JPWO2014115818A1 - Image projection optical system and image projection apparatus - Google Patents

Abstract

The image projection optical system (PL) is an image projection optical system (PL) that enlarges an image displayed on the image display element and projects the image on the projection surface from an oblique direction, and is projected from the image display element side along the optical axis. A rotationally symmetric lens group (G1) composed of rotationally symmetric lenses formed in rotation symmetry with respect to the central axis, and a free curved surface lens group composed of free curved surface lenses formed in a non-rotational symmetry with respect to the central axis. (G2) and a free-form surface mirror (M) having a reflection surface formed non-rotationally symmetric with respect to the central axis, and the free-form surface lens group (G2) are arranged in order from the image display element side. The first free-form surface lens (L21), the second free-form surface lens (L22), and the third free-form surface lens (L23), and the second free-form surface lens (L22) moves along the optical axis. Is possible.

Description

  The present invention relates to an image projection optical system and an image projection apparatus.

  In the image projection apparatus, so-called oblique projection is performed, in which an image is projected under the condition that the optical axis of the image projection optical system is not perpendicular to the screen. In oblique projection, there is a problem that a rectangular screen is projected into a trapezoid. There are two known methods for correcting such trapezoidal distortion, so-called keystone correction, that is, a method of correcting by image processing and a method of correcting by an optical element having a non-rotationally symmetric optical surface with respect to the central axis.

  A method of correcting by image processing is a method in which trapezoidal distortion that is opposite to trapezoidal distortion that occurs in an optical system is previously applied to a display image by image processing and canceled. This method has the advantage of not requiring a new burden on the optical system, but has the major drawback of degrading the image quality of the projected image. Therefore, it cannot be adopted for an image projection apparatus having a large incident angle on the screen, that is, a large amount of correction of trapezoidal distortion. On the other hand, the method of correcting with an optical element requires an optical surface that is non-rotationally symmetric with respect to the central axis (see Patent Document 1). This method has an advantage that the image quality of the projected image does not deteriorate even if the keystone distortion is corrected.

Japanese Unexamined Patent Publication No. 2012-14127

  In the image projection apparatus of Patent Document 1, the image projection apparatus is reduced in size, but the image projection optical system has a single focal point and the projection size on the screen is fixed.

According to the first aspect of the present invention, the image projection optical system for enlarging the image displayed on the image display element and projecting the image on the projection surface from an oblique direction is arranged in order from the image display element side along the optical axis. A rotationally symmetric lens group composed of rotationally symmetric lenses formed rotationally symmetrically with respect to the central axis, a free-form surface lens group composed of free-form curved lenses formed non-rotatically symmetric about the central axis, and the central axis A free-form surface mirror having a reflection surface formed in a non-rotationally symmetric manner, and the free-form surface lens group is arranged in order from the image display element side, a first free-form surface lens, a second free-form surface lens, Three free-form surface lenses, and the second free-form surface lens is movable along the optical axis.
According to the second aspect of the present invention, in the image projection optical system according to the first aspect, the lens surfaces on both sides of the second free-form surface lens are the optical axis and free-form surface between the free-form surface lens group and the free-form surface mirror. It is preferable that the first cross section passing through the optical axis between the mirror and the projection surface and the second cross section perpendicular to the first cross section have a shape with a substantially concave surface facing the image display element side. .
According to the third aspect of the present invention, in the image projection optical system of the second aspect, the coordinate axis in the optical axis direction in which the direction from the image display element toward the free-form surface mirror is positive is the z ₁ axis, and the first section And the coordinate axis perpendicular to the z ₁ axis is the y ₁ axis, and the coordinate axis perpendicular to the z ₁ axis and the y ₁ axis is the x ₁ axis, the lens surface on the image display element side of the second free-form surface lens and the optical axis Is defined as a local coordinate system (x ₁ , y ₁ , z ₁ ) with the origin as the origin, m and n are natural numbers including 0, and C ₁ (m, n is a coefficient of a polynomial including x ₁ and y ₁ ) Represents the sag amount of the lens surface on the image display element side of the second free-form surface lens as the following equation (1):
When expressed as (2)
C ₁ (2,0) <0, C ₁ (0,2) <0 (2)
And the coordinate axis in the optical axis direction with the direction from the image display element toward the free-form surface mirror being positive is defined as z ₂ axis, and the coordinate axis perpendicular to the z ₂ axis along the first cross section is defined as y _2. The local coordinate system (x ₂ , x ₂ , x ₂ , x ₂ , the coordinate axis perpendicular to the z ₂ axis and the y ₂ axis is the x ₂ axis, and the origin is the intersection of the lens surface on the free curved mirror side of the second free curved lens y ₂ , z ₂ ), natural numbers including 0 are m and n, and coefficients of polynomials including x ₂ and y ₂ are C ₂ (m, n), the free curved mirror side of the second free curved lens The expression for the sag amount on the lens surface of
When expressed as (4)
C ₂ (2,0) <0, C ₂ (0,2) <0 (4)
It is preferable to satisfy the following conditions.
According to the fourth aspect of the present invention, in the image projection optical system of the second or third aspect, the coordinate axis in the optical axis direction in which the direction from the image display element toward the free-form surface mirror is positive is the z ₁ axis, and the first The coordinate surface perpendicular to the z ₁ axis along the cross-section of the second free-form surface lens is defined as the y ₁ axis, and the coordinate axis perpendicular to the z ₁ axis and the y ₁ axis is defined as the x ₁ axis. In the local coordinate system (x ₁ , y ₁ , z ₁ ) whose origin is the intersection with the axis, an expression representing the shape of the lens surface on the image display element side of the second free-form surface lens is z ₁ = f ₁ (x ₁ , Y ₁ ), in the region where the light from the image display element passes, the following equation (9)
F ₁ (0, α ₁ ) satisfying the following condition exists, and a variable conversion is performed such that y ₁ ′ = y ₁ −α ₁ with respect to an expression representing the shape of the lens surface on the image display element side of the second free-form surface lens. Assuming that the performed equation is z ₁ = f ₁ ′ (x ₁ , y ₁ ′), in the region through which light from the image display element passes, when x ₁ = 0, the following equation (10)
When y ₁ = 0 in the region where the light from the image display element passes and the following equation (11) is satisfied:
And the coordinate axis in the optical axis direction with the direction from the image display element toward the free-form surface mirror being positive is defined as z ₂ axis, and the coordinate axis perpendicular to the z ₂ axis along the first cross section is defined as y _2. The local coordinate system (x ₂ , x ₂ , x ₂ , x ₂ , the coordinate axis perpendicular to the z ₂ axis and the y ₂ axis is the x ₂ axis, and the origin is the intersection of the lens surface on the free curved mirror side of the second free curved lens In y ₂ , z ₂ ), when an expression representing the shape of the lens surface of the second free-form surface lens on the free-form surface mirror side is z ₂ = f ₂ (x ₂ , y ₂ ), the light from the image display element is In the passing region, the following equation (12)
F ₂ (0, α ₂ ) satisfying the following condition exists, and a variable transformation is set such that y ₂ ′ = y ₂ −α ₂ with respect to the expression representing the shape of the lens surface of the second free-form surface lens on the free-form surface mirror side. Assuming that the performed equation is z ₂ = f ₂ ′ (x ₂ , y ₂ ′), when x ₂ = 0 in the region through which light from the image display element passes, the following equation (13)
When y ₂ = 0 in the region where the light from the image display element passes and the following condition (14) is satisfied:
It is preferable to satisfy the following conditions.
According to the fifth aspect of the present invention, in the image projection optical system according to any one of the first to fourth aspects, the focal length of the rotationally symmetric lens group is f _G1 , and the rotational symmetry of the rotationally symmetric lens group closest to the image display element side. When the focal length of the lens is _fL11 , the following equation (5)
0.8 ≦ f _L11 / f _G1 ≦ 1.4 (5)
It is preferable to satisfy the following conditions.
According to the sixth aspect of the present invention, in the image projection optical system according to any one of the first to fifth aspects, it is preferable that the image display element is movable in the optical axis direction with respect to the image projection optical system.
According to the seventh aspect of the present invention, in the video projection optical system according to any one of the first to sixth aspects, the first free-form surface lens is integrally movable with the second free-form surface lens in the optical axis direction. It is preferable.
According to the eighth aspect of the present invention, in the image projection optical system according to any one of the first to seventh aspects, the entire rotationally symmetric lens group or the rotationally symmetric lens closest to the image display element in the rotationally symmetric lens group is in the optical axis direction. It is preferable that it is movable.
According to the ninth aspect of the present invention, in the image projection optical system according to any one of the first to eighth aspects, it is preferable that the free-form surface mirror is movable in the optical axis direction with respect to the image display element.
According to the tenth aspect of the present invention, in the image projection optical system according to any one of the first to ninth aspects, when the central curvature radius of the free-form surface mirror is MR, the following formula (6)
−0.1 <2 / MR <−0.005 (6)
It is preferable to satisfy the following conditions.
According to the eleventh aspect of the present invention, an image is projected from an oblique direction on the same surface as the installation surface or on a surface substantially parallel to the installation surface, according to the projection size. An image projection apparatus having a focusable mechanism includes the image projection optical system according to any one of the first to tenth aspects.

  According to the present invention, it is possible to refocus even if the projection size is changed, and to correct the trapezoidal distortion of the projected image satisfactorily even though the configuration is compact.

