JPH09281429A - Mounting-on-head type image display device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide observed images which are distinct even at a wide angle of view and have decreased distortions. SOLUTION: This device is constituted by having an image display element 6 and an eyepiece optical system 7 which introduces the image formed by this image display element 6 to the observer's eyeball position without forming intermediate images so that the images may be observed as virtual images. In such a case, the eyepiece optical system 7 has at least one reflection surfaces of a nonrotationally symmetric surface shape having no rotational symmetrical axis both within its face and off the face and the deviation in the Y direction differential value on the periphery of the screen with respect to the center of the screen of the nonrotationally symmetric surface is limited within the prescribed value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image display device, and more particularly to a head- or face-mounted image display device that can be held on an observer's head or face.

[0002]

2. Description of the Related Art As a conventional well-known head- or face-mounted image display device, there is JP-A-3-101709. The entire optical system is shown in FIG.
This image display device transmits a display image of an image display element as an aerial image by a relay optical system composed of a positive lens, and an eyepiece optical system composed of a concave reflecting mirror. The aerial image is enlarged and projected into the eyeball of the observer.

Another conventional type is disclosed in US Pat. No. 4,669,810. As shown in FIG. 25, this device forms an intermediate image of a CRT image through a relay optical system, and projects the image on a viewer's eye by a combiner having a reflective holographic element and a hologram surface.

Another conventional type of image display device is disclosed in JP-A-62-214782. In this device, as shown in FIGS. 26A and 26B, the image display element is magnified by an eyepiece lens so that the image can be directly observed.

Further, another conventional type of image display device is disclosed in US Pat. No. 4,026,641. As shown in FIG. 27, this device transmits an image of an image display element to a curved object plane by a transmission element and projects the object plane in the air by a toric reflection surface.

Another conventional type of image display device is US Pat. No. 27,356.
As shown in FIG. 28, this device is an eyepiece optical system that projects an object plane onto an exit pupil by a semitransparent concave mirror and a semitransparent plane mirror.

Others, US Pat. No. 4,322,135
U.S. Pat. No. 4,969,724, European Patent No. 0,
Nos. 583 and 116A2 and JP-A-7-333551 are also known.

[0008]

However, in these prior arts, the reflecting surface and the transmitting surface constituting the optical system are composed of a spherical surface, a rotationally symmetric aspherical surface, a toric surface, an anamorphic surface, etc. It was impossible to correct aberration and distortion at the same time.

If the aberration of the observed image is satisfactorily corrected and the distortion is not satisfactorily corrected, the observer may observe the observed image as being distorted, and if the left and right eyes are not symmetrically distorted. , You ca n’t fuse
When a figure or the like is displayed, the figure or the like is distorted and observed, and the correct shape cannot be recognized.

The present invention has been made in view of the above-mentioned problems of the prior art, and an object of the present invention is to provide a head-mounted image display device which provides a clear and less distorted observation image even at a wide angle of view. To provide.

[0011]

A head-mounted image display device of the present invention that achieves the above-mentioned object is provided with an image display element and an observer's eyeball so that an image formed by the image display element can be observed as a virtual image. A head-mounted image display device having an eyepiece optical system for guiding an intermediate image to a position without forming an intermediate image, wherein the eyepiece optical system has a non-rotationally symmetric surface shape having neither a rotational symmetry axis in-plane nor out-of-plane. Z has a reflection surface of at least one surface, the axial direction of the axial chief ray from the screen center of the image display element is emitted from the eyepiece optical system and reaches the observer's eyeball position center is the Z axis, A direction perpendicular to the Z axis is defined as a Y axis, and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when the axial chief ray is reflected by the reflecting surface. When defined, the non-rotationally symmetric surface is It is characterized in that to satisfy the matter. -0.2 <DY _max4 <0.2 (4-1) However, with the Y-axis direction as the vertical direction, an axial chief ray in the Z-axis direction at the center of the screen, a chief ray at the screen upper center angle of view The effective area is defined as the area where the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. Differentiated values DY2, DY1, DY4, DY5, DY6 of the position where each principal ray hits the surface of a value that is differentiated with respect to the Y axis that is in the eccentric direction of the surface of the expression that defines the shape of the surface in the effective area.
When it is DY3, DY2-DY1, DY2-DY3,
_Let all the values of _DY2 -DY4, _DY2-DY5, and _DY2-DY6 be DY _max4 .

Another head-mounted image display device of the present invention forms an intermediate image at an observer's eyeball position so that the image display element and the image formed by the image display element can be observed as a virtual image. In a head-mounted image display device having an eyepiece optical system to guide without, the last reflection surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element, The in-plane and out-of-plane reflection-shaped surfaces having no rotationally symmetric axis have a non-rotationally symmetric surface shape, and the axial chief ray from the center of the screen of the image display element is emitted from the eyepiece optical system to the observer's eyeball. The extension direction of the line segment reaching the position center is the Z axis, the Y axis is the direction perpendicular to the Z axis in the plane including the folded line segment when the axial chief ray is reflected by the reflecting surface. The direction perpendicular to the axis and the Y-axis is the X-axis When you define the surface of the non-rotationally symmetric surface shape is characterized in that the following condition is satisfied. 0.55 <DDXY11 <4.0 (20-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction of the screen center, the chief ray at the screen upper center angle of view, and the screen upper right corner The effective area is defined as the area where the chief ray at the angle of view, the chief ray at the right angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. With respect to the Y axis that is in the eccentric direction of the surface of the equation that defines the shape of that surface with 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY11
And

Still another head-mounted image display device of the present invention forms an intermediate image at an observer's eyeball position so that the image display element and the image formed by the image display element can be observed as a virtual image. In a head-mounted image display device having an eyepiece optical system that guides without any matter, other than the last reflecting surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element. The reflecting surface is composed of a non-rotationally symmetric reflecting surface that does not have a rotational symmetry axis both in-plane and out-of-plane, and an axial chief ray from the center of the screen of the image display element is emitted from the eyepiece optical system. And a direction perpendicular to the Z axis in a plane including a line segment that is folded when the axial chief ray is reflected by the reflecting surface. Y axis, Z
When the direction perpendicular to the axis and the Y-axis is defined as the X-axis,
The surface of the non-rotationally symmetric surface shape satisfies the following conditions. 0.55 <D ² XY12 <5 (21-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction of the screen center, the chief ray at the screen upper center angle of view, and the screen upper right corner The effective area is defined as the area where the chief ray at the angle of view, the chief ray at the right angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. With respect to the Y axis that is in the eccentric direction of the surface of the equation that defines the shape of that surface with 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY12
And

Hereinafter, the reason and operation of the above-described configuration, particularly, the configuration using a plane-symmetric free-form surface in the eyepiece optical system of the head-mounted image display device in the present invention will be described. First, for convenience of description, typical eyepiece optical systems used in the head-mounted image display device of the present invention are illustrated in FIGS.

In the case of FIG. 15, the eyepiece optical system 7 is composed of the first surface 3, the second surface 4 and the third surface 5, and the light flux emitted from the image display element 6 is refracted at the third surface 5. The light enters the eyepiece optical system 7, is internally reflected by the first surface 3, and is reflected by the second surface 4,
It again enters the first surface 3 and is refracted, and is projected into the eyeball of the observer as the exit pupil 1 at the iris position of the observer's pupil or the center of rotation of the eyeball.

In the case of FIG. 16, the eyepiece optical system 7 comprises the first surface 3, the second surface 4, the third surface 5 and the fourth surface 9, and the light flux emitted from the image display element 6 is the third surface. The light is refracted at 5 and enters the eyepiece optical system 7, is internally reflected at the fourth surface 9, is incident on the second surface 4 and is internally reflected, and is incident on the first surface 3 and is refracted, so that the pupil of the observer is refracted. The iris position or the center of rotation of the eyeball is projected into the eyeball of the observer as the exit pupil 1.

In the case of FIG. 17, the eyepiece optical system 7 comprises the first surface 3, the second surface 4, the third surface 5 and the fourth surface 9, and the light flux emitted from the image display element 6 is the third surface. The light is refracted at 5, enters the eyepiece optical system 7, is internally reflected at the fourth surface 9, is incident on the third surface 5 this time is internally reflected, and is incident on the second surface 4 is internally reflected. The light enters the surface 3 and is refracted, and is projected into the eyeball of the observer as the exit pupil 1 at the iris position of the observer's pupil or the center of rotation of the eyeball.

In the case of FIG. 18, the eyepiece optical system 7 comprises the first surface 3, the second surface 4, the third surface 5 and the fourth surface 9, and the light flux emitted from the image display element 6 is the third surface. Refraction at 5 and incidence on the eyepiece optical system 7, internal reflection at the second surface 4, incidence on the fourth surface 9 and internal reflection, incidence at the second surface 4 again and internal reflection, first surface The light enters the lens 3 and is refracted, and is projected into the observer's eyeball by using the iris position of the observer's pupil or the center of rotation of the eyeball as the exit pupil 1.

In the case of FIG. 19, the eyepiece optical system 7 is composed of the first surface 3, the second surface 4, the third surface 5 and the fourth surface 9, and the light flux emitted from the image display element 6 is the second surface. The light is refracted at 4, enters the eyepiece optical system 7, is internally reflected at the third surface 5, is internally reflected at the second surface 4, is internally reflected at the fourth surface 9, and is again incident on the second surface 4. Then, the light is internally reflected, is incident on the first surface 3, is refracted, and is projected into the eyeball of the observer as the exit pupil 1 at the iris position of the observer's pupil or the center of rotation of the eyeball.

In the case of FIG. 20, the ray bundle emitted from the image display element 6 is refracted by the third surface 5 and enters the eyepiece optical system 7, is internally reflected by the first surface 3, and is again reflected by the third surface 5. And then internally reflected, then internally reflected by the first surface 3, reflected by the second surface 4, incident on the first surface 3 three times and refracted, and the iris position of the observer's pupil or The center of rotation of the eyeball is projected as the exit pupil 1 into the eyeball of the observer.

In the case of FIG. 21, the ray bundle emitted from the image display element 6 is refracted by the first surface 3 and enters the eyepiece optical system 7, is internally reflected by the third surface 5, and is again reflected by the first surface 3. And then internally reflected again, then internally reflected again on the third surface 5, three times incident on the first surface 3 and internally reflected, and then reflected on the second surface 4,
It is incident on the first surface 3 and is refracted four times, and is projected into the eyeball of the observer as the exit pupil 1 at the iris position of the observer's pupil or the center of rotation of the eyeball.

In the case of FIG. 22, the eyepiece optical system 7 comprises the first surface 3, the second surface 4 and the third surface 5, and the light flux emitted from the image display element 6 is refracted on the third surface 5. It is incident on the eyepiece optical system 7, internally reflected by the second surface 4, internally reflected by the first surface 3,
The light is reflected again by the second surface 4, re-enters the first surface 3, is refracted, and is projected into the eyeball of the observer as the exit pupil 1 at the iris position of the observer's pupil or the center of rotation of the eyeball.

As described above, in the present invention, the surface numbers of the eyepiece optical system are, in principle, given in the order of the backward ray tracing from the exit pupil 1 to the image display element 6, and typically,
Description will be given on the premise of the eyepiece optical system 7 of FIG. 15, but of course the present invention is not limited to the optical system of FIG. 15, and the optical systems of FIGS. 16 to 22 and other known optical systems. Is applicable to.

Next, the coordinate system used in the following description will be described. As shown in FIG. 15, the axial chief ray that passes through the center of the exit pupil 1 and reaches the center of the image display element 6 that is an image forming means for forming an observed image exits the pupil 1 and the first eyepiece optical system 7 A visual axis 2 defined by a straight line until it intersects the surface 3 is defined as a Z axis, and an axis in the decentered plane of each surface that is orthogonal to the Z axis and that constitutes the eyepiece optical system 7 is defined as a Y axis. ,
An axis orthogonal to the visual axis 2 and orthogonal to the Y axis is taken as the X axis. In the following description, the ray tracing direction is
Unless otherwise specified, the backward ray tracing from the pupil 1 toward the image forming means 6 for forming the observed image will be described.

Generally, in order to satisfactorily correct aberrations with a small number of surfaces, an aspherical surface or the like is used. Generally, a spherical lens system is configured to correct spherical aberration, coma, field curvature, and other aberrations that occur on a spherical surface on another surface.
Therefore, an aspherical surface is used in order to reduce various aberrations generated on this spherical surface. This is to reduce the occurrence of various aberrations occurring on one surface, reduce the number of surfaces for aberration correction, and reduce the total number of constituent surfaces.

