JPH09113801A - Optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optical system capable of exactly measuring a surface shape and having a rotary asymmetric optical surface whose center of external size is not in coincidence with the center of the surface shape. SOLUTION: This optical system has a rotary asymmetric surface shape such as an anamorphic surface, is arranged obliquely to the optical axis 2 and has at least one surface of optical surfaces 3, 4 whose center of surface determined by its external size is not coincident with the center 14 of the surface shape. A point 14 at which the surface shape becomes symmetric in two orthogonal directions in at least an arbitraty area on the optical surfaces 3, 4 exists on the optical surfaces 3, 4. When the symmetric point 14 is constituted so as to actually exist on the optical surfaces 3, 4, since the positioning of the optical surface is performed on the basis of this point without using approxamation, exact measurement of the surface shape is performed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical system usable as an eyepiece optical system or an imaging optical system, and more particularly to an optical system having a decentered rotationally asymmetric optical surface.

[0002]

2. Description of the Related Art In recent years, with technological innovation in various fields, new optical systems that have never existed before are required. In order to respond to this, various special optical systems have been developed. Among them, there are rotationally asymmetric optical surfaces, and various designs have been made.

For example, in an optical system such as a head- or face-mounted image display device, which is required to be small and lightweight, a concave mirror arranged at an angle with respect to the optical axis may be used for downsizing. At this time, tilting the concave mirror causes large aberrations such as coma and astigmatism. In order to correct these aberrations, it is conceivable that the surface shape of the concave mirror or other surface is a rotationally asymmetric surface such as an anamorphic surface or a toric surface. However, simply tilting the optical surface causes asymmetrical distortion in the eccentric direction. That is, as shown in FIG. 22, the optical axis 32 direction of the optical system is the Z axis, and the Y axis is the eccentric direction of the optical system.
When the X axis is taken perpendicular to the Y and Z axes, the center 3 of the surface shape
Due to the rotationally asymmetric optical surface 31 having 3, the asymmetric distortion is generated in the Y-axis direction. In order to correct this, as shown in FIG. 23, the rotationally asymmetric optical surface 3
It can be corrected by arranging the center 33 of the surface shape of No. 1 so as to be displaced from the optical axis 32. Here, the center 33 of the surface shape is the origin of a mathematical expression expressing the surface shape in an anamorphic surface, a toric surface, or the like, and more generally, the surface shape is symmetrical in at least two directions orthogonal to each other in a certain region. It is a point. Further, when the center of the surface shape is displaced with respect to the optical axis as described above, it is general that the center determined by the outer shape of the optical surface does not coincide with the center of the surface shape. The center determined by the outer shape of the optical surface here is the center of the circle when the outer diameter of the optical surface is a circle, and is the intersection of the diagonal lines of the quadrangle if the outer diameter of the optical surface is a quadrangle. is there.

[0004]

However, when the surface shape center and the center determined by the outer shape of the optical surface are displaced from each other, the following problems occur. When measuring the surface shape after processing the rotationally asymmetric optical surface, a so-called three-dimensional shape measuring machine is often used. This measuring machine is capable of measuring the X,
The Y, Z three-dimensional coordinates are measured, and the deviation from the design formula is measured from those coordinates. If the center of the outer shape of the optical surface and the center of the surface shape match, the position of the optical surface that is the object to be measured can be accurately determined based on the outer shape. Can be compared accurately.

However, if the center of the outer shape of the optical surface does not coincide with the center of the surface shape, the optical surface cannot be positioned on the basis of the outer shape, and therefore the position of the optical surface with respect to the measuring machine is The estimation is performed from the surface shape measurement result of the optical surface, for example, a fitting method such as the least square method of the coordinate data of thousands to tens of thousands that is the measurement result of the surface shape design formula. In this method, since the position of the object to be measured is approximated, the exact position of the optical surface is unknown, and therefore the measurement accuracy deteriorates. Especially,
Since the reflective surface is required to have a particularly strict surface accuracy, high accuracy is required for the measurement, but it has been a serious problem that the position of the non-measuring object cannot be accurately determined as described above.

The present invention has been made in view of the above-mentioned problems of the prior art, and an object thereof is to enable accurate surface shape measurement and to perform rotation in which the center of the outer shape of the optical surface does not coincide with the center of the surface shape. An object is to provide an optical system having an asymmetrical optical surface.

[0007]

A first optical system of the present invention which achieves the above object has a rotationally asymmetric surface shape, is inclined with respect to an optical axis, and has a surface determined by an outer shape. In an optical system having at least one optical surface whose center does not coincide with the center of the surface shape, the point where the surface shape is symmetrical with respect to two directions orthogonal to each other in at least an arbitrary region on the optical surface is the optical surface. It is characterized by being present above.

In this case, the position of the above-mentioned point in the cross section of the optical surface cut along one of the symmetry planes at the point where the surface shape is symmetric with respect to two directions orthogonal to each other in at least some arbitrary region is as follows. It is desirable to satisfy the formula of. 0.05 × D <L ₀ <0.25 × D (1) where L ₀ is the distance from one end of the cross section close to the point to the point, and D is the outside of the cross section. Is the diameter.

A second optical system of the present invention has a rotationally asymmetric surface shape having at least one symmetrical surface, is arranged to be inclined with respect to the optical axis, and has a center and a surface shape determined by the outer shape. In an optical system having at least one optical surface whose center does not match, when the shape of the optical surface cut along the plane of symmetry is represented by any of the following mathematical formulas, at least one local maximum or minimum of the mathematical formula It is characterized in that points are present in the optical surface. However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
CY is a Y-axis direction curvature, ak is a conic coefficient, and ac (n) is an aspherical surface coefficient. However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
C _0n is a coefficient of each term.

In this case, it is desirable that the position of at least one of the maximum point and the minimum point in the mathematical formula representing the shape cut in the symmetry plane satisfies the following formula. 0.05 × D <L ₀ <0.25 × D (4) where L ₀ is the distance from one end of the cross section on the side close to the point to the point, and D is the outside of the cross section. Is the diameter.

A third optical system of the present invention is an optical system having a rotationally asymmetric surface shape, arranged so as to be inclined with respect to the optical axis, and in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape. In an optical system having at least one surface, the surface shape is an anamorphic surface or a toric surface, and the origin of the surface shape is in the optical surface.

In this case, it is desirable that the position of the origin in the cross section of the optical surface cut by either the plane of symmetry of the anamorphic surface or the toric surface satisfies the following equation. 0.05 × D <L ₀ <0.25 × D (8) where L ₀ is the distance from one end on the side close to the origin to the origin, and D is the outer diameter of the cross section. is there.

In the above-mentioned first to third optical systems, the rotationally asymmetrical optical surface can be used as the reflecting surface.

Further, the optical system can be used together with the image display device in a head- or face-mounted image display device.

In that case, the optical system has at least two surfaces, a first surface forming a transmission surface and a second surface forming a reflection surface, said at least two surfaces being the observer. Is arranged so as to be inclined with respect to the visual axis which is the central direction of the projected image to be observed, and the region between the first surface and the second surface is filled with a medium having a refractive index larger than 1. Can be one.

Further, the optical system may have at least two reflecting mirrors arranged eccentrically with respect to each other, and at least one of them may be a concave mirror.

Further, the optical system has at least one concave mirror arranged at an angle with respect to the visual axis which is the central direction of the projected image observed by the observer, and between the concave mirror and the image display element. At least one optical element having a positive refractive power may be arranged.

Further, the optical system has at least three surfaces, and in the order in which the light rays emitted from the image display element pass, at least a third surface forming a transmission surface and a second surface forming a reflection surface. And a first surface forming a transmissive surface. In this case, the first surface of the optical system may form the reflective surface at the same time as the transmissive surface.

Further, the optical system has at least three surfaces, and in the order in which the light rays emitted from the image display element pass, at least a second surface which forms a reflective surface and a reflective surface at the same time as a transmissive surface, and a reflective surface are formed. A fourth surface that forms a transparent surface and a first surface that forms a transparent surface.
And a surface. In this case, the light ray is transmitted once and reflected twice on the second surface, and
The reflection can be performed twice on the fourth surface.

Further, the optical system has at least three surfaces, and in the order in which the light rays emitted from the image display device pass, at least a second surface forming a reflecting surface at the same time as a transmitting surface, and at the same time as the reflecting surface. It may include a first surface forming a transmissive surface and a fourth surface forming a reflective surface.

Further, the optical system has at least four surfaces, and in the order in which the light rays emitted from the image display element pass, at least a third surface forming a transmitting surface and a fourth surface forming a reflecting surface. And a second surface forming a reflecting surface and a first surface forming a transmitting surface. In this case, the light ray can be reflected twice on the second surface. Further, the third surface may also be formed as a reflective surface at the same time as the transmissive surface.