1 is a perspective view showing an outline of an image projection apparatus according to an embodiment of the present invention. It is sectional drawing which shows the outline inside the video projector shown in FIG. It is explanatory drawing which shows an example of a local coordinate system. It is yz sectional drawing of the image projection optical system which concerns on 1st Example. It is xz sectional drawing of the image projection optical system which concerns on 1st Example. FIG. 5 is an optical path diagram of the image projection optical system according to the first example when the projection surface is at the first position. FIG. 5 is an optical path diagram of the image projection optical system according to the first example when the projection surface is at a third position. It is a spot diagram of the image projection optical system according to the first example when the projection surface is at the first position. It is a figure which shows the two-dimensional image simulation image of the lattice point in the image | video projection optical system which concerns on 1st Example when a projection surface exists in a 1st position. It is a spot diagram of the image projection optical system according to the first example when the projection surface is at the second position. It is a figure which shows the two-dimensional image simulation image of the grating | lattice point in the image projection optical system which concerns on 1st Example when a projection surface exists in a 2nd position. It is a spot diagram of the image projection optical system according to the first example when the projection surface is at the third position. It is a figure which shows the two-dimensional image simulation image of the lattice point in the image | video projection optical system which concerns on 1st Example when a projection surface exists in a 3rd position. It is yz sectional drawing of the image projection optical system which concerns on 2nd Example. It is xz sectional drawing of the image projection optical system which concerns on 2nd Example. It is an optical path diagram of the image projection optical system according to the second example when the projection surface is at the first position. It is an optical path diagram of the image projection optical system according to the second example when the projection surface is at the third position. It is a spot diagram of the image projection optical system according to the second example when the projection surface is at the first position. It is a figure which shows the two-dimensional image simulation image of the grating | lattice point in the image projection optical system which concerns on 2nd Example when a projection surface exists in a 1st position. It is a spot diagram of the image projection optical system according to the second example when the projection surface is at the second position. It is a figure which shows the two-dimensional image simulation image of the grating | lattice point in the image projection optical system which concerns on 2nd Example when a projection surface exists in a 2nd position. It is a spot diagram of the image projection optical system according to the second example when the projection surface is at the third position. It is a figure which shows the two-dimensional image simulation image of the lattice point in the image | video projection optical system which concerns on 2nd Example when a projection surface exists in a 3rd position. It is yz sectional drawing of the image projection optical system which concerns on 3rd Example. It is xz sectional drawing of the image projection optical system which concerns on 3rd Example. It is an optical path diagram of the image projection optical system according to the third example when the projection surface is at the first position. It is an optical path diagram of the image projection optical system according to the third example when the projection surface is at the third position. It is a spot diagram of the image projection optical system according to the third example when the projection surface is at the first position. It is a figure which shows the two-dimensional image simulation image of the grating | lattice point in the image projection optical system which concerns on 3rd Example when a projection surface exists in a 1st position. It is a spot diagram of the image projection optical system according to the third example when the projection surface is at the second position. It is a figure which shows the two-dimensional image simulation image of the lattice object point in the image | video projection optical system which concerns on 3rd Example when a projection surface exists in a 2nd position. It is a spot diagram of the image projection optical system according to the third example when the projection surface is at the third position. It is a figure which shows the two-dimensional image simulation image of the grating | lattice point in the image projection optical system which concerns on 3rd Example when a projection surface exists in a 3rd position.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a perspective view showing a schematic configuration of a video projection apparatus PRJ according to the present embodiment. FIG. 2 is a cross-sectional view showing a schematic configuration inside the image projection apparatus PRJ shown in FIG. The image projection apparatus PRJ includes a cylindrical box-shaped housing BD having a window W on the front surface, an image display element DS and an image projection optical system PL housed in the housing BD, respectively. Configured. The image projection device PRJ is used in a state where it is installed on an arbitrary installation surface Q such as the upper surface of a table (or desk) or a wall surface near the whiteboard. The image projection apparatus PRJ reflects light (light) from a light source (not shown) by the image display element DS and then reflects the image (light) obtained by the image display element DS to the image projection optical system PL and the window. Via the portion W, the projection screen (screen) SC is configured to be enlarged and projected from an oblique direction.

  The projection plane SC is set on the same plane as the installation plane Q of the image projection device PRJ (housing BD) or on a plane substantially parallel to the installation plane Q. In the image projection apparatus PRJ, the projection size can be changed by changing the position of the projection surface SC (the distance from the image projection optical system PL to the projection surface SC). In other words, the image projection device PRJ has a mechanism that can focus on the projection size. This will be described in detail later.

  As the light source (not shown) of the image projection device PRJ, 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 image projection optical system PL includes a rotationally symmetric lens group G1, a free-form surface lens group G2, and a free-form surface mirror M, which are arranged in order from the image display element DS side along the optical axis. The rotationally symmetric lens group G1 is composed of a plurality of rotationally symmetric lenses that are rotationally symmetric with respect to the central axis. The free-form surface lens group G2 includes a plurality of free-form surface lenses formed in a non-rotational symmetry with respect to the central axis. The free-form surface mirror M has a reflecting surface formed in a non-rotational symmetry with respect to the central axis.

  In such an image projection optical system PL, the light emitted from the image display element DS is transmitted through the rotationally symmetric lens group G1 and the free-form surface lens group G2, reflected by the free-form surface mirror M in an oblique direction, and projected onto the projection surface SC. Is projected onto the screen.

  The free-form surface lens group G2 includes, in order from the image display element DS side, a first free-form surface lens, a second free-form surface lens, and a third free-form surface lens, and the second free-form surface lens is along the optical axis. It is configured to be movable. The image projection optical system PL is configured such that the second free-form surface lens moves along the optical axis so that it can be refocused even if the position of the projection surface SC is changed and the projection size is changed. .

  Here, the local coordinate system of each lens and mirror will be described. In this description, for example, as shown in FIG. 3, the local coordinate system of each lens and mirror is an (x, y, z) coordinate system (right-handed system) with the intersection point of each lens surface or reflecting surface and the optical axis as the origin. ). In this local coordinate system, the coordinate axis in the optical axis direction in which the direction from the image display element DS toward the free-form surface mirror M is positive is the z axis. Further, along the cross section passing through the optical axis between the free-form surface lens group G2 and the free-form surface mirror M and the optical axis between the free-form surface mirror M and the projection surface SC, the coordinate axis perpendicular to the z-axis is the y-axis. To do. A coordinate axis perpendicular to the z axis and the y axis is taken as an x axis. A cross section of each lens or mirror passing through the x axis and the z axis is referred to as an xz cross section, a cross section of each lens or mirror passing through the y axis and the z axis is referred to as a yz cross section, and the x axis and the y axis are referred to. The cross section of each lens or mirror that passes through is called the xy cross section.

For convenience of explanation, x = x ₁ , y = y ₁ , z = z ₁ and local coordinates of the lens surface on the image display element DS side of the second free-form surface lens (hereinafter referred to as display element side lens surface). Define the system (x ₁ , y ₁ , z ₁ ). The local coordinate system (x ₁ , y ₁ , z ₁ ) has an origin at the intersection of the display element side lens surface and the optical axis. Further, assuming that x = x ₂ , y = y ₂ , and z = z ₂ , the local coordinate system (x ₂ , x ₂ , y ₂ ) of the lens surface on the free curved mirror M side of the second free curved surface lens (hereinafter referred to as the mirror side lens surface). y ₂ , z ₂ ) is defined. In the local coordinate system (x ₂ , y ₂ , z ₂ ), the origin is the intersection of the mirror side lens surface and the optical axis.

In the present embodiment, the sag amount z ₁ of the display element side lens surface of the second free-form surface lens satisfies the following conditional expression (2) in the local coordinate system (x ₁ , y ₁ , z ₁ ). preferable. In Equation (1), m and n are natural numbers including 0, and C ₁ (m, n) is a coefficient of an x, y polynomial.

C ₁ (2,0) <0, C ₁ (0,2) <0 (2)

Conditional expression (2) is a conditional expression for defining the sag amount in the xz section and the yz section on the display element side lens surface. Display In x-z cross section and y-z cross-section near the optical axis contribution decreases the higher-order terms in equation (1), the value of C ₁ (2, 0) and C ₁ (0, 2) in each section The amount of sag on the element side lens surface is determined. Therefore, by satisfying conditional expression (2), the shape of the display element side lens surface in the xz cross section and the yz cross section in the vicinity of the optical axis becomes a shape in which the concave surface is directed to the video display element DS.

In the present embodiment, when the sag amount z ₂ of the mirror side lens surface of the second free-form surface lens is expressed by the following expression (3) in the local coordinate system (x ₂ , y ₂ , z ₂ ): It is preferable that the following conditional expression (4) is satisfied. In Equation (3), m and n are natural numbers including 0, and C ₂ (m, n) is a coefficient of an x, y polynomial.

C ₂ (2,0) <0, C ₂ (0,2) <0 (4)

Conditional expression (4) is a conditional expression for defining the sag amount in the xz section and the yz section on the mirror side lens surface. In x-z cross section and y-z cross-section near the optical axis where the contribution of higher-order terms in equation (3) is relatively small, the number is the section of _{C 2} (2, 0) and _{C 2} (0, 2) The sag amount of the mirror side lens surface is determined. Therefore, when the conditional expression (4) is satisfied, the shape of the mirror side lens surface in the xz section and the yz section in the vicinity of the optical axis becomes a shape in which the concave surface is directed to the image display element DS.

In the present embodiment, in the local coordinate system (x ₁ , y ₁ , z ₁ ), an expression representing the shape of the display element side lens surface of the second free-form surface lens is expressed as z ₁ = f ₁ (x ₁ , y ₁ ), it is preferable that f ₁ (0, α ₁ ) satisfying the following conditional expression (9) exists in a region through which light from the video display element DS passes.

Then, an expression obtained by performing variable transformation with respect to the expression representing the shape of the lens surface on the display element side as y ₁ ′ = y ₁ −α ₁ is z ₁ = f ₁ ′ (x ₁ , y ₁ ′). In the region where light from the image display element DS passes, it is preferable that the following conditional expression (10) is satisfied when x ₁ = 0.

