JP5987459B2 - Optical system for image projection device and image projection device - Google Patents

Description

  The present invention relates to an image projection apparatus that enlarges and projects an image or the like of an image display element.

  In an image projection apparatus, in order to project an image displayed on an image display element onto a screen (projection surface) without distortion, the optical axis of the projection optical system is generally perpendicular to the screen. . However, in some cases, the image projection apparatus is configured under the condition that the optical axis of the projection optical system is not perpendicular to the screen in order to reduce the size, ease of use, and cost of the image projection apparatus. This is so-called oblique projection. In this case, there arises a problem that the rectangular image display area is projected into a trapezoid. There are two well-known methods for correcting such trapezoidal distortion: a method of correcting by image processing and a method of correcting by an optical element having an optical surface that is non-rotationally symmetric with respect to the central axis.

  The method of correcting by image processing is to cancel the trapezoidal distortion that is opposite to the trapezoidal distortion that occurs in the optical system by applying it to the display image in advance by image processing. Although correction by this method has an advantage of not requiring a new burden on the optical system, it has a great disadvantage that the image quality of the projected image is deteriorated. Therefore, it cannot be adopted for a projection apparatus having a large incident angle on the screen, that is, a large correction amount of trapezoidal distortion. On the other hand, a method for correcting optically non-rotationally symmetric trapezoidal distortion (see, for example, Patent Document 1) requires an optical surface that is nonrotationally symmetric with respect to the central axis. The correction by this method has an advantage that the image quality of the projected image does not deteriorate even if the keystone distortion is corrected.

JP 2010-266482 A

  However, in such a conventional image projection apparatus, the apparatus cannot be miniaturized by oblique projection.

  The present invention has been made in view of such problems, and has an optical system for a video projection device capable of satisfactorily correcting trapezoidal distortion of a projected image, and a video projection provided with the same, while having a compact configuration. An object is to provide an apparatus.

In order to achieve such an object, according to an aspect of the present invention, an optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction, An optical element group arranged in order from the image display element side along the optical axis, a free-form surface lens group having a free-form surface lens formed non-rotationally symmetric with respect to the center axis, and non-rotation with respect to the center axis The optical element group includes an aspherical mirror having an aspherical reflecting surface formed rotationally symmetrically with respect to the central axis, and satisfies the following conditional expression: An optical system for a video projection device is provided.
−0.10 <2 / MR <−0.01
20 ° <| α | <45 °
However,
MR: radius of curvature of the reflection surface of the aspherical mirror,
α: An angle formed by the optical axis between the image display element and the aspherical mirror and the central axis of the aspherical mirror.
An optical system for an image projection apparatus that enlarges an image displayed on the image display element and projects the image on a predetermined projection plane from an oblique direction, and is arranged in order from the image display element side along the optical axis. An optical element group comprising: an element group; a free-form surface lens group having a free-form surface lens formed non-rotationally symmetric with respect to the central axis; and a free-form surface mirror formed non-rotationally symmetric with respect to the central axis. Are arranged in order from the image display element side along the optical axis, and an aspherical mirror having an aspherical reflecting surface formed rotationally symmetrically with respect to the central axis, and formed rotationally symmetrically with respect to the central axis There is provided an optical system for an image projection apparatus, which comprises a cemented lens having a positive refractive power formed by bonding a convex lens and a concave lens, and satisfies the following conditional expression.
1.00 <fdu / F1 <2.00
However,
fdu: focal length of the cemented lens,
F1: The combined focal length of the optical element group.

Further, according to an aspect of the present invention, the image is projected from an oblique direction on a surface that is used on a predetermined installation surface and is substantially the same as the installation surface or substantially parallel to the installation surface. There is provided an image projection apparatus, wherein the optical system constituting the image projection apparatus is the optical system for an image projection apparatus according to the present invention.

  According to the present invention, it is possible to satisfactorily correct the trapezoidal distortion of a projected image while having a compact configuration.

It is an optical path figure of the optical system for image projection apparatuses concerning the 1st example. It is an enlarged view of the optical system for image projection apparatuses concerning the 1st example. It is a spot diagram of the optical system for image projection apparatuses concerning the 1st example. It is a figure which shows the distortion of the optical system for image projection apparatuses which concerns on 1st Example. It is an optical path figure of the optical system for image projection apparatuses concerning the 2nd example. It is an enlarged view of the optical system for image projection apparatuses which concerns on 2nd Example. It is a spot diagram of the optical system for video projectors concerning the 2nd example. It is a figure which shows the distortion of the optical system for image projection apparatuses which concerns on 2nd Example. It is an optical path figure of the optical system for image projection apparatuses concerning the 3rd example. It is an enlarged view of the optical system for image projection apparatuses which concerns on 3rd Example. It is a spot diagram of the optical system for video projectors concerning the 3rd example. It is a figure which shows the distortion of the optical system for image projection apparatuses which concerns on 3rd Example. It is a perspective view of a video projection device. It is sectional drawing which shows the inside of an image projection apparatus. It is explanatory drawing which shows an example of a local coordinate system.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. An image projection apparatus PRJ of this embodiment is shown in FIGS. 13 is a perspective view of the image projection device PRJ, and FIG. 14 is a cross-sectional view showing the inside of the image projection device PRJ.

  The image projection apparatus PRJ shown in FIGS. 13 and 14 includes a cylindrical box-shaped housing BD having a window portion W on the front surface, an image display element DS accommodated in the inside of the housing BD, and an image projection. And an apparatus optical system PL. Such an image projection device PRJ is used in a state where it is installed on a predetermined installation surface Q such as the upper surface of a table (or desk) or a wall surface in the vicinity of a whiteboard, and light from a light source (not shown). After the image is reflected by the image display element DS, the image (light) obtained by the reflection by the image display element DS is projected through the image projection apparatus optical system PL and the window W, which will be described in detail later. The apparatus PRJ (housing BD) is configured to be enlarged and projected from an oblique direction onto a projection surface R (screen) set on the same surface as the installation surface Q.

  As the light source (not shown), for example, a lamp that generates white light with high luminance, such as a mercury lamp or a halogen lamp, an LED (Light Emitting Diode) light source, or the like is used. Further, as the video display element DS, for example, a DMD (Digital Micromirror Device) element capable of displaying video (or images) input from an external input device (such as a personal computer or a storage device), a reflective liquid crystal display element, or the like Is used.

The optical system PL for an image projection apparatus includes an optical element group G1 having a mirror or a lens formed in a rotationally symmetric manner with respect to the central axis, arranged in order from the video display element DS side along the optical axis, and the central axis. And a free-form surface lens group G2 having a free-form surface lens formed non-rotationally symmetric, and a free-form surface mirror M2 formed non-rotationally symmetric with respect to the central axis. In such an image projection apparatus optical system PL, the light emitted from the image display element DS passes through the optical element group G1 and the free-form surface lens group G2, and is reflected by the free-form surface mirror M2 in an oblique direction and projected onto the projection surface R ( Is projected on the screen.

  In the present embodiment, the optical element group G1 includes an aspherical mirror M1 having an aspherical reflecting surface formed rotationally symmetrically with respect to the central axis. According to such a configuration, by providing the aspherical mirror M1 in the optical element group G1, the Petzval sum can be reduced, and the field curvature can be corrected well.

  In the present embodiment, it is preferable that the condition represented by the following conditional expression (1) is satisfied.