However, in an eccentrically arranged optical system such as the eyepiece optical system used in the head-mounted image display apparatus of the present invention, aberrations due to decentering which cannot be corrected by the conventional rotationally symmetric aspherical surface occur. Aberrations that occur due to decentering include coma, astigmatism, image distortion, and field curvature.
In the conventional one, there are examples of using a toric surface or an anamorphic surface to correct these aberrations.
Astigmatism caused by decentering is emphasized, and there is no one that is compact with a wide angle of view and has sufficient aberration correction even for image distortion.

Means for aberration correction that have been performed up to now are introduced here. The fact that the arrangement of the concave mirror and the convex mirror exerts a good effect on the field curvature aberration is that the applicant has a Japanese Patent Application No. 5-264.
No. 828 is described in detail, and the aberration generated by the inclined concave mirror is described in Japanese Patent Application No. 6-127453. The astigmatism generated by the inclined concave mirror is also described in Japanese Patent Application Nos. 6-210167 and 6-256676 of the present applicant. Further, a trapezoidal or bow-shaped image distortion caused by an inclined concave mirror is described in JP-A-5-303056.

However, to correct these aberrations simultaneously and satisfactorily, satisfactory results could not be obtained on toric surfaces, anamorphic surfaces, rotationally symmetric aspherical surfaces, and spherical surfaces.

In order to correct the above-mentioned aberrations simultaneously and satisfactorily, the present invention does not have a rotational symmetry axis both inside and outside the plane,
Moreover, it is characterized by using a plane-symmetric free-form surface having only one plane of symmetry.

Here, the free-form surface of the present invention is defined by the following equation. Z = C ₂ + C ₃ y + C ₄ x + C ₅ y ² + C ₆ yx + C ₇ x ² + C ₈ y ³ + C ₉ y ² x + C ₁₀ yx ² + C ₁₁ x ³ + C ₁₂ y ⁴ + C ₁₃ y ³ x + C ₁₄ y ² x ² + C ₁₅ yx ³ + C ₁₆ x ⁴ + C ₁₇ y ⁵ + C ₁₈ y ⁴ x + C ₁₉ y ³ x ² + C ₂₀ y ² x ³ + C ₂₁ yx ⁴ + C ₂₂ x ⁵ + C ₂₃ y ⁶ + C ₂₄ y ⁵ x + C ₂₅ y ⁴ x ² + C ₂₆ y ³ x ³ + C ₂₇ y ² x ⁴ + C ₂₈ yx ⁵ + C ₂₉ x ⁶ + C ₃₀ y ⁷ + C ₃₁ y ⁶ x + C ₃₂ y ⁵ x ² + C ₃₃ y ⁴ x ³ + C ₃₄ y ³ x ⁴ + C ₃₅ y ² x ⁵ + C ₃₆ yx ⁶ + C ₃₇ x ⁷ ... (a) By using such a free-form surface as a reflecting surface having at least one reflecting function, an inclined reflecting surface, for example, described later On the second surface of the embodiment, as described above, the eccentric direction is the Y axis, the line of sight of the observer's eye is the Z axis, and the axis orthogonal to the Y axis and the Z axis. When X-axis, it is possible to provide a gradient in the Y direction at an arbitrary position on the X-axis arbitrarily. This can correct the image distortion that occurs in the eccentrically arranged concave mirror, in particular, the image distortion that changes depending on the image height in the X-axis direction and that occurs in the Y-axis direction. In other words, as a result, it is possible to satisfactorily correct the image distortion observed when the horizontal line is bowed.

Next, the trapezoidal distortion generated by the eccentrically arranged concave mirror will be described. This image distortion will be explained by backtracking from the eyeball of the observer. A light ray emitted from the eyeball and having a spread in the X-axis direction hits the eccentrically arranged second surface and is reflected. Due to the difference in the optical path lengths of the light ray in the positive axis direction and the light ray in the negative Y axis direction, the spread in the X axis direction is greatly different and then reflected by the second surface. Therefore, the image size in the Y-axis positive direction and the image size in the Y-axis negative direction are formed differently, and as a result, the observed image has a trapezoidal distortion.

This distortion can also be corrected by using a free-form surface. This is because the free-form surface has an odd-order term of Y and an even-order term of X whose curvature can be arbitrarily changed in the X-axis direction depending on whether the Y-axis is positive or negative, as is clear from the definition formula (a). is there.

Next, rotationally symmetric image distortion will be described. As in the eyepiece optical system of the present invention, for example, in an optical system having a pupil of the optical system at a position distant from the concave surface of the second surface and having a wide angle of view, pincushion rotational symmetry in backward ray tracing from the pupil surface side. Large image distortion occurs. The occurrence of such image distortion can be suppressed by changing the inclination of the surface around the reflecting surface.

Further, astigmatism can be obtained by appropriately changing the difference between the secondary differential in the X-axis direction and the secondary differential in the Y-axis direction.

Further, coma can be corrected by giving the inclination in the Y direction of an arbitrary point on the X axis in the same way as the above-mentioned bow image distortion.

More preferably, in consideration of manufacturability of optical parts, it is desirable that the free-form surface is minimized.
Therefore, one of the at least three surfaces, for example, the second surface may be the free-form surface, and the other surface may be a flat surface, a spherical surface, or an eccentric rotationally symmetric surface to improve manufacturability. .

The second surface, which is the reflecting surface facing the exit pupil of the eyepiece optical system, has a stronger catadioptric power than other surfaces.
The free-form surface is effective for suppressing the occurrence of aberration.

Further, the coma aberration can be suppressed by forming the first surface, which is also used as the refracting surface and the reflecting surface, facing the exit pupil of the eyepiece optical system, into a free-form surface. this is,
This is because when the first surface acts as a reflecting surface, it is arranged with a large inclination with respect to the axial chief ray.

Further, by making the third surface a free-form surface, the occurrence of image distortion can be corrected. this is,
This is because the third surface is arranged close to the image forming position, so that a good result can be obtained in correcting image distortion without deteriorating other aberrations.

Further, it goes without saying that each aberration can be further corrected by making the two surfaces free-form. For example, if the second surface and the third surface are free-form surfaces, the first surface can be a flat surface, and the manufacturability of the optical element forming the eyepiece optical system can be improved. Further, the first surface can be a spherical surface or a rotationally symmetric aspherical surface.

In the present invention, the above-mentioned free-form surface is used as at least one reflecting surface having a reflecting action, and in that case, the surface shape of the reflecting surface is the rotational symmetry axis both inside and outside the surface. And a plane-symmetric free-form surface having only one plane of symmetry. This is shown in FIG.
When a coordinate system such as 5 is used, a free-form surface such that the YZ plane, which is a plane including the eccentric direction of the eccentrically arranged plane, is a symmetric surface, and thus an image forming plane in the backward ray tracing is obtained. This is because the YZ plane of the image can also be symmetrical on both sides as a plane of symmetry, and the labor for aberration correction can be greatly reduced.

The reflecting surface having a reflecting function in the present invention includes all reflecting surfaces having a reflecting function such as a total reflection surface, a mirror coat surface and a semi-transmissive reflecting surface.

Further, in the coordinate system as described above, it is desirable that the reflecting surface of the free curved surface satisfies one or both of the following conditions (1) and (2).

| Φx |> 0 (1) | φy |> 0 (2) where φx is the YZ plane of the area where the axial chief ray is reflected in the reflecting surface. Is the catadioptric power in the plane perpendicular to, and φy is the catadioptric power in the YZ plane of the region where the axial chief ray is reflected in the catoptric surface.

This is because the distance between the pupil and the image forming surface (image display element surface) is set by making the catadioptric power of the reflecting surface as such a plane-symmetric free-form surface for the axial principal ray other than zero. Is a condition set so that the head-mounted image display device can be made compact and lightweight.

It is desirable that the plane-symmetric free-form surface satisfies the following condition (3).

| Φx |> 0.005 (1 / mm) (3) It should be noted that the catadioptric power in the YZ plane for the axial principal ray of the reflecting surface as a plane-symmetric free-form surface, and It is desirable that at least one, and preferably both, of the catadioptric powers in the plane perpendicular to the YZ plane are positive. By doing so, the plane-symmetric free-form surface of the present invention is introduced into the concave mirror of the second surface, which has the largest refractive power of the eyepiece optical system of the head-mounted image display device, and the image distortion of the entire system is reduced. It is possible to excellently correct various aberrations such as point aberration and coma.

As described above, when a plane-symmetric free-form surface having only one symmetry plane is used as at least one reflection surface of the eyepiece optical system, the wide image can be obtained by satisfying the following conditions. It is possible to provide an eyepiece optical system that is angular and has aberrations corrected.

First, according to the above definition, the X axis, the Y axis, and the Z axis.
When the axis is determined, the center of the pupil position is emitted, and among the principal rays incident on the image display element, the angle of view in the X direction is zero, the maximum angle of view in the X direction, the maximum angle of view in the positive Y direction, the angle of view in the Y direction is zero, and Y The following Table-1 shows the combination of the maximum angle of view in the X direction and the Y direction in the negative direction.
The six chief rays are determined like.

[0050]

That is, as described in Table 1 above, the axial principal ray in the visual axis direction at the center of the screen is defined as the principal ray of the upper central angle of view, and the principal ray of the upper right angle of view is the right center. The chief ray of view angle is the chief ray of the lower right view angle, and the chief ray of the lower central view angle is. Then, an area where these chief rays intersect with each surface is defined as an effective area, and an expression defining the shape of each surface in the effective area (an expression in which the Z axis is the axis of the surface, or that surface is Assuming no eccentricity, Z = f
A value obtained by differentiating the surface of (X, Y) in the eccentric direction of the surface with respect to the Y-axis (differential value in the YZ plane) is the differential value of the position where each ray hits the surface DY1. ~ D
The Y6,2-order differential value and D ² Y1~D ² Y6. Also,
Differentiated values (differential values in a plane perpendicular to the YZ plane) differentiated with respect to the X axis orthogonal thereto are DX1 to DX6 as the differential values at the positions where the respective principal rays 〜 hit the surface, and the secondary differential value is D ² X
1 to D ² X6.

First, on the second surface which is the reflecting surface facing the exit pupil of the eyepiece optical system, the values of DY1 to DY6 are changed to DY.
_If it is expressed by _max1 , it is important that all of them satisfy the condition of −10 <DY _max1 <1.0 (1-1).

This limits the inclination of the second surface having a relatively strong catadioptric power in the Y direction in the eyepiece optical system.
If the effective area of the second surface having the main catadioptric power is too inclined in the eyepiece optical system, there will be a portion where the resolution of the entire observation angle of view is insufficient. The upper limit of the conditional expression (1-1) is 1.
When the value exceeds 0, the inclination of the reflecting surface of the principal ray of each image height passing through the center of the pupil becomes too large, and aberrations due to decentering become too large, making it impossible to correct it by other surfaces. . On the contrary, when the lower limit of -10 is exceeded, it becomes impossible to guide the chief ray of each image height to the image forming means, and the observation angle of view becomes extremely small.

More preferably, it is important to satisfy the conditional expression of -1.0 <DY _max1 <0.5 (1-2).

More preferably, it is important to satisfy the conditional expression of -0.5 <DY _max1 <0.3 (1-3).

Both of the above conditional expressions are necessary for obtaining a good observation image in a wide observation angle of view. In particular, it is preferable that the conditional expression (1-2) becomes important in the observation angle of view of 20 ° or more, and the conditional expression (1-3) is satisfied in the observation angle of view of 30 ° or more.

More preferably, it is preferable that all the reflecting surfaces of the eyepiece optical system satisfy one of the above conditional expressions (1-1) to (1-3). The meaning and reason for setting the upper and lower limits are the same.

Next, the change in the horizontal direction from the view angle of zero to the maximum view angle in the XZ plane on the second surface will be defined. The inclination in the Y direction, that is, the difference between the differential values is DY1-DY
4, DY2-DY5, DY3-DY6, and these values are represented by DY _max2 , all satisfy the condition of -0.2 <DY _max2 <0.2 (2-1). It is preferable.

