargement and projection. When to project is to conduct enlargement and projection in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of enlarging and projecting an image onto a surface to be projected on.
(59) A projection optical system according to the first embodiment of the present invention includes a first optical system which forms a first image conjugate to an object and has an optical axis and a second optical axis which forms a second image conjugate to the first image onto a surface to be projected on. In an optical path for a projection optical system according to the first embodiment of the present invention, for example, an object, a first optical system, a first image, a second optical system, and a second image may be arranged in order.
(60) In a projection optical system according to the first embodiment of the present invention, a first optical system is an optical system which forms a first image conjugate to an object and has an optical axis. Herein, a first optical system, for example, includes a refractive optical system which forms a first image conjugate to an object and has an optical axis. A refractive optical system is, for example, a lens system. The number of lenses included in a lens system is not particularly limited. A shape of a surface composing a lens included in a lens system is not particularly limited. A shape of a surface composing a lens may be a spherical surface or an aspheric surface. An aspheric surface may be a rotationally symmetric aspheric surface. A refractive optical system preferably has a positive power. When a refractive optical system has a positive power, a first image is a real image.
(61) In a projection optical system according to the first embodiment of the present invention, a second optical system is an optical system which projects a second image conjugate to a first image onto a surface to be projected on. Herein, a second optical system, for example, includes a reflection optical system which projects and reflects a second image conjugate to a first image onto a surface to be projected on. A reflection optical system is, for example, a mirror system. The number of mirrors included in a mirror system is not particularly limited. A shape of a surface composing a mirror included in a mirror system is not particularly limited. A shape of a surface composing a mirror may be a spherical surface or an aspheric surface. An aspheric surface may be a rotationally symmetric aspheric surface or a free-form surface. A free-form surface may be a rotationally asymmetric aspheric surface. A reflection optical system preferably has a positive power. When a reflection optical system has a positive power, a second image is a real image.
(62) In a projection optical system according to the first embodiment of the present invention, a first image satisfies a condition of ImTr1.70.
(63) In a projection optical system according to the first embodiment of the present invention, Im denotes a length of a first image in a direction of an optical axis of a first optical system which is normalized by a focal length of the first optical system (a length of a first image in a direction of an optical axis of a first optical system/a focal length of the first optical system). A length of a first image in a direction of an optical axis of a first optical system is a distance between a position of an image point nearest the first optical system in a direction of the optical axis of the first optical system and a position of an image point nearest a second optical system in a direction of the optical axis of the first optical system among image points for the first image which are provided by a meridional light ray and a sagittal light ray from an object point for an object.
(64) In a projection optical system according to the first embodiment of the present invention, Tr denotes a throw ratio for the projection optical system. A throw ratio is a ratio of a distance from a principal point of a second optical system at a surface-to-be-projected-on side to the surface to be projected on to a size of a second image projected on the surface to be projected on in a horizontal direction.
(65) According to the first embodiment of the present invention, it may be possible to provide a more compact projection optical system capable of projecting a better image onto a surface to be projected on at a shorter distance, because a first image satisfies a condition of ImTr1.70, wherein Im denotes a length of the first image in a direction of an optical axis of a first optical system which is normalized by a focal length of the first optical system and Tr denotes a throw ratio of a projection optical system. For example, it may be possible to provide a projection optical system with a further reduced total length. A total length of a projection optical system is a distance from an object point for an object to a last end of a second optical system in a direction of an optical axis of a first optical system with respect to a principal light ray of a light beam nearest the optical axis of the first optical system included in the projection optical system.
(66) In a projection optical system according to the first embodiment of the present invention, a first image preferably satisfies a condition of ImTr1.50.
(67) When a first image satisfies a condition of ImTr1.50 in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a more compact projection optical system.
(68) In a projection optical system according to the first embodiment of the present invention, a first image preferably satisfies a condition of 0.50ImTr.
(69) When a first image satisfies a condition of 0.50ImTr in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on.
(70) In a projection optical system according to the first embodiment of the present invention, the projection optical system preferably satisfies a condition of Tr0.7.
(71) When a projection optical system satisfies a condition of Tr0.7 in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of projecting an image onto a surface to be projected on at a shorter distance.
(72) In a projection optical system according to the first embodiment of the present invention, a first optical system preferably includes an aspheric surface.
(73) When a first optical system includes an aspheric surface in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on.
(74) In a projection optical system according to the first embodiment of the present invention, a Petzval sum for a first optical system is preferably less than or equal to 0.010 mm.sup.1.
(75) When a Petzval sum for a first optical system is less than or equal to 0.010 mm.sup.1 in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on. A Petzval sum for a first optical system is more preferably less than or equal to 0.012 mm.sup.1. When a Petzval sum for a first optical system is less than or equal to 0.012 mm.sup.1, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on. A Petzval sum for a first optical system is preferably greater than or equal to 0.037 mm.sup.1. When a Petzval sum for a first optical system is greater than or equal to 0.037 mm.sup.1, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on.
(76) In a projection optical system according to the first embodiment of the present invention, a second optical system preferably includes a reflection surface with a free-form surface shape. When a second optical system includes a reflection surface with a free-form surface shape in a projection optical system according to the first embodiment of the present invention, it may be possible to provide a projection optical system capable of projecting a better image onto a surface to be projected on.
(77) A second embodiment of the present invention is an image projecting apparatus including an image forming part which forms an image and a projection optical system which projects an image onto a surface to be projected on, wherein the projection optical system is a projection optical system according to the first embodiment of the present invention.
(78) In an image projecting apparatus according to the second embodiment of the present invention, an image forming part which forms an image is not particularly limited. Herein, an image forming part may be, for example, a displaying device (light valve) such as a transmission-type or reflection-type dot matrix liquid crystal or a digital micro-mirror device (DMD).
(79) In an image projecting apparatus according to the second embodiment of the present invention, an image is not particularly limited. Herein, an image may be, for example, an image displayed on a displaying device as described above.
(80) In an image projecting apparatus according to the second embodiment of the present invention, a surface to be projected on is not particularly limited. Herein, a surface to be projected on may be, for example, a flat surface or screen.
(81) In an image projecting apparatus according to the second embodiment of the present invention, to project includes to conduct enlargement and projection, to conduct projection at a same magnification, or to conduct reduction and projection, and preferably is to conduct enlargement and projection. When to project is to conduct enlargement and projection in an image projecting apparatus according to the second embodiment of the present invention, it may be possible to provide an image projecting apparatus capable of enlarging and projecting an image onto a surface to be projected on.
(82) According to the second embodiment of the present invention, it may be possible to provide a more compact image projecting apparatus capable of projecting a better image onto a surface to be projected on at a shorter distance, because a projection optical system is a projection optical system according to the first embodiment of the present invention.
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(84) A projector as an image projecting apparatus illustrated in
(85) The projection optical system illustrated in
(86) Additionally, X, Y, and Z for a coordinate system in
(87) If a projection distance of a projection optical system increases, an image to be projected may be blocked by a presenter standing between a projector and the screen 4 for presentation, etc., or a shade of a presenter standing between a projector and the screen 4 for presentation, etc., may be projected onto the screen 4.
(88) A throw ratio is used as a parameter for indicting a projection distance of a projection optical system and an enlargement factor of a projection optical system in a projector. A throw ratio is a ratio of a size of an image projected on a screen in a horizontal direction (a width of an image projected on a screen) to a projection distance of a projection optical system. In the projection optical system illustrated in
(89)
(90) As illustrated in
(91) As illustrated in
(92) In the projection optical system illustrated in
(93) A value Im of a length of an intermediate image in a Z-direction divided by a focal length of the first optical system 2 tends to increase when a throw ratio for a projection optical system included in a projector is reduced.
(94)
(95) As illustrated in
(96) In the projection optical system illustrated in
(97) When a throw ratio Tr for a projection optical system included in a projector is reduced, an angle of incidence of a light ray to be projected onto the screen 4 tends to increase. When an angle of incidence of a light ray to be projected onto the screen 4 increases, an astigmatic aberration for a projection optical system tends to increase. When a distance from an optical axis of the first optical system 2 in a direction of a transverse axis of the screen 4 increases (increases in a +Y-direction), an angle of incidence of a light ray incident on the screen 4 tends to increase. For example, when a projection distance of a projection optical system included in a projector is reduced, an angle of incidence of a light ray incident on the screen tends to increase, and when a distance from an optical axis of the first optical system 2 increases in a +Y-direction, an increase in an angle of incidence of a light ray incident on the screen 4 tends to be more significant and an astigmatic aberration for the projection optical system tends to increase.
(98) Then, a value Im of a length of an intermediate image in a Z-direction divided by a focal length of the first optical system 2 is increased in a projection optical system illustrated in
(99) As illustrated in
(100) Thus, in the projection optical system illustrated in
(101) Hence, in a projection optical system including the first optical system 2 which forms an intermediate image conjugate to an image formed on the image forming part 1 and has an optical axis and the second optical system 3 which projects an image conjugate to the intermediate image onto the screen 4, the intermediate image satisfies a condition of ImTr1.70, whereby it may be possible to provide a more compact projection optical system capable of projecting a better image onto the screen 4 at a shorter distance or a more compact image projecting apparatus capable of projecting a better image onto the screen 4 at a shorter distance.
(102) In the projection optical system illustrated in
(103) In the projection optical system illustrated in
(104) In the projection optical system illustrated in
(105) In the projection optical system illustrated in
(106) In the projection optical system illustrated in
PRACTICAL EXAMPLES
(107) In each practical example according to an embodiment of the present invention, a size, aspect ratio, and enlargement factor of an image to be projected onto a screen are 0.64 inches, 16:10, and 94, respectively. Herein, an enlargement factor is an approximate ratio of a size of an image projected on a screen to a size of an image formed on an image forming part. Furthermore, practical examples 1-7, 10, and 11 are examples of a projection optical system with F2.5 while practical examples 8 and 9 are examples of a projection optical system with F4.
Practical Example 1
(108) Table 1 illustrates the data of a projection optical system in practical example 1.