−0.10 <2 / MR <−0.01 (1)
However,
MR: the radius of curvature of the center of the reflecting surface of the aspherical mirror M1.

Conditional expression (1) is a conditional expression that defines an appropriate value of the central curvature radius of the aspherical mirror M1 in the optical element group G1. When the condition is less than the lower limit value of the conditional expression (1), the power of the aspherical mirror M1 becomes too large, so that the off-axis spherical aberration cannot be corrected. In order to better correct the spherical aberration of the entire system, it is desirable to set the lower limit of conditional expression (1) to −0.05 [mm ⁻¹ ]. On the other hand, when the condition exceeds the upper limit value of the conditional expression (1), the power of the aspherical mirror M1 becomes too small, so that the field curvature generated in the optical element group G1 increases. In order to correct this field curvature more satisfactorily, it is desirable to set the upper limit value of conditional expression (1) to −0.03 [mm ⁻¹ ].

  In the present embodiment, it is preferable that the condition represented by the following conditional expression (2) is satisfied.

20 ° <| α | <45 ° (2)
However,
α: An angle formed by the optical axis between the image display element DS and the aspherical mirror M1 and the central axis of the aspherical mirror M1.

  Conditional expression (2) is a conditional expression that defines an appropriate angle at which the aspherical mirror M1 turns back the light beam emitted from the video display element DS. When the condition is less than the lower limit value of the conditional expression (2), α is too small, and the light beam interferes with the lens or the prism. In order to configure the optical system with a margin, it is desirable to set the lower limit of conditional expression (2) to 25 °. On the other hand, when the condition exceeds the upper limit value of the conditional expression (2), α becomes too large, so that it is difficult to correct spherical aberration and coma generated on the reflecting surface of the aspherical mirror M1. In addition, the entire optical system becomes large. In order to correct various aberrations better, it is desirable to set the upper limit of conditional expression (2) to 40 °.

  In the present embodiment, when the optical element group G1 includes an aspherical mirror M1 and a cemented lens having a positive refractive power, which are arranged in order from the image display element DS side along the optical axis, the following conditional expression ( It is preferable to satisfy the condition represented by 3). The cemented lens is a cemented doublet formed by bonding a convex lens and a concave lens that are formed rotationally symmetrically with respect to the central axis.

1.00 <fdu / F1 <2.00 (3)
However,
fdu: focal length of the cemented lens,
F1: The combined focal length of the optical element group G1.

  Conditional expression (3) is a condition that defines an appropriate combined focal length of the cemented lens (junction type doublet) in the optical element group G1. When the condition exceeds the upper limit value of the conditional expression (3), the focal length of the cemented lens becomes too large, which increases the power burden of the aspherical mirror M1, and as a result, it is difficult to correct spherical aberration and coma aberration. Become. In order to correct various aberrations better, it is desirable to set the upper limit of conditional expression (3) to 1.60. On the other hand, when the condition is lower than the lower limit value of the conditional expression (3), the focal length of the cemented lens becomes too small, so that it is difficult to correct the curvature of field that occurs in the optical element group G1. In order to correct this curvature of field more satisfactorily, it is desirable to set the lower limit of conditional expression (3) to 1.40.

  Further, when the optical element group G1 includes the aspherical mirror M1 and a cemented lens having a positive refractive power, it is preferable that the condition represented by the following conditional expression (4) is satisfied.

0.10 <Nen-Nep <0.30 (4)
However,
Nep: refractive index of the convex lens material for the e-line,
Nen: Refractive index with respect to e-line of the material of the concave lens.

Conditional expression (4) is a conditional expression that defines an appropriate combination of a convex lens and a concave lens in a cemented lens (a cemented doublet) by a refractive index difference based on e-line. When the condition exceeds the upper limit value of the conditional expression (4), chromatic aberration increases and it becomes difficult to correct spherical aberration due to the wavelength difference. In order to better correct spherical aberration due to the wavelength difference, it is desirable to set the upper limit of conditional expression (4) to 0.20. On the other hand, when the condition is lower than the lower limit value of the conditional expression (4), the refractive index difference becomes too small, and it becomes difficult to correct the spherical aberration. In order to correct spherical aberration better, it is desirable to set the lower limit of conditional expression (4) to 0.15.

  Further, when the optical element group G1 includes the aspherical mirror M1 and a cemented lens having a positive refractive power, it is preferable to satisfy the condition expressed by the following conditional expression (5).

20 <νep−νen <50 (5)
However,
νep: Abbe number for the e-line of the convex lens material,
νen: Abbe number for the e-line of the material of the concave lens.

Conditional expression (5) is a conditional expression that defines an appropriate combination of a convex lens and a concave lens in a cemented lens (a cemented doublet) by a difference in dispersion on the basis of e-line. When the condition exceeds the upper limit value of conditional expression (5), the chromatic aberration is excessively corrected. In order to correct chromatic aberration more satisfactorily, it is desirable to set the upper limit of conditional expression (5) to 45. On the other hand, when the condition is lower than the lower limit value of the conditional expression (5), the chromatic aberration is insufficiently corrected. In order to correct chromatic aberration more satisfactorily, it is desirable to set the lower limit of conditional expression (5) to 30.

  In the present embodiment, the free-form surface lens group G2 may include a diffractive optical element and a free-form surface lens that are arranged in order from the image display element DS side along the optical axis. According to such a configuration, the chromatic aberration can be favorably corrected according to the free-form surface shape by the diffractive optical element.

  The diffractive optical element is a close-contact multilayer diffractive optical element, and preferably satisfies the condition represented by the following conditional expression (6). The close-contact multilayer diffractive optical element has a first optical material having a relatively high refractive index and a small dispersion, and a relatively low refractive index and a large dispersion relative to the first optical material. And a second optical material.

Ne1−Ne2 ≧ 0.010 (6)
However,
Ne1: refractive index of the first optical material with respect to e-line
Ne2: Refractive index for the e-line of the second optical material.

Conditional expression (6) is a conditional expression that defines an appropriate combination of materials of the diffractive optical element by the refractive index difference based on the e-line. When the condition is less than the lower limit value of the conditional expression (6), the grating height on the diffraction surface becomes too large, so that the diffraction efficiency in a wide wavelength range is lowered and flare is increased. Moreover, it becomes difficult to process the diffractive optical element. In order to obtain a better adhesion multilayer diffractive optical element, it is desirable to set the lower limit of conditional expression (6) to 0.020.

  The diffractive optical element is a close-contact multilayer diffractive optical element, and preferably satisfies the condition represented by the following conditional expression (7).

(NF'2-NC'2)-(NF'1-NC'1) ≥0.0015 (7)
However,
NF′1: Refractive index of the first optical material with respect to the F ′ line,
NC'1: Refractive index with respect to C 'line of the first optical material,
NF′2: refractive index of the second optical material with respect to the F ′ line,
NC'2: Refractive index with respect to the C 'line of the second optical material.

  Conditional expression (7) is a conditional expression that defines an appropriate combination of materials of the diffractive optical element by a difference in dispersion of the materials. When the condition is lower than the lower limit value of the conditional expression (7), the difference in dispersion of the materials to be combined becomes too small, so that it is difficult to maintain high diffraction efficiency in a wide wavelength range, and the conditional expression (6) Similarly, flare increases. In order to obtain better diffraction efficiency, it is desirable to set the lower limit of conditional expression (7) to 0.0020.