Further, on the display element side lens surface, it is preferable that the following conditional expression (11) is satisfied when y ₁ = 0 in a region through which light from the image display element DS passes.

  Conditional expressions (9) and (10) are conditional expressions for defining the shape of the display element side lens surface in the yz section. By satisfying the conditional expressions (9) and (10), the shape of the display element side lens surface in the yz section becomes a shape in which the concave surface is directed to the video display element DS. Conditional expression (11) is a conditional expression for defining the shape of the display element side lens surface in the xz section. By satisfying conditional expression (11), the shape of the display element side lens surface in the xz cross section becomes a shape in which the concave surface is directed to the image display element DS.

In the present embodiment, in the local coordinate system (x ₂ , y ₂ , z ₂ ), an expression representing the shape of the mirror side lens surface of the second free-form surface lens is z ₂ = f ₂ (x ₂ , y ₂ ), It is preferable that f ₂ (0, α ₂ ) satisfying the following conditional expression (12) exists in a region through which light from the image display element DS passes.

Then, when an expression obtained by performing variable transformation with y ₂ ′ = y ₂ −α ₂ on the expression representing the shape of the mirror side lens surface is z ₂ = f ₂ ′ (x ₂ , y ₂ ′) In the region where the light from the image display element DS passes, it is preferable that the following conditional expression (13) is satisfied when x ₂ = 0.

Further, on the mirror side lens surface, it is preferable that the following conditional expression (14) is satisfied when y ₂ = 0 in a region through which light from the image display element DS passes.

  Conditional expressions (12) and (13) are conditional expressions for defining the shape of the mirror side lens surface in the yz section. When the conditional expressions (12) and (13) are satisfied, the shape of the mirror side lens surface in the yz section is a shape in which the concave surface is directed to the image display element DS. Conditional expression (14) is a conditional expression for defining the shape of the mirror side lens surface in the xz section. When the conditional expression (14) is satisfied, the shape of the mirror side lens surface in the xz section becomes a shape in which the concave surface is directed to the image display element DS.

  As described above, in the present embodiment, the second free-form surface lens has a shape in which the lens surfaces on both sides are substantially concave on the image display element DS side in the xz cross section and the yz cross section. It is preferable to have such a shape. As a result, in the image projection optical system PL, when the focus is adjusted by moving the second free-form surface lens as the projection size is changed by changing the position of the projection surface SC, coma aberration, distortion aberration, or the like may be caused. Degradation of image performance can be reduced.

Further, in the present embodiment, the focal length f _G1 rotationally symmetric lens group G1, the most image display element DS side of the rotationally symmetric lens in rotational symmetry lens group G1 (hereinafter, referred to as a display device side lens) focal length f _L11 of Preferably satisfies the following conditional expression (5).
0.8 ≦ f _L11 / f _G1 ≦ 1.4 (5)

Conditional expression (5) is an expression for defining an appropriate value of the focal length _fL11 of the display element side lens. When f _L11 / f _G1 is lower than the lower limit of the conditional expression (5), the focal length f _L11 of the display element side lens becomes too short with respect to the focal length f _{G1 of the} entire rotationally symmetric lens group G1, and correction of coma aberration is performed. Not only becomes difficult, but the position of the entrance pupil becomes too close to the image display element DS side, and shading increases. If f _L11 / f _G1 exceeds the upper limit of the conditional expression (5), the focal length f _L11 of the display element side lens becomes too long with respect to the focal length f _{G1 of the} entire rotationally symmetric lens group G1, and rotationally symmetric. The configuration of the lens group G1 makes it difficult to correct field curvature. In order to more effectively correct various aberrations, it is desirable to set the lower limit of conditional expression (5) to 0.9 and the upper limit to 1.3.

When the center curvature of the free-form mirror M is negative (that is, a concave surface at the center), it is preferable to satisfy the following conditional expression (6). In conditional expression (6), MR is the center curvature radius of the reflecting surface of the free-form curved mirror M.
−0.1 <2 / MR <−0.005 (6)

  Conditional expression (6) is an expression for defining an appropriate value of the central radius of curvature of the reflecting surface of the free-form surface mirror M. When 2 / MR is below the lower limit of conditional expression (6), the positive refractive power of the free-form surface mirror M becomes too strong, and it becomes difficult to correct spherical aberration and coma aberration, and the Petzval sum is negative. Becomes too large to increase the field curvature. On the other hand, if 2 / MR exceeds the upper limit of the conditional expression (6), the positive refractive power of the free-form surface mirror M becomes too weak to correct the field curvature generated in the rotationally symmetric lens group G1. In order to more effectively reduce the Petzval sum, reduce the burden on the free-form surface lens group G2, and correct the curvature of field satisfactorily, the lower limit value of conditional expression (6) is set to −0.05, and the upper limit value is set to -0.02 is desirable.

  In the present embodiment, the first free-form surface lens of the free-form surface lens group G2 may be integrally movable with the second free-form surface lens in the optical axis direction. In this case, the image projection optical system PL moves the first free-form surface lens and the second free-form surface lens integrally in the optical axis direction when the projection size is changed by changing the position of the projection surface SC. Configured so that the focus can be adjusted.

  In the present embodiment, the entire rotationally symmetric lens group G1 or the rotationally symmetric lens (display element side lens) closest to the image display element DS in the rotationally symmetric lens group G1 may be movable in the optical axis direction. Good. In this case, when the projection size is changed by changing the position of the projection surface SC, the image projection optical system PL moves the second free-form surface lens and the entire rotationally symmetric lens group G1 or the display element side lens in the optical axis direction. By doing so, the focus can be adjusted.

-Example-
Hereinafter, each example according to the present embodiment will be described. 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, an aspheric surface that is rotationally symmetric with respect to the optical axis (center axis) is defined by the following equation (7) in the above-mentioned local coordinate system. In the following formula (7), 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 a conic _constant, a 4 _{to a 12} are aspherical coefficients of fourth-order 12-order.

Next, an aspherical surface (free curved surface) that is non-rotationally symmetric with respect to the central axis is defined by the following equation (8) in the local coordinate system described above. In the following equation (8), 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 .

<First embodiment>
First, the first embodiment will be described. FIG. 4 is a yz sectional view of the image projection optical system PL according to the first example. FIG. 5 is an xz sectional view of the image projection optical system PL according to the first example. The image projection optical system PL according to the first example includes a rotationally symmetric lens group G1, a free-form surface lens group G2, and a free-form surface mirror M arranged in order from the image display element DS side along the optical axis. .

  4 and 5, two parallel flat plates P1 and P2 are disposed in the vicinity of the video display element DS. The parallel flat plates P1 and P2 are the face plate of the video display element DS and the color synthesis prism. , PBS (polarization beam splitter) and the like. An aperture stop S is disposed between the rotationally symmetric lens group G1 and the free-form surface lens group G2.

  The rotationally symmetric lens group G1 is arranged in order from the image display element DS side, a first meniscus lens L11, a cemented meniscus lens obtained by bonding the second rotationally symmetric lens L12 and the third rotationally symmetric lens L13, and a fourth rotation. And a symmetric lens L14. The first rotationally symmetric lens L11 is a biconvex lens, and the shape of the lens surface on the emission side is a rotationally symmetric aspherical surface. The second rotationally symmetric lens L12 is a biconvex lens. The third rotationally symmetric lens L13 is a biconcave lens. The fourth rotationally symmetric lens L14 is a meniscus lens having a concave surface directed toward the image display element DS, and the shape of the incident-side lens surface is a rotationally symmetric aspherical surface.

  The free-form surface lens group G2 includes a first free-form surface lens L21, a second free-form surface lens L22, and a third free-form surface lens L23 arranged in order from the image display element DS side. The first free-form surface lens L21 has a substantially positive refractive power, and both the shape of the lens surfaces on the entrance side and the exit side are non-rotationally symmetric aspheric surfaces (free-form surfaces). The second free-form surface lens L22 is a non-rotationally symmetric aspheric surface (free-form surface) in which both the incident side and the exit side lens surfaces have a substantially concave surface facing the image display element DS. The third free-form surface lens L23 has a substantially positive refractive power, and the shapes of the lens surfaces on the entrance side and the exit side are both non-rotationally symmetric aspheric surfaces (free-form surfaces). Note that, in the third free-form surface lens L23, the lens surface on the emission side has a shape in which the concave surface is directed to the image display element DS.

  The divergent light beam emitted from each object point on the display area of the image display element DS passes through the rotationally symmetric lens group G1 and the free-form surface lens group G2, is reflected by the free-form surface mirror M, and becomes a convergent light beam as a projection surface. The image is formed on the SC.

  In the image projection optical system PL according to the first example, when the second free-form surface lens L22 of the free-form surface lens group G2 moves in the optical axis direction, the position of the projection surface SC is changed and the projection size is changed. It is also possible to focus.

  6 and 7 are optical path diagrams in the yz plane of the image projection optical system PL according to the first example. FIG. 6 shows a case where the position of the projection surface SC is the first position, and FIG. 7 shows a case where the position of the projection surface SC is the third position. When the position of the projection surface SC is the first position, the distance from the free-form surface mirror M to the projection surface SC is 350 mm, and the projection size is 420 mm × 262.5 mm. When the position of the projection surface SC is the third position, the distance from the free-form surface mirror M to the projection surface SC is 700 mm, and the projection size is 840 mm × 525 mm. Thus, in the image projection optical system PL, the projection size is changed from 420 mm × 262.5 mm (first position) to 840 mm × by changing the position of the projection surface SC (the distance from the free-form curved mirror M to the projection surface SC). The area can be enlarged to 4 times up to 525 mm (third position).