(109) TABLE-US-00001 TABLE 1 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 20.55 4.27 1.51 63.90 1.33 SURFACE 4 ASPHERIC 41.49 0.10 SURFACE STOP SPHERE 0.10 6 SPHERE 72.85 1.00 1.84 40.06 7 SPHERE 12.34 7.48 1.49 70.44 8 SPHERE 18.76 0.10 9 SPHERE 21.86 3.52 1.77 35.62 10 SPHERE 115.34 0.10 11 SPHERE 30.65 6.00 1.58 41.19 12 SPHERE 13.07 1.30 1.83 43.06 13 SPHERE 28.60 0.10 14 SPHERE 295.75 5.79 1.61 60.99 15 SPHERE 32.44 8.41 16 SPHERE 17.34 5.13 1.70 29.10 17 SPHERE 46.19 2.00 18 SPHERE 28.23 4.25 1.84 27.35 19 SPHERE 15.76 4.70 20 ASPHERIC 16.05 1.35 1.53 55.80 SURFACE 21 ASPHERIC 228.23 6.10 SURFACE 22 ASPHERIC 41.02 5.20 1.53 55.80 SURFACE 23 ASPHERIC 17.59 0.10 SURFACE 24 SPHERE 90.00 25 xy- 92.08 170.11 REFLECTION 70.15 56.16 POLYNOMIAL SURFACE 26 SPHERE 0.00
(110) In Table 1, a shift indicates an amount of shift decentering in a y-direction and a tilt indicates an amount of tilt decentering about an x-axis as an axis of rotation. In Table 1, the units of a radius of curvature, a surface distance, and an amount of shift decentering are mm and the unit of an amount of tilt decentering is degrees. Furthermore, with respect to signs for a shift and a tilt in Table 1, a shift in a positive direction in a direction of a Y-axis has a + sign and a tilt in a counterclockwise rotation about an X-axis has a + sign. The definitions and units of a shift and a tilt and the units of a radius of curvature, a surface distance, and an amount of shift decentering in any of practical examples 2-11 are similar to those in practical example 1.
(111) Aspheric surfaces used for a third surface, a fourth surface, and twentieth to twenty-third surfaces of a projection optical system in practical example 1 are rotationally symmetric aspheric surfaces. A rotationally asymmetric aspheric surface may be used instead of a rotationally symmetric aspheric surface.
(112) A rotationally symmetric aspheric surface is an aspheric surface represented by a formula of:
Z=c.Math.r.sup.2/[1+{square root over ( )}{1(1+k)c.sup.2r.sup.2}]+Ar.sup.4+Br.sup.6+Cr.sup.8+ . . . Z denotes a depth of a rotationally symmetric aspheric surface in a direction of an optical axis thereof. c denotes a paraxial radius of curvature of a rotationally symmetric aspheric surface. r denotes a distance from an optical axis in a direction orthogonal to the optical axis. k denotes a cone coefficient or constant of a rotationally symmetric aspheric surface. A, B, C, . . . , etc., denote higher-order aspheric surface coefficients of a rotationally symmetric aspheric surface. A shape of a rotationally symmetric aspheric surface is specified by determining values of c, k, A, B, C, . . . , etc. The definition of a rotationally symmetric aspheric surface in any of practical examples 2-11 is also similar to that of practical example 1. When an aspheric surface lens is used for a first optical system, a freedom of design of a first optical system may be higher, and hence, a quality of an image projected on a screen may be improved.
(113) Table 2 illustrates coefficients of an aspheric surface for a projection optical system in practical example 1.
(114) TABLE-US-00002 TABLE 2 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 3.67E05 4.19E05 1.30E04 8.27E06 1.15E04 3.64E05 COEFFICIENT (A) 6th ORDER 3.18E09 1.38E08 3.81E06 1.19E06 5.72E07 6.30E07 COEFFICIENT (B) 8th ORDER 5.57E10 1.22E10 1.16E07 1.35E08 6.91E09 1.08E08 COEFFICIENT (C) 10th ORDER 1.25E12 2.75E11 2.45E09 1.86E10 2.88E13 1.40E10 COEFFICIENT (D) 12th ORDER 2.90E14 6.12E13 2.76E11 1.14E12 7.37E14 1.11E12 COEFFICIENT (E) 14th ORDER 1.05E15 5.38E15 1.53E13 5.19E16 6.28E16 4.49E15 COEFFICIENT (F) 16th ORDER 1.11E17 1.33E17 3.20E16 1.96E17 3.92E18 7.14E18 COEFFICIENT (G)
(115) A reflection surface in practical example 1 is an anamorphic polynomial free-form surface. When a reflection surface having a positive power in a second optical system is an anamorphic polynomial free-form surface, is may be possible to adjust a shape of a reflection for each light, beam corresponding to an image point of an intermediate image, and hence, it may be possible to improve a performance of aberration correction for a projection optical system. An anamorphic polynomial free-form surface is a surface represented by a formula of:
Z=X2.Math.x.sup.2+Y2.Math.y.sup.2+X2Y.Math.x.sup.2y+Y3.Math.y.sup.3+X4.Math.x.sup.4+X2Y2.Math.x.sup.2y.sup.2+Y4.Math.y.sup.4+X4Y.Math.x.sup.4y+X2Y3.Math.x.sup.2y.sup.3+Y5.Math.y.sup.5+X6.Math.x.sup.6+X4Y2.Math.x.sup.4y.sup.2+X2Y4.Math.x.sup.2y.sup.4+Y6.Math.y.sup.6+ . . . (1) While an image projected on a screen is a reference, a top or bottom direction, a left or right direction, and a direction of a depth of surface are a Y-direction, an X-direction, and a Z-direction, respectively, and X2, Y2, X2Y, Y3, X2Y2, . . . , etc., are coefficients of a polynomial free-form surface.
(116) Table 3 illustrates coefficients of a polynomial free-form surface of a projection optical system in practical example 1. The definition of an anamorphic polynomial free-form surface in any of practical examples 2-11 is also similar to that of practical example 1.
(117) TABLE-US-00003 TABLE 3 COEFFICIENT VALUE X2 4.20E04 Y2 3.13E03 X2Y 3.00E05 Y3 2.53E07 X4 1.22E07 X2Y2 2.04E08 Y4 4.35E07 X4Y 2.32E09 X2Y3 2.08E09 Y5 1.03E08 X6 1.57E10 X4Y2 4.50E11 X2Y4 6.07E10 Y6 5.01E10 X6Y 1.88E12 X4Y3 2.31E13 X2Y5 2.94E11 Y7 4.35E11 X8 9.63E14 X6Y2 1.03E13 X4Y4 3.23E13 X2Y6 3.55E13 Y8 1.27E12 X8Y 1.34E15 X6Y3 1.05E15 X4Y5 1.83E14 X2Y7 9.39E15 Y9 1.88E14 X10 2.99E17 X8Y2 5.25E17 X6Y4 2.20E17 X4Y6 3.39E16 X2Y8 3.08E16 Y10 1.43E16 X10Y 2.57E19 X8Y3 3.59E19 X6Y5 2.43E18 X4Y7 2.20E18 X2Y9 3.08E18 Y11 4.65E19 X12 3.72E21 X10Y2 8.83E21 X8Y4 1.14E20 X6Y6 2.84E20 X4Y8 1.29E21 X2Y10 1.02E20 Y12 2.28E22
(118) TABLE-US-00004 TABLE 4 POSITION OF LIGHT RAY xfo yfo f1 127.9 125.5 f2 99.8 63.3 f3 63.5 8.1 f4 93.6 115.2 f5 91.9 47.8 f6 59.4 3.7 f7 41.7 88.1 f8 17.9 71.0 f9 50.9 5.3
(119) A value of ImTr for a projection optical system in practical example 1 will be obtained.
(120)
(121) In practical example 1, a projection distance of a projection optical system is a distance in a Z-direction from a reflection point on a reflection surface of a second optical system to a screen with respect to a principal light ray of a light beam nearest an optical axis of a first optical system among light beams from an image forming part. In practical example 1, a projection distance of a projection optical system is 226.5 mm. A projection optical system in practical example 1 is to project a 60-inch image. Hence, a throw ratio Tr for a projection optical system in practical example 1 is 0.18.
(122) Accordingly, a value of ImTr for a projection optical system in practical example 1 is 5.010.18=0.90.
(123)
(124) As illustrated in
(125) In any of practical examples 1-7, a first optical system included in a projection optical system is composed of eleven lenses and a stop but the number of lenses composing a lens element in a first optical system included in a projection optical system is not necessarily needed to be eleven. Also, a position of a stop in a first optical system included in a projection optical system is not necessarily needed to be a position illustrated in
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Practical Example 2
(129) Table 5 illustrates the data of a projection optical system in practical example 2. In practical example 2, a projection distance of a projection optical system and a size of an image projected on a screen are 295 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 2 is 0.23.
(130) TABLE-US-00005 TABLE 5 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 18.83 4.28 1.51 63.90 1.57 SURFACE 4 ASPHERIC 47.71 0.10 SURFACE STOP SPHERE 0.10 6 SPHERE 54.82 1.00 1.84 42.36 7 SPHERE 11.67 5.89 1.49 70.38 8 SPHERE 22.39 0.10 9 SPHERE 38.57 7.00 1.75 35.13 10 SPHERE 212.66 3.98 11 SPHERE 23.16 6.00 1.58 40.77 12 SPHERE 16.53 1.51 1.83 43.00 13 SPHERE 48.44 0.10 14 SPHERE 84.87 3.60 1.55 45.37 15 SPHERE 85.22 1.58 16 SPHERE 22.24 4.46 1.69 29.62 17 SPHERE 38.35 1.59 18 SPHERE 30.70 2.98 1.84 29.69 19 SPHERE 18.82 5.17 20 ASPHERIC 18.35 1.80 1.53 55.80 SURFACE 21 ASPHERIC 66.43 7.48 SURFACE 22 ASPHERIC 27.22 3.86 1.53 55.80 SURFACE 23 ASPHERIC 17.94 0.10 SURFACE 24 SPHERE 90.00 25 xy- 91.82 254.12 REFLECTION 51.93 59.29 POLYNOMIAL SURFACE 26 SPHERE 0.00
(131) Table 6 illustrates coefficients of an aspheric surface for a projection optical system in practical example 2.
(132) TABLE-US-00006 TABLE 6 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 2.48E05 4.12E05 5.34E05 1.57E08 9.05E05 4.06E05 COEFFICIENT (A) 6th ORDER 1.24E08 1.55E08 3.30E06 6.62E07 6.39E07 6.27E07 COEFFICIENT (B) 8th ORDER 6.45E10 7.35E12 1.20E07 1.55E08 6.71E09 1.10E08 COEFFICIENT (C) 10th ORDER 7.68E13 2.71E11 2.45E09 1.82E10 3.24E12 1.35E10 COEFFICIENT (D) 12th ORDER 2.12E14 6.21E13 2.74E11 1.11E12 3.90E14 1.13E12 COEFFICIENT (E) 14th ORDER 1.10E15 5.32E15 1.54E13 6.55E16 5.81E16 4.51E15 COEFFICIENT (F) 16th ORDER 1.03E17 1.37E17 3.34E16 1.76E17 8.32E19 6.86E18 COEFFICIENT (G)
(133) Table 7 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 2.