In addition, the optical system has a second surface having at least four surfaces and performing at least one transmission and two reflections in the order in which the light rays emitted from the image display element pass, and a reflection surface. A fifth surface forming a surface and a fourth surface forming a reflecting surface
A surface and a first surface forming a transparent surface may be included.

The reason why the above structure is adopted and its function will be described below. From the measurement result of the surface shape of the optical surface, it is possible to easily and accurately extract a point where the surface shape is symmetric with respect to two directions orthogonal to each other in a given arbitrary region. Therefore, if this point of symmetry is configured to actually exist on the optical surface, the positioning of the optical surface with respect to the measuring device can be performed with this point as a reference without depending on approximation. Therefore, accurate surface shape measurement can be performed.

For example, in the surface shape as shown in FIG. 24, there are a plurality of points 41 in which a surface shape is symmetrical with respect to two directions orthogonal to each other in a certain region.
If at least one of them is in the optical plane,
The object of the present invention is achieved.

Here, in a surface shape in which there are continuous points whose surface shapes are symmetrical with respect to two orthogonal directions, it is impossible to set one point as a reference for positioning. Naturally, such a surface shape is different from the surface shape of the present invention. For example, like a so-called cylindrical surface, a surface shape in which a cross-sectional shape in a certain direction is a straight line corresponds to it.

As described above, when a point whose surface shape is symmetric with respect to two directions orthogonal to each other in an arbitrary area actually exists on the optical surface, one of the symmetry planes at that point It is desirable that the position of the point on the cross section of the optical surface cut by the step satisfies the following formula. 0.05 × D <L ₀ <0.25 × D (1) where L ₀ is the distance from one end on the side close to the point of symmetry of the above cross section to D, and D is the above The outer diameter of the cross section. With such a relationship, the asymmetrical distortion can be effectively removed, and at the same time, the positioning of the optical surface can be accurately performed, and highly accurate surface shape measurement can be performed.

Now, from the measurement result of the surface shape of the optical surface having at least one symmetry plane, it is possible to easily and accurately extract the maximum point or the minimum point in the shape cut in the symmetry plane. Therefore, if the maximum point or the minimum point exists in the optical surface, the optical surface can be accurately positioned with reference to the maximum point or the minimum point, and highly accurate surface shape measurement can be performed. It can be performed.

As described above, when the maximum point or the minimum point in the shape cut in the symmetric surface of the optical surface having at least one symmetric surface is configured to exist in the optical surface, the maximum point. It is desirable that the position of at least one of the points or the minimum points satisfies the following formula. 0.05 × D <L ₀ <0.25 × D (4) where L ₀ is the distance from one end on the side close to the maximum or minimum point of the cross section, and D is the cross section Is the outer diameter of. With such a relationship, the asymmetrical distortion can be effectively removed, and at the same time, the positioning of the optical surface can be accurately performed, and highly accurate surface shape measurement can be performed.

When the rotationally asymmetric surface shape is an anamorphic surface or toric surface and the origin of the surface shape is in the optical surface, the anamorphic surface or the anamorphic surface is determined from the measurement result of the surface shape of the optical surface. The origin of the surface shape of the toric surface can be extracted easily and accurately. Therefore, the optical surface can be accurately positioned with reference to this origin, and highly accurate surface shape measurement can be performed.

The surface shapes of the anamorphic surface and the toric surface are expressed by the following equations. (Anamorphic surface type) 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. (Toric surface expression) Z = -Sign (Rx) · {(Rx-G (y)) 2 -x 2} However ^{1/2 + Rx ··· (6),} Z is from a plane tangent to the origin of the surface shape The shift amount, Rx is the radius of curvature in the X axis direction, Sign (Rx) is the sign of the radius of curvature in the X axis direction, and G (y) is Where CY is the Y-axis direction curvature, ak is the conic coefficient, and ac (n) is the aspherical surface coefficient.

As described above, when the rotationally asymmetric surface shape is an anamorphic surface or a toric surface and the origin of the surface shape is in the optical surface, a symmetric surface of the anamorphic surface or toric surface is symmetrical. It is preferable that the position of the origin of the cross section of the optical surface cut by either of the above satisfies the following formula. 0.05 × D <L ₀ <0.25 × D (8) where L ₀ is the distance from one end on the side close to the origin of the cross section to the origin, and D is the outer diameter of the cross section. With such a relationship, the asymmetrical distortion can be effectively removed, and at the same time, the positioning of the optical surface can be accurately performed, and highly accurate surface shape measurement can be performed.

By the way, since the reflecting surface is required to have a higher precision than the transmitting surface, if the optical surface having the above rotationally asymmetric shape is used as the reflecting surface,
More effective.

In the head- or face-mounted image display device, an eccentric concave mirror is considered to be used because an optical system that is smaller and has a well-corrected aberration is used. Therefore, as shown in FIG. 25, the optical system according to the present invention is configured as an eyepiece optical system 21, and the image display device 2
It is more effective to use the same in the head or face-mounted image display device together with 2.

By adopting the constitutions of Examples 1 to 21 described later, it is possible to observe clearly in a wide angle of view, the brightness of the image is hardly deteriorated, and further, it is very possible. It is possible to realize an optical system that is compact and lightweight, and that can be used in a head- or face-mounted image display device that does not easily cause fatigue.

[0035]

BEST MODE FOR CARRYING OUT THE INVENTION Several embodiments of the optical system of the present invention will be described below. The following examples all use the optical system of the present invention as an eyepiece optical system of a head- or face-mounted image display device.

In the constituent parameters of each embodiment described later, as shown in FIG. 1, the observer's pupil position 1 is the origin of the optical system, and the observer's visual axis 2 is the Z axis. In addition, the pupil 1
The direction away from is positive. In addition, the Y-axis is set in the plane of the figure so that the top of the figure is positive and is orthogonal to the Z-axis. Further, so as to be orthogonal to the Y axis and the Z axis, that is,
The X axis is assumed to be perpendicular to the figure. The ray tracing is performed by reverse tracing with the eyeball 1 side of the observer as the object side and the image display element 8 side as the image plane side.

Then, with respect to the surface on which the eccentricity amounts Y and Z and the inclination amount θ are described, the observer pupil 1 which is the origin of the optical system.
Represents the amount of deviation from and the tilt angle with respect to the Z axis. The tilt angle is positive in the counterclockwise direction.

The surface on which the eccentricity amounts Y and Z and the inclination amount θ are not described is coaxial with the surface immediately before that surface, and is defined by the surface distance along the central axis of the surface immediately before that surface. . It should be noted that the sign of the surface interval is positive when the light exits from the pupil 1, and thereafter, the sign is inverted every time the light passes through the reflecting surface.

The shape of the anamorphic surface is defined by the following formula. 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. In addition, the term relating to the aspherical surface for which no data is given is 0. The refractive index for d-line (wavelength 587.56 nm) is shown.

Further, as shown in FIG. 26, the position of the center of the surface shape with respect to the outer diameter of the optical surface in a certain cross section is from the center 53 of the surface shape with respect to the straight line connecting both ends 52 of the optical surface having the cross section 51. It is determined by the position of the intersection with the lowered perpendicular. That is, in FIG. 26, the following values are the center positions of the surface shapes.

If a <b, then a / (a + b) If a> b, then b / (a + b) The origin of the anamorphic surface, which is the center of the surface shape of the optical surface, is in two orthogonal directions. The surface shape is symmetrical with respect to the Y-axis direction and the X-axis direction, and has a maximum value or a minimum value on the Y-axis.

Example 1 A sectional view of this example is shown in FIG. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and passes through a third surface 5 which is a transmissive surface arranged facing the image display element 8. Display light from the image display element 8 that has entered the optical system is reflected by the first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, and then, The reflected light is incident on and reflected by the second surface 4 of the reflecting surface that is eccentrically arranged so as to face the observer's pupil 1 on the observer's visual axis 2. The light exits and advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axes of the first surface 3 and the second surface 4 forming the anamorphic surface,
Reference numeral 14 indicates the center of those surface shapes.

By setting the origin 14 of the surface shape of the anamorphic surface of the first surface 3 and the second surface 4 to the following positions with respect to the outer shape of the optical surface, it becomes possible to measure the surface shape with high accuracy. At the same time, it removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) First side: 20% Second side: 20%
.