The conditional expression (2-1) defines the maximum value of the inclination of the surface in the Y direction with respect to the X direction. This represents the difference in inclination between the vicinity of the maximum value of the X-axis in the effective area and that on the Y-axis. It corresponds. When the upper limit of 0.2 to condition (2-1) is exceeded, the left and right edges of the observed image change in the Y direction, making it impossible to correct on other surfaces, resulting in a distorted observed image. . Lower limit of -0.2
The same applies to.

More preferably, it is preferable that the conditional expression of -0.1 <DY _max2 <0.1 (2-2) is satisfied. This is particularly important when observing an observation image with little image distortion when trying to secure an observation angle of view of 20 ° or more.

More preferably, it is preferable that the conditional expression of -0.05 <DY _max2 <0.05 (2-3) is satisfied. This is particularly important when observing an observation image with little image distortion when trying to secure an observation angle of view of 30 ° or more.

It is more preferable that the conditional expression of -0.02 <DY _max2 <0.02 (2-4) is satisfied. This is particularly important when observing an observation image with almost no image distortion when trying to secure an observation angle of view of 30 ° or more. In the case of a toric surface, it will be 0, but there are many coma aberrations,
Good imaging characteristics cannot be obtained.

More preferably, it is preferable that all the reflecting surfaces of the eyepiece optical system satisfy any of the above conditional expressions (2-1) to (2-4). The meaning and reason for setting the upper and lower limits are the same.

Next, on the second surface, the (DY
When 1-DY4)-( _DY3-DY6 ) is DY _max3 , the value of DY _max3 of the second surface satisfies the conditional expression of -0.1 <DY _max3 <1 (3-1). This is very important.

This represents the difference in inclination in the Y direction with respect to the Y axis from the vicinity of the maximum value of the X axis in the effective area. When the Y axis is taken in the vertical direction of the observer, It corresponds to the vertical symmetry in the lower right. When the lower limit of -0.1 is exceeded,
The length in the up-down direction becomes too long, and as a result, a large image distortion of the pincushion type occurs. If the upper limit of 1 is exceeded,
On the other hand, barrel-shaped image distortion will occur.

More preferably, it is important that the conditional expression of -0.05 <DY _max3 <0.5 (3-2) is satisfied, especially in the case of an observation angle of view exceeding 20 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (3-1).

More preferably, it is important that the conditional expression of -0.02 <DY _max3 <0.1 (3-3) is satisfied, especially in the case of an observation angle of view exceeding 30 °. It is important to satisfy this condition. The meaning of the upper and lower limits of this conditional expression is the same as that of the conditional expression (3-1). In this case,
In the case of a toric surface, it becomes 0, but coma aberration is often generated, and good imaging characteristics cannot be obtained.

For the second surface, DY2-DY1 and DY2, which are the differences in the Y-direction differential values between the screen center and the screen periphery.
-DY3, DY2-DY4, DY2-DY5, DY2-
When _DY6 is represented by DY _max4 , it is important that all of them satisfy the conditional expression of −0.2 <DY _max4 <0.2 (4-1).

This represents the deviation of the differential value in the Y direction around the screen with respect to the center of the screen. If this value exceeds the upper limit of 0.2, bow-shaped image distortion will occur significantly. Lower limit −
When it exceeds 0.2, a large bow-shaped image distortion occurs in the opposite direction, and it becomes impossible to correct other surfaces.

More preferably, it is important that the conditional expression of -0.16 <DY _max4 <0.16 (4-2) is satisfied, especially in the case of an observation angle of view exceeding 20 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (4-1).

On the second surface, the difference DY2 in the Y direction between the center of the screen and the right end of the X direction maximum angle of view on the X axis.
When -DY5 is set to DY _max5 , it is important to satisfy the conditional expression -0.5 <DY _max5 <0.08 (5-1).

This is a straight line in the left-right direction passing through the center of the screen,
For example, a horizontal line or the like is curved in a bow shape, resulting in image distortion observed. If this numerical value exceeds the upper limit of 0.08, bow-shaped image distortion is largely convex downward. If the lower limit of -0.5 is exceeded, a large bow-shaped image distortion in the opposite direction will occur in a convex shape, and it will be impossible to correct it on other surfaces.

More preferably, it is important to satisfy the conditional expression of -0.1 <DY _max5 <0.05 (5-2), especially in the case of an observation angle of view exceeding 20 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (5-1).

More preferably, it is important to satisfy the conditional expression of -0.02 <DY _max5 <0.01 (5-3), especially in the case of an observation angle of view exceeding 30 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (5-1).

Next, the conditional expression for the differential value DX in the X-axis direction will be described. When the difference DX4-DX6 differential value DX4 in the X-axis direction of the right edge of the screen above and below the DX6 and DX _max1, DX _max1 of the second _{side, -0.16 <DX max1 <1.4 ···} ( 6-1) It is important to satisfy the following conditional expression.

This is X near the maximum value on the X axis of the effective area.
It represents the difference in inclination in the axial direction, and when the Y axis is taken in the vertical direction of the observer, it corresponds to the symmetry in the horizontal direction of the upper right and lower right of the observed image. If the lower limit of −0.16 is exceeded, the horizontal lengths of the observed image differ greatly between the top and bottom of the observed image, resulting in a large amount of trapezoidal image distortion with a long base. If the upper limit of 1.4 is exceeded, on the contrary, a large trapezoidal image distortion with a long upper side will occur.

More preferably, it is important that the conditional expression of -0.1 <DX _max1 <1 (6-2) is satisfied, and this condition is particularly satisfied when the observation angle of view exceeds 20 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (6-1).

More preferably, it is important that the conditional expression of -0.05 <DX _max1 <0.05 (6-3) is satisfied, especially in the case of an observation angle of view exceeding 30 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (6-1).

More preferably, when DX4-DX6 on all the reflecting surfaces of the eyepiece optical system is DX _{max1 '} , DX _max1' is -0.16 <DX _{max1 '} <1.4 ( 7-1) It is important to satisfy the following condition.

This condition can be relatively easily corrected on other surfaces if the trapezoidal distortion generated on the second surface having the main catadioptric power in the entire optical system is suppressed to some extent small. This is a condition for enabling all the aberrations to be well balanced. The upper limit and the lower limit are the same as in conditional expression (6-1).

More preferably, it is important that the conditional expression of -0.1 <DX _{max1 '} <1 (7-2) is satisfied. Especially, in the case of an observation angle of view exceeding 20 °, this It is important to meet the conditions. The meaning of the upper and lower limits is the same as that of the conditional expression (6-1).

More preferably, it is important that the conditional expression of -0.05 <DX _{max1 '} <0.05 (7-3) is satisfied, especially when the observation angle of view exceeds 30 °. Is important to meet this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (6-1).

Next, the astigmatism will be described. Astigmatism occurs because the curvature of the tilted concave mirror in the X-axis direction and the curvature in the Y-axis direction are different for the light rays. In order to satisfactorily correct this, it is important to appropriately make the curvature in the X-axis direction and the curvature in the Y-axis direction different at the position where the light ray strikes.
The difference D ² of the axial principal ray is the second derivative of the second derivative and the Y-axis direction of the X-axis direction position corresponding reflecting surface X2-D ² Y2 and D ²
When XY, when D ² XY of the maximum absolute value is D ² XY _max1 , -0.02 <D ² XY _max1 <0.04 (1 / mm) (8-1) It is important to satisfy the following conditional expression.

If there is a reflecting surface in the eyepiece optical system that exceeds the upper limit of 0.04 and the lower limit of -0.02 of conditional expression (8-1),
The astigmatism generated by the tilted concave mirror becomes too large to be corrected by another surface.

More preferably, it is important that the conditional expression of -0.01 <D ² XY _max1 <0.02 (1 / mm) (8-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (8-1).

More preferably, it is important that the conditional expression of -0.005 <D ² XY _max1 <0.01 (1 / mm) (8-3) is satisfied, and in particular, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (8-1).

More preferably, it is important to satisfy the conditional expression of -0.005 <D ² XY _max1 <0.005 (1 / mm) ··· (8-4), especially for observations exceeding 35 °. In the case of the angle of view, it is important to satisfy this condition. For the meaning of the upper and lower limits, the above conditional expression (8
Same as -1).

Next, the conditions relating to D ² XY _max1 on the second surface will be described. This surface has a relatively strong catadioptric power as compared with other surfaces, and since light rays are incident obliquely, astigmatism often occurs. Therefore, D ² X on the second surface
When Y _max1 is D ² XY _{max1 ′} , it is important to satisfy −0.02 <D ² XY _{max1 ′} <0.04 (1 / mm) (9-1).

The second surface has the upper limit of 0.04 and the lower limit of −.
When it exceeds 0.02, the astigmatism generated by the tilted concave mirror becomes too large to be corrected by another surface.

More preferably, it is important to satisfy the conditional expression of -0.01 <D ² XY _{max1 '} <0.02 (1 / mm) (9-2), and in particular 20 ° It is important to satisfy this condition when the observation angle of view exceeds. The meaning of the upper and lower limits is the same as that of the conditional expression (9-1).

More preferably, it is important to satisfy the conditional expression of -0.005 <D ² XY _{max1 '} <0.01 (1 / mm) ·· (9-3), and particularly, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (9-1).

More preferably, it is important that the conditional expression of -0.005 <D ² XY _{max1 '} <0.005 (1 / mm) · (9-4) is satisfied, and in particular, observation exceeding 35 ° In the case of the angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (9-1).

On the second surface, D ² Y1 to D ²
When the value of Y6 is D ² Y _max1 , it is important that all of them satisfy the condition of −0.03 <D ² Y _max1 <0.06 (1 / mm) (10-1). Becomes

This represents a change in the tilt of the second surface in the Y direction. When the upper limit of 0.06 and the lower limit of -0.03 in the above conditional expression are exceeded, the curvature of the surface in the effective region is too different. ,
In the eyepiece optical system, the curvature of the entire effective region of the second surface having the main catadioptric power changes too much, and it becomes impossible to observe a wide and flat observation image over the entire observation angle of view.

More preferably, it is important to satisfy the conditional expression: -0.03 <D ² Y _max1 <0.05 (1 / mm) (10-2).

More preferably, it is important to satisfy the conditional expression -0.025 <D ² Y _max1 <0 (1 / mm) (10-3).

Both the conditional expressions (10-2) and (10-3) are necessary for obtaining a good observation image in a wide observation angle of view. In particular, the conditional expression (10-2) is 20 °
It becomes important in the above observation angle of view, and the conditional expression (10-
It is preferable that 3) is satisfied at an observation angle of view of 30 ° or more.

Next, on the second surface, from D ² X1 to D
^When the value of ² X6 is D ² X _max2 , all of them must satisfy the condition of −0.03 <D ² X _max2 <0.1 (1 / mm) (11-1). preferable.

The above conditional expression defines the maximum value of the change in the inclination of the second surface in the X direction. This is related to the field curvature at the left and right ends of the observed image. If the upper limit of 0.1 is exceeded, the image forming position is too far from the optical system, and if the lower limit of -0.03 is exceeded, the optical system is lowered. And the observation image plane is curved as a result.

More preferably, it is preferable that the conditional expression of -0.02 <D ² X _max2 <0.01 (1 / mm) (11-2) is satisfied. This is particularly important when observing an observation image with little field curvature when trying to secure an observation angle of view of 20 ° or more.

It is more preferable that the conditional expression of -0.02 <D ² X _max2 <-0.005 (1 / mm) (11-3) is satisfied. This is particularly important when observing an observation image with little field curvature when trying to secure an observation angle of view of 30 ° or more.

More preferably, it is preferable that the conditional expression of -0.015 <D ² X _max2 <-0.005 (1 / mm) · (11-4) is satisfied. This is particularly important when observing an observation image with almost no field curvature when trying to secure an observation angle of view of 30 ° or more. In the case of a toric surface, it becomes 0, but coma is often generated and good imaging characteristics cannot be obtained.

Next, D ² X1-D ² X4, D ^{2 of} the second surface
^{X2-D 2 X5, D 2} X3-D 2 value of the X6 D ² X _max3
Then, it is important that all of them satisfy the conditional expression of −0.05 <D ² X _max3 <0.05 (1 / mm) (12-1).