  Table 1 below shows various data of the image projection optical system PL according to the first example. The surface numbers 1 to 18 in Table 1 correspond to the surfaces 1 to 18 in FIG. In the tables shown in the following examples, “* A” indicates that the surface is a rotationally symmetric aspheric surface, and “* F” indicates that the surface is a rotationally symmetric aspheric surface (free-form surface). It represents something. Further, the curvature radius “∞” indicates a plane or an opening, and the refractive index of air is omitted. The variable data indicates data when the position of the projection plane (image plane) SC changes to the first position, the second position, and the third position.

<Table 1>
(Overall specifications)
F number 2.3
Image display area 9.696mm x 6.06mm
(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
0: (Object surface) ∞ 1.410000
1: ∞ 0.650000 1.50900 62.7
2: ∞ 14.000000 1.51872 64.0
3: ∞ 11.400000
4: 34.99300 5.300000 1.68082 55.1
5: * A -32.30900 12.300000
6: 13.40020 4.400000 1.73234 55.5
7: -54.61100 2.000000 1.80633 29.6
8: 12.90030 2.370000
9: * A -39.99900 2.500000 1.69661 53.0
10: -18.50920 0.500000
11: (Aperture) ∞ 2.850000
12: * F ∞ 4.000000 1.53113 55.7
13: * F ∞ 5th interval / variable
14: * F ∞ 4.500000 1.53113 55.7
15: * F ∞ 6th interval / variable
16: * F ∞ 10.000000 1.53113 55.7
17: * F ∞ 40.420000
18: * F (reflective surface) ∞ B. F / variable
19: (image plane) ∞
(Variable data)
Projection plane position 1st position 2nd position 3rd position 5th interval 16.90000 21.84281 24.20000
6th interval 14.50000 9.55719 7.20000
B. F -350.00000 -525.00000 -700.00000
Projection size 420mm × 262.5mm 630mm × 393.75mm 840mm × 525mm

  In the image projection optical system PL, when the position of the projection surface SC (image surface) changes, the distance from the reflection surface (18th surface) of the free-form surface mirror M to the image surface (19th surface) (BF: back focus ) And the projection size change. At this time, since the second free-form surface lens L22 (14th surface and 15th surface) moves, the distance from the 13th surface to the 14th surface (fifth interval) and the 15th surface to the 16th surface The distance (sixth interval) changes.

  As shown in the lens data in Table 1, among the lens surfaces (fourth to tenth surfaces) of the rotationally symmetric lens group G1, the fifth surface and the ninth surface are rotationally symmetric aspheric surfaces. Table 2 below shows the aspherical coefficients of the fifth and ninth surfaces.

<Table 2>
(Aspheric data)
Aspheric coefficient 5th surface 9th surface K 0.000000 0.000000
A ₄ 1.675255E-05 -3.181507.E-05
A ₆ -2.349383E-08 -1.756659.E-06
A ₈ 1.252354E-10 3.599902.E-08
A ₁₀ -3.589638E-13 -4.187286.E-10
A ₁₂ 0.000000 0.000000

As shown in the lens data in Table 1, the lens surface of the free-form surface lens group G2 and the reflection surfaces (the 12th to 18th surfaces) of the free-form surface mirror M are non-rotationally symmetric aspheric surfaces (free-form surfaces). It is. Table 3 below shows the coefficients of these free-form surface aspheric terms x ^m y ⁿ .

<Table 3>
(Free curved surface data 1)
Each coefficient 12th surface 13th surface 14th surface 15th surface
c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) 0.000000 0.000000 0.000000 0.000000
C (2,0) 2.508830E-02 5.157404E-02 -4.476107E-02 -3.435438E-02
C (0,2) 1.963383E-02 4.086798E-02 -5.080941E-02 -3.399970E-02
C (2,1) -2.103879E-03 -4.185413E-03 -1.585316E-03 -1.325429E-03
C (0,3) -2.359498E-03 -4.497759E-03 -7.171970E-04 -7.029510E-04
C (4,0) -4.122587E-04 -5.698777E-04 -5.398541E-05 -2.905489E-05
C (2,2) -8.191440E-04 -1.024766E-03 -1.230434E-04 -4.640560E-05
C (0,4) -4.456241E-04 -4.969219E-04 -5.888743E-05 -1.793727E-05
C (4,1) -1.444565E-05 1.401912E-05 -4.066319E-06 -2.655920E-06
C (2,3) -2.439606E-05 3.944797E-05 1.974772E-06 -3.369896E-07
C (0,5) -1.414309E-05 2.190379E-05 2.382461E-06 -1.869447E-07
C (6,0) 4.815875E-06 7.745351E-06 -1.235063E-07 -4.723111E-08
C (4,2) 1.065860E-05 1.885204E-05 -4.788292E-07 -1.205591E-07
C (2,4) 9.780335E-06 1.796857E-05 -8.376748E-07 -2.998470E-07
C (0,6) 3.605721E-06 6.990157E-06 1.278414E-07 2.840478E-08
C (6,1) 1.632369E-07 -8.836931E-08 -1.098441E-08 -1.031499E-08
C (4,3) 2.064593E-07 -5.958086E-07 -6.198195E-08 -2.947823E-08
C (2,5) 1.981346E-07 -6.948675E-07 -3.535209E-08 -1.380039E-08
C (0,7) 1.309074E-07 -2.082092E-07 -8.340497E-09 -7.552196E-10
C (8,0) -3.578915E-08 -6.017559E-08 8.901556E-10 2.163701E-10
C (6,2) -7.466681E-08 -1.717513E-07 -1.241104E-09 -1.164189E-09
C (4,4) -1.050531E-07 -2.401001E-07 -3.242764E-10 -5.821983E-10
C (2,6) -7.008747E-08 -1.598576E-07 -1.583906E-09 -2.127023E-10
C (0,8) -2.353642E-08 -5.587009E-08 -5.000872E-10 -3.119740E-11
(Free curved surface data 2)
Each coefficient 16th surface 17th surface 18th surface
c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) 0.000000 0.000000 0.000000
C (2,0) 8.469105E-03 -9.010033E-03 9.258086E-03
C (0,2) 2.050889E-03 -1.310580E-02 1.503976E-03
C (2,1) 1.025339E-03 7.853203E-04 2.626100E-04
C (0,3) 5.480642E-04 3.951016E-04 6.195973E-05
C (4,0) -8.744144E-06 -2.231304E-06 -2.142705E-06
C (2,2) 3.620787E-06 1.237842E-05 5.910080E-06
C (0,4) -2.245115E-05 -1.403945E-05 2.046666E-06
C (4,1) -3.502511E-07 2.514377E-07 -1.176948E-07
C (2,3) 8.212073E-08 1.000201E-06 1.269391E-07
C (0,5) -1.542889E-06 -6.972717E-07 7.031074E-08
C (6,0) 8.057165E-09 -2.300051E-10 5.233323E-10
C (4,2) -1.793361E-08 -3.200337E-08 -3.920219E-09
C (2,4) 7.295111E-08 1.439549E-08 1.568623E-09
C (0,6) -1.619323E-08 -2.494842E-08 1.678322E-09
C (6,1) -8.632349E-11 -1.182743E-10 5.436521E-11
C (4,3) -2.037259E-09 -1.739811E-09 -1.176181E-10
C (2,5) -1.821661E-11 -7.373674E-10 9.924704E-12
C (0,7) 1.171163E-09 7.524217E-10 2.286754E-11
C (8,0) -3.461698E-12 -1.752394E-13 2.605019E-13
C (6,2) 3.142403E-12 -1.129677E-11 9.480340E-13
C (4,4) -8.678698E-11 -4.759386E-11 -1.774152E-12
C (2,6) -5.620357E-11 -2.789020E-11 2.465374E-13
C (0,8) 4.936275E-11 3.958599E-11 1.127335E-13

  Furthermore, the eccentricity in the local coordinate system of the 12th surface to the 19th surface is shown in Table 4 below. The type of eccentricity is rotation around the x axis (referred to as α rotation). The positive direction of the α rotation is counterclockwise when facing the positive direction of the x axis. In the 12th to 17th surfaces, the optical axis does not change only by the eccentricity of each surface. Since the eighteenth surface is a reflecting surface, the direction in which light rays incident along the optical axis are reflected when the first-order term of the expression representing the surface is 0 is the optical axis after the eccentric operation. The decentering of the 19th surface (image surface) is to decenter only the image surface, and the optical axis does not change.

<Table 4>
(Eccentric data)
Surface number α rotation (unit: °)
Side 12 -15.000
Side 13 -11.238
Side 14 5.000
15th -5.000
16th surface 8.704
17th surface 11.902
18th surface (reflective surface) 35.000
19th surface (image surface) -60.000

In the first example, C ₁ (2,0) = − 4.476107E-02, C ₁ (0,2) = − about the display element side lens surface (14th surface) of the second free-form surface lens L22. Since it is 5.080941E-02, the conditional expression (2) is satisfied. Further, with respect to the mirror side lens surface (fifteenth surface) of the second free-form surface lens L22, C ₂ (2,0) = − 3.4435438E-02 and C ₂ (0,2) = − 3.999970E-02. Conditional expression (4) is satisfied. Therefore, in the first embodiment, as described above, the lens surfaces on both sides of the second free-form surface lens L22 have a meniscus shape with concave surfaces facing the image display element DS. Therefore, when the second free-form surface lens L22 is moved to adjust the focus, it is possible to reduce the deterioration of the imaging performance.

In the first example, f _L11 / f _G1 = 1.2565 for the rotationally symmetric lens group G1 and the display element side lens (the first rotationally symmetric lens L11) in the rotationally symmetric lens group G1, so the conditional expression (5 ) Is satisfied. Therefore, in the first example, as described above, the focal length fL11 of the first rotationally symmetric lens _L11 is an appropriate value, and various aberrations can be corrected effectively.