[Embodiment 2] A sectional view of this embodiment is shown in FIG. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and passes through a third surface 5 which is a transmissive surface arranged facing the image display element 8. Display light from the image display element 8 that has entered the optical system is reflected by the first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, and then, The reflected light is incident on and reflected by the second surface 4 of the reflecting surface that is eccentrically arranged so as to face the observer's pupil 1 on the observer's visual axis 2. The light exits and advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the first surface 3 forming the anamorphic surface, and reference numeral 14
Indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the first surface 3 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time.
Asymmetrical distortion is removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) First surface: 14% This example is the same optical system as Example 1 of Japanese Patent Application No. 7-120034, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 3] A sectional view of this embodiment is shown in FIG. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and passes through a third surface 5 which is a transmissive surface arranged facing the image display element 8. Display light from the image display element 8 that has entered the optical system is reflected by the first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, and then, The reflected light is incident on and reflected by the second surface 4 of the reflecting surface that is eccentrically arranged so as to face the observer's pupil 1 on the observer's visual axis 2. The light exits and advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the third surface 5 forming the anamorphic surface, and reference numeral 14
Indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the third surface 5 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time.
Asymmetrical distortion is removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Third surface: 20% This example is the same optical system as Example 3 of Japanese Patent Application No. 7-120034, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 4] A sectional view of this embodiment is shown in FIG. This optical system is composed of four surfaces 3, 4, 5, and 6, and a space between them is filled with a medium having a refractive index of more than 1, and the third of the transmission surfaces is arranged facing the image display element 8.
The display light from the image display element 8 that has entered the optical system through the surface 5 is reflected by the fourth surface 6 of the reflecting surface, and then decentered on the viewer's visual axis 2 so as to face the pupil 1 of the viewer. The light is incident on and reflected by the second surface 4 of the arranged reflecting surface, and the reflected light is the first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2. Through the optical system, travels along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the second surface 4 and the third surface which form the anamorphic surface.
The axes of the surface 5 and the fourth surface 6 are shown, and the reference numeral 14 shows the center of these surface shapes.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4, the fourth surface 6, and the third surface 5 to the following position with respect to the outer shape of the optical surface, the surface shape can be accurately adjusted. It enables measurement. Further, the action of the fourth surface 6 removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface ... 47% Third surface ... 4% Fourth surface ... 16% This example is the same optical system as Example 2 of Japanese Patent Application No. 7-127896, and the difference in the constituent parameters. Is due to the difference in the definition of the coordinate system.

[Embodiment 5] A sectional view of this embodiment is shown in FIG. This optical system is composed of four surfaces 3, 4, 5, and 6, and a space between them is filled with a medium having a refractive index of more than 1, and the third of the transmission surfaces is arranged facing the image display element 8.
The display light from the image display element 8 that has entered the optical system through the surface 5 is reflected by the fourth surface 6 of the reflecting surface, and then decentered on the viewer's visual axis 2 so as to face the pupil 1 of the viewer. The light is incident on and reflected by the second surface 4 of the arranged reflecting surface, and the reflected light is the first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2. Through the optical system, travels along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the second surface 4 and the fourth surface 4 which form the anamorphic surface.
The axis of the surface 6 is shown, and the reference numeral 14 shows the center of those surface shapes.

By setting the origin 14 of the anamorphic surface of the second surface 4 and the fourth surface 6 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy. There is. Further, the action of the fourth surface 6 removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 48% Fourth surface: 19% Note that this embodiment is the same optical system as the fourth embodiment of Japanese Patent Application No. 7-127896, and the difference in the constituent parameters is the definition of the coordinate system. It is due to the difference.

[Embodiment 6] A sectional view of this embodiment is shown in FIG. This optical system is composed of four surfaces 3, 4, 5, and 6, and a space between them is filled with a medium having a refractive index of more than 1, and the third of the transmission surfaces is arranged facing the image display element 8.
The display light from the image display element 8 that has entered the optical system through the surface 5 enters the second surface 4 of the reflecting surface that is eccentrically arranged on the visual axis 2 of the viewer so as to face the pupil 1 of the viewer. After being reflected, after being reflected, it is reflected by the fourth surface 6 of the reflecting surface, and then is incident on the second surface 4 and reflected, and the reflected light is observed as the second surface 4 on the observer's visual axis 2. Through the first surface 3 arranged between the viewer's pupil 1 and the optical system, and travels along the observer's visual axis 2.
The light enters the observer's pupil 1 without forming an intermediate image and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 39% Note that this example is the same as Example 4 of Japanese Patent Application No. 7-158897.
The optical system is the same as, and the difference in the configuration parameters is due to the difference in the definition of the coordinate system.

[Embodiment 7] A sectional view of this embodiment is shown in FIG. This optical system is composed of four surfaces 3, 4, 5, and 6, and a space between them is filled with a medium having a refractive index of more than 1, and the third of the transmission surfaces is arranged facing the image display element 8.
The display light from the image display element 8 that has entered the optical system via the surface 5 is reflected by the fourth surface 6 of the reflective surface, then enters the third surface 5, and is reflected this time, and then the observer. The second surface 4 of the reflecting surface, which is eccentrically arranged so as to face the pupil 1 of the observer on the visual axis 2.
Incident on the observer's visual axis 2 and then transmitted through the first surface 3 disposed between the second surface 4 and the observer's pupil 1 to exit from the optical system for observation. Go along the visual axis 2
The light enters the observer's pupil 1 without forming an intermediate image and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 21% Note that this example is the same as Example 6 of Japanese Patent Application No. 7-158897.
The optical system is the same as, and the difference in the configuration parameters is due to the difference in the definition of the coordinate system.

[Embodiment 8] A sectional view of this embodiment is shown in FIG. This optical system is composed of three surfaces 3, 4, and 6, and a space between them is filled with a medium having a refractive index larger than 1. The optical system is arranged so as to face the image display element 8 and is on the observer's visual axis 2. Display light from the image display element 8 that has entered the optical system through the second surface 4 that is eccentrically arranged so as to face the observer's pupil 1 is reflected by the fourth surface 6 of the reflection surface, and then the second light. The light is incident on the surface 4 and is then reflected, and then is reflected again on the fourth surface 6. Then, it is incident on the second surface 4 and is reflected again. The light passes through the first surface 3 arranged between the observer's pupil 1 and exits from the optical system, advances along the observer's visual axis 2, and enters the observer's pupil 1 without forming an intermediate image. Then, a display image is formed on the retina of the observer. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 33% This example is the same optical system as Example 7 of Japanese Patent Application No. 7-158897, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 9] A sectional view of this embodiment is shown in FIG. This optical system is composed of four surfaces 3, 4, 6, and 7, and a space between them is filled with a medium having a refractive index larger than 1. The optical system is arranged so as to face the image display element 8, and the observer's visual axis 2 is provided. A second eccentric arrangement facing the pupil 1 of the observer
The display light from the image display element 8 that has entered the optical system via the surface 4 is reflected by the fifth surface 7 of the reflective surfaces, then enters the second surface 4 and is then reflected, and then the reflective surface. Is reflected by the fourth surface 6 of the above, is incident on the second surface 4 again, is reflected again, and after the reflection, is placed between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2. The light passes through the first surface 3, exits from the optical system, advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. Image. In the figure, reference numeral 13 indicates the axis of the fourth surface 6 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the fourth surface 6 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Fourth surface ... 37% This example is the same optical system as Example 9 of Japanese Patent Application No. 7-158897, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 10] FIG. 1 is a sectional view of this embodiment.
0 is shown. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and the third of the transmission surfaces arranged facing the image display element 8 is provided.
The display light from the image display element 8 that has entered the optical system through the surface 5 enters the second surface 4 of the reflecting surface that is eccentrically arranged on the visual axis 2 of the viewer so as to face the pupil 1 of the viewer. It is reflected, passes through the first surface 3 disposed between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, exits from the optical system, and advances along the observer's visual axis 2. , Enters the observer's pupil 1 without forming an intermediate image and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axes of the first surface 3 and the second surface 4 forming the anamorphic surface, and the reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the anamorphic surface of the first surface 3 and the second surface 4 at the following position with respect to the outer shape of the optical surface, it becomes possible to measure the surface shape with high accuracy. At the same time, it removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) First surface: 45% Second surface: 14% Note that this embodiment is the same optical system as the first embodiment of Japanese Patent Application No. 6-290892, and the difference in the constituent parameters is the definition of the coordinate system. It is due to the difference.

[Embodiment 11] A sectional view of this embodiment is shown in FIG.
It is shown in FIG. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and the third of the transmission surfaces arranged facing the image display element 8 is provided.
The display light from the image display element 8 that has entered the optical system through the surface 5 enters the second surface 4 of the reflecting surface that is eccentrically arranged on the visual axis 2 of the viewer so as to face the pupil 1 of the viewer. It is reflected, passes through the first surface 3 disposed between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, exits from the optical system, and advances along the observer's visual axis 2. , Enters the observer's pupil 1 without forming an intermediate image and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axes of the first surface 3 and the third surface 5 forming the anamorphic surface, and the reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the anamorphic surface of the first surface 3 and the third surface 5 at the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy. There is.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) First surface: 9% Third surface: 48% It should be noted that this embodiment is the same optical system as the fourth embodiment of Japanese Patent Application No. 6-290892, and the difference in the constituent parameters is the definition of the coordinate system. It is due to the difference.