This shows how much the difference in the second derivative in the X direction between X = 0 and the vicinity of the maximum X value in the effective area has a width above and below in the Y axis direction. This corresponds to the vertical symmetry of the field curvature of the upper right and lower right of the observed image when the Y axis is taken in the vertical direction of the observer. When the lower limit of -0.05 of the above conditional expression is exceeded, the image surface becomes too close to the optical system and correction cannot be performed by other surfaces. On the contrary, when the upper limit of 0.05 is exceeded, the image is transferred from the optical system. The surfaces are too far apart to be corrected by the other surfaces, and it becomes impossible to obtain a flat image surface together.

More preferably, it is important that the conditional expression of -0.02 <D ² X _max3 <0.02 (1 / mm) (12-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (12-1).

More preferably, it is important to satisfy the conditional expression of -0.01 <D ² X _max3 <0.01 (1 / mm) (12-3), and particularly, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (12-1). In this case, too, in the case of a toric surface, it will be 0, but coma will often occur,
Good imaging characteristics cannot be obtained.

Next, D ² Y1-D ² Y4, D ^{2 on} the second surface
Y2-D ² Y5, the value of ^{D 2 Y3-D 2 Y6 D} 2 Y max4
Then, it is important to satisfy the conditional expression of −0.03 <D ² Y _max4 <0.05 (1 / mm) (13-1).

This shows how wide the difference in the second derivative in the Y direction between X = 0 and the vicinity of the maximum X value in the effective area is in the vertical direction in the Y axis direction. This also corresponds to the vertical symmetry of the field curvature of the upper right and lower right of the observed image when the Y axis is taken in the vertical direction of the observer. Lower limit of -0.0
When the value exceeds 3, the image surface becomes too close to the optical system and cannot be corrected by the other surface. On the other hand, when the value exceeds the upper limit of 0.05, the image surface is too far from the optical system and the other surface is not corrected. It becomes impossible to correct, and it becomes impossible to obtain a flat image plane.

More preferably, it is important that the conditional expression of -0.02 <D ² Y _max4 <0.03 (1 / mm) (13-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (13-1).

More preferably, it is important that the conditional expression of -0.01 <D ² Y _max4 <0.01 (1 / mm) (13-3) is satisfied, and in particular, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (13-1).

For all reflecting surfaces, D ² X1-D ² X3, D ² X4-D ² X6 relating to the difference in the second-order differential in the X-direction of X = 0 in the vertical direction of the Y-axis and the X-maximum part To D
^{When 2} X _max5 , it is important that all satisfy the conditional expression -0.05 <D ² X _max5 <0.05 (1 / mm) (14-1).

This is a condition necessary for reducing the inclination of the image plane in the vertical direction of the screen. This value is the upper limit of 0.
If the value of 05 and the lower limit of -0.05 are exceeded, the tilt of the image plane becomes too large, and the tilt of the image plane is corrected unless the image display element forming the observed image is tilted with respect to the axial chief ray. As a result, the size of the device cannot be increased and the device becomes large.

More preferably, it is important that the conditional expression of -0.03 <D ² X _max5 <0.03 (1 / mm) (14-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (14-1).

More preferably, it is important that the conditional expression of -0.02 <D ² X _max5 <0.02 (1 / mm) (14-3) is satisfied, and in particular, it exceeds 25 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (14-1).

More preferably, it is important that the conditional expression of -0.01 <D ² X _max5 <0.01 (1 / mm) (14-4) is satisfied, and in particular, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (14-1).

More preferably, it is important that the conditional expression of -0.005 <D ² X _max5 <0.005 (1 / mm) (14-5) is satisfied, and in particular, it exceeds 35 °. In the case of the observation angle of view, it is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (14-1).

Next, the difference between the second-order differentials in the Y direction of X = 0 and the maximum X portion in the vertical direction of the Y-axis D ² Y 1 -D ² Y 3, D
When the difference between the ² Y4-D ² Y6 and _D ² Y max6, all values of _D ² Y max6 of all the reflecting _{^{surfaces, -0.03 <D 2 Y max6 <}} 0.03 (1 / mm) · · It is important to satisfy the conditional expression (15-1).

This is also a necessary condition for reducing the inclination of the image plane in the vertical direction of the screen. If this value exceeds the upper limit of 0.03 and the lower limit of -0.03, the inclination of the image plane becomes too large, and the image display element forming the observed image must be arranged with a large inclination with respect to the axial chief ray. The tilt of the image plane cannot be corrected, resulting in an increase in size of the apparatus.

More preferably, it is important that the conditional expression of -0.02 <D ² Y _max6 <0.02 (1 / mm) (15-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is acceptable to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (15-1).

More preferably, it is important that the second surface satisfies the conditional expression of -0.01 <D ² Y _max6 <0.01 (1 / mm) (15-3), and particularly It is important to satisfy this condition when the observation angle of view exceeds 30 °. The meaning of the upper and lower limits is the same as that of the conditional expression (15-1).

Next, the difference between the second derivative in the X direction and the second derivative in the Y direction, where each ray in the effective surface strikes the surface, is D ² X
When n−D ² Yn (n is 1 to 6) is D ² XY _max7 , all the values of D ² XY _max7 of all reflecting surfaces are −0.02 <D ² XY _max7 <0.1 (1 / Mm) (16-1) It is important to satisfy the conditional expression.

This is the image formation position in the X direction of the effective area and Y.
This is a condition that corresponds to the image forming position in the direction and that the astigmatism is well corrected. When the lower limit of -0.02 is exceeded,
A light ray in the X direction is imaged closer to a light ray in the Y direction on the optical system side, and astigmatism increases. vice versa,
If the upper limit of 0.1 is exceeded, rays in the X direction will be imaged farther than rays in the Y direction from the optical system, and conversely large astigmatism will occur, both of which will be corrected by other surfaces. It becomes impossible. However, in the case of a surface having symmetry with respect to both the Y and X axes, such as a toric surface, coma aberration and image distortion are increased although this condition is satisfied.

More preferably, it is important that the conditional expression of -0.018 <D ² XY _max7 <0.05 (1 / mm) (16-2) is satisfied, and in particular, it exceeds 20 °. In the case of the observation angle of view, it is important to satisfy this condition.

More preferably, it is important that the conditional expression of -0.015 <D ² XY _max7 <0.02 (1 / mm) (16-3) is satisfied, and in particular, it exceeds 25 °. In the case of the observation angle of view, it is important to satisfy this condition.

More preferably, it is important that the conditional expression of -0.01 <D ² XY _max7 <0.01 (1 / mm) (16-4) is satisfied, and in particular, it exceeds 30 °. In the case of the observation angle of view, it is important to satisfy this condition.

Regarding the conditional expression (16-1), when the value on the second surface is D ² XY _{max7 '} , -0.1 <D ² XY _max7' <0.08 (1 / mm) ( 17-1) It is important to satisfy the following conditional expression.

The meanings of the upper limit of 0.08 and the lower limit of -0.1 are the same as in conditional expression (16-1) above. In particular, astigmatism often occurs on the second surface, which has the strongest positive catadioptric power in the optical system and is arranged at an inclination, so that by satisfying this conditional expression, It is important to correct the occurrence in a balanced manner. However, if this surface is also a surface having symmetry with respect to both the Y and X axes, such as a toric surface, this condition is satisfied, but coma aberration and image distortion are increased.

More preferably, it is important to satisfy the conditional expression: -0.1 <D ² XY _{max7 '} <0.05 (1 / mm) (17-2), and especially 20 ° It is important to satisfy this condition when the observation angle of view exceeds.

More preferably, it is important to satisfy the conditional expression of -0.05 <D ² XY _{max7 '} <0.02 (1 / mm) (17-3), and in particular 25 ° It is important to satisfy this condition when the observation angle of view exceeds.

More preferably, it is important that the conditional expression of -0.01 <D ² XY _{max7 '} <0.01 (1 / mm) (17-4) is satisfied, and especially 30 ° is set. It is important to satisfy this condition when the observation angle of view exceeds.

Next, the reflecting surface (the first transmitting surface in the case of FIGS. 15 and 20) facing the image display element of the eyepiece optical system.
The surface also serves. ) D ² X2 / D ² X2 value of the second surface is D
^{When 2} × 9, it is important to satisfy the condition of 0.13 <D ² X9 <1.15 (18-1).

This condition represents the ratio of the second derivative in the X direction of the reflecting surface facing the image display element having the main catadioptric power in the entire optical system and the reflecting surface facing the exit pupil. This condition is related to the conventional paraxial power arrangement that is required to increase the distance from the optical system to the pupil position and bring the exit principal ray tilt angle on the observed image side closer to the display surface of the observed image perpendicularly. If the lower limit of 0.13 is exceeded, the front focal position of the optical system becomes large, but the rear focal length becomes too short, and the surface displaying the observed image interferes with the optical system body, making it impossible to arrange. On the other hand, when the upper limit of 1.15 is exceeded, the rear focal length becomes large, but conversely the front focal position of the optical system becomes too small, making it difficult to observe with glasses.

More preferably, it is important that the conditional expression of 0.2 <D ² X9 <1 (18-2) is satisfied, and this condition is particularly satisfied when the observation angle of view exceeds 20 °. Is important to satisfy. Regarding the upper and lower limits, the above conditional expression (1
It is the same as 8-1).

More preferably, it is important that the conditional expression of 0.3 <D ² X9 <0.8 (18-3) is satisfied, especially in the case of an observation angle of view exceeding 30 °. It is important to satisfy this condition. Regarding the upper and lower limits, the above conditional expression (1
It is the same as 8-1).

Next, the value of D ² Y2 of the reflecting surface facing the image display element of the eyepiece optical system / D ² Y2 of the second surface is set to D ² Y10.
Then, it is important to satisfy the condition of 0.14 <D ² Y10 <5 (19-1).

This condition represents the ratio of the second derivative in the Y direction of the reflecting surface facing the image display element having the main catadioptric power and the reflecting surface facing the exit pupil in the entire optical system. This condition is related to the conventional paraxial power arrangement, which is necessary to increase the distance from the system to the pupil position and to make the exit principal ray tilt angle on the observed image side closer to the display surface of the observed image perpendicularly. When the lower limit of 0.14 is exceeded, the front focal position of the optical system becomes large, but the rear focal length becomes too short, and the surface displaying the observed image interferes with the optical system main body, making it impossible to arrange. On the other hand, when the upper limit of 5 is exceeded, the rear focal length becomes large, but on the contrary, the front focal position of the optical system becomes too small,
It becomes difficult to observe with glasses.

More preferably, it is important that the conditional expression 0.15 <D ² Y10 <4 (19-2) is satisfied, and this condition is particularly satisfied when the observation angle of view exceeds 20 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (19-1).

More preferably, it is important that the conditional expression of 0.2 <D ² Y10 <3 (19-3) is satisfied, especially in the case of an observation angle of view exceeding 25 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (19-1).

More preferably, it is important that the conditional expression of 0.25 <D ² Y10 <1 (19-4) is satisfied. Especially, in the case of an observation angle of view exceeding 30 °, this condition is satisfied. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (19-1).

Next, when the value of D ² X2 / D ² Y2 of the reflecting surface facing the image display element of the eyepiece optical system is D ² XY11, 0.55 <D ² XY11 <4.0 ... It is important to satisfy the condition (20-1).

This condition is the refraction of the portion of the entire optical system in which the principal rays in the X and Y directions are incident on the axial principal ray of the reflecting surface facing the image display element on which the axial principal ray is most inclined. Corresponds to force and mainly relates to astigmatism. The lower limit of 0.
When the value exceeds 55 and the upper limit is more than 4.0, the astigmatism generated when reflecting on this surface becomes too large, and it becomes difficult to correct it on other surfaces.

More preferably, it is important to satisfy the conditional expression 0.6 <D ² XY11 <3.5 (20-2), especially in the case of an observation angle of view exceeding 20 °. It is important to satisfy this condition. Regarding the meaning of the upper and lower limits, the above conditional expression (2
It is the same as 0-1).

More preferably, it is important that the conditional expression of 0.7 <D ² XY11 <3.0 (20-3) is satisfied, especially in the case of an observation angle of view exceeding 25 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (20-1).

More preferably, it is important that the conditional expression 0.8 <D ² XY11 <2.5 (20-4) is satisfied, especially in the case of an observation angle of view exceeding 30 °. It is important to satisfy this condition. The meaning of the upper and lower limits is the same as that of the conditional expression (20-1).

Next, D ² X2 / of the second surface facing the exit pupil
When the value of D ² Y2 is D ² XY12, it is important to satisfy the condition of 0.55 <D ² XY12 <5 (21-1).