In the first example, since C ₁ (0,1) = 0 for the display element side lens surface (14th surface), α ₁ = 0 for conditional expression (9). Similarly, with respect to the mirror side lens surface (fifteenth surface), since C ₁ (0,1) = 0, α ₂ = 0 with respect to the conditional expression (11). Further, the values relating to the conditional expressions (10), (11), (13), and (14) are shown in the following table for the display element side lens surface (14th surface) and the mirror side lens surface (15th surface).

  As shown in this table, on the 14th and 15th surfaces, conditional expressions (10) and (13) are satisfied in the yz cross section of the effective diameter through which the light beam passes, and x− of the effective diameter through which the light beam passes. Conditional expressions (11) and (14) are satisfied in the z cross section. Therefore, in the first embodiment, the lens surfaces on both sides of the second free-form surface lens L22 have a shape in which concave surfaces are directed toward the image display element DS in both the yz section and the xz section. .

  Here, the spot diagrams when the position of the projection surface SC is the first position, the second position, and the third position so that the image formation state and the trapezoidal distortion state on the projection surface (image surface) SC can be understood. 8, 10, and 12. In addition, FIGS. 9, 11 and 13 show two-dimensional image simulation images of lattice object points when the position of the projection plane SC is the first position, the second position, and the third position.

  8, 10, and 12 are e-line monochromatic spot diagrams of the image projection optical system PL 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, -1.515), (-2.424, -1.515), (-2.424,0.00), (-2.424,1.515), ( 0.00,1.515), (0.00, -3.030), (-2.424, -3.030), (-4.848, -3.030), (-4.848, -1.515), (-4.848,0.00), (-4.848,1.515), (-4.848,3.030), (-2.424,3.030), (0.00,3.030). Although the x coordinate is ½ because of y-axis symmetry, it corresponds to the video display element DS having a diagonal of 0.45 inches.

  9, FIG. 11 and FIG. 13 represent images when a grid is displayed over the entire image 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 FIGS. 9, 11, and 13, the lattice line width of the object is about 0.01 mm.

  According to FIGS. 8 to 13 described above, in the first embodiment, the trapezoidal distortion is satisfactorily corrected regardless of the position of the projection surface SC in any of the first position to the third position, and excellent imaging performance is achieved. It can be seen that

<Second embodiment>
Next, a second embodiment will be described. FIG. 14 is a yz sectional view of the image projection optical system PL according to the second example. FIG. 15 is an xz sectional view of the image projection optical system PL according to the second example. In the image projection optical system PL of the second embodiment, the same components as those in the first embodiment are denoted by the same reference numerals as those in the first embodiment, and detailed description thereof is omitted. In the second embodiment, unlike the first embodiment, the entire rotationally symmetric lens group G1 and the second free-form surface lens L22 of the free-form surface lens group G2 are moved in the optical axis direction to adjust the focus. It has become. It is confirmed by calculation that even if the movement of the first rotationally symmetric lens L11 alone is not the movement of the entire rotationally symmetric lens group G1, the same effect as the movement of the entire rotationally symmetric lens group G1 is obtained. .

  16 and 17 are optical path diagrams on the yz plane of the image projection optical system PL according to the second example. FIG. 16 shows the time when the position of the projection surface SC is the first position, and FIG. 17 shows the time when the position of the projection surface SC is the third position. The distance from the free-form surface mirror M to the projection plane (image plane) SC and the projection size are the same as those in the first embodiment at each position, and thus the description thereof is omitted.

Table 5 below shows various data of the image projection optical system PL according to the second example. The surface numbers 1 to 18 in Table 5 correspond to the surfaces 1 to 18 in FIG.
<Table 5>
(Overall specifications)
F number 2.3
Image display area 9.696mm x 6.06mm
(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
0: (Object surface) ∞ 1.410000
1: ∞ 0.650000 1.50900 62.7
2: ∞ 14.000000 1.51872 64.0
3: ∞ 1st interval / variable
4: 35.00000 5.117805 1.68082 55.1
5: * A‐38.33586 14.180950
6: 15.62618 5.012496 1.75844 52.1
7: -32.98129 2.000000 1.80633 29.6
8: 16.56141 3.411572
9: * A -14.82741 3.000000 1.69661 53.0
10: -11.00000 0.500000
11: (Aperture) ∞ 4th interval / variable
12: * F ∞ 4.000000 1.53113 55.7
13: * F ∞ 5th interval / variable
14: * F ∞ 5.500000 1.53113 55.7
15: * F ∞ 6th interval / variable
16: * F ∞ 10.000000 1.53113 55.7
17: * F ∞ 33.955054
18: * F (reflective surface) ∞ B. F / variable
19: (image plane) ∞
(Variable data)
Projection plane position 1st position 2nd position 3rd position 1st interval 8.93745 8.73600 8.63982
4th interval 2.80000 3.00145 3.09763
5th interval 23.55187 26.00790 27.28705
6th interval 11.97281 9.51678 8.23762
B. F -350.00000 -525.00000 -700.00000
Projection size 420mm × 262.5mm 630mm × 393.75mm 840mm × 525mm

  In the image projection optical system PL, when the position of the projection surface (image surface) SC changes, the distance (BF: back focus) from the reflection surface (18th surface) of the free-form surface mirror M to the image surface (19th surface). ) And the projection size changes. At this time, since the entire rotationally symmetric lens group G1 (fourth surface to tenth surface) and the aperture stop (eleventh surface) move together, the distance from the third surface to the fourth surface (first interval) ) And the distance (fourth interval) from the eleventh surface to the twelfth surface changes. At this time, since the second free-form surface lens L22 (14th surface and 15th surface) moves, the distance from the 13th surface to the 14th surface (fifth interval) and the 15th surface to the 16th surface The distance (sixth interval) also changes.

  Further, as shown in the lens data in Table 5, among the lens surfaces (fourth to tenth surfaces) of the rotationally symmetric lens group G1, the fifth surface and the ninth surface are rotationally symmetric aspheric surfaces. Table 6 below shows the aspheric coefficients of the fifth and ninth surfaces.

<Table 6>
(Aspheric data)
Aspheric coefficient 5th surface 9th surface K 0.000000 0.000000
A ₄ 1.431332E-05 -1.843052.E-04
A ₆ -1.190678E-08 -6.386215E-07
A ₈ 1.414341E-11 7.669655E-09
A ₁₀ -5.207302E-14 -1.544189E-10
A ₁₂ 0.000000 0.000000

As shown in the lens data of Table 5, the lens surface of the free-form surface lens group G2 and the reflection surfaces (the 12th to 18th surfaces) of the free-form surface mirror M are non-rotationally symmetric aspheric surfaces (free-form surfaces). It is. Table 7 below shows the coefficients of the aspheric terms x ^m y ⁿ of these free-form surfaces.

<Table 7>
(Free curved surface data 1)
Each coefficient 12th surface 13th surface 14th surface 15th surface
c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) 0.000000 0.000000 0.000000 0.000000
C (2,0) 3.243288E-02 4.598112E-02 -6.165401E-02 -3.546819E-02
C (0,2) 4.066493E-02 5.747610E-02 -5.951304E-02 -2.524541E-02
C (2,1) -1.643960E-03 -3.050000E-03 -1.532907E-03 -7.378099E-04
C (0,3) -1.287953E-03 -2.684356E-03 -1.569374E-03 -6.192209E-04
C (4,0) -1.528613E-05 -1.403116E-04 -6.449545E-05 -1.155376E-05
C (2,2) -5.403842E-05 -2.608902E-04 -5.715099E-05 3.447517E-05
C (0,4) -1.098857E-05 -8.013954E-05 -2.109919E-05 2.901366E-05
C (4,1) -7.042119E-07 1.261027E-05 -6.924880E-06 -1.316785E-06
C (2,3) -5.175777E-06 2.095148E-05 -1.047877E-06 3.189579E-07
C (0,5) -4.265106E-06 6.734423E-06 -7.440807E-06 -2.049358E-06
C (6,0) 1.250506E-06 2.491100E-06 -1.413658E-07 8.568508E-09
C (4,2) 3.844072E-06 6.865635E-06 -4.193468E-07 8.006768E-08
C (2,4) 4.078317E-06 7.040898E-06 -3.461588E-07 -9.197651E-08
C (0,6) 1.495938E-06 2.662879E-06 -5.246130E-07 -6.781026E-08
C (6,1) -5.221901E-08 -2.525476E-07 1.946792E-08 5.409437E-09
C (4,3) -1.689645E-07 -8.668216E-07 -4.063205E-08 -8.052398E-10
C (2,5) -1.318273E-07 -8.401018E-07 -5.730905E-08 -4.335797E-09
C (0,7) -4.482892E-08 -3.218456E-07 -1.882585E-08 3.635616E-09
C (8,0) -1.256593E-08 -1.835236E-08 6.845784E-10 1.045973E-10
C (6,2) -4.263649E-08 -4.692627E-08 1.962337E-09 -5.998261E-11
C (4,4) -5.907196E-08 -4.121774E-08 3.121062E-11 5.941790E-11
C (2,6) -3.469703E-08 -1.016130E-08 -4.490353E-09 -4.411121E-10
C (0,8) -8.177375E-09 2.344446E-09 -6.314697E-10 3.433510E-11
(Free curved surface data 2)
Each coefficient 16th surface 17th surface 18th surface
c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) 0.000000 0.000000 0.000000
C (2,0) 2.605499E-03 -1.441996E-02 8.697655E-03
C (0,2) -4.859934E-03 -2.148224E-02 1.221026E-03
C (2,1) 7.337605E-04 5.414362E-04 2.407397E-04
C (0,3) 2.546943E-04 1.275926E-04 5.184920E-05
C (4,0) -1.147906E-05 -3.591818E-06 -1.862400E-06
C (2,2) 1.541870E-05 1.681719E-05 4.561951E-06
C (0,4) 1.389432E-06 -3.767671E-06 1.364151E-06
C (4,1) -5.674932E-07 -9.229992E-09 -1.002536E-07
C (2,3) -3.444716E-07 7.727935E-07 8.869047E-08
C (0,5) -1.045564E-06 -3.269574E-07 5.269547E-08
C (6,0) 1.317183E-08 -1.308703E-09 2.556637E-10
C (4,2) -7.408957E-09 -2.654469E-08 -2.585053E-09
C (2,4) 4.597696E-09 1.465654E-09 2.069172E-09
C (0,6) -4.057305E-08 -1.498766E-08 1.625417E-09
C (6,1) 4.315421E-10 3.138984E-10 2.555736E-11
C (4,3) -3.982129E-10 -8.210486E-10 -4.557457E-11
C (2,5) 6.528097E-10 -1.019077E-09 3.917974E-11
C (0,7) 4.790521E-11 -3.239008E-10 2.715467E-11
C (8,0) -4.007155E-12 4.930926E-12 1.631463E-13
C (6,2) 1.057214E-11 2.986960E-11 3.890704E-13
C (4,4) -2.365447E-11 -4.267349E-12 -4.653979E-13
C (2,6) 1.674616E-11 -3.252133E-11 3.695700E-13
C (0,8) 1.619537E-11 -1.458121E-11 1.844515E-13