(134) TABLE-US-00007 TABLE 7 COEFFICIENT VALUE X2 1.16E03 Y2 2.93E03 X2Y 4.21E05 Y3 9.02E06 X4 1.15E07 X2Y2 3.60E07 Y4 5.38E07 X4Y 2.67E09 X2Y3 1.03E09 Y5 1.18E08 X6 1.31E10 X4Y2 7.72E12 X2Y4 6.83E10 Y6 5.15E10 X6Y 1.17E12 X4Y3 1.26E12 X2Y5 2.60E11 Y7 4.32E11 X8 9.76E14 X6Y2 7.45E14 X4Y4 1.73E13 X2Y6 3.79E13 Y8 1.27E12 X8Y 1.94E15 X6Y3 1.86E15 X4Y5 1.36E14 X2Y7 7.82E15 Y9 1.89E14 X10 3.48E17 X8Y2 8.29E17 X6Y4 6.21E17 X4Y6 3.62E16 X2Y8 2.65E16 Y10 1.42E16 X10Y 6.40E19 X8Y3 3.01E19 X6Y5 2.12E19 X4Y7 2.82E18 X2Y9 2.10E18 Y11 4.60E19 X12 5.11E21 X10Y2 2.59E20 X8Y4 8.01E21 X6Y6 1.95E20 X4Y8 4.66E21 X2Y10 1.31E22 Y12 5.67E22
(135) A value of ImTr for a projection optical system in practical example 2 will be obtained.
(136) Table 8 illustrates xfo and yfo for a projection optical system in practical example 2.
(137) TABLE-US-00008 TABLE 8 POSITION OF LIGHT RAY xfo yfo f1 112.0 110.0 f2 90.4 64.8 f3 61.8 17.4 f4 88.8 103.2 f5 84.4 53.6 f6 58.3 12.6 f7 50.6 82.4 f8 28.6 68.6 f9 50.3 2.0
(138) In practical example 2, a projection distance for a projection optical system and a size of an image projected on a screen are 295 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 2 is 0.23. Furthermore, from Table 8, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 2 is |xfo of f1yfo of f9|=112.0 mm2.0 mm=110.0 mm. A focal length of a first optical system included in a projection optical system in practical example 2 is 27.53 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 2 is 110.0 mm/27.53 mm=4.00. A value of ImTr for a projection optical system in practical example 2 is 4.000.23=0.92.
(139)
(140)
(141)
Practical Example 3
(142) Table 9 illustrates the data of a projection optical system in practical example 3. In practical example 3, a projection distance of a projection optical system and a size of an image projected on a screen are 388 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 3 is 0.30.
(143) TABLE-US-00009 TABLE 9 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 22.53 4.06 1.51 63.90 1.43 SURFACE 4 ASPHERIC 41.04 0.10 SURFACE STOP SPHERE 0.10 6 SPHERE 42.98 1.00 1.84 37.52 7 SPHERE 11.60 5.94 1.49 69.89 8 SPHERE 21.42 0.10 9 SPHERE 46.44 1.00 1.83 40.93 10 SPHERE 90.04 0.10 11 SPHERE 24.10 6.00 1.58 41.05 12 SPHERE 14.23 1.62 1.84 42.98 13 SPHERE 78.11 3.07 14 SPHERE 54.23 1.00 1.64 58.93 15 SPHERE 116.29 0.10 16 SPHERE 21.68 4.00 1.71 28.89 17 SPHERE 28.89 1.58 18 SPHERE 23.00 7.00 1.84 28.73 19 SPHERE 31.05 3.66 20 ASPHERIC 21.17 2.77 1.53 55.80 SURFACE 21 ASPHERIC 26.39 9.87 SURFACE 22 ASPHERIC 56.37 2.46 1.53 55.80 SURFACE 23 ASPHERIC 27.89 0.10 SURFACE 24 SPHERE 90.00 25 xy- 79.58 375.60 REFLECTION 29.12 38.41 POLYNOMIAL SURFACE 26 SPHERE 0.00
(144) Table 10 illustrates coefficients of an aspheric surface for a projection optical system in practical example 3.
(145) TABLE-US-00010 TABLE 10 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 4.77E05 4.88E05 2.88E05 8.18E06 1.01E04 7.57E05 COEFFICIENT (A) 6th ORDER 3.05E08 1.84E08 3.05E06 7.00E07 3.71E07 5.65E07 COEFFICIENT (B) 8th ORDER 4.70E10 1.20E10 1.20E07 1.76E08 6.32E09 1.22E08 COEFFICIENT (C) 10th ORDER 5.49E13 2.74E11 2.38E09 1.59E10 1.79E12 1.32E10 COEFFICIENT (D) 12th ORDER 3.91E14 6.03E13 2.79E11 1.20E12 2.64E14 1.13E12 COEFFICIENT (E) 14th ORDER 1.08E15 5.49E15 1.54E13 1.93E16 4.70E16 4.56E15 COEFFICIENT (F) 16th ORDER 8.81E18 1.62E17 2.91E16 2.20E17 1.50E18 6.62E18 COEFFICIENT (G)
(146) Table 11 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 3.
(147) TABLE-US-00011 TABLE 11 COEFFICIENT VALUE X2 4.44E03 Y2 1.49E03 X2Y 1.65E04 Y3 4.61E05 X4 8.73E09 X2Y2 3.07E06 Y4 3.86E07 X4Y 1.59E08 X2Y3 7.19E08 Y5 2.00E08 X6 3.03E11 X4Y2 6.59E10 X2Y4 1.92E09 Y6 1.90E09 X6Y 2.62E11 X4Y3 2.52E11 X2Y5 7.16E11 Y7 7.80E12 X8 1.89E13 X6Y2 5.76E13 X4Y4 1.72E12 X2Y6 2.02E12 Y8 5.36E12 X8Y 2.33E14 X6Y3 4.55E14 X4Y5 1.29E13 X2Y7 1.07E14 Y9 3.95E14 X10 2.71E16 X8Y2 3.95E16 X6Y4 1.55E15 X4Y6 1.10E15 X2Y8 5.02E15 Y10 9.56E15 X10Y 1.04E17 X8Y3 2.85E17 X6Y5 7.25E17 X4Y7 2.76E17 X2Y9 5.53E18 Y11 5.39E17 X12 1.15E19 X10Y2 2.36E19 X8Y4 3.95E19 X6Y6 7.48E19 X4Y8 3.52E18 X2Y10 2.35E18 Y12 5.91E18
(148) A value of ImTr for a projection optical system in practical example 3 will be obtained.
(149) Table 12 illustrates xfo and yfo for a projection optical system in practical example 3.
(150) TABLE-US-00012 TABLE 12 POSITION OF LIGHT RAY xfo yfo f1 86.6 85.9 f2 74.8 61.5 f3 55.9 26.2 f4 75.0 81.9 f5 70.9 54.2 f6 53.3 21.2 f7 51.4 69.3 f8 35.6 60.6 f9 46.5 8.6
(151) In practical example 3, a projection distance for a projection optical system and a size of an image projected on a screen are 388 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 3 is 0.30. Furthermore, from Table 12, a length of an intermediate image in a direction of an optical axis of a first optical system for a. projection optical system in practical example 3 is |xfo of f1yfo of f9|=86.6 mm8.6 mm=78.0 mm. A focal length of a first optical system included in a projection optical system in practical example 3 is 31.34 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 3 is 78.0 mm/31.34 mm=2.49. A value of ImTr for a projection optical system in practical example 3 is 2.490.30=0.75.
(152)
(153)
(154)
Practical Example 4
(155) Table 13 illustrates the data of a projection optical system in practical example 4. In practical example 4, a projection distance of a projection optical system and a size of an image projected on a screen are 517 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 4 is 0.40.
(156) TABLE-US-00013 TABLE 13 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 19.48 4.24 1.51 63.90 1.57 SURFACE 4 ASPHERIC 45.02 0.10 SURFACE STOP SPHERE 0.10 6 SPHERE 62.87 1.00 1.84 42.36 7 SPHERE 12.05 5.77 1.49 70.23 8 SPHERE 23.07 0.18 9 SPHERE 114.92 4.56 1.81 40.60 10 SPHERE 39.65 0.10 11 SPHERE 19.89 6.00 1.57 41.87 12 SPHERE 15.85 1.00 1.84 39.09 13 SPHERE 74.97 3.31 14 SPHERE 25.40 1.00 1.62 56.11 15 SPHERE 97.76 0.10 16 SPHERE 26.72 3.54 1.73 27.51 17 SPHERE 28.47 1.27 18 SPHERE 24.50 7.00 1.84 28.24 19 SPHERE 26.58 3.28 20 ASPHERIC 26.58 6.39 1.53 55.80 SURFACE 21 ASPHERIC 29.38 2.13 SURFACE 22 ASPHERIC 175.02 3.22 1.53 55.80 SURFACE 23 ASPHERIC 33.44 0.10 SURFACE 24 SPHERE 90.00 25 xy- 76.48 496.82 REFLECTION 40.89 42.62 POLYNOMIAL SURFACE 26 SPHERE 0.00
(157) Table 14 illustrates coefficients of an aspheric surface for a projection optical system in practical example 4.
(158) TABLE-US-00014 TABLE 14 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 2.76E05 4.40E05 4.30E05 8.27E06 1.03E04 7.45E05 COEFFICIENT (A) 6th ORDER 6.90E09 2.05E08 2.77E06 6.23E07 5.08E07 6.61E07 COEFFICIENT (B) 8th ORDER 5.29E10 1.15E10 1.18E07 1.49E08 6.43E09 1.14E08 COEFFICIENT (C) 10th ORDER 7.03E13 2.67E11 2.42E09 1.91E10 5.55E14 1.34E10 COEFFICIENT (D) 12th ORDER 2.99E14 6.12E13 2.77E11 1.08E12 3.92E14 1.11E12 COEFFICIENT (E) 14th ORDER 1.09E15 5.45E15 1.55E13 8.19E16 6.57E16 4.64E15 COEFFICIENT (F) 16th ORDER 9.34E18 1.53E17 3.24E16 1.38E17 1.10E18 6.47E18 COEFFICIENT (G)
(159) Table 15 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 4.
(160) TABLE-US-00015 TABLE 15 COEFFICIENT VALUE X2 1.74E03 Y2 2.72E03 X2Y 9.20E05 Y3 1.14E05 X4 8.68E08 X2Y2 1.02E07 Y4 2.02E07 X4Y 7.12E09 X2Y3 4.63E08 Y5 1.10E08 X6 2.92E10 X4Y2 4.42E10 X2Y4 9.40E10 Y6 4.12E10 X6Y 4.20E12 X4Y3 5.76E12 X2Y5 3.36E11 Y7 4.25E11 X8 1.23E13 X6Y2 6.92E13 X4Y4 1.63E12 X2Y6 4.27E13 Y8 1.32E12 X8Y 1.63E15 X6Y3 1.84E14 X4Y5 2.34E14 X2Y7 1.22E14 Y9 1.81E14 X10 1.30E16 X8Y2 1.09E15 X6Y4 4.44E16 X4Y6 2.96E16 X2Y8 2.05E16 Y10 1.48E16 X10Y 6.66E19 X8Y3 1.47E17 X6Y5 2.44E17 X4Y7 1.79E18 X2Y9 4.51E19 Y11 4.20E19 X12 1.02E19 X10Y2 4.14E19 X8Y4 4.68E19 X6Y6 5.21E19 X4Y8 1.36E19 X2Y10 2.11E20 Y12 9.56E23
(161) A value of ImTr for a projection optical system in practical example 4 will be obtained.