Similar to the above condition (20-1), this condition also relates to astigmatism, and has an upper limit of 5 and a lower limit of 0.55.
Is the same as the condition (20-1).

More preferably, it is important that the conditional expression 0.6 <D ² XY12 <4 (21-2) is satisfied, and this condition is particularly satisfied when the observation angle of view exceeds 20 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (20-1).

More preferably, it is important that the conditional expression 0.7 <D ² XY12 <3 (21-3) is satisfied, and this condition is particularly satisfied when the observation angle of view exceeds 25 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (20-1).

More preferably, it is important that the conditional expression 0.8 <D ² XY12 <2 (21-4) is satisfied, especially in the case of an observation angle of view exceeding 30 °. Is important to satisfy. The meaning of the upper and lower limits is the same as that of the conditional expression (20-1).

Now, from the above conditions (1-1) to (21-
As for 4), the surface shape of any of the reflecting surfaces constituting the eyepiece optical system does not have an axis of rotational symmetry in and out of the surface, and only a plane-symmetric free-form surface having only one symmetry surface. Not only when it is formed with an anamorphic surface that does not have a rotational symmetry axis both in-plane and out-of-plane, that is, in which it has a non-rotational symmetric surface shape that does not have a rotational symmetry axis in-plane and out-of-plane Can also be applied to. In particular, the above (4
Regarding the conditions of -1) to (4-2), in the above description, the conditional expression is related to the reflecting surface facing the exit pupil of the eyepiece optical system, but any reflecting surface forming the eyepiece optical system may be used. When the in-plane and out-of-plane non-rotationally symmetric surface shapes have no axis of rotational symmetry, the non-rotationally symmetric surface shape reflecting surface can also be applied. In addition, (20-1) to (20
The condition -4) can be applied to the case where the reflecting surface facing the image display element is formed into a non-rotationally symmetric surface shape having no axis of rotational symmetry both inside and outside the surface. Further, with respect to the conditions (21-1) to (21-4), the non-rotational symmetry in which the reflection surface other than the reflection surface facing the image display element does not have a rotational symmetry axis in or out of the surface. It can also be applied to a surface shape.

Regarding the above various conditions, the first surface 3, the second surface 4, and the third surface 5 as shown in FIG. 15 are mainly used, and the refractive index (n) is larger than 1 between them. (N>
1) The description was made on the premise of the eyepiece optical system using the prism member 7 filled with the medium, but the same can be applied to the other prism members 7 as shown in FIGS. 16 to 22.

[0152]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments 1 to 5 of the head-mounted image display device of the present invention will be described below. In the configuration parameters of each example described later, as shown in FIG. 1, the optical axis 2 is the center of the display of the image display element 6 and the center of the exit pupil 1 with the exit pupil 1 of the eyepiece optical system 7 as the origin of the optical system. Defined as a ray passing through (origin), and the direction from the exit pupil 1 to the optical axis 2 is the Z-axis direction, the plane orthogonal to the Z axis, passing through the center of the exit pupil 1, and being bent by the eyepiece optical system 7. Is the Y-axis direction, the direction orthogonal to the Z-axis and the Y-axis and passing through the center of the exit pupil 1 is the X-axis direction, the direction from the exit pupil 1 to the eyepiece optical system 7 is the positive direction of the Z-axis, and from the optical axis 2. The direction of the image display device 6 is defined as the positive direction of the Y axis, and the direction forming the Z-axis and Y-axis and the right-handed system is defined as the positive direction of the X axis. Note that ray tracing is performed by reverse tracing with the exit pupil 1 side of the eyepiece optical system 7 as the object side and the image display element 6 side as the image plane side.

Then, for the surface on which the eccentricity amounts Y and Z and the tilt amount θ are described, the shift amount from the exit pupil 1 which is the origin of the optical system and the tilt angle with respect to the Z axis are shown. The tilt angle is positive in the counterclockwise direction. In addition,
The plane spacing has no meaning.

The shape of the anamorphic surface is defined by the following equation. A straight line passing through the origin of the surface shape and perpendicular to the optical surface is the axis of the anamorphic surface. Where Z is the amount of deviation of the surface shape from the tangent plane, CX is the curvature in the X-axis direction, CY is the curvature in the Y-axis direction, K _x is the conical coefficient in the X-axis direction, K _y is the conical coefficient in the Y-axis direction, and R _n Is an aspherical term rotationally symmetric component, and P _n is an aspherical term rotationally asymmetrical component. In the configuration parameters of the embodiment described later, _Rx : radius of curvature in the X-axis direction _Ry : radius of curvature in the Y-axis direction, and between the curvatures CX and CY, _Rx = 1 / CX, R _y = 1 / CY.

The shape of the free-form surface is defined by the following equation. The Z axis of the definition is the axis of the free-form surface. _{Z = C 2 + C 3 y} + C 4 x + C 5 y 2 + C 6 yx + C 7 x 2 + C 8 y 3 + C 9 y 2 x + C 10 yx 2 + C 11 x 3 + C 12 y 4 + C 13 y 3 x + C 14 y 2 x 2 + C ^{_{15 yx 3 + C 16 x 4}} + C 17 y 5 + C 18 y 4 x + C 19 y 3 x 2 + C 20 y 2 x 3 + C 21 yx 4 + C 22 x 5 + C 23 y 6 + C 24 y 5 x + C 25 y 4 x 2 + C ^{_{26 y 3 x 3 + C 27}} y 2 x 4 + C 28 yx 5 + C 29 x 6 + C 30 y 7 + C 31 y 6 x + C 32 y 5 x 2 + C 33 y 4 x 3 + C 34 y 3 x 4 + C 35 y 2 x ^{_{5 + C 36 yx 6 + C}} 37 x 7 ··· Note (a), the term with respect to aspheric surfaces on which no data is 0
It is. For the refractive index, d line (wavelength 587.56n
The one for m) is shown. The unit of the length is mm.

Now, the eyepiece optical system 7 of Examples 1 to 5 below.
Are composed of three surfaces, namely, a first surface 3, a second surface 4, and a third surface 5, and a space between them is filled with a medium having a refractive index higher than 1, and is arranged so as to face the image display element 6. The display light from the image display element 6 that has entered the optical system via the third surface 5 of the transmission surface is reflected by the first surface 3 disposed between the second surface 4 and the exit pupil 1 on the optical axis 2. Reflected, and then exit pupil 1 on optical axis 2
Is incident on and reflected by the second surface 4 of the reflecting surface which is eccentrically arranged so as to face the optical system 7 and passes through the first surface 3.
The light exits from the optical axis 2 and travels along the optical axis 2 to enter the pupil of the observer at the position of the exit pupil 1 without forming an intermediate image, and forms a display image on the retina of the observer.

1 to 5 are YZ sectional views including the optical axis 2 of Examples 1 to 5, respectively. Although constituent parameters will be described later, in Example 1, both the first surface and the second surface are anamorphic surfaces defined by the above formula (b), and the third surface is a flat surface.
In Example 2, all of the first surface 3, the second surface 4, and the third surface 5 are free-form surfaces defined by the formula (a), and in Examples 3 and 4, the first surface 3 is a flat surface and the second surface is a second surface. The fourth and third surfaces 5 are all free-form surfaces defined by the above equation (a), and the fifth embodiment is the first
The surface is a spherical surface, and the second surface 4 and the third surface 5 are all free-form surfaces defined by the equation (a). The observation angle of view of Example 1 is 57.8 ° for the horizontal angle of view, 34.5 ° for the vertical angle of view, and the pupil diameter is 4 mm.
The observation angle of view in Example 2 was 40 ° in the horizontal angle, the angle of view in the vertical direction was 30.5 °, and the pupil diameter was 8 mm. The angle of view in the Examples 3 and 5 was 40 ° in the horizontal angle of view. The vertical field angle is 30.5 °, the pupil diameter is 4 mm, and the observation field angle in Example 4 is the horizontal field angle 3
The angle of view is 5 °, the vertical angle of view is 26.6 °, and the pupil diameter is 4 mm.

The constituent parameters of Examples 1 to 5 are shown below. Example 1 Surface number Curvature radius Spacing Refractive index Abbe number (eccentricity) (tilt angle) 1 ∞ (pupil) 2 R _y -209.268 1.4922 57.50 (first surface) R _x -95.115 (from pupil position) K _y 0 Y -18.335 θ -12 ° K _x 0 Z 27.921 R ₂ 7.8387 × 10 ^-7 R ₃ 2.9947 × 10 ^-13 R ₄ 1.5297 × 10 ^-14 R ₅ -5.0289 × 10 ^-17 P ₂ -0.4499 P ₃ -7.9471 P ₄ 0.6545 P ₅ -0.1387 3 R _y -67.801 1.4922 57.50 (2nd surface) R _x -58.220 (From pupil position) (Reflecting surface) K _y 0 Y 9.356 θ 27.44 ° K _x 0 Z 38.348 R ₂ 4.2705 × 10 ^-7 R ₃ -7.7029 × 10 ^-11 R ₄ 4.0793 × 10 ^-22 R ₅ 1.0591 × 10 ^-17 P ₂ 0.1070 P ₃ 0.4967 P ₄ 119.38 P ₅ -0.0092 4 R _y -209.268 1.4922 57.50 (1st surface) R _x- 95.115 (from pupil position) (Reflecting surface) K _y 0 Y -18.335 θ -12 ° K _x 0 Z 27.921 R ₂ 7.8387 × 10 ^-7 R ₃ 2.9947 × 10 ^-13 R ₄ 1.5297 × 10 ^-14 R ₅ -5.0289 × 10 ^-17 P ₂ -0.4499 P ₃ -7.9471 P ₄ 0.6545 P ₅ -0.1387
5 ∞ (from the pupil position)
(Third surface) Y -27.164 θ -62.56 ° Z 27.921 6 ∞ (from pupil position) (Image display surface) Y -27.678 θ -46.89 ° Z 39.000.

Example 2 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (pupil) 2 Free-form surface 1.5254 56.25 (first surface) (from pupil position) Y 13.983 θ 9.46 ° Z 33.974 3 Free-form surface 1.5254 56.25 (2nd surface) (From pupil position) (Reflecting surface) Y 4.596 θ -15.22 ° Z 49.231 4 Free-form surface 1.5254 56.25 (1st surface) (From pupil position) (Reflecting surface) Y 13.983 θ 9.46 ° Z 33.974 5 Free-form surface (from pupil position) (3rd surface) Y 27.094 θ 79.39 ° Z 35.215 6 ∞ (from pupil position) (Image display surface) Y 29.266 θ 46.34 ° Z 46.318 Free-form surface C ₅ -2.6152 × 10 ^{_{-3 C 7 -3.9706 × 10 -3 C}} 8 -7.5434 × 10 -5 C 10 -1.5120 × 10 -6 C 12 2.6572 × 10 -7 C 14 1.3359 × 10 -6 C 16 1.7946 × 10 -7 C 17 - 2.9881 x 10 ^-9 C ₁₉ -3.0362 x 10 ^-9 C ₂₁ -2.0258 x 10 ^-7 C ₂₃ -3.8978 x 10 ^-10 C ₂₅ 1.4986 x 10 ^-9 C ₂₇ -3.8974 x 10 ^-9 C ₂₉ -2.5335 x 10 ^{_{-9 C 30 4.3101 × 10 -12 C}} 32 -1.4923 × 10 -11 ^{_{34 7.6026 × 10 -11 C 36 -4.2410}} × 10 -11 free curved surface ^{_{C 5 -6.2524 × 10 -3 C 7}} -7.5944 × 10 -3 C 8 -1.0605 × 10 -5 C 10 9.3276 × 10 -6 C 12 8.3882 _{^{× 10 -7 C 14 -5.6861 × 10}} -7 C 16 -4.9904 × 10 -7 C 17 -2.0403 × 10 -10 C 19 -8.0184 × 10 -9 C 21 -4.4196 × 10 -8 C 23 4.4149 × 10 - ¹⁰ C ₂₅ 3.8 170 × 10 ^-10 C ₂₇ 8.4 970 × 10 ^-11 C ₂₉ -2.8006 × 10 ^-10 C ₃₀ 1.3964 × 10 ^-12 C ₃₂ -1.7677 × 10 ^-10 C ₃₄ 3.3 220 × 10 ^-12 C ₃₆ 6.9401 × 10 ^-12 free curved surface ^{_{C 5 -1.2118 × 10 -2 C 7}} -3.7062 × 10 -3 C 8 -1.2290 × 10 -4 C 10 9.9763 × 10 -4 C 12 -8.0746 × 10 -5 C 14 -3.8939 × 10 - ⁵ C ₁₆ 2.6861 x 10 ^-5 C ₁₇ -1.7720 x 10 ^-6 C ₁₉ -3.4243 x 10 ^-6 C ₂₁ -3.5310 x 10 ^-7 C ₂₃ 1.2185 x 10 ^-7 C ₂₅ 1.0019 x 10 ^-7 C ₂₇ 1.4838 x 10 ^-7 C ₂₉ -5.3531 x 10 ^-8 .