  Further, the eccentricity of the twelfth to nineteenth surfaces in the local coordinate system is shown in Table 8 below. The type of eccentricity is rotation around the x axis (referred to as α rotation). The positive direction of the α rotation is counterclockwise when facing the positive direction of the x axis. In the 12th to 17th surfaces, the optical axis does not change only by the eccentricity of each surface. Since the eighteenth surface is a reflecting surface, the direction in which light rays incident along the optical axis are reflected when the first-order term of the expression representing the surface is 0 is the optical axis after the eccentric operation. The decentering of the 19th surface (image surface) is to decenter only the image surface, and the optical axis does not change.

<Table 8>
(Eccentric data)
Surface number α rotation (unit: °)
Side 12 -15.000
Side 13 -12.401
14th surface -8.961
15th -20.000
Face 16 1.469
17th page 6.613
18th surface (reflective surface) 35.000
19th surface (image surface) -60.000

In the second embodiment, C ₁ (2,0) =-6.165401E-02, C ₁ (0,2) = − about the display element side lens surface (14th surface) of the second free-form surface lens L22. Since it is 5.951304E-02, the conditional expression (2) is satisfied. Further, with respect to the mirror side lens surface (fifteenth surface) of the second free-form surface lens L22, C ₂ (2,0) = − 3.546819E-02 and C ₂ (0,2) = − 2.524541E-02. Conditional expression (4) is satisfied. Therefore, in the second embodiment, as described above, the lens surfaces on both sides of the second free-form surface lens L22 have a meniscus shape with concave surfaces facing the image display element DS. Therefore, when the second free-form surface lens L22 is moved to adjust the focus, it is possible to reduce the deterioration of the imaging performance.

In the second example, since f _L11 / f _G1 = 1.1721 for the rotationally symmetric lens group G1 and the display element side lens (first rotationally symmetric lens L11) in the rotationally symmetric lens group G1, conditional expression (5 ) Is satisfied. Therefore, in the second example, as described above, the focal length fL11 of the first rotationally symmetric lens _L11 is an appropriate value, and various aberrations can be corrected effectively.

In the second example, since C ₁ (0,1) = 0 for the display element side lens surface (14th surface), α ₁ = 0 for conditional expression (9). Similarly, with respect to the mirror side lens surface (fifteenth surface), since C ₁ (0,1) = 0, α ₂ = 0 with respect to the conditional expression (11). Further, the values relating to the conditional expressions (10), (11), (13), and (14) are shown in the following table for the display element side lens surface (14th surface) and the mirror side lens surface (15th surface).

  As shown in this table, on the 14th and 15th surfaces, conditional expressions (10) and (13) are satisfied in the yz cross section of the effective diameter through which the light beam passes, and x− of the effective diameter through which the light beam passes. Conditional expressions (11) and (14) are satisfied in the z cross section. Therefore, in the second embodiment, the lens surfaces on both sides of the second free-form surface lens L22 have a shape in which concave surfaces are directed toward the image display element DS in both the yz section and the xz section. .

  Here, the spot diagrams when the position of the projection surface SC is the first position, the second position, and the third position so that the image formation state and the trapezoidal distortion state on the projection surface (image surface) SC can be understood. 18, 20, and 22. In addition, FIGS. 19, 21, and 23 show two-dimensional image simulation images of lattice object points when the position of the projection surface SC is the first position, the second position, and the third position.

  18, 20, and 22 are e-line monochromatic spot diagrams of the image projection optical system PL 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.

  19, FIG. 21, and FIG. 23 represent images when a grid is displayed over the entire image 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. 19, FIG. 21, and FIG. 23, the lattice line width of the object is about 0.01 mm.

  As shown in FIGS. 18 to 23, in the second embodiment, the trapezoidal distortion is corrected well and the imaging performance is excellent even if the position of the projection surface SC is any of the first position to the third position. It can be seen that

<Third embodiment>
Next, a third embodiment will be described. FIG. 24 is a yz sectional view of the image projection optical system PL according to the third example. FIG. 25 is an xz sectional view of the image projection optical system PL according to the third example. In the image projection optical system PL of the third embodiment, the same components as those of the first and second embodiments are denoted by the same reference numerals as those of the first and second embodiments, and detailed description thereof is omitted. In the third example, unlike the first and second examples, the first free-form surface lens L21 and the second free-form surface lens L22 of the free-form surface lens group G2 move together in the optical axis direction. The focus is adjusted.

  Further, unlike the first and second embodiments, the reflecting surface of the free-form curved mirror M in the third embodiment has a negative (concave) center curvature. The divergent light beam emitted from each object point on the display area of the image display element DS is collected by the rotationally symmetric lens group G1, passes through the free-form surface lens group G2, forms an intermediate image, and is reflected by the free-form surface mirror M. Incidently incident on the projection surface SC and re-imaged.

  26 and 27 are optical path diagrams on the yz plane of the image projection optical system PL according to the third example. FIG. 26 shows the time when the position of the projection surface SC is the first position, and FIG. 27 shows the time when the position of the projection surface SC is the third position. Note that the distance from the free-form surface mirror M to the projection plane (image plane) SC and the projection size are the same as those in the first and second embodiments at each position, and thus the description thereof is omitted.

Table 9 below shows various data of the image projection optical system PL according to the third example. The surface numbers 1 to 19 in Table 9 correspond to the surfaces 1 to 18 in FIG.
<Table 9>
(Overall specifications)
F number 2.3
Image display area 9.856mm × 6.16mm
(Lens data)
Surface number Curvature radius Surface spacing Refractive index (e-line) Abbe number (νe)
0: (Object surface) ∞ 1.410000
1: ∞ 0.650000 1.50900 62.7
2: ∞ 14.000000 1.51872 64.0
3: ∞ 5.000000
4: 53.29483 5.000000 1.68082 55.1
5: * A -21.35546 2.456684
6: 13.96854 5.000000 1.82017 46.4
7: -102.41896 1.000000 1.81643 22.6
8: 13.54101 8.173801
9: * A -9.29920 2.000000 1.69661 53.0
10: -9.00000 0.500000
11: (Aperture) ∞ 4th interval / variable
12: * F ∞ 3.000000 1.53113 55.7
13: * F ∞ 18.309515
14: * F ∞ 4.200000 1.53113 55.7
15: * F ∞ 6th interval / variable
16: * F ∞ 7.000000 1.53113 55.7
17: * F ∞ 50.000000
18: * F (reflective surface) -73.08994 B. F / variable
19: (image plane) ∞
(Variable data)
Projection plane position 1st position 2nd position 3rd position 4th interval 7.79344 10.54563 11.86153
6th interval 14.50656 11.75437 10.43847
B. F -350.00000 -525.00000 -700.00000
Projection size 420mm × 262.5mm 630mm × 393.75mm 840mm × 525mm

  In the image projection optical system PL, when the position of the projection surface (image surface) SC changes, the distance (BF: back focus) from the reflection surface (18th surface) of the free-form surface mirror M to the image surface (19th surface). ) And the projection size changes. At this time, since the first free-form curved lens L21 (the twelfth and thirteenth surfaces) and the second free-form curved lens L22 (the fourteenth and fifteenth surfaces) move together, the eleventh to the first The distance to the 12th surface (fourth interval) and the distance from the fifteenth surface to the sixteenth surface (sixth interval) change.

  Further, as shown in the lens data of Table 9, among the lens surfaces (fourth to tenth surfaces) of the rotationally symmetric lens group G1, the fifth surface and the ninth surface are rotationally symmetric aspheric surfaces. Table 10 below shows the aspherical coefficients of the fifth surface and the ninth surface.

<Table 10>
(Aspheric data)
Aspheric coefficient 5th surface 9th surface K 0.000000 0.000000
A ₄ 2.414263E-05 -9.622804E-05
A ₆ -1.873343E-09 -1.801724E-06
A ₈ 1.109369E-10 2.556471E-08
A ₁₀ -3.716152E-13 -5.085332E-10
A ₁₂ 0.000000 0.000000

Further, as shown in the lens data of Table 9, the lens surface of the free-form surface lens group G2 and the reflection surfaces (the 12th to 18th surfaces) of the free-form surface mirror M are non-rotationally symmetric aspheric surfaces (free-form surfaces). It is. Table 11 below shows the coefficients of the aspheric terms x ^m y ⁿ of these free-form surfaces.