  The diffractive optical element is preferably disposed in the vicinity of the entrance pupil of the optical system for image projection apparatus PL, and the diffractive surface of the diffractive optical element is preferably formed in a non-rotational symmetry with respect to the central axis. According to such a configuration, it is possible to satisfactorily correct the chromatic aberration of the as component (the focus difference between the x-axis direction and the y-axis direction described later) due to different wavelengths.

  Here, the local coordinate system of the diffractive optical element will be described. In this embodiment, the local coordinate system of the diffractive optical element is, for example, as shown in FIG. 15, an (x, y) coordinate system with the intersection point between the diffractive surface of the diffractive optical element and the optical axis as the origin. At this time, the coordinate axis perpendicular to the optical axis along the plane passing through the optical axis between the image display element DS and the aspherical mirror M1 and the optical axis between the aspherical mirror M1 and the free-form mirror M2 is defined as the y axis. The coordinate axis perpendicular to the optical axis and the y axis is taken as the x axis.

In such a local coordinate system, the phase shape of the diffractive surface of the diffractive optical element is defined by the following equation (A). In the following equation (A), the phase shape of the diffraction surface of the diffractive optical element is φ, the reference wavelength is λ ₀ , the diffraction order is m, natural numbers including 0 are i and j, and x and y are Let D (i, j) be the coefficient of the polynomial that contains it.

In the diffractive optical element of this embodiment, it is preferable that the condition represented by the following conditional expression (8) is satisfied.

  Conditional expression (8) is a conditional expression that defines the diffractive optical surface. When the condition (8) is not within the upper limit and lower limit values, astigmatism is greatly generated, and it is difficult to correct astigmatism and chromatic aberration generated by the free-form surface lens group. In order to obtain a better correction effect, it is desirable to set the lower limit of conditional expression (8) to 2.90. In order to obtain a better correction effect, it is desirable to set the upper limit of conditional expression (8) to 5.0.

  As described above, according to the present embodiment, the optical system PL for a video projection apparatus that can satisfactorily correct the trapezoidal distortion of a projected image, and the video projection apparatus PRJ including the same, with a compact configuration. Can be obtained.

  Embodiments of the present application will be described below with reference to the accompanying drawings. In each embodiment, an aspherical surface that is rotationally symmetric with respect to the optical axis (center axis) and an aspherical surface that is not rotationally symmetric with respect to the central axis (free curved surface) are used. Therefore, before describing each embodiment, these defining formulas will be described.

  First, the aspherical surface rotationally symmetric with respect to the optical axis (center axis) is defined by the following equation (B). In the following formula (B), z is a sag amount in the optical axis direction from the apex of the lens surface, h is a distance from the optical axis, c is a curvature (the reciprocal of the radius of curvature), and K is It is a conic constant, and A to E are coefficients related to each power series term of h.

Next, an aspheric surface (free curved surface) that is non-rotationally symmetric with respect to the central axis is defined by the following equation (C). In the following formula (C), z is the sag amount in the optical axis direction from the apex of the lens surface, h is the distance from the optical axis, c is the curvature (the reciprocal of the radius of curvature), and K is It is a conic constant, and C (m, n) is a coefficient of the aspheric term x ^m y ⁿ .

In each embodiment, the eccentricity is performed in the local coordinate system of each surface. In the local coordinates, the coordinate axis in the optical axis direction in which the direction from the image display element DS toward the aspherical mirror M1 is positive is the z axis, the optical axis between the image display element DS and the aspherical mirror M1, and the aspherical mirror M1. The coordinate axis perpendicular to the z axis along the plane passing through the optical axis between the free curved mirror M2 and the free curved mirror M2 and the optical axis between the free curved mirror M2 and the projection plane is the y axis, and perpendicular to the z axis and the y axis. This is a coordinate system (right-handed system) translated along the optical axis with the coordinate axis as the x axis (see FIG. 15). Note that the origin of each local coordinate is the intersection of each surface and the optical axis. The type of eccentricity is rotation about the x-axis (referred to as α rotation), and when turning in the positive direction of the x-axis, the counterclockwise direction is the positive direction of α rotation.

(First embodiment)
1st Example of this application is described using FIGS. 1-4 and Table 1-Table 4. FIG. FIG. 1 is an optical path diagram of an optical system for an image projection apparatus according to the first embodiment, and FIG. 2 is an enlarged view of the optical system for an image projection apparatus according to the first embodiment. The optical system PL (PL1) for a video projection apparatus according to the first embodiment is an optical element having an optical surface that is arranged in order from the video display element DS side along the optical axis and that is rotationally symmetric with respect to the central axis. Consists of a group G1, a free-form surface lens group G2 having a lens surface formed non-rotationally symmetric with respect to the central axis, and a free-form surface mirror M2 having a reflection surface formed non-rotationally symmetric with respect to the central axis Is done. The optical system PL for a video projection apparatus according to each embodiment utilizes, for example, a projection capability and a reduction in size due to a large screen incident angle, and is installed on a desk, for example, and the desk is used as a screen (image plane I). It is used for a desktop projector that projects an image (image) without trapezoidal distortion from a position that does not interfere with the visual field.

  Two parallel flat plates P1 and P2 are arranged in the vicinity of the video display element DS. The plane parallel plates P1 and P2 correspond to a face plate of a display element, a color synthesis prism, a PBS (polarization beam splitter), and the like, and are irrelevant to the essence of the present invention. An aperture stop S is arranged between the optical element group G1 and the free-form surface lens group G2.

  The optical element group G1 includes an aspherical mirror M1 and a cemented lens L10 having positive refractive power, which are arranged in order from the image display element DS side along the optical axis. The aspherical mirror M1 has an aspherical reflecting surface formed rotationally symmetrical with respect to the central axis. The cemented lens L10 is a cemented doublet formed by bonding a convex lens L11 and a concave lens L12 that are formed rotationally symmetrically with respect to the central axis.

  The free-form surface lens group G2 is arranged in order from the image display element DS side and has a first positive curved surface lens L21 having a substantially positive refractive power (having a converging effect) and a substantially negative refractive power (having a diverging effect). ) The second free-form surface lens L22 and a third free-form surface lens L23 having a substantially negative refractive power (having a diverging action). The entrance-side (object plane side) and exit-side (image plane side) lens surfaces of the first to third free-form surface lenses L21 to L23 have lens surface shapes that are non-rotationally symmetric with respect to the central axis.

  The light beam emitted from the video display element DS is reflected by the reflecting surface of the aspherical mirror M1, and is bent at a predetermined angle. The light beam reflected by the reflecting surface of the aspherical mirror M1 passes through the cemented lens L10 and the first to third free-form surface lenses L21 to L23 and is reflected by the reflecting surface of the free-form surface mirror M2. The light beam reflected by the reflecting surface of the free-form mirror M2 forms an image on the screen (image surface I).

  Table 1 below shows various data of the optical system PL1 for the image projection apparatus according to the first example. In the tables (numerical data of optical systems) shown in the following examples, “* A” written therein represents that the surface is a rotationally symmetric aspheric surface, and “* F” represents It represents that the surface is a non-rotationally symmetric aspherical surface (free-form surface). In each surface, it is assumed that the radius of curvature is positive when the center of curvature is in the positive direction of the optical axis (Z-axis). The curvature radius “∞” indicates a plane, and the refractive index of air is omitted. The radius of curvature of the aspheric surface indicates the central radius of curvature of the aspheric surface. Further, the surface numbers 1 to 15 in Table 1 correspond to the surfaces 1 to 15 in FIG.