Example 3 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (pupil) 2 ∞ 1.5254 56.25 (first surface) (from pupil position) Y 0.000 θ 20.65 ° Z 37.527 3 Free-form surface 1.5254 56.25 (2nd surface) (From pupil position) (Reflecting surface) Y 1.760 θ -9.37 ° Z 49.700 4 ∞ 1.5254 56.25 (1st surface) (From pupil position) (Reflecting surface) Y 0.000 θ 20.65 ° Z 37.527 5 Free curved surface (from pupil position) (3rd surface) Y 25.997 θ 74.58 ° Z 46.184 6 ∞ (from pupil position) (Image display surface) Y 33.670 θ 51.85 ° Z 45.021 Free curved surface C ₅ -4.5817 × 10 ^-3 C ₇ -5.0 260 x 10 ^-3 C ₈ 3.2015 x 10 ^-5 C ₁₀ 2.2441 x 10 ^-5 C ₁₂ -1.8792 x 10 ^-7 C ₁₄ 7.9 815 x 10 ^-7 C ₁₆ 5.0 435 x 10 ^-7 C ₁₇ -6.8 674 x 10 ^-8 C ₁₉ 1.0002 x 10 ^-8 C ₂₁ -6.6719 x 10 ^-9 C ₂₃ 1.3063 x 10 ^-9 C ₂₅ -2.2955 x 10 ^-9 C ₂₇ -1.9 103 x 10 ^-10 C ₂₉ -6.8281 x 10 ^-10 C ₃₀ 1.3784 x 10 ^-10 C ₃₂ -1.0577 x 10 ^-10 C ₃₄ 2.8 101 x 10 ^-11 C ₃₆ 1.2847 × 10 ^-11 Free-form surface C ₅ 4.249 3 × 10 ^-4 C ₇ -2.0055 × 10 ^-2 C ₈ -1.1201 × 10 ^-3 C ₁₀ 1.5646 × 10 ^-4 C ₁₂ -1.0605 × 10 ^-4 C ₁₄ 4.3806 × 10 ^-5 C ₁₆ 2.6464 × 10 ^-5 C ₁₇ 2.1338 × 10 ^-5 C ₁₉ -8.0966 × 10 ^-7 C ₂₁ -1.4461 × 10 ^-6 C ₂₃ -1.0841 × 10 ^-6 C ₂₅ -1.2023 × 10 ^-7 C ₂₇ -1.6090 x 10 ^-8 C ₂₉ -5.5701 x 10 ^-9 C ₃₀ 1.8180 x 10 ^-8 C ₃₂ 5.1816 x 10 ^-9 C ₃₄ 1.0613 x 10 ^-9 C ₃₆ 6.6826 x 10 ^-10 .

Example 4 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (pupil) 2 ∞ 1.5254 56.25 (first surface) (from pupil position) Y 0.000 θ 22.10 ° Z 39.619 3 Free-form surface 1.5254 56.25 (2nd surface) (From pupil position) (Reflecting surface) Y -8.143 θ -13.23 ° Z 50.124 4 ∞ 1.5254 56.25 (1st surface) (From pupil position) (Reflecting surface) Y 0.000 θ 22.10 ° Z 39.619 5 free-form surface (from pupil position) (third surface) Y 25.826 θ 92.97 ° Z 51.879 6 ∞ ( from pupil position) (image display surface) Y 35.497 θ 50.34 ° Z 48.576 free curved surface C ₅ -4.6506 × 10 ^{- 3} C ₇ -4.7935 × 10 ^-3 C ₈ 2.6669 × 10 ^-6 C ₁₀ 1.6974 × 10 ^-5 C ₁₂ 5.4534 × 10 ^-7 C ₁₄ -4.6491 × 10 ^-7 C ₁₆ -3.5840 × 10 ^-7 C ₁₇ 1.8802 × 10 ^-8 C ₁₉ 4.4645 × 10 ^-8 C ₂₁ -7.6909 × 10 ^-9 C ₂₃ -1.5994 × 10 ^-9 C ₂₅ -5.2799 × 10 ^-11 C ₂₇ 1.1706 × 10 ^-9 C ₂₉ 1.3813 × 10 ^-11 C _{30 ^{2.9144 × 10 -11 C 32 -4.6116 ×}} 10 -11 C 34 -5.5362 × 10 - ¹¹ C ₃₆ 4.7568 × 10 ^-12 Free-form surface C ₅ 1.9719 × 10 ^-2 C ₇ -7.7622 × 10 ^-3 C ₈ 2.3734 × 10 ^-5 C ₁₀ -5.0 317 × 10 ^-4 C ₁₂ -2.0 110 × 10 ^-4 C _{14 ^{6.3593 × 10 -5 C 16 4.5581 ×}} 10 -5 C 17 1.6122 × 10 -5 C 19 -1.3368 × 10 -6 C 21 -3.0966 × 10 -6 C 23 -5.2286 × 10 -7 C 25 -6.5949 × 10 - ⁸ C ₂₇ 5.9 680 × 10 ^-9 C ₂₉ -2.7181 × 10 ^-8 C ₃₀ 6.2 758 × 10 ^-9 C ₃₂ 2.4 299 × 10 ^-9 C ₃₄ 2.2 116 × 10 ^-9 C ₃₆ 2.0886 × 10 ^-9 .

Example 5 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Inclination angle) 1 ∞ (Pupil) 2 -87.879 1.5254 56.25 (First surface) (From pupil position) Y 0.000 θ 4.83 ° Z 38.369 3 Free-form surface 1.5254 56.25 (2nd surface) (From pupil position) (Reflecting surface) Y -3.704 θ -23.79 ° Z 46.813 4 -87.879 1.5254 56.25 (1st surface) (From pupil position) (Reflecting surface) Y 0.000 θ 4.83 ° Z 38.369 5 Free-form surface (from pupil position) (3rd surface) Y 19.042 θ 46.94 ° Z 47.204 6 ∞ (from pupil position) (Image display surface) Y 27.507 θ 55.57 ° Z 45.930 Free-form surface C ₅ -9.8620 × 10 ^-3 C ₇ -9.1521 x 10 ^-3 C ₈ 6.2235 x 10 ^-5 C ₁₀ 8.0917 x 10 ^-6 C ₁₂ 9.2182 x 10 ^-7 C ₁₄ -1.5968 x 10 ^-6 C ₁₆ -1.1413 x 10 ^-6 C ₁₇ -9.8234 x 10 ^-8 C ₁₉ 1.3883 x 10 ^-8 C ₂₁ 1.1992 x 10 ^-8 C ₂₃ -1.0379 x 10 ^-8 C ₂₅ -5.0580 x 10 ^-9 C ₂₇ -2.3570 x 10 ^-9 C ₂₉ -1.5443 x 10 ^{_{-10 C 30 4.6063 × 10 -10 C}} 32 1.4306 × 10 -10 C 34 5.9077 10 ^-11 C ₃₆ 1.5553 × 10 ^-12 free curved surface ^{_{C 5 -3.4909 × 10 -3 C 7}} -1.8708 × 10 -3 C 8 -7.3195 × 10 -5 C 10 1.7538 × 10 -4 C 12 -5.3578 × 10 - ⁴ C ₁₄ 1.1 140 x 10 ^-4 C ₁₆ 4.0 203 x 10 ^-5 C ₁₇ -3.3457 x 10 ^-6 C ₁₉ -4.3054 x 10 ^-6 C ₂₁ 8.6 126 x 10 ^-6 C ₂₃ 6.3802 x 10 ^-6 C ₂₅ -2.1983 x 10 ^-7 C ₂₇ -2.7202 x 10 ^-7 C ₂₉ -1.5211 x 10 ^-8 C ₃₀ -2.8038 x 10 ^-7 C ₃₂ 1.8870 x 10 ^-8 C ₃₄ 3.0331 x 10 ^-8 C ₃₆ -2.9737 x 10 ^-8 .

Next, the lateral aberration charts of Examples 1, 2, 3, 4, and 5 are shown in FIGS. 6 to 8, 9 to 11, and 12, respectively.
It shows in FIG. 13, FIG. In these lateral aberration diagrams, the numbers in parentheses are (horizontal (X direction) angle of view, vertical (Y
Direction) angle of view), and lateral aberration at that angle of view.

The values of the parameters relating to the conditional expressions (1) to (21-1) in the respective examples of the present invention are shown below (for the conditional expressions (1) and (2), the reflection and refraction of each reflecting surface). Regarding the conditional expressions showing the force and the other two upper and lower values, the upper part shows the minimum value and the lower part shows the maximum value.)

[0165]

In the above embodiments, the above defined formula (a),
Although it is composed of the free-form surface and the anamorphic surface of (b),
It goes without saying that curved surfaces of any definition can be used. However, no matter what definition formula was used, the aberration was corrected very well by satisfying any of the conditions shown in the present invention and by satisfying some of them. It goes without saying that an eyepiece optical system can be obtained. In addition, the conditional expression used in the conventional non-eccentric system such as the curvature of the surface defined by the center of the definition coordinate system of the surface ignoring the eccentricity, the focal length of the surface is such that each surface is largely eccentric as in the present invention. If so, it has no meaning.

A pair of left and right eyepiece optical systems and image display elements according to the present invention as described above are prepared, and they are supported at a distance of the eye radiation distance so that they can be observed by both eyes. It can be configured as a portable image display device such as a partially mounted image display device. FIG. 23 shows the overall configuration of an example of such a portable image display device. The display device main body 50 is provided with a pair of left and right eyepiece optical systems as described above, and an image display element composed of a liquid crystal display element is arranged on the image plane corresponding to them. A temporal frame 51 as shown in the figure is provided on the main body 50 continuously on the left and right. The temporal frames 51 on both sides are connected by a parietal frame 52. A rear frame 54 is provided through the rear frame 54, and the rear frame 54 is applied to the rear portions of both ears of the observer like a pair of spectacles.
2 on the top of the observer, the display device body 5
0 can be held in front of the observer's eyes. A top pad 55 made of an elastic body such as a sponge is attached inside the top frame 52, and a similar pad is attached inside the rear frame 54 in the same manner. It does not feel uncomfortable when attached to the camera.

A speaker 56 is mounted on the rear frame 54.
Is provided so that stereophonic sound can be heard together with image observation. As described above, the display device main body 50 having the speaker 56 has a video / audio transmission code 57.
The viewer 58 holds the playback device 58 at an arbitrary position such as a belt position as shown in FIG.
You can enjoy the sound. 5 shown
Reference numeral 9 denotes an adjustment unit such as a switch and a volume of the playback device 58. Note that electronic components such as a video processing / audio processing circuit are built in the top frame 52.

The cord 57 may be attached to an existing video deck or the like by using the tip as a jack. Furthermore, it is connected to a tuner for TV radio wave reception,
It may be used for viewing, or may be connected to a computer to receive computer graphics images, message images from the computer, and the like. Also, in order to reject an obstructive code, an antenna may be connected to receive an external signal by radio waves.

The head-mounted image display device of the present invention described above can be configured as follows, for example. [1] Head-mounted image display having an image display element and an eyepiece optical system that guides an image formed by the image display element as a virtual image without forming an intermediate image at an observer's eyeball position In the apparatus, the eyepiece optical system has at least one non-rotationally symmetric reflecting surface having neither a rotational symmetry axis in-plane nor an out-of-plane reflection axis, and an axial chief ray from the screen center of the image display device. Is an extension direction of a line segment which is emitted from the eyepiece optical system and reaches the observer's eyeball position center in the Z axis, and in a plane including a folded line segment when the axial chief ray is reflected by the reflecting surface. When the direction perpendicular to the Z-axis is defined as the Y-axis and the direction perpendicular to the Z-axis and the Y-axis is defined as the X-axis, the non-rotationally symmetric surface shape satisfies the following conditions. Head-mounted image display device.