<Table 11>
(Free curved surface data 1)
Each coefficient 12th surface 13th surface 14th surface 15th surface
c 0.000000 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000 0.000000
C (0,1) -2.000000E-01 -1.501338E-01 -1.901294E-01 -2.356788E-01
C (2,0) 1.660926E-02 -3.935345E-03 -8.854417E-02 -5.173742E-02
C (0,2) 2.674969E-02 1.110750E-03 -9.837711E-02 -6.292070E-02
C (2,1) 2.496584E-03 2.776639E-03 -4.963320E-03 -2.353832E-03
C (0,3) 1.844795E-03 2.177712E-03 -4.724449E-03 -2.262237E-03
C (4,0) -4.588676E-05 -6.814823E-05 6.788245E-05 4.814856E-05
C (2,2) -1.457480E-04 -1.664710E-04 8.069055E-05 5.388783E-05
C (0,4) -6.726787E-05 -7.148696E-05 7.154381E-05 5.349039E-05
C (4,1) 1.250749E-05 5.841080E-06 -3.956399E-05 -1.077592E-05
C (2,3) 1.987129E-05 6.280142E-06 -5.751769E-05 -1.122715E-05
C (0,5) 1.114466E-05 6.247984E-06 -1.797101E-05 -6.083334E-06
C (6,0) 3.881765E-08 1.211324E-07 1.895460E-07 7.689734E-08
C (4,2) 8.949947E-07 1.503762E-06 6.949495E-08 9.676614E-08
C (2,4) -3.733054E-07 1.926072E-07 7.359587E-07 7.693300E-07
C (0,6) -5.940411E-07 -4.272913E-07 -5.351885E-07 -4.576820E-07
C (6,1) 1.011073E-07 9.934412E-08 2.620133E-07 6.579987E-08
C (4,3) 2.915402E-07 2.989641E-07 4.781203E-07 9.036046E-08
C (2,5) 2.507952E-07 2.174302E-07 4.761958E-07 1.121736E-07
C (0,7) 1.319082E-07 1.134788E-07 4.266284E-07 1.804909E-07
C (8,0) -1.261462E-09 -1.216761E-09 2.681246E-10 -1.954245E-10
C (6,2) -5.125781E-09 2.456627E-09 2.511190E-08 6.432003E-09
C (4,4) 8.357396E-10 1.916012E-08 -9.676340E-09 2.342589E-09
C (2,6) 2.077726E-10 1.157889E-08 3.789384E-08 1.008124E-08
C (0,8) -8.638139E-10 5.353558E-09 2.926229E-08 3.070161E-09
(Free curved surface data 2)
Each coefficient 16th surface 17th surface 18th surface
c 0.000000 0.000000 0.000000
K 0.000000 0.000000 0.000000
C (0,1) 4.579867E-01 4.882112E-01 0.000000
C (2,0) -2.620386E-03 -1.741742E-02 -2.713774E-03
C (0,2) 6.877148E-03 -1.421746E-02 1.627566E-03
C (2,1) 4.184938E-05 1.209973E-04 -1.046419E-04
C (0,3) -1.197508E-03 -1.142636E-03 -3.273417E-05
C (4,0) -2.369128E-05 -9.219561E-06 1.332504E-07
C (2,2) -1.102911E-05 3.971734E-05 -1.726484E-06
C (0,4) 7.570781E-05 7.955227E-05 -8.340865E-07
C (4,1) -2.885199E-06 -3.074426E-06 1.248715E-08
C (2,3) 1.605967E-06 -1.797292E-06 -2.942482E-08
C (0,5) -5.366710E-06 -7.948611E-06 -2.461114E-08
C (6,0) 1.627190E-07 9.717786E-08 -8.705697E-11
C (4,2) -1.277483E-07 -1.007888E-07 3.605850E-10
C (2,4) -3.807164E-07 -2.137959E-07 3.452167E-10
C (0,6) -1.198319E-06 -5.402778E-07 -3.295427E-10
C (6,1) 3.547214E-09 8.605540E-10 -4.090185E-12
C (4,3) 1.397208E-08 1.828407E-08 5.308053E-12
C (2,5) 5.121552E-08 3.687527E-08 2.688415E-11
C (0,7) 9.687843E-08 5.495618E-08 -3.529102E-12
C (8,0) -9.276799E-11 5.413772E-11 -3.845458E-15
C (6,2) 9.527918E-11 6.813421E-11 -8.406395E-14
C (4,4) -8.631176E-10 -7.909944E-10 8.305402E-14
C (2,6) -6.717070E-10 -9.540200E-10 4.724024E-13
C (0,8) -2.567534E-09 -1.129137E-09 -1.309966E-14

  Further, the eccentricity of the 18th surface and the 19th surface (image surface) in the local coordinate system is shown in Table 12 below. The type of eccentricity is rotation around the x axis (referred to as α rotation). The positive direction of the α rotation is counterclockwise when facing the positive direction of the x axis. Since the eighteenth surface is a reflecting surface, the direction in which light rays incident along the optical axis are reflected when the first-order term of the expression representing the surface is 0 is the optical axis after the eccentric operation. The decentering of the 19th surface (image surface) is to decenter only the image surface, and the optical axis does not change.

<Table 12>
(Eccentric data)
Surface number α rotation (unit: °)
18th surface (reflective surface) -25.000
19th surface (image surface) -60.000

In the third example, C ₁ (2,0) =-8.854417E-02, C ₁ (0,2) = − about the display element side lens surface (14th surface) of the second free-form surface lens L22. Since it is 9.837711E-02, the conditional expression (2) is satisfied. Further, with respect to the mirror side lens surface (fifteenth surface) of the second free-form surface lens L22, C ₂ (2,0) = − 5.173742E-02 and C ₂ (0,2) = − 6.292070E-02. Conditional expression (4) is satisfied. Therefore, in the third embodiment, as described above, the lens surfaces on both sides of the second free-form surface lens L22 have a meniscus shape with concave surfaces facing the image display element DS. Therefore, when the second free-form surface lens L22 is moved to adjust the focus, it is possible to reduce the deterioration of the imaging performance.

In the third example, since f _L11 / f _G1 = 1.2812 for the rotationally symmetric lens group G1 and the display element side lens (first rotationally symmetric lens L11) in the rotationally symmetric lens group G1, the conditional expression (5 ) Is satisfied. Therefore, in the third example, as described above, the focal length fL11 of the first rotationally symmetric lens _L11 is an appropriate value, and various aberrations can be corrected effectively.

  In the third embodiment, since the free-form surface mirror M is 2 / MR = −0.02736, the conditional expression (6) is satisfied. Therefore, in the third embodiment, as described above, the center curvature radius MR of the free-form surface mirror M is an appropriate value, and various aberrations can be effectively corrected.

In the third example, α ₁ = 1.048 with respect to the conditional expression (9) for the display element side lens surface (14th surface). With respect to the mirror side lens surface (fifteenth surface), α ₂ = 2.140 with respect to conditional expression (11). Further, the values relating to the conditional expressions (10), (11), (13), and (14) are shown in the following table for the display element side lens surface (14th surface) and the mirror side lens surface (15th surface).

  As shown in this table, on the 14th and 15th surfaces, conditional expressions (10) and (13) are satisfied in the yz cross section of the effective diameter through which the light beam passes, and x− of the effective diameter through which the light beam passes. Conditional expressions (11) and (14) are satisfied in the z cross section. Therefore, in the third embodiment, the lens surfaces on both sides of the second free-form surface lens L22 have a shape in which concave surfaces are directed toward the image display element DS in both the yz section and the xz section. .

  Here, FIG. 28 shows a spot diagram when the position of the projection plane SC is the first position, the second position, and the third position so that the image formation state and the trapezoidal distortion state on the projection plane SC can be understood. 30 and 32. In addition, FIGS. 29, 31, and 33 show two-dimensional image simulation images of lattice object points when the position of the projection surface SC is the first position, the second position, and the third position.

  28, 30 and 32 are e-line monochromatic spot diagrams of the image projection optical system PL 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 (0.00,0.00), (0.00, -1.54), (-2.464, -1.54), (-2.464,0.00), (-2.464,1.54), ( 0.00,1.54), (0.00, -3.08), (-2.464, -3.08), (-4.928, -3.08), (-4.928, -1.54), (-4.928,0.00), (-4.928,1.54), (-4.928,3.08), (-2.464,3.08), (0.00,3.08).

  FIG. 29, FIG. 31, and FIG. 33 represent images when a grid is displayed over the entire image 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. 29, 31 and 33, the lattice line width of the object is about 0.01 mm.

  According to FIGS. 28 to 33 described above, in the third embodiment, the trapezoidal distortion is corrected well and the imaging performance is excellent regardless of the position of the projection surface SC from the first position to the third position. It can be seen that

According to the embodiment described above, the following operational effects can be obtained.
(1) The image projection optical system PL includes a rotationally symmetric lens group G1, a free-form surface lens group G2, and a free-form surface mirror M, which are arranged in order from the image display element DS side along the optical axis. The curved lens group G2 includes a first free-form surface lens L21, a second free-form surface lens L22, and a third free-form surface lens L23 arranged in order from the image display element DS side, and the second free-form surface lens L22. Is movable along the optical axis. As a result, the trapezoidal distortion of the projected image can be satisfactorily corrected while having a compact configuration, and the second free-form surface lens L22 moves in the optical axis direction, so that the focus can be maintained even if the projection size is changed. Can be recombined.