(Table 1)
(Overall specifications)
F number 2.3
Image display area 4.93 [mm] x 3.70 [mm]
Screen 270 [mm] x 202.5 [mm]

(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
Object plane ∞ 1.410000
1 ∞ 0.650000 1.50900 62.7
2 ∞ 10.000000 1.51872 64.0
3 ∞ 10.248448
4 * A -65.64259 -11.000000 Reflective surface
5 -11.66101 -3.532777 1.49845 81.1
6 17.64110 -1.000000 1.67718 37.9
7 168.25529 -5.542219
8 (Aperture) ∞ -1.000000
9 * F ∞ -4.435885 1.53340 55.3
10 * F ∞ -4.364562
11 * F ∞ -5.000000 1.53340 55.3
12 * F ∞ -9.666656
13 * F ∞ -4.457901 1.53340 55.3
14 * F ∞ -40.000000
15 * F ∞ 200.000000 Reflection surface Image surface ∞

In the lens data of Table 1, the fourth surface to the seventh surface are the lens surfaces or reflecting surfaces of the optical element group G1, and the fourth surface is the reflecting surface of the rotationally symmetric aspherical mirror M1. . Table 2 below shows the aspherical coefficients of the fourth surface. In each table below, “En” is “× 10 ⁻ⁿ
Is shown.

(Table 2)
(Aspheric data)
Aspheric coefficient 4th surface K 0.000000
A (4th) 5.627182E-06
B (6th) -5.134480E-08
C (8th) 2.715186E-11
D (10th order) -8.763494E-13
E (12th order) 0.000000

  In the lens data of Table 1, the ninth to fifteenth surfaces are non-rotationally symmetric aspheric surfaces (free curved surfaces). In the present embodiment, the fifteenth surface is the reflecting surface of the free-form surface mirror M2. Table 3 below shows each term coefficient of these free-form surfaces.

(Table 3)
(Free curved surface data 1)
Each coefficient 9th surface 10th surface 11th surface 12th surface c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) 5.148173E-02 2.308014E-02 -5.025392E-02 -2.852182E-02
C (2,0) -2.937228E-02 -4.711872E-02 -6.989631E-02 -7.949807E-02
C (0,2) -1.894080E-02 -4.650062E-02 8.033168E-02 7.816443E-02
C (2,1) 1.396806E-02 2.063164E-02 -8.473578E-03 -1.031970E-02
C (0,3) 1.167677E-02 1.880279E-02 1.575032E-03 6.696790E-04
C (4,0) 3.709295E-04 3.009881E-04 -4.876147E-05 -5.973960E-04
C (2,2) 1.634327E-03 7.302935E-04 1.480021E-03 5.626504E-04
C (0,4) 5.573566E-04 -1.972216E-04 1.836759E-03 3.161885E-04
C (4,1) 8.036593E-05 9.666960E-05 -4.744175E-05 -2.362004E-04
C (2,3) 6.291705E-05 -2.337218E-04 -3.147218E-04 -7.318666E-05
C (0,5) -7.242086E-05 -1.919848E-04 -1.429849E-04 -2.032247E-05
C (6,0) 2.962023E-06 1.350676E-06 -1.591020E-06 -1.663527E-05
C (4,2) -2.075704E-05 -8.824057E-05 1.941558E-05 2.950168E-05
C (2,4) -3.701313E-05 -9.232971E-05 -4.215870E-05 -2.775712E-05
C (0,6) -1.787244E-05 -3.175778E-06 -2.696655E-06 -2.503408E-06
C (6,1) -1.637241E-06 -1.475774E-06 -3.358678E-07 -2.444223E-06
C (4,3) -4.904205E-06 1.451216E-05 -6.051581E-06 1.900763E-06
C (2,5) -1.511312E-06 2.239830E-05 -9.171867E-06 -3.493655E-07
C (0,7) 1.368977E-06 6.806315E-06 -3.419959E-06 4.137932E-07
C (8,0) -1.793895E-08 7.429723E-09 4.708347E-08 -1.356529E-07
C (6,2) -1.272910E-07 1.204503E-07 -6.711180E-07 -1.121788E-07
C (4,4) -1.809962E-07 -2.102193E-07 2.444797E-06 3.263891E-07
C (2,6) 2.270762E-07 -2.248388E-06 1.539900E-06 1.727802E-07
C (0,8) 3.059935E-07 -5.847885E-07 3.233059E-07 -7.373199E-08

(Free curved surface data 2)
Each coefficient 13th surface 14th surface 15th surface c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) -0.15 -0.15 0.000000
C (2,0) 1.277650E-01 7.954907E-02 -1.308227E-02
C (0,2) -2.473396E-02 -5.411641E-02 -1.829500E-03
C (2,1) 9.786682E-03 4.562533E-03 -5.819697E-04
C (0,3) -3.788662E-04 -2.613505E-03 -1.266214E-04
C (4,0) 9.597456E-04 1.974206E-04 1.165172E-05
C (2,2) -3.397097E-05 -4.275910E-04 -1.766879E-05
C (0,4) -8.557827E-05 1.344918E-04 -5.264988E-06
C (4,1) 1.655594E-04 4.190430E-05 1.037640E-06
C (2,3) -5.524408E-05 -7.918923E-05 -3.100960E-07
C (0,5) 1.204902E-05 1.843350E-05 -1.498002E-07
C (6,0) 8.157403E-06 1.298398E-06 -1.160682E-08
C (4,2) 3.707107E-05 6.339190E-06 4.281360E-08
C (2,4) -3.590358E-06 5.497379E-06 7.984223E-09
C (0,6) -1.437177E-06 -2.318703E-06 -3.496029E-09
C (6,1) -7.065887E-06 -9.710311E-07 -1.133160E-09
C (4,3) 2.734848E-06 -6.178305E-07 1.160775E-09
C (2,5) 1.294144E-06 1.937084E-06 8.122962E-10
C (0,7) -3.043315E-07 -5.017731E-07 -9.735252E-11
C (8,0) -1.119206E-06 -8.204081E-08 5.760487E-12
C (6,2) 1.313329E-06 1.476638E-07 -4.267118E-11
C (4,4) -9.750863E-07 -3.174904E-07 2.846439E-11
C (2,6) 3.397909E-07 2.114011E-07 1.529598E-11
C (0,8) 3.742289E-08 4.888751E-09 -2.252242E-12

  The amount of eccentricity of each surface in this example is shown in Table 4 below. Since the fourth surface and the fifteenth surface are reflection surfaces, the direction in which the light rays incident along the optical axis are reflected when the first-order term of the mathematical expression representing the surface is 0 is determined after the eccentric operation. The optical axis. Further, the decentering of the image plane is for decentering only the image plane, and the optical axis does not change.

(Table 4)
(Eccentric data)
Surface number α rotation (unit: °)
4th surface -30.000
15th -45.000
Image plane 60.000

  The corresponding values for each conditional expression are shown below.

Conditional expression (1) 2 / MR = −0.0305 [mm ⁻¹ ]
Conditional expression (2) | α | = 30 °
Conditional expression (3) fdu / F1 = 1.494
Conditional expression (4) Nen-Nep = 0.18773
Conditional expression (5) νep−νen = 43.2

  As described above, in this example, it is understood that the conditional expressions (1) to (5) are satisfied.