[Embodiment 12] A sectional view of this embodiment is shown in FIG.
It is shown in FIG. This optical system is composed of three surfaces 3, 4 and 5, and a space between them is filled with a medium having a refractive index larger than 1, and the third of the transmission surfaces arranged facing the image display element 8 is provided.
The display light from the image display element 8 that has entered the optical system through the surface 5 enters the second surface 4 of the reflecting surface that is eccentrically arranged on the visual axis 2 of the viewer so as to face the pupil 1 of the viewer. It is reflected, passes through the first surface 3 disposed between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2, exits from the optical system, and advances along the observer's visual axis 2. , Enters the observer's pupil 1 without forming an intermediate image and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 9% This example is the same optical system as Example 5 of Japanese Patent Application No. 6-290892, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 13] A sectional view of this embodiment is shown in FIG.
3 is shown. This optical system is composed of three surfaces 3, 4, and 6, and a space between them is filled with a medium having a refractive index larger than 1. The optical system is arranged so as to face the image display element 8 and is on the observer's visual axis 2. Second eccentric arrangement facing the observer's pupil 1
Display light from the image display element 8 that has entered the optical system via the surface 4 is reflected by the fourth surface 6 of the reflecting surface, then enters the second surface 4 and is reflected this time. A first surface 3 arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2.
Through the optical system, travels along the observer's visual axis 2, and enters the observer's pupil 1 without forming an intermediate image,
A display image is formed on the observer's retina. In the figure, reference numeral 13
Indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 27% This example is the same optical system as Example 3 of Japanese Patent Application No. 7-212594, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 14] A sectional view of this embodiment is shown in FIG.
It is shown in FIG. This optical system is composed of three surfaces 3, 4, and 6, a fourth surface 6 is a rear surface mirror, and a first surface 3 and a second surface 4 are provided.
Also, the space between the fourth surface 6 and the surface 15 facing the rear surface mirror is filled with a medium having a refractive index larger than 1, and is arranged so as to face the image display element 8 and is observed on the observer's visual axis 2. The display light from the image display element 8 that has entered the optical system through the second surface 4 that is eccentrically arranged so as to face the human pupil 1 passes through the surface 15, and is reflected by the fourth surface 6 of the rear surface mirror. Next, the light is incident on the second surface 4 through the surface 15 and is reflected this time, and after the reflection, the first surface arranged between the second surface 4 and the observer's pupil 1 on the observer's visual axis 2. The light passes through the surface 3 and exits from the optical system, and the observer's visual axis 2
The observer's pupil 1 without forming an intermediate image.
To form a display image on the retina of the observer. In the figure,
Reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface ... 7% This example is the same optical system as Example 4 of Japanese Patent Application No. 7-212594, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 15] A sectional view of this embodiment is shown in FIG.
It is shown in FIG. This optical system is composed of three surfaces 3, 4, 6 and is filled with two kinds of media having a refractive index larger than 1 between them, and is arranged so as to face the image display element 8, and
Display light from the image display element 8 that has entered the optical system through the second surface 4 that is eccentrically arranged so as to face the viewer's pupil 1 on the viewer's visual axis 2 is reflected by the fourth surface 6 of the reflecting surface. And then the second
The light is incident on the surface 4 and is then reflected. After the reflection, the light is transmitted through the second surface 4 and the first surface 3 arranged between the observer's pupil 1 and the optical system from the optical system. The light exits and advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 13% This example is the same optical system as Example 6 of Japanese Patent Application No. 7-212594, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 16] A sectional view of this embodiment is shown in FIG.
6 is shown. This optical system is composed of three surfaces 3, 4, 6 and is filled with three kinds of media having a refractive index larger than 1 between them. The optical system is arranged so as to face the image display element 8, and
Display light from the image display element 8 that has entered the optical system through the second surface 4 that is eccentrically arranged so as to face the viewer's pupil 1 on the viewer's visual axis 2 is reflected by the fourth surface 6 of the reflecting surface. And then the second
The light is incident on the surface 4 and is then reflected. After the reflection, the light is transmitted through the second surface 4 and the first surface 3 arranged between the observer's pupil 1 and the optical system from the optical system. The light exits and advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the second surface 4 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the second surface 4 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy and at the same time, perform asymmetric distortion. Have been removed.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Second surface: 25% This example has the same optical system as that of Example 9 of Japanese Patent Application No. 7-212594, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 17] FIG. 1 is a sectional view of this embodiment.
FIG. This optical system is composed of three surfaces 3, 4, and 6, and a space between them is filled with a medium having a refractive index larger than 1. The optical system is arranged so as to face the image display element 8 and is on the observer's visual axis 2. Second eccentric arrangement facing the observer's pupil 1
Display light from the image display element 8 that has entered the optical system via the surface 4 is reflected by the first surface 3 arranged on the observer's visual axis 2 between the second surface 4 and the observer's pupil 1. , Is reflected by the fourth surface 6 of the reflecting surface, then is incident on the second surface 4 and is then reflected,
After the reflection, this time, the light passes through the first surface 3, exits from the optical system, travels along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms the observer's retina. Form a display image on top. In the figure, reference numeral 13 indicates the axis of the first surface 3 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface of the first surface 3 to the following position with respect to the outer shape of the optical surface, it is possible to measure the surface shape with high accuracy.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) First surface: 27% The present embodiment is the same optical system as the third embodiment of Japanese Patent Application No. 7-178657, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 18] A sectional view of this embodiment is shown in FIG.
8 shows. This optical system comprises two reflecting mirrors 9 and 10, of which the first reflecting mirror 9 is a surface mirror and the second reflecting mirror 1 is a mirror.
0 is a rear surface mirror, and the display light from the image display element 8 that has entered the optical system through the surface of the second reflecting mirror 10 that is arranged so as to face the image displaying element 8 is reflected by the second reflecting mirror 10. The front surface, the back surface, and the front surface are transmitted, reflected, and transmitted in this order, and then are reflected by the first reflecting mirror 9 that is eccentrically arranged on the observer's visual axis 2 so as to face the pupil 1 of the observer, and the optical system Exits from, advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axes of the front surface and the back surface of the second reflecting mirror 10 forming the anamorphic surface, and the reference numeral 14 indicates the center of those surface shapes.

High accuracy measurement of the surface shape is possible by setting the origin 14 of the surface shape of the anamorphic surface on the front surface and the back surface of the second reflecting mirror 10 to the following position with respect to the outer shape of the optical surface. At the same time, it removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) The surface of the second reflecting mirror ... 9% The back surface of the second reflecting mirror ... 11% In addition, this Example is Example 8 of Japanese Patent Application No. 7-43847.
The optical system is the same as, and the difference in the configuration parameters is due to the difference in the definition of the coordinate system.

[Embodiment 19] FIG. 1 is a sectional view of this embodiment.
9 shows. This optical system includes an optical element (junction lens) 12 having a positive refracting power and a concave mirror 11 formed of a rear surface mirror, and the concave mirror 11 is arranged to face the image display element 8.
The display light from the image display element 8 that has entered the optical system via the surface of the concave mirror 11 is transmitted, reflected, and transmitted in the order of the front surface, the rear surface, and the front surface of the concave mirror 11. An optical element 12 having a positive refractive power, which is eccentrically arranged so as to face the pupil 1.
Through the optical system, travels along the observer's visual axis 2, and enters the observer's pupil 1 without forming an intermediate image,
A display image is formed on the observer's retina. In the figure, reference numeral 13
Indicates the axis of the surface of the concave mirror 11 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

By setting the origin 14 of the surface shape of the anamorphic surface on the surface of the concave mirror 11 to the following position with respect to the outer shape of the optical surface, the surface shape can be measured with high accuracy.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Surface of concave mirror ... 14% This example is the same optical system as Example 7 of Japanese Patent Application No. 7-34, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. .

[Embodiment 20] A sectional view of this embodiment is shown in FIG.
0 is shown. This optical system is composed of an optical element (junction lens) 12 having a positive refractive power and a concave mirror 11 made of a surface mirror. Display light from the image display element 8 that has passed through and entered the optical system is reflected by a concave mirror 11 that is eccentrically arranged on the observer's visual axis 2 so as to face the pupil 1 of the observer, and is emitted from the optical system. It advances along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. In the figure, reference numeral 13 indicates the axis of the reflecting surface of the concave mirror 11 forming the anamorphic surface, and reference numeral 14 indicates the center of the surface shape.