-0.2 <DY _max4 <0.2 (4-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center and the screen upper central view angle The effective area is defined as the area where the chief ray, the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of view of the screen, the chief ray at the lower right angle of view of the screen, and the chief ray at the lower central angle of view of the screen intersect with the target surface. Then, a differential value DY2, DY1, DY4, DY5 of a position where each of the principal rays hits the surface of a value obtained by differentiating with respect to the Y axis that is in the eccentric direction of the surface of the expression defining the shape of the surface in the effective area, DY6,
When it is DY3, DY2-DY1, DY2-DY3,
_Let all the values of _DY2 -DY4, _DY2-DY5, and _DY2-DY6 be DY _max4 .

[2] Head wearing having an image display element and an eyepiece optical system for guiding an image formed by the image display element as a virtual image without forming an intermediate image at the observer's eyeball position In the image display device, the last reflecting surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element,
The in-plane and out-of-plane reflection-shaped surfaces having no rotationally symmetric axis have a non-rotationally symmetric surface shape, and the axial chief ray from the center of the screen of the image display element is emitted from the eyepiece optical system to the observer's eyeball. The extension direction of the line segment reaching the position center is the Z axis, the Y axis is the direction perpendicular to the Z axis in the plane including the folded line segment when the axial chief ray is reflected by the reflecting surface. A head-mounted image display device, characterized in that, when the direction perpendicular to the axis and the Y-axis is defined as the X-axis, the non-rotationally symmetric surface shape satisfies the following conditions.

0.55 <DDXY11 <4.0 (20-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction of the screen center and the chief ray at the screen upper central angle of view. , The area where the chief ray of the screen upper right angle of view, the chief ray of the screen right central angle of view, the chief ray of the screen lower right angle of view, and the chief ray of the lower screen central angle of view intersect the target surface, 2 about the Y-axis that corresponds to the eccentric direction of the surface of the equation that defines the shape of that surface in the effective area
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY11
And

[3] Wearing a head having an image display element and an eyepiece optical system for guiding an image formed by the image display element as a virtual image without forming an intermediate image at the observer's eyeball position In the image display apparatus, the reflecting surfaces other than the last reflecting surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element are rotated both in-plane and out-of-plane. It consists of a non-rotationally symmetric reflecting surface having no axis of symmetry, and the axial chief ray from the screen center of the image display element exits from the eyepiece optical system and reaches the observer eyeball position center line segment. The extension direction is the Z-axis, and the direction perpendicular to the Z-axis is the Y-axis in a plane that includes a line segment that is folded when the axial chief ray is reflected by the reflecting surface.
Axis, and a direction perpendicular to the Z-axis and the Y-axis is defined as an X-axis, the non-rotationally symmetric surface shape surface satisfies the following conditions: .

0.55 <D ² XY12 <5 (21-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction at the screen center and the chief ray at the screen upper central angle of view. , The area where the chief ray of the screen upper right angle of view, the chief ray of the screen right central angle of view, the chief ray of the screen lower right angle of view, and the chief ray of the lower screen central angle of view intersect with the target surface, 2 about the Y-axis that corresponds to the eccentric direction of the surface of the equation that defines the shape of that surface in the effective area
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY12
And

[4] The above [1], wherein the non-rotationally symmetric surface is an anamorphic surface.
The head-mounted image display device according to [2] or [3].

[5] The head mounting according to the above [1], [2] or [3], wherein the non-rotationally symmetric surface is a plane-symmetric free-form surface having only one symmetry surface. Type image display device.

[6] The extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element is emitted to the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] ,
The head-mounted image display device according to [2] or [3].

-10 <DY _max1 <1.0 (1-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center and the principal ray at the screen upper central angle of view. , The area where the chief ray of the screen upper right angle of view, the chief ray of the screen right central angle of view, the chief ray of the screen lower right angle of view, and the chief ray of the lower screen central angle of view intersect the target surface, Differentiated values DY2, DY1, DY4, DY5, DY6 of the position where each principal ray hits the surface of a value obtained by differentiating with respect to the Y axis that is in the eccentric direction of the surface of the expression that defines the shape of the surface in the effective area.
When set to DY3, all values from DY1 to DY6 are DY
_Set to _max1 .

[7] An extension direction of a line segment from the eyepiece optical system in which an axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is the axial chief ray. When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] ,
The head-mounted image display device according to [2] or [3].

-0.2 <DY _max2 <0.2 (2-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center and the screen upper central angle of view The effective area is defined as the area where the chief ray, the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of view of the screen, the chief ray at the lower right angle of view of the screen, and the chief ray at the lower central angle of view of the screen intersect with the target surface. Then, a differential value DY2, DY1, DY4, DY5 of a position where each of the principal rays hits the surface of a value obtained by differentiating with respect to the Y axis that is in the eccentric direction of the surface of the expression defining the shape of the surface in the effective area, DY6,
When it is DY3, DY1-DY4, DY2-DY5,
Let all the values of _DY3 to _DY6 be DY _max2 .

[8] An extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] ,
The head-mounted image display device according to [2] or [3].

-0.1 <DY _max3 <1 (3-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center and the principal ray at the screen upper central angle of view. , The area where the chief ray of the screen upper right angle of view, the chief ray of the screen right central angle of view, the chief ray of the screen lower right angle of view, and the chief ray of the lower screen central angle of view intersect with the target surface, Differentiated values DY2, DY1, DY4, DY5, DY6 of the position where each principal ray hits the surface of a value obtained by differentiating with respect to the Y axis that is in the eccentric direction of the surface of the expression that defines the shape of the surface in the effective area.
When set to DY3, (DY1-DY4)-(DY3-D
Y6) is DY _max3 .

[0184]

[9] The axial chief ray from the center of the screen of the image display device is emitted from the eyepiece optical system to the extension direction of a line segment reaching the observer eyeball position center is the Z axis, and the axial chief ray is the When the direction perpendicular to the Z-axis is defined as the Y-axis and the direction perpendicular to the Z-axis and the Y-axis is defined as the X-axis in the plane including the folding line segment when reflected by the reflecting surface, the observation In the first reflective surface of the eyepiece optical system when viewed in the order of back ray tracing from the pupil of the human eye to the image display element, the following condition is satisfied [1],
The head-mounted image display device according to [2] or [3].

-0.5 <DY _max5 <0.08 (5-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction at the screen center and the screen upper central angle of view The effective area is defined as the area where the chief ray, the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of view of the screen, the chief ray at the lower right angle of view of the screen, and the chief ray at the lower central angle of view of the screen intersect with the target surface. Then, a differential value DY2, DY1, DY4, DY5 of a position where each of the principal rays hits the surface of a value obtained by differentiating with respect to the Y axis that is in the eccentric direction of the surface of the expression defining the shape of the surface in the effective area, DY6,
When it is _DY3 , _DY2-DY5 is DY _max5 .

[10] The axial chief ray from the center of the screen of the image display element is emitted from the eyepiece optical system and reaches the observer's eyeball position center in the extension direction of the Z axis, and the axial chief ray When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.16 <DX _max1 <1.4 (6-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center and the screen upper central angle of view The effective area is defined as the area where the chief ray, the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of view of the screen, the chief ray at the lower right angle of view of the screen, and the chief ray at the lower central angle of view of the screen intersect with the target surface. X, which is in the direction perpendicular to the eccentric direction of the surface of the expression that defines the shape of that surface in the effective area
Differentiated values DX2, DX1, DX4, DX at the positions where the respective principal rays hit the surface of the values differentiated with respect to the axis
5, DX6, DX3, DX4-DX6 is DX
_Set to _max1 .

[11] The extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is the axial chief ray. When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized in that all reflecting surfaces of the eyepiece optical system satisfy the following conditions.

−0.16 <DX _{max1 ′} <1.4 (7-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction at the screen center and the screen upper-side center angle of view The principal ray of the screen, the chief ray of the upper right angle of view of the screen, the chief ray of the right central angle of view of the screen, the chief ray of the lower right angle of view of the screen, and the area where the chief ray of the lower central angle of view of the screen intersects the target surface as the effective area. X that hits in a direction perpendicular to the eccentric direction of the surface of the expression that defines the shape of that surface in its effective area
Differentiated values DX2, DX1, DX4, DX at the positions where the respective principal rays hit the surface of the values differentiated with respect to the axis
5, DX6, DX3, DX4-DX6 is DX
_{max1 '}

[12] The axial principal ray from the center of the screen of the image display device is emitted from the eyepiece optical system to the extension direction of the line segment reaching the observer's eyeball position center is the Z axis, and the axial principal ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

-0.02 <D ² XY _max1 <0.04 (1 / mm) (8-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and the Y-axis, which corresponds to the eccentric direction of the surface of the equation that defines the shape of the surface in the effective area, is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
3 and then, when the D ² X2-D ² Y2 and D ² XY, the maximum D ² XY value of those absolute values of D ² XY at all reflecting surfaces of the ocular optical system and D ² XY _max1 .

[13] An extension direction of a line segment from the eyepiece optical system in which an axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.02 <D ² XY _{max1 '} <0.04 (9-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction of the screen center and the screen upper center Effective areas where the chief ray of view angle, the chief ray of view angle on the screen, the chief ray of view angle on the right center of the screen, the chief ray of view angle on the lower right side of the screen, and the chief ray of view angle on the lower side of the screen intersect the target surface. 2) about the Y-axis which corresponds to the eccentric direction of the surface of the formula which defines the area and defines the shape of that surface in the effective area
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
3, and when D ² X2-D ² Y2 is D ² XY, D
The ² X2-D ² Y2 and D ² XY _{max1 '.}

[14] An extension direction of a line segment from the eyepiece optical system in which an axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.03 <D ² Y _max1 <0.06 (1 / mm) (10-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and the Y-axis, which corresponds to the eccentric direction of the surface of the equation that defines the shape of the surface in the effective area, is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
^{When 2} Y5, D ² Y6, and D ² Y3, all the values of D ² Y1 to D ² Y6 are D ² Y _max1 DY _max1 .

[15] An extension direction of a line segment, in which an axial chief ray from the screen center of the image display element is emitted from the eyepiece optical system and reaches the observer's eyeball position center, is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.03 <D ² X _max2 <0.1 (1 / mm) (11-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and X that corresponds to the direction perpendicular to the eccentric direction of the surface of the formula that defines the shape of that surface in the effective area
The value obtained by differentiating twice about the axis is the second derivative D ² X2, D ² X1, of the position where each principal ray hits the surface.
When D ² X4, D ² X5, D ² X6, D ² X3,
Let all the values of D ² X1 to D ² X6 be D ² X _max2 .

[16] The extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.05 <D ² X _max3 <0.05 (1 / mm) (12-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and X that corresponds to the direction perpendicular to the eccentric direction of the surface of the formula that defines the shape of that surface in the effective area
The value obtained by differentiating twice about the axis is the second derivative D ² X2, D ² X1, of the position where each principal ray hits the surface.
When D ² X4, D ² X5, D ² X6, D ² X3,
^{D 2 X1-D 2 X4,} D 2 X2-D 2 X5, D 2 X3-
Let all values of D ² X6 be D ² X _max3 .

[17] The extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display device reaches the observer's eyeball position center is the Z axis, and the axial chief ray is the axial chief ray. When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.03 <D ² Y _max4 <0.05 (1 / mm) (13-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and the Y-axis, which corresponds to the eccentric direction of the surface of the equation that defines the shape of the surface in the effective area, is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, D ² Y1-D
² Y4, all values of ^{D 2 Y2-D 2 Y5,} D 2 Y3-D 2 Y6 and D ² Y _max4.

[18] The extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

-0.05 <D ² X _max5 <0.05 (1 / mm) (14-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and X that corresponds to the direction perpendicular to the eccentric direction of the surface of the formula that defines the shape of that surface in the effective area
The value obtained by differentiating twice about the axis is the second derivative D ² X2, D ² X1, of the position where each principal ray hits the surface.
When D ² X4, D ² X5, D ² X6, D ² X3,
D ² X 1 -D ^{2 on} all reflecting surfaces of the eyepiece optical system
X3, the value of D ² X4-D ² X6 and D ² X _max5.