A spot diagram is shown in FIG. 3 and a two-dimensional image simulation image of the lattice points is shown in FIG. 4 so that the imaging state on the screen and the trapezoidal distortion state can be understood. FIG. 3 is an e-line monochromatic spot diagram of the optical system PL1 for image projection apparatus according to the first embodiment. The length of the straight line displayed at the bottom of the spot diagram corresponds to 1 mm on the screen. Corresponding object point positions are (0.00, 0.00), (0.00, 0.925) from the bottom of the spot diagram.
), (1.235, 0.925), (1.235, 0.00), (1.235, -0.925), (0.00, -0.925), (0.00, 1.85), (1.235, 1.85), (2.47, 1.85), (2.47, 0.925) ), (2.47, 0.00), (2.47, -0.925), (2.47, -1.85), (1.235, -1.85), (0.00, -1.85).

  FIG. 4 represents an image (distortion) when a grid is displayed over the entire display area. In the actual calculation, since the convolution integral of the object image and the point image intensity distribution of the optical system is calculated, not only the trapezoidal distortion state but also the resolving power is expressed. In FIG. 4, the lattice line width of the object is about 0.01 mm. 3 and 4, it can be seen that in the first example, the trapezoidal distortion is corrected well and the imaging performance is excellent.

(Second embodiment)
A second embodiment of the present application will be described with reference to FIGS. 5 to 8 and Tables 5 to 8. FIG. FIG. 5 is an optical path diagram of the optical system for the image projection apparatus according to the second embodiment, and FIG. 6 is an enlarged view of the optical system for the image projection apparatus according to the second embodiment. The optical system PL (PL2) for the image projection apparatus according to the second embodiment has an optical element having an optical surface that is arranged in order from the image display element DS side along the optical axis and is formed rotationally symmetrical with respect to the central axis. Consists of a group G1, a free-form surface lens group G2 having a lens surface formed non-rotationally symmetric with respect to the central axis, and a free-form surface mirror M2 having a reflection surface formed non-rotationally symmetric with respect to the central axis Is done.

Two parallel flat plates P1 and P2 are arranged in the vicinity of the video display element DS. The plane parallel plates P1 and P2 correspond to a face plate of a display element, a color synthesis prism, a PBS (polarization beam splitter), and the like, and are irrelevant to the essence of the present invention. An aperture stop S is arranged between the optical element group G1 and the free-form surface lens group G2.

  The optical element group G1 includes an aspherical mirror M1 and a cemented lens L10 having positive refractive power, which are arranged in order from the image display element DS side along the optical axis. The aspherical mirror M1 has an aspherical reflecting surface formed rotationally symmetrical with respect to the central axis. The cemented lens L10 is a cemented doublet formed by bonding a convex lens L11 and a concave lens L12 that are formed rotationally symmetrically with respect to the central axis.

  The free-form surface lens group G2 is arranged in order from the image display element DS side and has a first positive curved surface lens L21 having a substantially positive refractive power (having a converging effect) and a substantially negative refractive power (having a diverging effect). ) The second free-form surface lens L22 and a third free-form surface lens L23 having a substantially negative refractive power (having a diverging action). The entrance-side (object plane side) and exit-side (image plane side) lens surfaces of the first to third free-form surface lenses L21 to L23 have lens surface shapes that are non-rotationally symmetric with respect to the central axis.

  The light beam emitted from the video display element DS is reflected by the reflecting surface of the aspherical mirror M1, and is bent at a predetermined angle. The light beam reflected by the reflecting surface of the aspherical mirror M1 passes through the cemented lens L10 and the first to third free-form surface lenses L21 to L23 and is reflected by the reflecting surface of the free-form surface mirror M2. The light beam reflected by the reflecting surface of the free-form mirror M2 forms an image on the screen (image surface I).

  Table 5 below shows various data of the optical system PL2 for the image projection apparatus according to the second example. The surface numbers 1 to 15 in Table 5 correspond to the surfaces 1 to 15 in FIG.

(Table 5)
(Overall specifications)
F number 2.3
Image display area 4.93 [mm] x 3.70 [mm]
Screen 270 [mm] x 202.5 [mm]

(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
Object plane ∞ 1.410000
1 ∞ 0.650000 1.50900 62.7
2 ∞ 10.000000 1.51872 64.0
3 ∞ 10.248448
4 * A -73.09341 -11.000000 Reflecting surface
5 -12.32593 -3.880976 1.49845 81.1
6 17.21008 -1.000000 1.67718 37.9
7 170.54732 -6.981641
8 (Aperture) ∞ -1.000000
9 * F ∞ -4.732251 1.53340 55.3
10 * F ∞ -6.000000
11 * F ∞ -5.000000 1.53340 55.3
12 * F ∞ -5.405131
13 * F ∞ -5.000000 1.53340 55.3
14 * F ∞ -40.000000
15 * F ∞ 200.000000 Reflection surface Image surface ∞

  In the lens data in Table 5, the fourth surface to the seventh surface are lens surfaces or reflecting surfaces of the optical element group G1, and among these, the fourth surface is a reflecting surface of the rotationally symmetric aspherical mirror M1. . Table 6 below shows the aspherical coefficients of the fourth surface.

(Table 6)
(Aspheric data)
Aspheric coefficient 4th surface K 0.000000
A (4th) 1.802282E-06
B (6th) -2.170337E-08
C (8th) -1.719167E-10
D (10th order) 1.178557E-12
E (12th order) 0.000000

  In the lens data of Table 5, the ninth to fifteenth surfaces are non-rotationally symmetric aspheric surfaces (free curved surfaces). In the present embodiment, the fifteenth surface is the reflecting surface of the free-form surface mirror M2. Table 7 below shows each term coefficient of these free-form surfaces.

(Table 7)
(Free curved surface data 1)
Each coefficient 9th surface 10th surface 11th surface 12th surface c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) 0.1 6.292720E-02 0.1 -6.368413E-02
C (2,0) -3.615332E-02 -4.891854E-02 -5.392192E-02 -5.197375E-02
C (0,2) -3.320069E-02 -6.990084E-02 8.847487E-02 7.354578E-02
C (2,1) 1.116885E-02 1.316880E-02 -1.772246E-02 -1.281312E-02
C (0,3) 1.192766E-02 1.836762E-02 -6.155899E-03 1.869901E-03
C (4,0) 3.609911E-04 3.524979E-04 2.572059E-04 3.189900E-04
C (2,2) 1.598202E-03 1.390082E-03 3.211056E-03 6.739473E-04
C (0,4) 8.693220E-04 4.122332E-04 2.617272E-03 3.427012E-04
C (4,1) 1.381821E-04 2.112115E-04 -1.749671E-04 -1.424435E-04
C (2,3) 2.282880E-04 4.394939E-06 -6.508579E-04 -5.082844E-05
C (0,5) 3.867255E-05 -9.873252E-05 -1.812487E-04 -3.073041E-05
C (6,0) 3.478526E-06 4.075746E-07 -1.836645E-06 -1.984394E-05
C (4,2) -4.067949E-06 -7.353821E-05 7.520969E-05 -7.914945E-06
C (2,4) -1.269135E-05 -1.119612E-04 6.764676E-05 -7.369728E-06
C (0,6) -1.359583E-05 -4.344457E-05 6.484832E-06 -4.427154E-06
C (6,1) -1.207197E-06 -3.428414E-06 -2.745069E-06 -1.805659E-06
C (4,3) -5.659167E-06 -3.321441E-06 -2.121549E-05 -1.887919E-06
C (2,5) -3.156474E-06 1.718841E-05 -1.216814E-05 8.724066E-07
C (0,7) 6.732389E-07 1.288942E-05 -2.528640E-07 1.081543E-06
C (8,0) 5.998389E-09 4.133237E-08 6.528619E-08 1.529932E-07
C (6,2) -1.702915E-07 9.178278E-07 2.511683E-07 -7.254361E-07
C (4,4) -8.421610E-07 1.726206E-06 2.352654E-06 1.824121E-07
C (2,6) -5.920103E-07 -1.565017E-06 4.730967E-07 -1.307629E-07
C (0,8) 1.147581E-07 -1.020064E-06 -3.529055E-07 -1.011652E-07