On the reflecting surface of the concave mirror 11, the origin 14 of the surface shape of the anamorphic surface is set to the following position with respect to the outer shape of the optical surface, thereby enabling highly accurate measurement of the surface shape and at the same time asymmetrical. It removes all distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Reflecting surface of concave mirror 27% Note that this example is the same optical system as Example 4 of Japanese Patent Application No. 6-308980, and the difference in the constituent parameters is due to the difference in the definition of the coordinate system. is there.

[Embodiment 21] A sectional view of this embodiment is shown in FIG.
It is shown in FIG. This optical system is composed of an optical element (bonded lens) 12 having a positive refractive power and a concave mirror 11 made of a rear surface mirror, and an optical element 12 having a positive refractive power arranged facing the image display element 8. The display light from the image display element 8 that is transmitted and made incident on the optical system is transmitted in the order of the front surface, the rear surface, and the front surface of the concave mirror 11 that is eccentrically arranged so as to face the pupil 1 of the observer on the observer's visual axis 2. , Reflected, transmitted, emitted from the optical system, travels along the observer's visual axis 2, enters the observer's pupil 1 without forming an intermediate image, and forms a display image on the observer's retina. . In the drawing, reference numeral 13 indicates the axes of the front and back surfaces of the concave mirror 11 forming the anamorphic surface, and the reference numeral 14 indicates
The centers of their surface shapes are shown.

By setting the origin 14 of the surface shape of the anamorphic surface on the front surface and the back surface of the concave mirror 11 to the following position with respect to the outer shape of the optical surface, it becomes possible to measure the surface shape with high accuracy and at the same time. Removes asymmetric distortion.

(Position of center of surface shape with respect to outer shape: L ₀ /
D) Front surface of concave mirror ... 44% Back surface of concave mirror ... 6% This embodiment is the same optical system as the embodiment 5 of Japanese Patent Application No. 6-308980, and the difference in the constituent parameters is the definition of the coordinate system. It is due to the difference.

The constituent parameters of Examples 1 to 21 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 pupil position) ( 3 sides) 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) (Inclination angle) 1 ∞ (pupil) 2 R _y -108.187 1.4922 57.50 (first surface) R _x -73.105 (from pupil position) K _y 0 Y -24.028 θ -14.70 ° K _x 0 Z 26.360 R ₂ 5.5419 × 10 ^-7 R ₃ 8.1756 × 10 ^-11 P ₂ -0.0804 P ₃ -1.3795 3 R _y -69.871 1.4922 57.50 (2nd surface) R _x -60.374 (From the pupil position) (Reflecting surface) K _y -0.1368 Y 19.109 θ 36.66 ° K _x -0.1233 Z 33.339 R ₂ -7.2329 × 10 ^-11 R ₃ -4.5294 × 10 ^-12 P ₂ 29.0752 P ₃ -2.0854 4 R -108.187 1.4922 57.50 (1st surface) R _x -73.105 (from pupil position) (Reflecting surface) K _y 0 Y -24.028 θ -14.70 ° K _x 0 Z 26.360 R ₂ 5.5419 × 10 ^-7 R ₃ 8.1756 × 10 ^-11 P ₂ -0.0804 P ₃ -1.3795 5 77.772 (From pupil position) (3rd surface) Y -35.215 θ -47.77 ° Z 18.818 6 ∞ (From pupil position) (Image display surface) Y -30.892 θ -52.77 ° Z 43.084.

Example 3 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Inclination angle) 1 ∞ (pupil) 2 R _y -178.469 1.4922 57.50 (first surface) R _x -75.710 (from pupil position) K _y -4.7001 Y -42.983 θ -19.56 ° K _x -1.2227 Z 19.657 R ₂ 9.7123 × 10 ^-7 R ₃ -1.7919 × 10 ^-10 P ₂ -0.4268 P ₃ -0.3806 3 R _y -81.632 1.4922 57.50 (2nd surface) ) R _x -66.826 (from pupil position) (Reflecting surface) K _y -0.0705 Y 30.011 θ 40.46 ° K _x -0.5741 Z 26.362 R ₂ 3.9038 × 10 ^-11 R ₃ -2.9560 × 10 ^-13 P ₂ -62.1044 P ₃ 3.6860 4 R _y -178.469 1.4922 57.50 (1st surface) R _x -75.710 (From pupil position) (Reflecting surface) K _y -4.7001 Y -42.983 θ -19.56 ° K _x -1.2227 Z 19.657 R ₂ 9.7123 × 10 ^-7 R ₃ -1.7919 × 10 ^-10 P ₂ -0.4268 P ₃ -0.3806 5 R _y -78.809 (from pupil position) (3rd surface) R _x -15.380 Y -28.629 θ -69.21 ° K _y -12 Z 27.051 K _x -7.2014 R ₂ -9.3889 × 10 ^-7 R ₃ -3.4662 × 10 ^-9 P ₂ -0.9953 P ₃ 0.7065 6 ∞ (from pupil position) (image display surface) Y -30.077 θ -55.73 ° Z 38.578.

Example 4 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (Pupil) 2 76.063 1.4990 69.10 (First surface) (From pupil position) Y -0.946 θ 2.91 ° Z 32.522 3 R _y -156.527 1.4990 69.1
0 (2nd surface) _Rx- 98.656
(From pupil position) (reflection _{surface) K y -7.0734 Y 2.234 θ 36.99} ° K x -4.1863 Z 49.661 R 2 6.0317 × 10 -11 R 3 -3.1116 × 10 -21 P 2 -40.1178 P 3 1579.73 4 R y - 392.753 1.4990 69.10 (fourth surface) R _x -124.880 (from pupil position) (reflection _{surface) K y 26.6033 Y -9.745 θ 29.83} ° K x -2.9042 Z 33.260 R 2 -6.0811 × 10 -8 R 3 8.1091 × 10 - ¹¹ P ₂ 0.0131 P ₃ 0.2803 5 R _y 133.797 (From pupil position) (3rd surface) R _x 898.615 Y -40.684 θ -19.13 ° K _y -41.4052 Z 52.119 K _x -22.7620 R ₂ -8.6132 × 10 ^-6 R ₃ -1.1141 × 10 ^-9 P ₂ -0.6106 P ₃ 1.4040 6 ∞ (from pupil position) (image display surface) Y -32.358 θ 2.87 ° Z 62.534.

Example 5 Surface Number Curvature Radius Spacing Refractive Index Abbe's Number (Eccentricity) (Inclination Angle) 1 ∞ (Pupil) 2 -2227.303 1.4870 70.40 (First Surface) (From Pupil Position) Y 0 θ 0 ° Z 32.000 3 R _y -86.054 1.4870 70.40 (2nd surface) R _x -71.847 (From pupil position) (Reflection surface) K _y -0.8934 Y 3.478 θ 29.21 ° K _x -0.2048 Z 50 R ₂ -3.3277 × 10 ^-8 R ₃ -3.2956 × 10 ^-11 P ₂ 0.2624 P ₃ 0.6719 4 R _y -70.490 1.4870 70.40 (4th surface) R _x -52.620 (from pupil position) (Reflecting surface) K _y 0 Y -13 θ 18.37 ° K _x 0 Z 34 R ₂ -7.6251 × 10 ^-8 R ₃ -2.2778 × 10 ^-10 P ₂ -1.6010 P ₃ -1.5837 5 85.106 (From pupil position) (3rd surface) Y -32.132 θ -34.75 ° Z 40.966 6 ∞ (pupil (From the position) (Image display surface) Y -30.195 θ -19.83 ° Z 53.755.

Example 6 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Inclination Angle) 1 ∞ (Pupil) 2 57.185 1.5163 64.15 (First Surface) (From Pupil Position) Y 12 θ -43 ° Z 40 3 R _y 868.454 1.5163 64.15 (2nd surface) R _x ∞ (from pupil position) (Reflecting surface) K _y 0 Y -10 θ 28 ° K _x 0 Z 50 R ₂ 1.2469 × 10 ^-6 R ₃ -6.5241 × 10 ^-10 P ₂ -0.1657 P ₃ -0.3656 4 147.375 1.5163 64.15 (4th surface) (From pupil position) (Reflecting surface) Y -15 θ 23 ° Z 30 5 R _y 868.454 1.5163 64.15 (2nd surface) R _x ∞ (From pupil position) (Reflecting surface) K _y 0 Y -10 θ 28 ° K _x 0 Z 50 R ₂ 1.2469 × 10 ^-6 R ₃ -6.5241 × 10 ^-10 P ₂ -0.1657 P ₃ -0.3656 6 -79.539 ( From the pupil position) (Third surface) Y -51.862 θ 63.19 ° Z 93.453 7 ∞ (From pupil position) (Image display surface) Y -54.387 θ 52.33 ° Z 51.508.