[19] An extension direction of a line segment from the eyepiece optical system in which an axial chief ray from the screen center of the image display device reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

-0.03 <D ² Y _max6 <0.03 (1 / mm) (15-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and the Y-axis, which corresponds to the eccentric direction of the surface of the equation that defines the shape of the surface in the effective area, is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and D ² Y1-D ² Y3 and D ² Y4-D on all reflecting surfaces of the eyepiece optical system.
_Let the value of ² Y6 be D ² Y _max6 .

[20] The axial principal ray from the center of the screen of the image display device is emitted from the eyepiece optical system and extends in the direction of the line segment reaching the observer's eyeball position center, the Z axis, and the axial chief ray. When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

-0.02 <D ² XY _max7 <0.1 (1 / mm) (16-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction at the center of the screen. , The chief ray at the upper center angle of view of the screen, the chief ray at the upper right angle of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect with the target surface. The area to be defined is defined as the effective area, and the Y-axis, which corresponds to the eccentric direction of the surface of the equation that defines the shape of the surface in the effective area, is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, all the values of D ² Xn-D ² Yn (n is 1 to 6) on all the reflecting surfaces of the eyepiece optical system are D ² XY.
_Set to _max7 .

[21] An extension direction of a line segment from the eyepiece optical system in which the axial chief ray from the screen center of the image display element reaches the observer's eyeball position center is the Z axis, and the axial chief ray is When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The first reflecting surface of the eyepiece optical system, when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element, satisfies the following condition: [1] The head-mounted image display device according to [2] or [3].

-0.1 <D ² XY _{max7 '} <0.08 (1 / mm) (17-1) However, with the Y-axis direction as the vertical direction, the axial main axis in the Z-axis direction at the center of the screen is set. Rays, chief ray of screen upper center angle of view, chief ray of screen upper right angle of view, chief ray of screen right central angle of view, chief ray of screen lower right angle of view, principal ray of lower screen center angle of view The intersecting area is defined as the effective area, and the Y axis that corresponds to the eccentric direction of the surface of the formula that defines the shape of the surface in the effective area is 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
3 to ^{time, D 2 Xn-D 2 Yn} (n is 1 to 6) to all values of _D ² XY max7 _'.

[22] The axial chief ray from the center of the screen of the image display element is emitted from the eyepiece optical system and extends in the direction of the line segment reaching the observer's eyeball position center, the Z axis, and the axial chief ray. When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

0.13 <D ² X9 <1.15 (18-1) However, with the Y-axis direction as the up-down direction, the axial chief ray in the Z-axis direction of the screen center and the screen upper-side center angle of view The effective area is defined as the area where the chief ray, the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of view of the screen, the chief ray at the lower right angle of view of the screen, and the chief ray at the lower central angle of view of the screen intersect with the target surface. X, which is in the direction perpendicular to the eccentric direction of the surface of the expression that defines the shape of that surface in the effective area
The value obtained by differentiating twice about the axis is the second derivative D ² X2, D ² X1, of the position where each principal ray hits the surface.
When D ² X4, D ² X5, D ² X6, D ² X3,
Back light ray reaching the image display element from the pupil of the observer eyeball D ² X2 / the last reflecting surface of the eyepiece optical system when viewed in the order of tracing back ray rays from the pupil of the observer eyeball to the image display element The first of the eyepiece optical systems when viewed in the order of tracking
The value of D ² X2 of the th reflective surface is D ² X9.

[23] The axial chief ray from the center of the screen of the image display device is emitted from the eyepiece optical system and reaches the center of the observer's eyeball in the direction of extension of the Z axis, and the axial chief When a direction perpendicular to the Z axis is defined as a Y axis and a direction perpendicular to the Z axis and the Y axis is defined as an X axis in a plane including a folding line segment when a light ray is reflected by the reflecting surface, The head mounted image display device according to the above [1], [2] or [3], characterized by satisfying the following conditions.

0.14 <DDY10 <5 (19-1) However, with the Y-axis direction as the vertical direction, the axial principal ray in the Z-axis direction of the screen center, the principal ray of the screen upper central view angle, the screen The effective area is defined as the area where the chief ray with the upper right angle of view, the chief ray with the right central angle of view of the screen, the chief ray with the lower right angle of view of the screen, and the principal ray with the lower central angle of view of the screen intersect the target surface. 2 about the Y-axis that corresponds to the eccentric direction of the surface of the formula that defines the shape of that surface in the region
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, D ² Y2 / the above-mentioned last reflection surface of the eyepiece optical system when viewed in the order of back ray tracing from the pupil of the observer's eye to the image display element. The value of D ² Y2 on the first reflecting surface of the eyepiece optical system when viewed in the order of tracing back rays from the pupil of the observer's eye to the image display element is D ² Y10.

[0214]

As is apparent from the above description, according to the present invention, it is possible to provide a head-mounted image display device which provides an observation image which is clear even with a wide angle of view and has little distortion.

[Brief description of drawings]

FIG. 1 is a sectional view of a monocular optical system of a head mounted image display device using an eyepiece optical system according to a first embodiment of the present invention.

FIG. 2 is a sectional view of a monocular optical system of a head mounted image display device using an eyepiece optical system according to a second embodiment of the present invention.

FIG. 3 is a sectional view of a monocular optical system of a head mounted image display device using an eyepiece optical system according to a third embodiment of the present invention.

FIG. 4 is a sectional view of a monocular optical system of a head mounted image display device using an eyepiece optical system according to a fourth embodiment of the present invention.

FIG. 5 is a cross-sectional view of a monocular optical system of a head mounted image display device using an eyepiece optical system according to a fifth embodiment of the present invention.

FIG. 6 is a part of a lateral aberration diagram of the eyepiece optical system according to the first embodiment of the present invention.

FIG. 7 is the remaining part of the lateral aberration diagram of the eyepiece optical system according to the first embodiment of the present invention.

FIG. 8 is the remaining portion of the lateral aberration diagram of the eyepiece optical system according to the first embodiment of the present invention.

FIG. 9 is a part of a lateral aberration diagram of the eyepiece optical system according to the second embodiment of the present invention.

FIG. 10 is a remaining part of the lateral aberration diagram of the eyepiece optical system according to the second embodiment of the present invention.

FIG. 11 is the remaining portion of the lateral aberration diagram of the eyepiece optical system according to the second embodiment of the present invention.

FIG. 12 is a lateral aberration diagram of the eyepiece optical system according to Example 3 of the present invention.

FIG. 13 is a lateral aberration diagram of the eyepiece optical system according to Example 4 of the present invention.

FIG. 14 is a lateral aberration diagram of the eyepiece optical system according to the fifth embodiment of the present invention.

FIG. 15 is a sectional view showing an example of an eyepiece optical system to which the present invention can be applied.

FIG. 16 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 17 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 18 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 19 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 20 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 21 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 22 is a sectional view showing another example of an eyepiece optical system to which the present invention can be applied.

FIG. 23 is a diagram showing the overall configuration of an example of a head-mounted image display device according to the present invention.

FIG. 24 is a diagram showing an optical system of one conventional head-mounted image display device.

FIG. 25 is a diagram showing an optical system of another conventional head-mounted image display device.

FIG. 26 is a diagram showing an optical system of still another conventional head-mounted image display device.

FIG. 27 is a diagram showing an optical system of another conventional head-mounted image display device.

FIG. 28 is a diagram showing an optical system of another conventional head-mounted image display device.

[Explanation of symbols]

 1 ... Exit pupil position (observer pupil position) 2 ... Observer visual axis (axial chief ray) 3 ... First surface of eyepiece optical system 4 ... Second surface of eyepiece optical system 5 ... Third surface of eyepiece optical system 6 ... Image display element 7 ... Eyepiece optical system 9 ... 4th surface of eyepiece optical system 50 ... Display device main body 51 ... Temporal frame 52 ... Crown frame 53 ... Leaf spring 54 ... Rear frame 55 ... Crown pad 56 ... Speaker 57 ... Video / audio transmission code 58 ... Playback device 59 ... Control part for switches, volume, etc.

Claims (3)

[Claims] 1. A head-mounted type having an image display element and an eyepiece optical system for guiding an image formed by the image display element as a virtual image without forming an intermediate image at an observer's eyeball position. In the image display device, the eyepiece optical system has at least one non-rotationally symmetric reflecting surface having neither a rotational symmetry axis in-plane nor an out-of-plane axis, and an on-axis axis from a screen center of the image display element. A plane including an extension direction of a line segment in which a chief ray is emitted from the eyepiece optical system and reaches the observer's eyeball position center, and a folding line segment when the axial chief ray is reflected by the reflecting surface. Where the direction perpendicular to the Z-axis is defined as the Y-axis and the direction perpendicular to the Z-axis and the Y-axis is defined as the X-axis, the surface of the non-rotationally symmetric surface shape satisfies the following conditions. Head-mounted image display device characterized by: -0.2 <DY _max4 <0.2 (4-1) However, with the Y-axis direction as the vertical direction, an axial chief ray in the Z-axis direction at the center of the screen, a chief ray at the screen upper center angle of view The effective area is defined as the area where the chief ray at the upper right angle of view of the screen, the chief ray at the right central angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. Differentiated values DY2, DY1, DY4, DY5, DY6 of the position where each principal ray hits the surface of a value that is differentiated with respect to the Y axis that is in the eccentric direction of the surface of the expression that defines the shape of the surface in the effective area.
When it is DY3, DY2-DY1, DY2-DY3,
_Let all the values of _DY2 -DY4, _DY2-DY5, and _DY2-DY6 be DY _max4 . 2. A head-mounted type having an image display element and an eyepiece optical system for guiding an image formed by the image display element as a virtual image without forming an intermediate image at an observer's eyeball position. In the image display device, the last reflecting surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element does not have an axis of rotational symmetry both inside and outside the surface. A non-rotationally symmetric reflecting surface, wherein the axial chief ray from the screen center of the image display device is emitted from the eyepiece optical system and reaches the observer's eyeball position center in the extension direction of the Z axis. , A plane perpendicular to the Z axis in a plane including a folded line segment when the axial chief ray is reflected by the reflecting surface, a Y axis, and a direction perpendicular to the Z axis and the Y axis is an X axis. Is defined as A head mounted image display device characterized by satisfying the following conditions. 0.55 <DDXY11 <4.0 (20-1) However, with the Y axis direction as the vertical direction, the axial chief ray in the Z axis direction of the screen center, the chief ray at the screen upper center angle of view, and the screen upper right corner The effective area is defined as the area where the chief ray at the angle of view, the chief ray at the right angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. With respect to the Y axis that is in the eccentric direction of the surface of the equation that defines the shape of that surface with 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY11
And 3. A head-mounted type having an image display element and an eyepiece optical system for guiding an image formed by the image display element as a virtual image without forming an intermediate image at an observer's eyeball position. In the image display device, the reflection surfaces other than the last reflection surface of the eyepiece optical system when viewed in the order of the backward ray tracing from the pupil of the observer's eye to the image display element are rotationally symmetric both in-plane and out-of-plane. It is composed of a non-rotationally symmetric reflecting surface having no axis, and an axial chief ray from the screen center of the image display element is an extension of a line segment that reaches the observer's eyeball position center from the eyepiece optical system. The direction is the Z axis, the direction perpendicular to the Z axis is the Y axis in the plane including the folding line segment when the axial chief ray is reflected by the reflecting surface, and the direction perpendicular to the Z axis and the Y axis. When the direction is defined as the X axis, the non-rotational symmetry A head-mounted image display device characterized in that the surface of the surface shape satisfies the following conditions. 0.55 <D ² XY12 <5 (21-1) However, with the Y-axis direction as the vertical direction, the axial chief ray in the Z-axis direction of the screen center, the chief ray at the screen upper center angle of view, and the screen upper right corner The effective area is defined as the area where the chief ray at the angle of view, the chief ray at the right angle of the screen, the chief ray at the lower right angle of the screen, and the chief ray at the lower central angle of the screen intersect the target surface. With respect to the Y axis that is in the eccentric direction of the surface of the equation that defines the shape of that surface with 2
Second derivative values D ² Y2, D ² Y1, D ² Y4, D of the positions where the respective chief rays hit the surface of the differentiated value
² Y5, D ² Y6, D ² Y3, and a value obtained by differentiating twice with respect to the X axis, which is perpendicular to the eccentric direction, with respect to the position where each of the chief rays hits the surface D ² X
2, D ² X1, D ² X4, D ² X5, D ² X6, D ² X
When set to 3, set the value of D ² X2 / D ² Y2 to DDXY12
And