(162) Table 16 illustrates xfo and yfo for a projection optical system in practical example 4.
(163) TABLE-US-00016 TABLE 16 POSITION OF LIGHT RAY xfo yfo f1 91.5 90.9 f2 82.1 72.2 f3 66.5 44.3 f4 83.3 88.0 f5 79.0 66.6 f6 64.3 39.8 f7 64.9 78.1 f8 52.4 70.7 f9 58.4 27.6
(164) In practical example 4, a projection distance for a projection optical system and a size of an image projected on a screen are 517 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 4 is 0.40. Furthermore, from Table 16, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 4 is |xfo of f1yfo of f9|=91.5 mm27.6 mm=63.9 mm. A focal length of a first optical system included in a projection optical system in practical example 4 is 33.32 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 4 is 63.9 mm/33.32 mm=1.92. A value of ImTr for a projection optical system in practical example 4 is 1.920.40=0.77.
(165)
(166)
(167)
Practical Example 5
(168) Table 17 illustrates the data of a projection optical system in practical example 5. In practical example 5, a projection distance of a projection optical system and a size of an image projected on a screen are 672 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 5 is 0.52.
(169) TABLE-US-00017 TABLE 17 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 18.87 6.38 1.51 63.90 1.65 SURFACE 4 ASPHERIC 50.60 0.47 SURFACE STOP SPHERE 0.10 6 SPHERE 68.16 1.00 1.84 40.68 7 SPHERE 12.37 5.50 1.50 69.57 8 SPHERE 23.66 0.10 9 SPHERE 528.54 2.43 1.84 42.98 10 SPHERE 30.65 0.10 11 SPHERE 17.88 6.00 1.57 41.85 12 SPHERE 15.55 1.00 1.84 39.48 13 SPHERE 80.98 3.83 14 SPHERE 30.20 1.00 1.67 56.41 15 SPHERE 161.42 0.10 16 SPHERE 30.32 4.50 1.73 27.97 17 SPHERE 24.15 0.59 18 SPHERE 22.60 7.00 1.84 29.28 19 SPHERE 28.66 2.95 20 ASPHERIC 40.72 6.75 1.53 55.80 SURFACE 21 ASPHERIC 35.92 1.68 SURFACE 22 ASPHERIC 3108.00 3.28 1.53 55.80 SURFACE 23 ASPHERIC 38.32 0.10 SURFACE 24 SPHERE 90.00 25 xy- 65.67 666.95 REFLECTION 20.11 26.89 POLYNOMIAL SURFACE 26 SPHERE 0.00
(170) Table 18 illustrates coefficients of an aspheric surface for a projection optical system in practical example 5.
(171) TABLE-US-00018 TABLE 18 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 2.26E05 4.73E05 2.86E05 2.89E06 1.06E04 7.80E05 COEFFICIENT (A) 6th ORDER 2.35E08 8.14E09 2.62E06 5.41E07 4.79E07 6.18E07 COEFFICIENT (B) 8th ORDER 5.19E10 2.09E10 1.16E07 1.50E08 6.54E09 1.13E08 COEFFICIENT (C) 10th ORDER 1.04E13 2.89E11 2.39E09 1.96E10 2.43E12 1.34E10 COEFFICIENT (D) 12th ORDER 5.67E14 6.01E13 2.76E11 1.06E12 4.64E14 1.11E12 COEFFICIENT (E) 14th ORDER 8.68E16 5.57E15 1.61E13 8.72E16 6.46E16 4.68E15 COEFFICIENT (F) 16th ORDER 6.80E18 1.46E17 3.74E16 1.36E17 1.23E18 6.32E18 COEFFICIENT (G)
(172) Table 19 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 5.
(173) TABLE-US-00019 TABLE 19 COEFFICIENT VALUE X2 3.59E03 Y2 6.17E05 X2Y 1.60E04 Y3 8.37E05 X4 8.02E07 X2Y2 2.47E06 Y4 1.81E06 X4Y 1.60E08 X2Y3 3.61E08 Y5 4.08E08 X6 1.43E10 X4Y2 2.50E09 X2Y4 1.79E09 Y6 4.01E09 X6Y 8.35E11 X4Y3 1.82E12 X2Y5 1.33E11 Y7 5.83E11 X8 3.27E13 X6Y2 2.02E12 X4Y4 6.79E13 X2Y6 7.31E12 Y8 9.10E12 X8Y 7.56E14 X6Y3 7.64E14 X4Y5 1.25E13 X2Y7 1.55E13 Y9 4.66E14 X10 1.16E15 X8Y2 2.68E15 X6Y4 2.20E15 X4Y6 4.68E15 X2Y8 4.00E14 Y10 8.45E15 X10Y 1.97E17 X8Y3 1.22E16 X6Y5 1.05E16 X4Y7 4.67E16 X2Y9 9.33E17 Y11 1.30E16 X12 1.13E18 X10Y2 2.47E18 X8Y4 1.70E19 X6Y6 6.28E18 X4Y8 1.55E17 X2Y10 7.59E17 Y12 3.97E17
(174) A value of ImTr for a projection optical system in practical example 5 will be obtained.
(175) Table 20 illustrates xfo and yfo for a projection optical system in practical example 5.
(176) TABLE-US-00020 TABLE 20 POSITION OF LIGHT RAY xfo yfo f1 75.7 75.3 f2 69.0 62.4 f3 57.4 43.1 f4 70.2 73.2 f5 66.7 58.6 f6 55.7 39.8 f7 57.7 66.2 f8 48.9 60.6 f9 51.0 30.8
(177) In practical example 5, a projection distance for a projection optical system and a size of an image projected on a screen are 672 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 5 is 0.52. Furthermore, from Table 20, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 5 is |xfo of f1yfo of f9|=75.7 mm30.8 mm=44.9 mm. A focal length of a first optical system included in a projection optical system in practical example 5 is 33.91 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 5 is 44.9 mm/33.91 mm=1.32. A value of ImTr for a projection optical system in practical example 5 is 1.320.52=0.69.
(178)
(179)
(180)
Practical Example 6
(181) Table 21 illustrates the data of a projection optical system in practical example 6. In practical example 6, a projection distance of a projection optical system and a size of an image projected on a screen are 775 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 6 is 0.60.
(182) TABLE-US-00021 TABLE 21 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 18.63 8.73 1.51 63.90 1.75 SURFACE 4 ASPHERIC 56.15 1.01 SURFACE STOP SPHERE 0.10 6 SPHERE 84.00 0.95 1.84 38.05 7 SPHERE 13.02 5.17 1.50 69.09 8 SPHERE 23.85 0.10 9 SPHERE 540.12 1.00 1.84 42.98 10 SPHERE 29.48 0.10 11 SPHERE 18.26 5.38 1.58 41.14 12 SPHERE 14.18 0.80 1.84 40.28 13 SPHERE 53.33 3.83 14 SPHERE 48.74 0.95 1.75 49.79 15 SPHERE 53.80 0.10 16 SPHERE 24.17 5.83 1.70 29.29 17 SPHERE 18.69 0.10 18 SPHERE 18.54 6.60 1.84 30.09 19 SPHERE 30.47 2.72 20 ASPHERIC 36.43 7.11 1.53 55.80 SURFACE 21 ASPHERIC 28.35 1.40 SURFACE 22 ASPHERIC 710.28 3.61 1.53 55.80 SURFACE 23 ASPHERIC 40.21 0.10 SURFACE 24 SPHERE 90.00 25 xy- POLYNOMIAL 62.88 772.78 REFLECTION 13.70 19.51 SURFACE 26 SPHERE 0.00
(183) Table 22 illustrates coefficients of an aspheric surface for a projection optical system in practical example 6.
(184) TABLE-US-00022 TABLE 22 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 2.16E05 5.17E05 3.98E05 4.80E06 1.08E04 7.83E05 COEFFICIENT (A) 6th ORDER 2.78E08 1.86E08 2.55E06 5.27E07 4.79E07 5.97E07 COEFFICIENT (B) 8th ORDER 2.84E10 1.69E10 1.14E07 1.47E08 6.37E09 1.12E08 COEFFICIENT (C) 10th ORDER 1.00E12 2.99E11 2.37E09 1.99E10 3.01E12 1.35E10 COEFFICIENT (D) 12th ORDER 7.30E14 5.85E13 2.76E11 1.06E12 4.19E14 1.10E12 COEFFICIENT (E) 14th ORDER 7.31E16 5.60E15 1.64E13 9.08E16 6.05E16 4.66E15 COEFFICIENT (F) 16th ORDER 3.33E18 1.78E17 4.02E16 1.27E17 1.15E18 6.65E18 COEFFICIENT (G)
(185) Table 23 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 6.
(186) TABLE-US-00023 TABLE 23 (Table 23) COEFFICIENT VALUE X2 4.00E03 Y2 1.58E03 X2Y 1.62E04 Y3 1.11E04 X4 1.79E06 X2Y2 9.77E07 Y4 4.54E07 X4Y 1.06E07 X2Y3 6.69E08 Y5 3.57E08 X6 1.61E09 X4Y2 2.44E09 X2Y4 1.82E09 Y6 2.96E09 X6Y 1.22E10 X4Y3 1.01E10 X2Y5 1.53E10 Y7 2.05E10 X8 2.69E12 X6Y2 1.04E12 X4Y4 6.41E12 X2Y6 1.01E11 Y8 5.71E12 X8Y 1.25E13 X6Y3 5.60E14 X4Y5 3.14E14 X2Y7 1.09E12 Y9 5.70E13 X10 3.21E15 X8Y2 1.09E15 X6Y4 1.00E14 X4Y6 3.36E15 X2Y8 4.32E14 Y10 4.15E14 X10Y 7.47E17 X8Y3 2.47E17 X6Y5 3.62E16 X4Y7 4.39E17 X2Y9 5.62E15 Y11 5.68E15 X12 1.83E18 X10Y2 5.79E20 X8Y4 3.09E18 X6Y6 4.36E19 X4Y8 6.25E18 X2Y10 1.27E16 Y12 1.37E16
(187) A value of ImTr for a projection optical system in practical example 6 will be obtained.
(188) Table 24 illustrates xfo and yfo for a projection optical system in practical example 6.
(189) TABLE-US-00024 TABLE 24 POSITION OF LIGHT RAY xfo yfo f1 72.2 71.9 f2 66.4 60.8 f3 56.2 44.1 f4 67.7 70.2 f5 64.4 57.6 f6 54.7 41.3 f7 57.0 64.1 f8 49.2 59.1 f9 50.6 33.3
(190) In practical example 6, a projection distance for a projection optical system and a size of an image projected on a screen are 775 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 6 is 0.60. Furthermore, from Table 24, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 6 is |xfo of f1yfo of f9|72.2 mm33.3 mm=38.9 mm. A focal length of a first optical system included in a projection optical system in practical example 6 is 35.74 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 6 is 38.9 mm/35.74 mm=1.09. A value of ImTr for a projection optical system in practical example 6 is 1.090.60=0.65.