(Free curved surface data 2)
Each coefficient 13th surface 14th surface 15th surface c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) -0.15 6.542861E-02 0.000000
C (2,0) 7.013365E-02 5.150467E-02 -1.682587E-02
C (0,2) -5.129239E-02 -6.106159E-02 -1.831473E-03
C (2,1) 1.486557E-02 9.423129E-03 -7.637709E-04
C (0,3) 2.644636E-03 -3.414861E-03 -1.304184E-04
C (4,0) 5.673193E-04 -1.715218E-05 2.128705E-05
C (2,2) -3.079970E-04 -4.230305E-04 -1.860871E-05
C (0,4) 1.534514E-04 2.885222E-04 -5.734691E-06
C (4,1) 2.254569E-04 7.746436E-05 2.113120E-06
C (2,3) -2.155945E-04 -2.277955E-04 5.609346E-08
C (0,5) -6.093225E-05 -3.039918E-05 -1.216970E-07
C (6,0) -2.837928E-05 -7.073378E-06 -1.160682E-08
C (4,2) 3.091759E-05 1.569996E-05 6.896226E-08
C (2,4) -7.405109E-06 -8.466278E-06 4.045339E-08
C (0,6) 1.197878E-06 3.380346E-07 -7.615827E-10
C (6,1) -2.900777E-06 -4.001654E-07 -3.686499E-09
C (4,3) -4.206543E-06 -2.593639E-06 6.306152E-10
C (2,5) 2.600197E-06 3.070324E-06 2.533680E-09
C (0,7) 1.506264E-07 3.127900E-07 2.678283E-10
C (8,0) 2.356395E-07 8.287607E-09 -6.852655E-11
C (6,2) -5.152546E-07 -1.714849E-07 -4.267118E-11
C (4,4) -3.628126E-07 -2.826291E-07 -6.442610E-11
C (2,6) 2.437144E-07 2.817377E-07 8.430543E-11
C (0,8) 2.182210E-08 9.076565E-10 -2.789703E-13

  The amount of eccentricity of each surface in this example is shown in Table 8 below. Since the fourth surface and the fifteenth surface are reflection surfaces, the direction in which the light rays incident along the optical axis are reflected when the first-order term of the mathematical expression representing the surface is 0 is determined after the eccentric operation. The optical axis. Further, the decentering of the image plane is for decentering only the image plane, and the optical axis does not change.

(Table 8)
(Eccentric data)
Surface number α rotation (unit: °)
4th surface -40.000
15th -35.000
Image plane 60.000

  The corresponding values for each conditional expression are shown below.

Conditional expression (1) 2 / MR = −0.0273 [mm ⁻¹ ]
Conditional expression (2) | α | = 40 °
Conditional expression (3) fdu / F1 = 1.005
Conditional expression (4) Nen-Nep = 0.18773
Conditional expression (5) νep−νen = 43.2

  As described above, in this example, it is understood that the conditional expressions (1) to (5) are satisfied.

  A spot diagram is shown in FIG. 7 and a two-dimensional image simulation image of the lattice points is shown in FIG. 8 so that the imaging state on the screen and the trapezoidal distortion state can be understood. FIG. 7 is an e-line monochromatic spot diagram of the optical system PL2 for image projection apparatus according to the second embodiment. The length of the straight line displayed at the bottom of the spot diagram corresponds to 1 mm on the screen. Corresponding object point positions are the same as in the first embodiment.

  FIG. 8 represents an image (distortion) when a grid is displayed over the entire display area. In the actual calculation, since the convolution integral of the object image and the point image intensity distribution of the optical system is calculated, not only the trapezoidal distortion state but also the resolving power is expressed. In FIG. 8, the lattice line width of the object is about 0.01 mm. 7 and 8, it can be seen that in the second embodiment, the trapezoidal distortion is corrected well and the imaging performance is excellent.

(Third embodiment)
A third embodiment of the present application will be described with reference to FIGS. 9 to 12 and Tables 9 to 13. FIG. FIG. 9 is an optical path diagram of the optical system for the image projection apparatus according to the third embodiment, and FIG. 10 is an enlarged view of the optical system for the image projection apparatus according to the third embodiment. The optical system PL (PL3) for image projection apparatus according to the third embodiment has an optical element having an optical surface that is arranged in order from the image display element DS side along the optical axis and that is rotationally symmetric with respect to the central axis. Consists of a group G1, a free-form surface lens group G2 having a lens surface formed non-rotationally symmetric with respect to the central axis, and a free-form surface mirror M2 having a reflection surface formed non-rotationally symmetric with respect to the central axis Is done.

  Two parallel flat plates P1 and P2 are arranged in the vicinity of the video display element DS. The plane parallel plates P1 and P2 correspond to a face plate of a display element, a color synthesis prism, a PBS (polarization beam splitter), and the like, and are irrelevant to the essence of the present invention. An aperture stop S is disposed in the free-form surface lens group G2.

  The optical element group G1 includes only an aspherical mirror M1. The aspherical mirror M1 has an aspherical reflecting surface formed rotationally symmetrical with respect to the central axis.

  The free-form surface lens group G2 includes a close-contact multilayer diffractive optical element L2D arranged in order from the image display element DS side, a first free-form surface lens L21 having a substantially positive refractive power (having a converging function), The second free-form lens L22 having a negative refractive power (having a diverging action) and a third free-form surface lens L23 having a substantially negative refractive power (having a diverging action). The entrance-side (object plane side) and exit-side (image plane side) lens surfaces of the first to third free-form surface lenses L21 to L23 have lens surface shapes that are non-rotationally symmetric with respect to the central axis.

  Although not shown in detail, the close-contact multilayer diffractive optical element L2D includes a first grating made of a first optical material having a relatively high refractive index and low dispersion between two planar glass plates. The second grating made of the second optical material having a relatively low refractive index and a large dispersion with respect to the first optical material is closely laminated. A relief type diffractive surface is formed non-rotationally symmetric with respect to the central axis at the interface between the first grating and the second grating. The diffractive optical element L2D is disposed in the vicinity of the entrance pupil of the optical system PL3 for image projection apparatus according to the third example.

  The light beam emitted from the video display element DS is reflected by the reflecting surface of the aspherical mirror M1, and is bent at a predetermined angle. The light beam reflected by the reflecting surface of the aspherical mirror M1 passes through the diffractive optical element L2D and the first to third free-form surface lenses L21 to L23, and is reflected by the reflecting surface of the free-form surface mirror M2. The light beam reflected by the reflecting surface of the free-form mirror M2 forms an image on the screen (image surface I).