(2) In the image projection optical system PL, the lens surfaces on both sides of the second free-form surface lens L22 are an optical axis between the free-form surface lens group G2 and the free-form surface mirror M, and an optical axis between the free-form surface mirror M and the projection surface SC. And a second cross section (xz cross section) perpendicular to the first cross section with a substantially concave surface facing the image display element DS side. To have. Thereby, when the focus is adjusted by moving the second free-form surface lens L22 as the projection size is changed by changing the position of the projection surface SC, the degradation of imaging performance such as coma and distortion is reduced. can do.

(3) In the image projection optical system PL, and the focal length _{f G1} of the entire group rotationally symmetrical lens G1, the focal length _{f L11} of the first rotationally symmetrical lens L11 on the most image display element DS side in rotationally symmetric lens group G1, The conditional expression (5) was satisfied. Thereby, various aberrations such as coma and curvature of field can be corrected.

(4) In the image projection optical system PL, when the center curvature of the reflection surface of the free-form surface mirror M is negative, the center curvature radius MR of the reflection surface of the free-form surface mirror M satisfies the conditional expression (6). I tried to do it. As a result, the Petzval sum can be reduced and the field curvature can be corrected well.

-Modification-
The image display element DS may be movable in the optical axis direction with respect to the image projection optical system PL. Moving the image display element DS when changing the projection size by changing the position of the projection surface SC is advantageous in correcting various aberrations.

  The free-form surface mirror M may be movable in the optical axis direction with respect to the image display element DS. When changing the projection size by changing the position of the projection surface SC, the free-form surface mirror M is also moved, which is advantageous for adjusting the projection size.

  The above description is merely an example, and the present invention is not limited to the configuration described above, and various aspects may be changed. For example, the number of lenses constituting each lens group, the radius of curvature of each lens, the surface interval, the glass material, and the like may be appropriately changed. Moreover, you may combine suitably the structure of each modification with embodiment mentioned above.

The disclosure of the following priority application is hereby incorporated by reference.
Japan Patent Application 2013-10403 (filed January 23, 2013)
Japanese patent application 2013 No.48040 (filed on March 11, 2013)

PRJ: video projection device, DS: video display element, PL: video projection optical system, G1: rotationally symmetric lens group, L11: first rotationally symmetric lens, L12: second rotationally symmetric lens, L13: third rotationally symmetric lens, L14: Fourth rotationally symmetric 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, M ... Free-form surface mirror

According to the first aspect of the present invention, the image projection optical system includes a rotationally symmetric lens group composed of rotationally symmetric lenses arranged in order from the image display element side and formed rotationally symmetric with respect to the optical axis, and the optical axis. non-rotating is formed symmetrically with the free-form surface lens group consisting of free-form surface lens, and a free-form surface mirror having a reflecting surface formed on the non-rotationally symmetrical to the optical axis, the free-form surface lens with respect to group, wherein arranged from the image display element side in order, a first free-form surface lens, a second free-form surface lens, and a third free curved lens, the second free-form surface lens along said optical axis By moving, the distance between the second free-form surface lens and the first free-form surface lens and the distance between the second free-form surface lens and the third free-form surface lens are changed .
According to a second aspect of the present invention, the image projection device is used in a state of being installed in a setting surface, and project images obliquely onto a plane substantially parallel to the same plane or on the installation surface and the installation surface , have a focusing mechanism capable to fit the projection size comprises a video projection optical system of the first aspect.

Claims (11)

An image projection optical system for enlarging an image displayed on an image display element and projecting the image on a projection surface from an oblique direction,
A rotationally symmetric lens group composed of rotationally symmetric lenses formed in a rotationally symmetric manner with respect to the central axis and arranged in order from the image display element side along the optical axis, and a free rotationally symmetric lens formed with respect to the central axis A free-form surface lens group composed of a curved lens, and a free-form surface mirror having a reflecting surface formed non-rotationally symmetric with respect to the central axis,
The free-form surface lens group includes a first free-form surface lens, a second free-form surface lens, and a third free-form surface lens arranged in order from the image display element side, and the second free-form surface lens is a light beam. An image projection optical system that is movable along an axis. The image projection optical system according to claim 1,
The lens surfaces on both sides of the second free-form surface lens have a first cross section passing through an optical axis between the free-form surface lens group and the free-form surface mirror and an optical axis between the free-form surface mirror and the projection surface. And a second cross section perpendicular to the first cross section, the image projection optical system having a shape with a substantially concave surface facing the image display element side. The image projection optical system according to claim 2,
The coordinate axis in the optical axis direction that is positive in the direction from the image display element toward the free-form curved mirror is z ₁ axis, the coordinate axis perpendicular to the z ₁ axis along the first cross section is y ₁ axis, and A coordinate system perpendicular to the z ₁ axis and the y ₁ axis is defined as an x ₁ axis, and a local coordinate system (x ₁ , x ₂ , x ₂₎ having an origin at the intersection between the optical surface and the lens surface of the second free-form surface lens on the image display element side. y ₁ , z ₁ ), m and n are natural numbers including 0, and C ₁ (m, n) is a coefficient of a polynomial including x ₁ and y _1. The following formula (1) expresses the sag amount of the lens surface on the element side.
When expressed as (2)
C ₁ (2,0) <0, C ₁ (0,2) <0 (2)
Satisfy the conditions of
Wherein the optical axis direction of the coordinate axis positive direction toward the free-form surface mirror from the image display element and z ₂ axis, the z ₂ axis perpendicular axes along the first section and y ₂ axes, wherein z ₂ axis and the y ₂ axis perpendicular coordinate axes as x ₂ axis, the second said free-form surface mirror side lens surface and the local coordinate system with the origin at the intersection of the optical axis of the free-form surface lens (x _2, y ₂ , z ₂ ), m and n are natural numbers including 0, and C ₂ (m, n) is a coefficient of a polynomial including x ₂ and y _2. The free curved surface of the second free curved lens An expression representing the sag amount of the lens surface on the mirror side is the following expression (3)
When expressed as (4)
C ₂ (2,0) <0, C ₂ (0,2) <0 (4)
An image projection optical system that satisfies the above conditions. In the image projection optical system according to claim 2 or 3,
The coordinate axis in the optical axis direction that is positive in the direction from the image display element toward the free-form curved mirror is z ₁ axis, the coordinate axis perpendicular to the z ₁ axis along the first cross section is y ₁ axis, and A coordinate system perpendicular to the z ₁ axis and the y ₁ axis is defined as an x ₁ axis, and the local coordinate system (x ₁ , x In y ₁ , z ₁ ), when the expression representing the shape of the lens surface of the second free-form surface lens on the image display element side is z ₁ = f ₁ (x ₁ , y ₁ ), from the image display element In the region through which the light passes, the following equation (9)
F ₁ (0, α ₁ ) satisfying the following condition exists, and y ₁ ′ = y ₁ −α ₁ with respect to the expression representing the shape of the lens surface of the second free-form surface lens on the image display element side Assuming that the converted expression is z ₁ = f ₁ ′ (x ₁ , y ₁ ′), in the region where the light from the image display element passes, when x ₁ = 0, the following expression (10)
When y ₁ = 0 in the region where the light from the image display element passes, the following formula (11) is satisfied:
Satisfy the conditions of
Wherein the optical axis direction of the coordinate axis positive direction toward the free-form surface mirror from the image display element and z ₂ axis, the z ₂ axis perpendicular axes along the first section and y ₂ axes, wherein z ₂ axis and the y ₂ axis perpendicular coordinate axes as x ₂ axis, the second said free-form surface mirror side lens surface and the local coordinate system with the origin at the intersection of the optical axis of the free-form surface lens (x _2, In y ₂ , z ₂ ), when the expression representing the shape of the lens surface of the second free-form surface lens on the free-form surface mirror side is z ₂ = f ₂ (x ₂ , y ₂ ), In the region through which the light passes, the following equation (12)
F ₂ (0, α ₂ ) satisfying the following condition exists, and a variable that sets y ₂ ′ = y ₂ −α ₂ to the expression representing the shape of the lens surface of the second free-form surface lens on the free-form surface mirror side When the converted expression is z ₂ = f ₂ ′ (x ₂ , y ₂ ′), in the region where the light from the image display element passes, when x ₂ = 0, the following expression (13)
When y ₂ = 0 in the region where the light from the image display element passes, the following formula (14) is satisfied:
An image projection optical system that satisfies the above conditions. In the image projection optical system according to any one of claims 1 to 4,
When the focal length of the rotationally symmetric lens group is f _G1 and the focal length of the rotationally symmetric lens closest to the image display element in the rotationally symmetric lens group is f _L11 , the following equation (5)
0.8 ≦ f _L11 / f _G1 ≦ 1.4 (5)
An image projection optical system that satisfies the above conditions. In the image projection optical system according to any one of claims 1 to 5,
An image projection optical system in which the image display element is movable in an optical axis direction with respect to the image projection optical system. In the image projection optical system according to any one of claims 1 to 6,
An image projection optical system in which the first free-form surface lens is integral with the second free-form surface lens and is movable in the optical axis direction. In the image projection optical system according to any one of claims 1 to 7,
An image projection optical system in which the entire rotationally symmetric lens group or the rotationally symmetric lens closest to the image display element in the rotationally symmetric lens group is movable in the optical axis direction. In the image projection optical system according to any one of claims 1 to 8,
An image projection optical system in which the free-form surface mirror is movable in the optical axis direction with respect to the image display element. In the image projection optical system according to any one of claims 1 to 9,
When the center curvature radius of the free-form curved mirror is MR, the following formula (6)
−0.1 <2 / MR <−0.005 (6)
An image projection optical system that satisfies the above conditions. An image having a mechanism that can be used in a state where it is installed on an installation surface, projects an image from an oblique direction on the same surface as the installation surface or a surface substantially parallel to the installation surface, and can be focused according to the projection size A projection device,
An image projection apparatus comprising the image projection optical system according to claim 1.