(191)
(192)
(193)
Practical Example 7
(194) Table 25 illustrates the data of a projection optical system in practical example 7. In practical example 7, a projection distance of a projection optical system and a size of an image projected on a screen are 795 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 7 is 0.62.
(195) TABLE-US-00025 TABLE 25 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 39.97 3 ASPHERIC 17.72 6.10 1.51 63.90 1.63 SURFACE 4 ASPHERIC 60.50 0.31 SURFACE STOP SPHERE 0.45 6 SPHERE 59.11 1.26 1.84 39.04 7 SPHERE 12.07 5.64 1.49 70.29 8 SPHERE 23.37 0.10 9 SPHERE 117.34 1.20 1.76 40.44 10 SPHERE 36.12 0.10 11 SPHERE 18.61 5.97 1.58 40.47 12 SPHERE 16.97 6.00 1.83 39.28 13 SPHERE 51.21 0.10 14 SPHERE 45.27 6.93 1.55 46.37 15 SPHERE 928.99 0.10 16 SPHERE 38.20 3.80 1.71 28.53 17 SPHERE 31.17 1.37 18 SPHERE 27.22 2.93 1.84 34.34 19 SPHERE 27.71 4.85 20 ASPHERIC 14.54 3.35 1.53 55.80 SURFACE 21 ASPHERIC 19.49 5.43 SURFACE 22 ASPHERIC 21.69 2.41 1.53 55.80 SURFACE 23 ASPHERIC 18.14 20.02 SURFACE 24 SPHERE 90.00 25 xy- 91.51 768.39 REFLECTION 62.29 40.52 POLYNOMIAL SURFACE 26 SPHERE 0
(196) Table 26 illustrates coefficients of an aspheric surface for a projection optical system in practical example 7.
(197) TABLE-US-00026 TABLE 26 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 1.20E05 4.38E05 3.91E05 1.66E05 9.47E05 5.66E05 COEFFICIENT (A) 6th ORDER 1.71E08 4.99E09 3.34E06 7.40E07 5.27E07 6.35E07 COEFFICIENT (B) 8th ORDER 6.61E10 2.26E10 1.20E07 1.51E08 6.53E09 1.17E08 COEFFICIENT (C) 10th ORDER 2.54E13 2.94E11 2.42E09 1.83E10 2.71E12 1.33E10 COEFFICIENT (D) 12th ORDER 4.38E14 6.05E13 2.76E11 1.13E12 2.97E14 1.12E12 COEFFICIENT (E) 14th ORDER 9.23E16 5.42E15 1.55E13 7.01E16 5.90E16 4.60E15 COEFFICIENT (F) 16th ORDER 8.13E18 1.32E17 3.12E16 1.90E17 3.96E19 6.41E18 COEFFICIENT (G)
(198) Table 27 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 7.
(199) TABLE-US-00027 TABLE 27 COEFFICIENT VALUE X2 2.48E04 Y2 2.44E03 X2Y 2.87E05 Y3 1.65E05 X4 4.62E08 X2Y2 1.58E07 Y4 5.31E07 X4Y 6.85E10 X2Y3 5.71E10 Y5 1.28E08 X6 9.70E11 X4Y2 8.13E11 X2Y4 7.49E10 Y6 5.24E10 X6Y 4.64E13 X4Y3 4.21E12 X2Y5 3.06E11 Y7 4.35E11 X8 8.12E14 X6Y2 5.16E14 X4Y4 2.02E13 X2Y6 2.84E13 Y8 1.26E12 X8Y 4.10E16 X6Y3 1.79E15 X4Y5 1.62E14 X2Y7 9.16E15 Y9 1.90E14 X10 3.83E17 X8Y2 5.33E17 X6Y4 1.21E16 X4Y6 3.81E16 X2Y8 2.36E16 Y10 1.45E16 X10Y 1.04E20 X8Y3 1.17E18 X6Y5 2.11E18 X4Y7 3.54E18 X2Y9 1.78E18 Y11 1.99E19 X12 7.01E21 X10Y2 2.29E21 X8Y4 9.93E21 X6Y6 1.13E20 X4Y8 1.03E20 X2Y10 3.42E21 Y12 5.20E22
(200) A value of ImTr for a projection optical system in practical example 7 will be obtained.
(201) Table 28 illustrates xfo and yfo for a projection optical system in practical example 7.
(202) TABLE-US-00028 TABLE 28 POSITION OF LIGHT RAY xfo yfo f1 100.0 100.2 f2 90.2 81.7 f3 72.6 51.0 f4 92.8 96.7 f5 86.8 76.0 f6 70.1 46.1 f7 74.5 85.9 f8 60.4 77.5 f9 63.1 32.4
(203) In practical example 7, a projection distance for a projection optical system and a size of an image projected on a screen are 795 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 7 is 0.62. Furthermore, from Table 28, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 7 is |xfo of f1yfo of f9|=100.2 mm32.4 mm=67.8 mm. A focal length of a first optical system included in a projection optical system in practical example 7 is 28.56 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 7 is 67.8 mm/28.56 mm=2.37. A value of ImTr for a projection optical system in practical example 7 is 2.370.62=1.47.
(204)
(205)
(206)
Practical Example 8
(207) Table 29 illustrates the data of a projection optical system in practical example 8. In practical example 8, a projection distance of a projection optical system and a size of an image projected on a screen are 200 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 8 is 0.15.
(208) TABLE-US-00029 TABLE 29 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 28.00 3 ASPHERIC 11.61 1.59 1.51 63.90 1.31 SURFACE 4 ASPHERIC 39.19 0.27 SURFACE STOP SPHERE 0.35 6 SPHERE 77.67 0.50 1.82 38.59 7 SPHERE 8.81 6.00 1.49 70.34 8 SPHERE 24.35 10.92 9 SPHERE 29.06 3.68 1.55 64.33 10 SPHERE 20.45 1.00 1.81 34.60 11 SPHERE 110.04 0.10 12 SPHERE 22.07 3.81 1.85 23.78 13 SPHERE 51.49 3.56 14 SPHERE 23.53 6.95 1.85 24.08 15 SPHERE 15.40 3.43 16 ASPHERIC 19.74 1.00 1.53 55.80 SURFACE 17 ASPHERIC 173.57 6.51 SURFACE 18 ASPHERIC 21.97 4.98 1.53 55.80 SURFACE 19 ASPHERIC 13.67 0.10 SURFACE 20 SPHERE 90.00 21 xy- 83.76 150.43 REFLECTION 62.93 54.93 POLYNOMIAL SURFACE 22 SPHERE 0.00
(209) Table 30 illustrates coefficients of an aspheric surface for a projection optical system in practical example 8.
(210) TABLE-US-00030 TABLE 30 SURFACE NUMBER 3 4 16 17 18 19 4th ORDER 2.75E04 2.76E04 1.83E04 6.41E05 1.48E04 5.30E05 COEFFICIENT (A) 6th ORDER 6.38E06 7.00E06 3.48E06 1.53E06 7.50E07 5.39E07 COEFFICIENT (B) 8th ORDER 1.13E07 1.88E07 1.12E07 1.78E08 1.00E08 7.45E09 COEFFICIENT (C) 10th ORDER 6.23E09 5.71E09 2.41E09 1.74E10 1.83E11 1.11E10 COEFFICIENT (D) 12th ORDER 1.12E10 1.20E10 2.82E11 1.20E12 7.28E15 1.08E12 COEFFICIENT (E) 14th ORDER 5.82E12 1.27E12 1.53E13 2.03E15 7.72E16 5.62E15 COEFFICIENT (F) 16th ORDER 5.19E13 6.93E13 2.46E16 3.96E17 6.96E19 1.41E17 COEFFICIENT (G)
(211) Table 31 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 8.
(212) TABLE-US-00031 TABLE 31 COEFFICIENT VALUE X2 5.33E04 Y2 3.64E03 X2Y 3.83E05 Y3 2.35E06 X4 3.42E10 X2Y2 1.87E07 Y4 3.66E07 X4Y 2.30E09 X2Y3 1.43E10 Y5 4.55E09 X6 5.36E11 X4Y2 1.29E10 X2Y4 3.86E10 Y6 5.01E10 X6Y 1.05E14 X4Y3 4.97E12 X2Y5 1.27E11 Y7 3.93E11 X8 3.93E14 X6Y2 1.10E13 X4Y4 2.57E13 X2Y6 1.21E13 Y8 1.20E12 X8Y 2.91E16 X6Y3 1.10E15 X4Y5 1.37E14 X2Y7 2.04E14 Y9 1.87E14 X10 1.44E17 X8Y2 4.27E17 X6Y4 4.42E17 X4Y6 2.33E16 X2Y8 5.07E16 Y10 1.44E16 X10Y 5.46E20 X8Y3 4.12E20 X6Y5 3.49E18 X4Y7 2.89E19 X2Y9 5.11E18 Y11 3.86E19 X12 2.01E21 X10Y2 6.10E21 X8Y4 1.30E20 X6Y6 5.13E20 X4Y8 1.52E20 X2Y10 1.73E20 Y12 4.40E22
(213) A value of ImTr for a projection optical system in practical example 8 will be obtained.
(214) Table 32 illustrates xfo and yfo for a projection optical system in practical example 8.
(215) TABLE-US-00032 TABLE 32 POSITION OF LIGHT RAY xfo yfo f1 123.9 120.4 f2 93.4 55.4 f3 58.1 3.9 f4 86.2 109.2 f5 85.7 39.9 f6 54.4 0.3 f7 33.6 81.8 f8 12.1 64.9 f9 47.4 6.9
(216) In practical example 8, a projection distance for a projection optical system and a size of an image projected on a screen are 200 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 8 is 0.15. Furthermore, from Table 32, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 8 is |xfo of f1yfo of f9|=123.9 mm(6.9 mm)=130.8 mm. A focal length of a first optical system included in a projection optical system in practical example 8 is 25.09 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 8 is 130.8 mm/25.09 mm=5.21. A value of ImTr for a projection optical system in practical example 8 is 5.210.15=0.78.
(217)
(218) In any of practical examples 8 and 9, a first optical system included in a projection optical system is composed of nine lenses and a stop but the number of a lens(es) composing a lens element in a first optical system included in a projection optical system is not necessarily needed to be nine. Also, a position of a stop in a first optical system included in a projection optical system is not necessarily needed to be a position illustrated in
(219)
(220)
Practical Example 9
(221) Table 33 illustrates the data of a projection optical system in practical example 9. In practical example 9, a projection distance of a projection optical system and a size of an image projected on a screen are 226.5 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 9 is 0.18.