Table 9 below shows various data of the optical system PL3 for image projection apparatus according to the third example. In addition,
In the table (lens data) shown in the third embodiment, “* D” written therein indicates that the surface is a non-rotationally symmetric diffraction surface. Further, the surface numbers 1 to 16 in Table 9 correspond to the surfaces 1 to 16 in FIG.

(Table 9)
(Overall specifications)
F number 2.3
Image display area 4.93 [mm] x 3.70 [mm]
Screen 270 [mm] x 202.5 [mm]

(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
Object plane ∞ 1.410000
1 ∞ 0.650000 1.50900 62.7
2 ∞ 10.000000 1.51872 64.0
3 ∞ 10.847303
4 * A -43.33824 -11.000000 Reflective surface
5 ∞ -2.000000 1.51872 64.0
6 ∞ -0.200000 1.55952 49.7
7 * D ∞ -0.200000 1.53117 34.3
8 ∞ -2.000000 1.51872 64.0
9 (Aperture) ∞ -5.100000
10 * F ∞ -4.000000 1.53340 55.3
11 * F ∞ -6.000000
12 * F ∞ -4.000000 1.53340 55.3
13 * F ∞ -15.314491
14 * F ∞ -6.000000 1.53340 55.3
15 * F ∞ -34.185509
16 * F ∞ 200.000000 Reflection surface Image surface ∞

  In the lens data of Table 9, the fourth surface is the reflecting surface of the rotationally symmetric aspherical mirror M1. Table 10 below shows the aspherical coefficients of the fourth surface.

(Table 10)
(Aspheric data)
Aspheric coefficient 4th surface K 0.000000
A (4th) 2.761640E-06
B (6th) 2.159610E-08
C (8th) -2.778690E-10
D (10th order) 1.325110E-12
E (12th order) 0.000000

  In the lens data of Table 9, the tenth to sixteenth surfaces are non-rotationally symmetric aspheric surfaces (free curved surfaces). In the present embodiment, the sixteenth surface is the reflecting surface of the free-form surface mirror M2. Table 11 below shows each term coefficient of these free-form surfaces.

(Table 11)
(Free curved surface data 1)
Each coefficient 10th surface 11th surface 12th surface 13th surface c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) -8.151211E-02 -1.000000E-01 -4.362286E-02 -1.000000E-01
C (2,0) -2.227068E-02 9.003893E-03 -6.002921E-02 -8.962254E-02
C (0,2) -6.284934E-02 -7.152796E-02 5.789446E-02 5.672609E-02
C (2,1) 6.356702E-03 2.973212E-03 -1.652923E-02 -1.293117E-02
C (0,3) 3.051455E-03 8.057268E-04 -3.705245E-03 9.510320E-04
C (4,0) 4.504302E-05 4.884778E-05 3.839637E-04 6.263245E-04
C (2,2) 1.054804E-03 2.391838E-03 2.545115E-03 5.332656E-04
C (0,4) 1.758918E-04 7.227359E-04 7.686204E-04 -2.050474E-05
C (4,1) 6.187495E-05 9.992876E-05 -1.383850E-04 -1.038152E-04
C (2,3) 1.714908E-04 2.308014E-04 -1.759300E-04 1.069443E-04
C (0,5) -8.875801E-06 -7.047297E-05 -1.744002E-05 4.714347E-05
C (6,0) -5.461069E-07 -2.131669E-06 -1.058808E-06 -7.044057E-06
C (4,2) 4.444867E-06 -1.666620E-05 5.992904E-06 -2.549457E-05
C (2,4) 4.090053E-06 -2.168276E-06 1.535737E-05 -1.785519E-05
C (0,6) -1.670659E-06 -2.608708E-06 -5.245131E-06 -9.296463E-06
C (6,1) 5.407970E-07 -3.570903E-07 -1.663601E-06 -2.597312E-06
C (4,3) 3.815478E-07 -5.292924E-06 2.490008E-06 4.109555E-06
C (2,5) -2.706481E-07 -2.388027E-06 7.123487E-06 3.822084E-06
C (0,7) 4.504526E-07 1.043037E-06 -7.270444E-07 9.305858E-07
C (8,0) 1.714598E-08 2.951818E-08 2.015010E-08 2.039171E-08
C (6,2) 1.715444E-07 2.514129E-07 -1.570572E-07 -6.474252E-07
C (4,4) 1.555826E-07 -5.386862E-21 -3.880917E-07 9.106516E-07
C (2,6) -6.916797E-08 -7.886033E-08 -1.528187E-06 -9.288357E-07
C (0,8) 2.362883E-08 1.653885E-07 3.497542E-07 -8.949595E-09

(Free curved surface data 2)
Each coefficient 14th surface 15th surface 16th surface c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) -1.070668E-01 -3.908875E-02 0.000000
C (2,0) 7.707403E-02 4.342214E-02 -1.312847E-02
C (0,2) -3.288645E-02 -4.571330E-02 -1.661226E-03
C (2,1) 1.260457E-02 6.792436E-03 -5.887746E-04
C (0,3) 1.690374E-03 1.305426E-04 -1.297690E-04
C (4,0) 7.658357E-04 7.733192E-05 1.247585E-05
C (2,2) 2.005835E-04 -2.172205E-04 -1.558160E-05
C (0,4) -1.047519E-04 -3.348316E-05 -6.372598E-06
C (4,1) 1.823793E-04 2.801893E-05 1.178576E-06
C (2,3) 1.759186E-05 -1.822806E-05 -1.882989E-07
C (0,5) -2.439998E-05 -3.126682E-05 -1.993496E-07
C (6,0) 1.705856E-05 9.393517E-07 -8.966307E-09
C (4,2) 3.589583E-05 9.431397E-06 4.145007E-08
C (2,4) 3.343790E-06 2.818633E-06 1.634530E-08
C (0,6) 1.058225E-06 9.804789E-07 -4.140721E-09
C (6,1) 3.309285E-06 -3.221474E-07 -1.320675E-09
C (4,3) 2.844258E-06 -1.983188E-07 8.399838E-10
C (2,5) 2.493830E-07 5.749357E-07 1.284779E-09
C (0,7) 3.351893E-08 3.604318E-08 -4.052271E-11
C (8,0) -7.132181E-08 -1.910213E-08 1.782195E-12
C (6,2) 2.221546E-07 -5.281545E-08 -4.828478E-11
C (4,4) 1.502272E-08 -1.165786E-07 1.920646E-11
C (2,6) 6.344319E-10 3.117683E-08 2.946707E-11
C (0,8) -2.126928E-09 -1.212857E-08 -1.652437E-12

In the lens data of Table 9, the seventh surface is a non-rotationally symmetric diffraction surface. Table 12 below shows each term coefficient when the phase shape φ of the diffractive surface is defined by the above-described equation (A). In the third embodiment, the reference wavelength λ ₀ = 546.074 nm and the diffraction order m = 1.