Example 7 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Tilt Angle) 1 ∞ (Pupil) 2 -99.012 1.5163 64.15 (First Surface) (From Pupil Position) Y 5.523 θ 0.34 ° Z 42.121 3 R _y -88.432 1.5163 64.15 (2nd surface) R _x -80.992 (from pupil position) (Reflecting surface) K _y 2.5380 Y -4.695 θ 27.73 ° K _x 2.3862 Z 59.773 R ₂ 4.2978 × 10 ^-7 R ₃ 2.1320 × 10 ^-10 P ₂ -0.0193 P ₃ -0.0400 4 -51.868 1.5163 64.15 (3rd surface) (From pupil position) (Reflecting surface) Y -17.331 θ 23.29 ° Z 42.790 5 -65.959 1.5163 64.15 (4th surface) (Pupil) (From position) (Reflecting surface) Y -13.843 θ -0.82 ° Z 62.191 6 -51.868 (From pupil position) (3rd surface) Y -17.331 θ 23.29 ° Z 42.790 7 ∞ (From pupil position) (Image display surface) Y -30.783 θ -5.46 ° Z 36.202.

Example 8 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Tilt Angle) 1 ∞ (Pupil) 2 167.297 1.5163 64.15 (First Surface) (From Pupil Position) Y 25 θ -18 ° Z 26.241 3 R _y 400 1.5163 64.15 (2nd surface) R _x 177.856 (from pupil position) (Reflecting surface) K _y -73.4978 Y -5.772 θ 38.27 ° K _x 92.5183 Z 41.698 R ₂ 1.7724 × 10 ^-7 R ₃ -5.6849 × 10 ^-11 P ₂ 2.3790 P ₃ 1.1041 4 R _y 200 1.5163 64.15 (4th surface) R _x 135.533 (from pupil position) (Reflecting surface) K _y -1.9711 Y 6.724 θ 31.39 ° K _x 14.6846 Z -5.146 R ₂ 1.5060 × 10 ^-8 R ₃ -1.6360 × 10 ^-11 P ₂ 2.7267 P ₃ -0.3094 5 R _y 400 1.5163 64.15 (2nd surface) R _x 177.856 (from pupil position) (Reflecting surface) K _y -73.4978 Y -5.772 θ 38.27 ° K _x 92.5183 Z 41.698 R ₂ 1.7724 × 10 ^-7 R ₃ -5.6849 × 10 ^-11 P ₂ 2.3790 P ₃ 1.1041 6 R _y 200 1.5163 64.15 (4th surface) R _x 135.533 (from pupil position) (Reflecting surface) ) K _y -1. 9711 Y 6.724 θ 31.39 ° K _x 14.6846 Z -5.146 R ₂ 1.5060 × 10 ^-8 R ₃ -1.6360 × 10 ^-11 P ₂ 2.7267 P ₃ -0.3094 7 R _y 400 (from pupil position) (2nd surface) R _x 177.856 Y -5.772 θ 38.27 ° K _y -73.4978 Z 41.698 K _x 92.5183 R ₂ 1.7724 × 10 ^-7 R ₃ -5.6849 × 10 ^-11 P ₂ 2.3790 P ₃ 1.1041 8 ∞ (from the pupil position) Y -6.101 θ 49.39 ° Z 66.376.

Example 9 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Inclination Angle) 1 ∞ (Pupil) 2 -297.47 1.5163 64.15 (First Surface) (From Pupil Position) Y 29.410 θ -0.23 ° Z 26.632 3 R _y -184.732 1.5163 64.15 (2nd surface) R _x -95.633 (from pupil position) (Reflecting surface) K _y -3.1978 Y 16.029 θ 33.92 ° K _x -4.1084 Z 31.944 R ₂ -1.3721 × 10 ^-7 R ₃ -4.8704 × 10 ^-14 P ₂ -0.8291 P ₃ -0.0071 4 R _y -391.72 1.5163 64.15 (4th surface) R _x -70.599 (From pupil position) (Reflecting surface) Y -18.905 θ 16.13 ° Z 28.517 5 R _y -184.732 1.5163 64.15 (2nd surface) R _x -95.633 (From pupil position) (Reflecting surface) K _y -3.1978 Y 16.029 θ 33.92 ° K _x -4.1084 Z 31.944 R ₂ -1.3721 × 10 ^-7 R ₃ -4.8704 × 10 ^-14 P ₂ -0.8291 P ₃ -0.0071 6 1829.412 1.5163 64.15 (Fifth surface) (From pupil position) (Reflecting surface) Y -58.589 θ 46.87 ° Z 57.831 7 R _y -184.732 (From pupil position) (No. 2) R _x -95.633 Y 16.029 θ 33.92 ° K _y -3.1978 Z 31.944 K _x -4.1084 R ₂ -1.3721 × 10 ^-7 R ₃ -4.8704 × 10 ^-14 P ₂ -0.8291 P ₃ -0.0071 8 ∞ (from the pupil position) (Image) Display surface) Y -37.269 θ 54.31 ° Z 67.891.

Example 10 Surface Number Curvature Radius Spacing Refractive Index Abbe's Number (Eccentricity) (Tilt Angle) 1 ∞ (Pupil) 2 R _y 276.464 1.5163 64.15 (First Surface) R _x 105.242 (From Pupil Position) K _y 176.2838 Y 2.792 θ -17.70 ° K _x 17.5964 Z 31.247 R ₂ 7.7034 × 10 ^-7 R ₃ -4.4238 × 10 ^-9 P ₂ 1.2490 P ₃ 0.0945 3 R _y -115.076 1.5163 64.15 (2nd surface) R _x -109.349 (pupil (From the position) (Reflecting surface) K _y -0.9556 Y -23.581 θ 12.16 ° K _x -6.1737 Z 64.552 R ₂ 1.5266 × 10 ^-10 R ₃ -2.1827 × 10 ^-13 P ₂ 15.6741 P ₃ -5.1396 4 R _y -84.948 (From the pupil position) (3rd surface) R _x -71.864 Y -39.205 θ 29.56 ° K _y 2.6905 Z 70.999 K _x -3.9975 R ₂ -1.7277 × 10 ^-6 R ₃ 8.9752 × 10 ^-10 P ₂ 0.6743 P ₃ 0.1087 5 ∞ (from pupil position) (image display surface) Y -33.951 θ 23.99 ° Z 26.499.

Example 11 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Inclination Angle) 1 ∞ (Pupil) 2 R _y 413.784 1.4870 70.40 (First Surface) R _x 100.922 (From Pupil Position) Y 15.589 θ -19.27 ° Z 38.060 3 -138.139 1.4870 70.40 (2nd surface) (From pupil position) (Reflecting surface) Y -6.269 θ 18.73 ° Z 58.402 4 R _y -97.085 (From pupil position) (3rd surface) R _x- 228.894 Y -17.728 θ 60.73 ° Z 42.458 5 ∞ (from pupil position) (Image display surface) Y -35.297 θ 21.06 ° Z 21.066.

Example 12 Surface number Curvature radius Spacing Refractive index Abbe number (Decentering amount) (Tilt angle) 1 ∞ (pupil) 2 ∞ 1.5163 64.15 (first surface) (from pupil position) Y -1.557 θ -13.01 ° Z 30 3 R _y -107.677 1.5163 64.15 (2nd surface) R _x -124.033 (From pupil position) (Reflecting surface) K _y 0.7139 Y -29.624 θ 16.99 ° K _x -1.3550 Z 67.452 R ₂ 3.6220 × 10 ^-10 R ₃ -7.4359 × 10 ^-15 P ₂ 29.8897 P ₃ 6.5074 4 R _y -311.976 (From pupil position) (3rd surface) R _x 90.339 Y -39.956 θ 53.11 ° K _y 22.5600 Z 76.999 K _x 0 R ₂ -7.6268 × 10 ^-7 R ₃ 2.0870 × 10 ^-10 P ₂ 1.9069 P ₃ 0.8633 5 ∞ (From the pupil position) (Image display surface) Y -43.950 θ 37.542 ° Z 32.513.