(222) TABLE-US-00033 TABLE 33 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT 0 SPHERE 1.11 1 SPHERE 1.05 1.51 63.35 2 SPHERE 28.00 3 ASPHERIC 17.54 1.55 1.51 63.90 1.30 SURFACE 4 ASPHERIC 222.17 0.10 SURFACE STOP SPHERE 0.10 6 SPHERE 29.48 0.48 1.83 37.35 7 SPHERE 7.98 2.16 1.49 70.10 8 SPHERE 54.88 10.14 9 SPHERE 33.62 2.89 1.55 64.40 10 SPHERE 19.77 1.00 1.81 33.16 11 SPHERE 106.64 0.19 12 SPHERE 20.93 3.51 1.85 23.78 13 SPHERE 39.86 3.55 14 SPHERE 19.30 3.55 1.82 24.64 15 SPHERE 15.76 2.21 16 ASPHERIC 34.26 1.00 1.53 55.80 SURFACE 17 ASPHERIC 113.40 5.49 SURFACE 18 ASPHERIC 22.77 3.98 1.53 55.80 SURFACE 19 ASPHERIC 12.65 0.10 SURFACE 20 SPHERE 90.00 21 xy- 83.29 187.65 REFLECTION 53.50 52.22 POLYNOMIAL SURFACE 22 SPHERE 0.00
(223) Table 34 illustrates coefficients of an aspheric surface for a projection optical system in practical example 9.
(224) TABLE-US-00034 TABLE 34 SURFACE NUMBER 3 4 16 17 18 19 4th ORDER 3.07E04 2.35E04 1.65E04 7.84E05 1.07E04 4.82E05 COEFFICIENT (A) 6th ORDER 3.30E06 3.20E06 3.88E06 1.43E06 4.76E07 4.68E07 COEFFICIENT (B) 8th ORDER 5.82E08 1.16E07 1.11E07 1.70E08 1.05E08 7.09E09 COEFFICIENT (C) 10th ORDER 5.85E09 3.09E09 2.40E09 1.74E10 1.65E11 1.09E10 COEFFICIENT (D) 12th ORDER 2.00E11 2.15E12 2.85E11 1.24E12 4.02E14 1.11E12 COEFFICIENT (E) 14th ORDER 1.47E11 3.01E12 1.49E13 2.29E15 9.74E16 5.29E15 COEFFICIENT (F) 16th ORDER 6.99E13 4.15E13 2.07E16 2.65E17 1.21E18 1.60E17 COEFFICIENT (G)
(225) Table 35 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 9.
(226) TABLE-US-00035 TABLE 35 COEFFICIENT VALUE X2 1.37E03 Y2 3.46E03 X2Y 5.53E05 Y3 5.02E06 X4 5.30E08 X2Y2 5.16E07 Y4 3.09E07 X4Y 3.79E09 X2Y3 4.29E09 Y5 4.03E09 X6 4.22E11 X4Y2 8.50E11 X2Y4 3.81E10 Y6 5.01E10 X6Y 7.98E13 X4Y3 6.30E12 X2Y5 8.90E12 Y7 3.82E11 X8 4.60E14 X6Y2 1.16E13 X4Y4 2.21E13 X2Y6 1.26E13 Y8 1.21E12 X8Y 1.09E16 X6Y3 1.83E15 X4Y5 1.78E14 X2Y7 2.37E14 Y9 1.92E14 X10 2.02E17 X8Y2 5.53E17 X6Y4 6.96E17 X4Y6 4.37E16 X2Y8 6.00E16 Y10 1.43E16 X10Y 4.73E20 X8Y3 4.03E19 X6Y5 6.29E18 X4Y7 1.47E18 X2Y9 5.10E18 Y11 3.61E19 X12 3.19E21 X10Y2 1.22E20 X8Y4 2.31E20 X6Y6 1.31E19 X4Y8 4.06E20 X2Y10 8.80E22 Y12 4.20E22
(227) A value of ImTr for a projection optical system in practical example 9 will be obtained.
(228) Table 36 illustrates xfo and yfo for a projection optical system in practical example 6.
(229) TABLE-US-00036 TABLE 32 POSITION OF LIGHT RAY xfo yfo f1 113.8 111.2 f2 89.7 60.0 f3 59.5 10.3 f4 85.3 102.5 f5 83.0 46.7 f6 56.1 6.0 f7 40.9 79.6 f8 19.5 65.7 f9 48.5 2.6
(230) In practical example 9, a projection distance for a projection optical system and a size of an image projected on a screen are 226.5 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 9 is 0.18. Furthermore, from Table 36, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 9 is |xfo of f1yfo of f9|=113.8 mm(2.6 mm)=116.4 mm. A focal length of a first optical system included in a projection optical system in practical example 9 is 25.57 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 9 is 116.4 mm/25.57 mm=4.55. A value of ImTr for a projection optical system in practical example 9 is 4.550.18=0.82.
(231)
(232)
(233)
Practical Example 10
(234) Table 37 illustrates the data of a projection optical system in practical example 10. In practical example 10, a projection distance of a projection optical system and a size of an image projected on a screen are 795 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 10 is 0.62.
(235) TABLE-US-00037 TABLE 37 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT SPHERE 1.11 CG SPHERE 1.05 1.51 63.35 P SPHERE 40.69 t ASPHERIC 19.33 4.50 1.51 63.90 1.49 SURFACE ASPHERIC 39.44 0.10 SURFACE SPHERE 0.10 L2 SPHERE 132.88 1.00 1.84 42.98 L3 SPHERE 12.74 5.81 1.49 70.44 SPHERE 21.45 0.24 L4 SPHERE 78.03 1.28 1.77 47.91 SPHERE 36.93 1.21 L5 SPHERE 19.07 5.44 1.58 41.19 L6 SPHERE 15.21 1.00 1.84 33.99 SPHERE 42.22 0.40 L7 SPHERE 28.24 1.00 1.59 39.71 SPHERE 100.59 0.10 L8 SPHERE 22.58 3.57 1.72 28.32 SPHERE 34.92 1.46 L9 SPHERE 27.67 1.92 1.84 30.11 SPHERE 19.86 5.58 L10 ASPHERIC 11.66 5.67 1.53 55.80 SURFACE ASPHERIC 14.14 2.90 SURFACE L11 ASPHERIC 23.15 2.60 1.53 55.80 SURFACE ASPHERIC 18.08 133.84 SURFACE SPHERE 90.00 M1 xy- 97.48 768.84 REFLECTION 71.17 35.45 POLYNOMIAL SURFACE SPHERE 0.00
(236) Table 38 illustrates coefficients of an aspheric surface for a projection optical system in practical example 10.
(237) TABLE-US-00038 TABLE 38 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 2.16E05 4.65E05 6.97E05 1.25E05 9.26E05 5.16E05 COEFFICIENT (A) 6th ORDER 3.56E08 2.25E08 3.19E06 7.98E07 4.84E07 6.53E07 COEFFICIENT (B) 8th ORDER 4.45E10 5.12E11 1.17E07 1.48E08 6.53E09 1.16E08 COEFFICIENT (C) 10th ORDER 1.87E12 2.77E11 2.42E09 1.89E10 5.28E13 1.33E10 COEFFICIENT (D) 12th ORDER 3.94E14 6.16E13 2.81E11 1.08E12 4.99E14 1.11E12 COEFFICIENT (E) 14th ORDER 9.43E16 5.30E15 1.50E13 7.26E16 7.47E16 4.67E15 COEFFICIENT (F) 16th ORDER 7.26E18 1.51E17 2.68E16 1.24E17 1.32E18 5.83E18 COEFFICIENT (G)
(238) Table 39 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 10.
(239) TABLE-US-00039 TABLE 39 COEFFICIENT VALUE X2 9.83E04 Y2 2.89E03 X2Y 2.14E05 Y3 1.36E05 X4 1.13E07 X2Y2 2.58E07 Y4 4.78E07 X4Y 1.78E09 X2Y3 1.53E09 Y5 1.15E08 X6 1.02E10 X4Y2 3.05E11 X2Y4 8.05E10 Y6 5.17E10 X6Y 1.93E12 X4Y3 3.85E12 X2Y5 3.18E11 Y7 4.33E11 X8 9.10E14 X6Y2 5.34E14 X4Y4 2.01E13 X2Y6 2.51E13 Y8 1.27E12 X8Y 7.07E16 X6Y3 1.99E15 X4Y5 1.64E14 X2Y7 9.17E15 Y9 1.90E14 X10 3.58E17 X8Y2 3.46E17 X6Y4 1.30E16 X4Y6 3.79E16 X2Y8 2.27E16 Y10 1.44E16 X10Y 7.08E20 X8Y3 6.30E19 X6Y5 2.30E18 X4Y7 3.55E18 X2Y9 1.90E18 Y11 4.10E19 X12 5.09E21 X10Y2 2.38E21 X8Y4 6.09E21 X6Y6 1.26E20 X4Y8 1.17E20 X2Y10 5.65E21 Y12 2.93E22
(240) A value of ImTr for a projection optical system in practical example 10 will be obtained.
(241) Table 40 illustrates xfo and yfo for a projection optical system in practical example 10.
(242) TABLE-US-00040 TABLE 40 POSITION OF LIGHT RAY xfo yfo f1 200.7 201.3 f2 190.0 181.8 f3 166.8 134.4 f4 195.0 197.3 f5 185.7 174.4 f6 163.2 126.2 f7 171.6 184.2 f8 149.1 173.4 f9 152.8 101.2
(243) In practical example 10, a projection distance for a projection optical system and a size of an image projected on a screen are 795 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 10 is 0.62. Furthermore, from Table 40, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 10 is |yfo of f1yfo of f9|=201.3 mm101.2 mm=100.1 mm. A focal length of a first optical system included in a projection optical system in practical example 10 is 39.30 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 10 is 100.1 mm/39.30 mm=2.55. A value of ImTr for a projection optical system in practical example 10 is 2.550.62=1.58.
(244)
(245)
(246)
Practical Example 11
(247) Table 41 illustrates the data of a projection optical system in practical example 11. In practical example 11, a projection distance of a projection optical system and a size of an image projected on a screen are 775 mm and 60 inches, respectively, and hence, a throw ratio for a projection optical system in practical example 11 is 0.60.
(248) TABLE-US-00041 TABLE 41 SURFACE SURFACE RADIUS OF SURFACE REFRACTIVE NUMBER SHAPE CURVATURE DISTANCE INDEX DISPERSION SHIFT TILT SPHERE 1.11 CG SPHERE 1.05 1.51 63.35 P SPHERE 40.22 t ASPHERIC 17.87 11.02 1.51 63.90 1.92 SURFACE ASPHERIC 82.56 2.10 SURFACE SPHERE 0.10 L2 SPHERE 90.91 0.90 1.84 34.26 L3 SPHERE 14.18 4.84 1.50 69.06 SPHERE 24.35 0.10 L4 SPHERE 200.44 1.00 1.83 43.13 SPHERE 30.99 0.10 L5 SPHERE 18.65 5.29 1.58 41.08 L6 SPHERE 14.10 0.80 1.84 41.33 SPHERE 41.13 2.14 L7 SPHERE 42.90 0.90 1.80 45.66 SPHERE 42.02 0.10 L8 SPHERE 23.47 7.47 1.68 30.43 SPHERE 16.32 0.10 L9 SPHERE 16.07 1.74 1.84 32.42 SPHERE 33.05 2.63 L10 ASPHERIC 33.09 7.39 1.53 55.80 SURFACE ASPHERIC 25.63 1.00 SURFACE L11 ASPHERIC 100.26 3.89 1.53 55.80 SURFACE ASPHERIC 61.42 0.10 SURFACE SPHERE 90.00 M1 xy- 59.65 774.60 REFLECTION 7.39 11.41 POLYNOMIAL SURFACE SPHERE 0.00
(249) Table 42 illustrates coefficients of an aspheric surface for a projection optical system in practical example 11.