(Table 12)
(Diffraction surface data)
Each coefficient 7th surface
D (2,0) -1.073977E-03
D (0,2) -3.685065E-04
D (2,1) 4.286725E-06
D (0,3) -3.211521E-05
D (4,0) 1.172544E-06
D (2,2) -5.302430E-06
D (0,4) 1.304254E-07
D (4,1) 1.195158E-06
D (2,3) 5.020064E-06
D (0,5) 5.323816E-06
D (6,0) -2.126839E-09
D (4,2) -4.454526E-07
D (2,4) 3.876746E-07
D (0,6) -5.363849E-07
D (6,1) 6.854850E-09
D (4,3) -1.847026E-07
D (2,5) -1.176489E-07
D (0,7) -9.348146E-08
D (8,0) -6.471787E-10
D (6,2) -7.235784E-09
D (4,4) -1.025453E-08
D (2,6) 8.736306E-09
D (0,8) 1.167841E-08

  Table 13 below shows the amount of eccentricity of each surface in this example. Since the fourth surface and the sixteenth surface are reflection surfaces, the direction in which light rays incident along the optical axis are reflected when the first-order term of the mathematical expression representing the surface is 0 is determined after the eccentric operation. The optical axis. Further, the decentering of the image plane is for decentering only the image plane, and the optical axis does not change.

(Table 13)
(Eccentric data)
Surface number α rotation (unit: °)
4th surface -30.000
16th face -45.000
Image plane 60.000

  The corresponding values for each conditional expression are shown below.

Conditional expression (1) 2 / MR = −0.0461 [mm ⁻¹ ]
Conditional expression (2) | α | = 30 °
Conditional expression (6) Ne1-Ne2 = 0.0284
Conditional expression (7) (NF'2-NC'2)-(NF'1-NC'1) = 0.004
Conditional expression (8) D (2,0) / D (0,2) = 2.914

  Thus, in the present Example, it turns out that conditional expression (1)-conditional expression (2) and conditional expression (6)-conditional expression (8) are satisfied.

  A spot diagram is shown in FIG. 11 and a two-dimensional image simulation image of the lattice points is shown in FIG. 12 so that the imaging state on the screen and the trapezoidal distortion state can be understood. FIG. 11 is an e-line monochromatic spot diagram of the optical system PL3 for image projection apparatus according to the third embodiment. The length of the straight line displayed at the bottom of the spot diagram corresponds to 1 mm on the screen. Corresponding object point positions are the same as in the first embodiment.

  FIG. 12 represents an image (distortion) when a grid is displayed over the entire display area. In the actual calculation, since the convolution integral of the object image and the point image intensity distribution of the optical system is calculated, not only the trapezoidal distortion state but also the resolving power is expressed. In FIG. 12, the lattice line width of the object is about 0.01 mm. 11 and 12, it can be seen that in the third example, the trapezoidal distortion is corrected well and the imaging performance is excellent.

  As described above, according to each of the embodiments, it is possible to realize the optical system PL for the image projection apparatus and the image projection apparatus PRJ including the image projection apparatus optical system PL that can satisfactorily correct the trapezoidal distortion of the projected image while having a compact configuration. it can.

  In each of the embodiments described above, the projection plane R (image plane I) is set on the same plane as the installation plane Q of the video projection device PRJ (housing BD), but the present invention is not limited to this. It may be set on a plane parallel to the installation surface Q.

PRJ image projection device DS image display element PL optical system for image projection device G1 optical element group L10 cemented lens G2 free-form surface lens group L21 first free-form surface lens L22 second free-form surface lens L23 third free-form surface lens L2D diffractive optical element M1 Aspherical mirror M2 Free-form surface mirror Q Installation surface

Claims (8)

An optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction,
An optical element group arranged in order from the image display element side along the optical axis, a free-form surface lens group having a free-form surface lens formed non-rotationally symmetric with respect to the center axis, and non-rotation with respect to the center axis With a free-form surface mirror formed symmetrically,
The optical element group has an aspherical mirror having an aspherical reflecting surface formed rotationally symmetrical with respect to the central axis ,
An optical system for an image projection apparatus, characterized by satisfying the following conditional expression:
−0.10 <2 / MR <−0.01
20 ° <| α | <45 °
However,
MR: radius of curvature of the reflection surface of the aspherical mirror,
α: An angle formed by the optical axis between the image display element and the aspherical mirror and the central axis of the aspherical mirror. An optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction,
An optical element group arranged in order from the image display element side along the optical axis, a free-form surface lens group having a free-form surface lens formed non-rotationally symmetric with respect to the center axis, and non-rotation with respect to the center axis With a free-form surface mirror formed symmetrically,
The optical element group is arranged in order from the image display element side along the optical axis, an aspherical mirror having an aspherical reflecting surface formed rotationally symmetrically with respect to the central axis, and the central axis It consists of a cemented lens with positive refractive power formed by bonding a convex lens and a concave lens formed in a rotational symmetry,
An optical system for an image projection apparatus, characterized by satisfying the following conditional expression:
1.00 <fdu / F1 <2.00
However,
fdu: focal length of the cemented lens,
F1: The combined focal length of the optical element group. The optical system for an image projection apparatus according to claim 2 , wherein the following conditional expression is satisfied.
0.10 <Nen-Nep <0.30
20 <νep−νen <50
However,
Nep: refractive index of the convex lens material with respect to e-line,
Nen: Refractive index with respect to e-line of the material of the concave lens,
νep: Abbe number for the e-line of the material of the convex lens,
νen: Abbe number for the e-line of the material of the concave lens. The optical system for an image projection apparatus according to claim 1 , wherein the free-form surface lens group includes a diffractive optical element and the free-form surface lens, which are arranged in order from the image display element side along an optical axis. system. The diffractive optical element includes a first optical material having a relatively high refractive index and a small dispersion, and a second optical material having a relatively low refractive index and a large dispersion relative to the first optical material; It is a contact multilayer type diffractive optical element formed using
The optical system for an image projection apparatus according to claim 4 , wherein the following conditional expression is satisfied.
Ne1-Ne2 ≧ 0.010
(NF'2-NC'2)-(NF'1-NC'1) ≥0.0015
However,
Ne1: Refractive index of the first optical material with respect to e-line,
NF′1: the refractive index of the first optical material with respect to the F ′ line,
NC′1: Refractive index with respect to the C ′ line of the first optical material,
Ne2: Refractive index with respect to e-line of the second optical material,
NF′2: Refractive index of the second optical material with respect to the F ′ line,
NC'2: Refractive index with respect to the C 'line of the second optical material. The diffractive optical element is disposed in the vicinity of an entrance pupil of the optical system for the image projection device,
6. The optical system for an image projection apparatus according to claim 4, wherein the diffractive surface of the diffractive optical element is formed non-rotationally symmetric with respect to the central axis. Between the aspherical mirror and the free-form surface mirror along a plane passing through the optical axis between the image display element and the aspherical mirror and the optical axis between the aspherical mirror and the free-form surface mirror And the coordinate axis perpendicular to the optical axis is the y-axis, the optical axis between the aspherical mirror and the free-form surface mirror and the coordinate axis perpendicular to the y-axis are the x-axis, and the diffractive surface and the optical axis of the diffractive optical element Is defined as a local coordinate system (x, y) with the origin as an origin, the phase shape of the diffraction surface of the diffractive optical element as φ, the reference wavelength as λ ₀ , the diffraction order as m, and a natural number including 0 The phase shape of the diffractive surface of the diffractive optical element is expressed by the following equation, where i and j are the coefficients of a polynomial including x and y:

When expressed as

The optical system for a video projector according to claim 4 , wherein the following condition is satisfied. An image projection device that is used in a state where it is installed on a predetermined installation surface and projects an image from an oblique direction on the same surface as the installation surface or a surface substantially parallel to the installation surface, the image projection device An image projection apparatus, wherein the optical system is the optical system for an image projection apparatus according to any one of claims 1 to 7 .

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