Example 13 Surface Number Curvature Radius Spacing Refractive Index Abbe's Number (Eccentricity) (Tilt Angle) 1 ∞ (Pupil) 2 R _y 143.843 1.4922 57.50 (First Surface) R _x 29.666 (From Pupil Position) K _y- 10.6789 Y -22.583 θ -0.80 ° K _x -4.1807 Z 21.322 R ₂ -1.3584 × 10 ^-8 R ₃ -5.1466 × 10 ^-10 P ₂ 8.4020 P ₃ -0.5529 3 R _y -184.192 1.4922 57.50 (2nd surface) R _x -456.655 (from pupil position) (Reflecting surface) K _y -2.9172 Y 5.564 θ 53.46 ° K _x -5.5396 Z 39.811 R ₂ -8.1467 × 10 ^-8 R ₃ 2.5671 × 10 ^-12 P ₂ 0.3561 P ₃ -0.5172 4 R _y 70.860 1.4922 57.50 (4th surface) R _x 166.306 (From pupil position) (Reflecting surface) K _y -8.7738 Y -13.573 θ 60 ° K _x -1.3858 Z 22.548 R ₂ 3.6912 × 10 ^-7 R ₃ -1.1704 × 10 ^-12 P ₂ -1.2644 P ₃ 1.5310 5 R _y -184.192 (from pupil position) (2nd surface) R _x -456.655 Y 5.564 θ 53.46 ° K _y -2.9172 Z 39.811 K _x -5.5396 R ₂ -8.1467 × 10 ^-8 R ₃ 2.5671 x 10 ^-12 P ₂ 0.3561 P ₃ -0.5172 6 ∞ (from pupil position) (Image display surface) Y -6.789 θ 68.00 ° Z 68.196.

Example 14 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (Pupil) 2 102.985 1.5093 68.07 (First surface) (From pupil position) Y 0.923 θ -2.81 ° Z 29.185 3 R _y 491.360 1.5093 68.07 (2nd surface) R _x ∞ (from pupil position) (Reflecting surface) K _y -23.545 Y 9.366 θ 49.18 ° K _x 0 Z 33.561 R ₂ -3.1250 × 10 ^-10 R ₃ 3.1733 × 10 ^-12 P ₂ -3.9952 P ₃ -0.5774 4 111.602 (from pupil position) Y -18.553 θ 74.81 ° Z 45.079 5 63.706 1.6619 32.68 (from pupil position) Y -24.901 θ 76.76 6 Zy 39.979 6 R _y 67.336 1.6619 32.68 (No. 4 side) R _x 82.918 (from pupil position) (reflection _{surface) K y -0.4537 Y -19.488 θ 60.27} ° K x -0.4663 Z 16.092 R 2 4.6318 × 10 -8 R 3 1.7137 × 10 -12 P 2 -0.3085 P ₃ -1.2267 7 63.706 (from pupil position) Y -24.901 θ 76.76 ° Z 39.979 8 111.602 1.5093 68.07 ( pupil position than) Y -18.553 θ 74.81 ° Z 45.079 9 R y 491.360 ( pupil Location from) (second _{surface) R x ∞ Y 9.366 θ 49.18} ° K y -23.545 Z 33.561 K x 0 R 2 -3.1250 × 10 -10 R 3 3.1733 × 10 -12 P 2 -3.9952 P 3 -0.5774 10 ∞ (From the pupil position) (Image display surface) Y 7.910 θ 97.72 ° Z 60.951.

Example 15 Surface Number Curvature Radius Spacing Refractive Index Abbe Number (Eccentricity) (Inclination Angle) 1 ∞ (Pupil) 2 108.105 1.5779 60.23 (First Surface) (From Pupil Position) Y 2.027 θ -3.83 ° Z 25.116 3 R _y 1676.967 1.5779 60.23 (2nd surface) R _x ∞ (from pupil position) (Reflecting surface) K _y -1.1352 Y 7.253 θ 48.56 ° K _x 0 Z 32.313 R ₂ -1.8564 × 10 ^-10 R ₃ -2.9541 × 10 ^-13 P ₂ -8.1079 P ₃ -2.4482 4 49.089 1.6619 32.68 (from pupil position) Y -25.370 θ 76.20 ° Z 38.548 5 R _y 97.125 1.6619 32.68 (4th surface) R _x 100.373 (from pupil position) (Reflecting surface) ) K _y -0.5142 Y -13.327 θ 56.84 ° K _x -0.7399 Z 5.687 R ₂ 5.5402 × 10 ^-8 R ₃ -5.2212 × 10 ^-12 P ₂ 0.0099 P ₃ 0.1219 6 49.089 1.5779 60.23 (from the pupil position) Y -25.370 θ 76.20 ° Z 38.548 7 R _y 1676.967 (from pupil position) (2nd surface) R _x ∞ Y 7.253 θ 48.56 ° K _y -1.1352 Z 32.313 K _x 0 R ₂ -1.8564 × 10 ^-10 R ₃ -2.9541 × 1 0 ^-13 P ₂ -8.1079 P ₃ -2.4482 8 ∞ (from pupil position) (image display surface) Y 5.841 θ 78.81 ° Z 59.335.

Example 16 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (Pupil) 2 104.277 1.6200 60.30 (First surface) (From pupil position) Y 6.01 θ -4.77 ° Z 23.327 3 -977.974 1.7201 46.70 (from pupil position) Y 12.778 θ -3 ° Z 26.314 4 R _y 731.548 1.7201 46.70 (2nd surface) R _x ∞ (from pupil position) (Reflecting surface) K _y 0 Y 2.779 θ 45.59 ° K _x 0 Z 38.175 R ₂ -1.0071 × 10 ^-8 R ₃ -3.2973 × 10 ^-11 P ₂ -1.9345 P ₃ -1.4200 5 45.954 1.7550 27.60 (from pupil position) Y -24.317 θ 74.19 ° Z 39.647 6 R _y 99.662 1.7550 27.60 (4th surface) R _x 114.270 (from pupil position) (Reflecting surface) K _y -0.8945 Y -10.489 θ 53.63 ° K _x -0.7173 Z 8.547 R ₂ 6.5273 × 10 ^-8
P ₂ 0.2247 P ₃ -0.9576 7 45.954 1.7201 46.70 (from pupil position) Y -24.317 θ 74.19 ° Z 39.647 8 R _y 731.548 (from pupil position) (2nd surface) R _x ∞ Y 2.779 θ 45.59 ° K _y 0 Z 38.175 K _x 0 R ₂ -1.0071 × 10 ^-8 R ₃ -3.2973 × 10 ^-11 P ₂ -1.9345 P ₃ -1.4200 9 ∞ (from pupil position) (image display surface) Y 5.982 θ 70.67 ° Z 60.426.

Example 17 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (pupil) 2 R _y -736.361 1.4870 70.40 (first surface) R _x -505.846 (from pupil position) K _y 0 Y -21.744 θ -2.45 ° K _x 0 Z 24.480 R ₂ -3.0670 × 10 ^-8 R ₃ 8.0969 × 10 ^-11 P ₂ 2.6398 P ₃ 0.0574 3 -553.259 1.4870 70.40 (2nd surface) (From pupil position) (Reflecting surface) Y 23.482 θ 53.27 ° Z 19.912 4 R _y 146.168 1.4870 70.40 (4th surface) R _x 128.931 (From pupil position) (Reflecting surface) K _y -0.0677 Y -42.800 θ 93.37 ° K _x -0.4075 Z- 6.534 R ₂ 5.5052 × 10 ^-9 R ₃ -1.5143 × 10 ^-12 P ₂ -1.5599 P ₃ 0.4377 5 R _y -736.361 1.4870 70.40 (first surface) R _x -505.846 (from pupil position) (reflection surface) K _y 0 Y -21.744 θ -2.45 ° K _x 0 Z 24.480 R ₂ -3.0670 × 10 ^-8 R ₃ 8.0969 × 10 ^-11 P ₂ 2.6398 P ₃ 0.0574 6 -553.259 (From pupil position) (2nd surface) Y 23.482 θ 53.27 ° Z 19.912 7 ∞ (Eyes (From the position) (Image display surface) Y 16.438 θ 58.43 ° Z 39.101.

Example 18 Surface number Curvature radius Spacing Refractive index Abbe number (Decentering amount) (Inclination angle) 1 ∞ (Pupil) 2 1275.444 (From pupil position) (Reflecting surface) Y -5 θ 40 ° Z 49.88 3 R _y 136.469 -4.580 1.4870 70.40 R _x 164.489 (From pupil position) K _y 0.7607 Y -45.956 θ 50 ° K _x -1.5983 Z 17.296 R ₂ 9.5727 × 10 ^-7 R ₃ -1.2540 × 10 ^-12 P ₂ -0.2493 P _3- 1.5581 4 R _y 114.274 4.580 1.4870 70.40 (Reflecting surface) R _x 114.451 K _y 0 K _x 0 R ₂ 3.1770 × 10 ^-7 R ₃ 6.1129 × 10 ^-13 P ₂ -0.2051 P ₃ 1.0083 5 R _y 136.469 R _x 164.489 K _y 0.7607 K _x -1.5983 R ₂ 9.5727 × 10 ^-7 R ₃ -1.2540 × 10 ^-12 P ₂ -0.2493 P ₃ -1.5581 6 ∞ (image display surface) (from pupil position) Y -22.440 θ 72.80 ° Z 71.052.