(250) TABLE-US-00042 TABLE 42 SURFACE NUMBER 3 4 20 21 22 23 4th ORDER 1.10E05 4.83E05 4.80E05 6.60E07 1.10E04 8.75E05 COEFFICIENT (A) 6th ORDER 8.76E10 1.13E08 2.48E06 5.23E07 4.85E07 5.94E07 COEFFICIENT (B) 8th ORDER 2.62E11 2.04E11 1.13E07 1.43E08 6.05E09 1.12E08 COEFFICIENT (C) 10th ORDER 1.29E12 3.02E11 2.37E09 2.01E10 3.82E12 1.37E10 COEFFICIENT (D) 12th ORDER 7.76E14 5.84E13 2.77E11 1.06E12 3.57E14 1.10E12 COEFFICIENT (E) 14th ORDER 7.70E16 5.50E15 1.65E13 9.57E16 5.45E16 4.64E15 COEFFICIENT (F) 16th ORDER 2.55E18 2.01E17 4.14E16 1.22E17 9.05E19 6.95E18 COEFFICIENT (G)
(251) Table 43 illustrates coefficients of a polynomial free-form surface for a projection optical system in practical example 11.
(252) TABLE-US-00043 TABLE 43 COEFFICIENT VALUE X2 5.03E03 Y2 3.81E03 X2Y 1.43E04 Y3 1.13E04 X4 2.73E06 X2Y2 1.69E06 Y4 1.54E07 X4Y 1.24E07 X2Y3 1.40E07 Y5 7.14E08 X6 2.36E09 X4Y2 5.55E10 X2Y4 7.70E10 Y6 7.54E09 X6Y 1.09E10 X4Y3 7.54E11 X2Y5 3.46E10 Y7 5.73E11 X8 4.14E12 X6Y2 7.69E13 X4Y4 4.38E12 X2Y6 8.66E12 Y8 6.13E12 X8Y 7.99E14 X6Y3 1.01E13 X4Y5 2.04E13 X2Y7 1.30E12 Y9 8.22E13 X10 7.52E15 X8Y2 1.32E16 X6Y4 1.29E14 X4Y6 2.80E16 X2Y8 4.90E14 Y10 5.51E14 X10Y 3.90E17 X8Y3 2.20E16 X6Y5 5.14E17 X4Y7 3.94E16 X2Y9 5.71E15 Y11 5.46E15 X12 5.92E18 X10Y2 6.89E18 X8Y4 6.28E18 X6Y6 1.12E18 X4Y8 7.19E18 X2Y10 1.11E16 Y12 1.05E16
(253) A value of ImTr for a projection optical system in practical example 11 will be obtained.
(254) Table 44 illustrates xfo and yfo for a projection optical system in practical example 11.
(255) TABLE-US-00044 TABLE 44 POSITION OF LIGHT RAY xfo yfo f1 71.2 70.7 f2 65.6 60.7 f3 56.5 48.4 f4 66.9 69.2 f5 63.9 58.0 f6 55.3 47.0 f7 57.9 63.8 f8 51.6 59.2 f9 52.0 42.3
(256) In practical example 11, a projection distance for a projection optical system and a size of an image projected on a screen are 775 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in practical example 11 is 0.60. Furthermore, from Table 44, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 11 is |xfo of f1yfo of f9|=71.2 mm42.3 mm=28.9 mm. A focal length of a first optical system included in a projection optical system in practical example 11 is 35.59 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in practical example 11 is 28.9 mm/35.59 mm=0.81. A value of ImTr for a projection optical system in practical example 11 is 0.810.60=0.49.
(257)
(258)
(259) Additionally, a spot on a screen in any of practical examples 1-10 is focused better than a spot on a screen in practical example 11. Furthermore, a value of a white MTF with respect to a frequency in a WXGA resolution in any of practical examples 1-10 is higher than a value of a white MTF with respect to a frequency in a WXGA resolution in practical example 11.
(260)
(261) Additionally, a distortion for a projection optical system in any of practical examples 1-10 is smaller than a distortion for a projection optical system in practical example 11.
Comparative Example 1
(262) A value of ImTr for a projection optical system in practical example 1 described in Japanese Patent Application Publication No. 2007-079524 as a comparative example 1 will be obtained.
(263) Table 45 illustrates xfo and yfo for a projection optical system in comparative example 1.
(264) TABLE-US-00045 TABLE 45 POSITION OF LIGHT RAY xfo yfo f1 230.6 189.1 f2 187.0 104.0 f3 141.2 38.4 f4 222.0 169.5 f5 180.5 92.8 f6 137.2 32.8 f7 122.3 196.6 f8 163.3 64.6 f9 126.9 18.4
(265) In comparative example 1, a projection distance for a projection optical system and a size of an image projected on a screen are 416 mm and 52.7 inches, respectively, and hence, a throw ratio Tr for a projection optical system in comparative example 1 is 0.36. Furthermore, from Table 45, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 1 is |xfo of f1yfo of f9|=230.6 mm18.4 mm=212.2 mm. A focal length of a first optical system included in a projection optical system in comparative example 1 is 35.87 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 1 is 212.2 mm/35.87 mm=5.92. A value of ImTr for a projection optical system in comparative example 1 is 5.920.36=2.13.
Comparative Example 2
(266) A value of ImTr for a projection optical system in practical example 1 described in Japanese Patent Application Publication No. 2008-116688 as a comparative example 2 will be obtained.
(267) Table 46 illustrates xfo and yfo for a projection optical system in comparative example 2.
(268) TABLE-US-00046 TABLE 46 POSITION OF LIGHT RAY xfo yfo f1 227.9 203.2 f2 185.4 119.2 f3 138.5 44.2 f4 217.5 180.3 f5 177.5 104.8 f6 133.9 36.6 f7 125.3 188.3 f8 157.3 69.2 f9 122.0 16.2
(269) In comparative example 2, a projection distance for a projection optical system and a size of an image projected on a screen are 501 mm and 63.4 inches, respectively, and hence, a throw ratio Tr for a projection optical system in comparative example 2 is 0.36. Furthermore, from Table 46, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 2 is |xfo of f1yfo of f9|=227.9 mm16.2 mm=211.7 mm. A focal length of a first optical system included in a projection optical system in comparative example 2 is 32.91 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 2 is 211.7 mm/32.91 mm=6.43. A value of ImTr for a projection optical system in comparative example 2 is 6.430.36=2.32.
Comparative Example 3
(270) A value of ImTr for a projection optical system in practical example 1 described in Japanese Patent Application Publication No. 2008-165187 as a comparative example 3 will be obtained.
(271) Table 47 illustrates xfo and yfo for a projection optical system in comparative example 3.
(272) TABLE-US-00047 TABLE 47 POSITION OF LIGHT RAY xfo yfo f1 108.3 105.0 f2 78.7 49.2 f3 35.9 7.3 f4 88.5 100.0 f5 72.4 38.5 f6 32.4 10.6 f7 47.4 77.6 f8 14.5 54.5 f9 23.4 17.9
(273) In comparative example 3, a projection distance for a projection optical system and a size of an image projected on a screen are 440 mm and 60 inches, respectively, and hence, a throw ratio Tr for a projection optical system in comparative example 3 is 0.36. Furthermore, from Table 47, a length of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 3 is |xfo of f1yfo of f9|=108.3 mm(17.9 mm)=126.2 mm. A focal length of a first optical system included in a projection optical system in comparative example 3 is 26.4 mm. A normalized length Im of an intermediate image in a direction of an optical axis of a first optical system for a projection optical system in comparative example 3 is 126.2 mm/26.4 mm=4.78. A value of ImTr for a projection optical system in comparative example 3 is 4.780.36=1.72.
(274) (Result)
(275) Table 48 illustrates throw ratios Tr, total lengths, and values of ImTr for projection optical systems in practical examples 1-11 and projection optical systems in comparative examples 1-3.
(276) TABLE-US-00048 TABLE 48 Tr TOTAL LENGTH Im Tr PRACTICAL 0.18 256 0.90 EXAMPLE 1 PRACTICAL 0.23 236 0.92 EXAMPLE 2 PRACTICAL 0.30 200 0.75 EXAMPLE 3 PRACTICAL 0.40 207 0.77 EXAMPLE 4 PRACTICAL 0.52 192 0.69 EXAMPLE 5 PRACTICAL 0.60 190 0.65 EXAMPLE 6 PRACTICAL 0.62 237 1.47 EXAMPLE 7 PRACTICAL 0.15 224 0.83 EXAMPLE 8 PRACTICAL 0.18 201 0.82 EXAMPLE 9 PRACTICAL 0.62 339 1.58 EXAMPLE 10 PRACTICAL 0.60 186 0.49 EXAMPLE 11 COMPARATIVE 0.36 575 2.13 EXAMPLE 1 COMPARATIVE 0.36 526 2.32 EXAMPLE 2 COMPARATIVE 0.36 385 1.72 EXAMPLE 3
(277) As illustrated in Table 48, any of projection optical systems in practical examples 1-11 and projection optical systems in comparative examples 1-3 satisfies a throw ratio Tr0.7. Hence, any of projection optical systems in practical examples 1-11 and projection optical systems in comparative examples 1-3 provides a more compact projection optical system capable of projecting an image onto a surface to be projected on at a shorter distance.
(278) However, as illustrated in Table 48, values of ImTr for projection optical systems in practical examples 1-11 are smaller than values of ImTr for projection optical systems in comparative examples 1-3. Herein, Im means a normalized length of an intermediate image in a direction of an optical axis of a first optical system.
(279) For example, when a projection optical system in practical example 4 has a value of Tr which is generally comparable to a value of Tr for a projection optical system in any of comparative examples 1-3 therewith, a value of ImTr (0.77) for a projection optical system in practical example 4 is smaller than any of values of ImTr (2.13, 2.32, and 1.72) for projection optical systems in comparative examples 1-3. A value of Im for a projection optical system in practical example 4 is generally smaller than any of values of Im for projection optical systems in comparative examples 1-3, because a value of Tr for a projection optical system in practical example 4 is generally comparable to any of values of Tr for projection optical systems in comparative examples 1-3. Furthermore, a value of total length (207) for a projection optical system in practical example 4 is smaller than any of values of total length (575, 525, and 385) for projection optical systems in comparative examples 1-3. It may be possible to reduce a distance from a last end of a first optical system included in a projection optical system in practical example 4 to a last end of a second optical system therein, compared to a distance from a last end of a first optical system included in a projection optical system in any of comparative examples 1-3 to a last end of a second optical system therein, because a value of Im for a projection optical system in practical example 4 is generally smaller than any of values of Im for projection optical systems in comparative examples 1-3. As a result, a value of total length for a projection optical system in practical example 4 is smaller than a value of total length for a projection optical system in any of comparative examples 1-3.
(280) Furthermore, as illustrated in Table 48, when a value of throw ratio Tr for a projection optical system is reduced, for example, when a projection distance of a projection optical system is reduced, a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system tends to increase. For example, when a projection distance of a projection optical system in any of comparative examples 1-3 is reduced, a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system increases and a total length of a projection optical system increase. As a result, a size and weight of an image projecting apparatus including a projection optical system in any of comparative examples 1-3 increases, and hence, an image projecting apparatus including a projection optical system in any of comparative examples 1-3 provides a user with an image projecting apparatus with a relatively low usability in such a manner that an image projecting apparatus including a projection optical system in any of comparative examples 1-3 occupies more space and/or it is not easy to carry an image projecting apparatus including a projection optical system in any of comparative examples 1-3, etc.
(281)
(282) In
(283)
(284) In
(285)
(286) In
(287) While any of projection optical systems in practical examples 1-11 and projection optical systems in comparative examples 1-3 satisfies a throw ratio less than or equal to 0.7 as illustrated in
(288) As illustrated in
(289) Thus, a condition that a value of ImTr for a projection optical system is less than or equal to 1.70 is satisfied, like a projection optical system in any of practical examples 1-11, and thereby, it may be possible to provide a more compact projection optical system capable of projecting an image onto a surface to be projected on at a shorter distance.
(290) On the other hand, when a value of ImTr for a projection optical system is greater than 1.70 like a projection optical system in any of comparative examples 1-3, a throw ratio Tr for a projection optical system or a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system increases, and hence, it may be difficult to provide a more compact projection optical system capable of projecting an image onto a surface to be projected on at a shorter distance.
(291) Furthermore, a value of ImTr for a projection optical system is preferably less than or equal to 1.50 to provide a more compact projection optical system capable of projecting an image onto a surface to be projected on at a shorter distance. When a value of ImTr for a projection optical system is less than or equal to 1.50, for example, it may be possible to further reduce a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system and it may be possible to reduce a total length of a projection optical system. As a result, it may be possible to provide a more compact projection optical system.
(292) For example, as illustrated in Table 48, a value of a throw ratio Tr of a projection optical system in practical example 7 is generally comparable to a value of a throw ratio Tr of a projection optical system in practical example 10. However, while a value of ImTr for a projection optical system in practical example 7 is less than or equal to 1.50, a value of ImTr for a projection optical system in practical example 10 is greater than 1.50. Hence, a value of Im for a projection optical system in practical example 7 is smaller than a value of Im for a projection optical system in practical example 10. As a result, a total length of a projection optical system in practical example 7 is smaller than a total length of a projection optical system in practical example 10.
(293) Furthermore, a value of ImTr for a projection optical system is preferably greater than or equal to 0.50. When a value of ImTr for a projection optical system is greater than or equal to 0.50, it may be possible to increase a throw ratio Tr for a projection optical system or increase a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system. When it may be possible to increase a throw ratio Tr for a projection optical system, it may be possible to reduce an angle of incidence of a light ray incident on a screen. As a result, it may be possible to reduce an aberration of a light beam incident on a screen and it may be possible to project a better image onto a screen. Furthermore, when it may be possible to increase a normalized length Im of an intermediate image in a direction of an optical axis of a first optical system included in a projection optical system, it may be possible to increase a cross-section of a light beam from an intermediate image in a second optical system included in a projection optical system. As a result, it may be possible to correct an aberration of a light beam from an intermediate image more readily by a second optical system and it may be possible to project a better image onto a screen.
(294) For example, as illustrated in Table 48, while a value of ImTr for a projection optical system in any of practical examples 1-10 is greater than or equal to 0.50, a value of ImTr for a projection optical system in practical example 11 is less than 0.50. Furthermore, a quality of an image projected onto a screen by a projection optical system in any of practical examples 1-10 is higher than a quality of an image projected onto a screen by a projection optical system in practical example 11. A projection optical system in any of practical examples 1-10 satisfies a condition that a value of ImTr for a projection optical system is greater than or equal to 0.50, and thereby, it may be possible to reduce an aberration (for example, an astigmatic aberration, a distortion aberration, etc.) for a light beam to be projected by a projection optical system, compared to a projection optical system in practical example 11.
(295) Table 49 illustrates a Petzval sum for a first optical system included in a projection optical system in any of practical examples 1-11 and comparative examples 1-3.
(296) TABLE-US-00049 TABLE 49 PRACTICAL 0.01135 EXAMPLE 1 PRACTICAL 0.01849 EXAMPLE 2 PRACTICAL 0.02992 EXAMPLE 3 PRACTICAL 0.03027 EXAMPLE 4 PRACTICAL 0.03444 EXAMPLE 5 PRACTICAL 0.03656 EXAMPLE 6 PRACTICAL 0.02461 EXAMPLE 7 PRACTICAL 0.01206 EXAMPLE 8 PRACTICAL 0.01732 EXAMPLE 9 PRACTICAL 0.02216 EXAMPLE 10 PRACTICAL 0.03640 EXAMPLE 11 COMPARATIVE 0.00705 EXAMPLE 1 COMPARATIVE 0.00982 EXAMPLE 2 COMPARATIVE 0.01191 EXAMPLE 3
(297) A Petzval sum PTZ for a first optical system included in a projection optical system is represented by a formula of:
(298)
(299) when the first optical system is composed of refractive surfaces which are a first surface to a k-th surface. Herein, s denotes a number of a refractive surface. ns denotes a refractive index at a s-th surface and ns1 denotes a refractive index at a s1-th surface. rs denotes a radius of curvature of a s-th surface.
(300) In a projection optical system according to an embodiment of the present invention, when a projection distance of a projection optical system is small and an angle of incidence of a light ray projected onto a surface to be projected on is large, an aberration such as an astigmatic aberration or a field curvature, etc., for a light beam projected onto the surface to be projected on is preferably corrected by a second optical system. In such a case, it is preferable to increase a cross-section of a light beam to be projected onto the surface to be projected on, in a second optical system. To that end, it is preferable to curve toward a first optical system an intermediate image which is imaged by the first optical system and increase a field curvature of the intermediate image which is imaged by the first optical system. That is, it is preferable that a sign of a Patzval sum of a first optical system included in a projection optical system according to an embodiment of the present invention is negative and an absolute value of a Petzval sum of a first optical system included in a projection optical system according to an embodiment of the present invention is large.
(301) From Table 49, a Petzval sum PTZ of a first optical system included in a projection optical system in any of practical examples 1-11 is less than or equal to 0.01135. When a Petzval sum PTZ of a first optical system included in a projection optical system is less than or equal to 0.01135, it may be possible to provide a projection optical system capable of projecting a better image onto a screen, such as a projection optical system in any of practical examples 1-11.
(302) Additionally, although a projection optical system with a fixed focal length is illustrated in any of practical examples 1-11, it may be possible to adjust a focal length of a projection optical system (or conduct adjustment of focusing for the projection optical system) due to movement of a first optical system or second optical system included in the projection optical system.
(303) [Appendix]
(304) <An Illustrative Embodiment(s) of a Projection Optical System and an Image Projecting apparatus>
(305) At least one illustrative embodiment of the present invention may relate to a projection optical system and an image projecting apparatus.
(306) One object of at least one illustrative embodiment of the present invention may be to provide a more compact projection optical system capable of projecting a better image onto a surface to be projected on at a shorter distance.
(307) Another object of at least one illustrative embodiment of the present invention may be to provide a more compact image projecting apparatus capable of projecting a better image onto a surface to be projected on at a shorter distance.
(308) According to one aspect of at least one illustrative embodiment of the present invention, there is provided a projection optical system including a first optical system which forms a first image conjugate to an object and has an optical axis and a second optical system which projects a second image conjugate to the first image onto a surface to be projected on, wherein the first image satisfies a condition of:
ImTr1.70,
wherein Im denotes a length of the first image in a direction of an optical axis of the first optical system which is normalized by a focal length of the first optical system and Tr denotes a throw ratio for the projection optical system.
(309) According to another aspect of at least one illustrative embodiment of the present invention, there is provided an image projecting apparatus including an image forming part which forms an image and a projection optical system which projects the image onto a surface to be projected on, wherein the projection optical system is a projection optical system according to one aspect of at least one illustrative embodiment of the present invention.
(310) According to one aspect of at least one illustrative embodiment of the present invention, it may be possible to provide a more compact projection optical system capable of projecting a better image onto a surface to be projected on at a shorter distance.
(311) According to another aspect of at least one illustrative embodiment of the present invention, it may be possible to provide a more compact image projecting apparatus capable of projecting a better image onto a surface to be projected on at a shorter distance.
(312) Illustrative embodiment (1) is a projection optical system including a first optical system which forms a first image conjugate to an object and has an optical axis and a second optical system which projects a second image conjugate to the first image onto a surface to be projected on, wherein the first image satisfies a condition of:
ImTr1.70,
wherein:
(313) Im denotes a length of the first image in a direction of an optical axis of the first optical system which is normalized by a focal length of the first optical system; and
(314) Tr denotes a throw ratio for the projection optical system.
(315) Illustrative embodiment (2) is the projection optical system as described in illustrative embodiment (1), wherein the first image satisfies a condition of:
ImTr1.50.
(316) Illustrative embodiment (3) is the projection optical system as described in illustrative embodiment (1) or (2), wherein the first image satisfies a condition of:
0.50ImTr.
(317) Illustrative embodiment (4) is the projection optical system as described in any of illustrative embodiments (1) to (3), wherein the projection optical system satisfies a condition of:
Tr0.7.
(318) Illustrative embodiment (5) is the projection optical system as described in any of illustrative embodiments (1) to (4), wherein a Petzval sum for the first optical system is less than or equal to 0.010 mm.sup.1.
(319) Illustrative embodiment (6) is the projection optical system as described in any of illustrative embodiments (1) to (5), wherein the second optical system includes a reflection surface with a free-form surface shape.
(320) Illustrative embodiment (7) is an image projecting apparatus including an image forming part which forms an image and a projection optical system which projects the image onto a surface to be projected on, wherein the projection optical system is the projection optical system as described in any of illustrative embodiments (1) to (6).
(321) Although the illustrative embodiments and specific examples of the present invention have been described with reference to the accompanying drawings, the present invention is not limited to any of the illustrative embodiments and specific examples of the present invention and the illustrative embodiments and specific examples of the present invention may be altered, modified, or combined without departing from the scope of the present invention.
(322) The present application claims the benefit of priority based on Japanese Patent Application No. 2011-201690 filed on Sep. 15, 2011, the entire content of which is hereby incorporated by reference herein.