Example 19 Surface number Curvature radius Spacing Refractive index Abbe number (Decentering amount) (Inclination angle) 1 ∞ (Pupil) 2 79.298 6 1.6200 60.30 (From pupil position) Y -3.096 θ -15 ° Z 22 3 -39.864 _{1 1.7550 27.60 4 -57.753 5 R y} -28.332 1.5163 64.15 R x ∞ ( from pupil _{position) K y -0.2141 Y -9.567 θ 15} ° K x 0 Z 46.148 R 2 2.6794 × 10 -6 R 3 -2.1462 × 10 - ⁹ P ₂ 0.4329 P ₃ 0.5870 6 R _y -39.619 1.5163 64.15 (Reflecting surface) R _x -67.799 (From pupil position) K _y 0 Y -20.032 θ 0.981 ° K _x 0 Z 50.073 R ₂ 2.1459 × 10 ^-6 R ₃ -3.2048 × 10 ^-10 P ₂ -0.1395 P ₃ -0.9573 7 R _y -28.332 (From the pupil position) R _x ∞ Y -9.567 θ 15 ° K _y -0.2141 Z 46.148 K _x 0 R ₂ 2.6794 × 10 ^-6 R ₃ -2.1462 × 10 ^-9 P ₂ 0.4329 P ₃ 0.5870 8 ∞ (From the pupil position) (Image display surface) Y -16.158 θ 37.54 ° Z 34.338.

Example 20 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Tilt angle) 1 ∞ (Pupil) 2 R _y -293.705 (From pupil position) (Reflecting surface) R _x -241.700 Y 6.356 θ 30 ° K _y -7.2572 Z 50 K _x -15.1102 R ₂ 1.163 × 10 ^-10 R ₃ 4.0479 × 10 ^-11 P ₂ 14.0494 P ₃ -0.0016 3 -54.382 -13.393 1.6200 60.30 (from pupil position) Y -20.251 θ 51.21 ° Z 39.883 4 53.673 -3 1.7550 27.60 5 127.245 6 ∞ (From the pupil position) (Image display surface) -62.547 θ -135.03 ° Z 11.874.

Example 21 Surface number Curvature radius Spacing Refractive index Abbe number (Eccentricity) (Inclination angle) 1 ∞ (pupil) 2 R _y -805.661 1.5254 56.25 R _x 203.470 (from pupil position) K _y 0 Y -3.531 θ 32.54 ° K _x 0 Z 50 R ₂ -2.6651 × 10 ^-7 R ₃ 4.5387 × 10 ^-10 P ₂ -0.0707 P ₃ -0.1071 3 R _y -405.815 1.5254 56.25 (Reflecting surface) R _x -878.408 (from pupil position) K _y 0 Y -15.839 θ 30 ° K _x 0 Z 59.698 R ₂ 3.4069 × 10 ^-9 R ₃ -3.7768 × 10 ^-11 P ₂ 2.7869 P ₃ 0.0200 4 R _y -805.661 (from the pupil position) R _x 203.470 Y- 3.531 θ 32.54 ° K _y 0 Z 50 K _x 0 R ₂ -2.6651 × 10 ^-7 R ₃ 4.5387 × 10 ^-10 P ₂ -0.0707 P ₃ -0.1071 5 -44.471 -12.023 1.6200 60.30 (from the pupil position) Y -17.314 θ 88.33 ° Z 36.979 6 66.167 -1.520 1.7550 27.60 7 -390.352 8 ∞ (from pupil position) (image display surface) -61.997 θ -122.81 ° Z 19.852.

The above optical system of the present invention can be constructed, for example, as follows. [1] An optical system having a rotationally asymmetric surface shape, arranged at an angle with respect to the optical axis, and having at least one optical surface in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape, An optical system characterized in that there is a point on the optical surface where the surface shape is symmetric with respect to two directions orthogonal to each other in at least an arbitrary region on the optical surface.

[2] In the above optical system, at least at a point where the surface shape is symmetric with respect to two directions orthogonal to each other in a given arbitrary region, the above-mentioned cross section of the optical surface cut along one of the symmetric planes. The optical system according to the above [1], wherein the positions of the points satisfy the following formula. 0.05 × D <L ₀ <0.25 × D (1) where L ₀ is the distance from one end of the cross section close to the point to the point, and D is the outside of the cross section. Is the diameter.

[3] Optical having a rotationally asymmetric surface shape having at least one symmetric surface, arranged so as to be inclined with respect to the optical axis, and in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape. In an optical system having at least one surface, when the shape of the optical surface cut at the symmetry plane is represented by any of the following mathematical expressions, at least one maximum point or minimum point of the mathematical expression exists in the optical surface. An optical system characterized by: However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
CY is a Y-axis direction curvature, ak is a conic coefficient, and ac (n) is an aspherical surface coefficient. However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
C _0n is a coefficient of each term.

[4] The optical system according to the above [3], wherein the position of at least one of the maximum point and the minimum point of the mathematical formula representing the shape cut in the symmetry plane satisfies the following formula. 0.05 × D <L ₀ <0.25 × D (4) where L ₀ is the distance from one end of the cross section on the side close to the point to the point, and D is the outside of the cross section. Is the diameter.

[5] Optical having a rotationally asymmetric surface shape, arranged at an inclination with respect to the optical axis, and having at least one optical surface in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape. In the system, the surface shape is an anamorphic surface or a toric surface, and the origin of the surface shape is in the optical surface.

[6] The position of the origin in the cross section of the optical surface cut by either the plane of symmetry of the anamorphic surface or the toric surface satisfies the following expression: 5] The optical system as described above. 0.05 × D <L ₀ <0.25 × D (8) where L ₀ is the distance from one end on the side close to the origin to the origin, and D is the outer diameter of the cross section. is there.

[7] The optical system according to any one of [1] to [6], wherein the optical surface having the rotationally asymmetric shape is a reflecting surface in the optical system.

[8] The optical system according to any one of [1] to [7], wherein the optical system is used in a head- or face-mounted image display device together with an image display element. system.

[0134]

[9] The optical system has at least two surfaces and includes a first surface that forms a transmission surface and a second surface that forms a reflection surface, and the at least two surfaces are observed by an observer. It is arranged so as to be inclined with respect to the visual axis that is the central direction of the projected image, and the region between the first surface and the second surface is filled with a medium having a refractive index larger than 1. The optical system according to [8] above.

[10] The optical system according to the above [8], wherein the optical system has at least two reflecting mirrors arranged eccentrically to each other, and at least one of them is a concave mirror.

[11] The optical system has at least one concave mirror that is arranged to be inclined with respect to the visual axis that is the central direction of the projection image observed by the observer, and the concave mirror and the image display element The optical system according to the above [8], wherein at least one optical element having a positive refractive power is arranged between them.

[12] The optical system has at least three surfaces, and in order of passage of the light rays emitted from the image display element, at least a third surface forming a transmission surface and a second surface forming a reflection surface. The optical system according to the above [8], which includes a surface and a first surface forming a transmission surface.

[13] The optical system according to the above [12], wherein the first surface of the optical system forms a reflecting surface at the same time as a transmitting surface.

[14] The optical system has at least three surfaces, and in order of passage of the light rays emitted from the image display element, at least a second surface forming a reflective surface and a reflective surface at the same time as a transmissive surface, and a reflective surface. The optical system according to [8] above, which includes a fourth surface to be formed and a first surface to form a transmission surface.

[15] The above-mentioned [14], wherein the optical system carries out a light transmission of once and a second reflection on the second surface and a second reflection of light on the fourth surface.
Optical system as described.

[16] The optical system has a second surface having at least three surfaces and forming a reflecting surface at least at the same time as a transmitting surface in the order in which the light rays emitted from the image display element pass, and a reflecting surface. The optical system according to the above [8], further comprising a first surface that forms a transmission surface and a fourth surface that forms a reflection surface at the same time.

[17] The optical system has at least four surfaces, and in order of passage of light rays emitted from the image display element, at least a third surface forming a transmission surface and a fourth surface forming a reflection surface. A surface, a second surface that forms a reflective surface, and a first surface that forms a transmissive surface. [8]
Optical system as described.

[18] The above-mentioned [1], wherein the optical system reflects the light rays twice on the second surface.
7] The optical system as described above.

[19] The optical system according to the above [17], wherein the third surface of the optical system forms a reflecting surface at the same time as a transmitting surface.

[20] A second surface having at least four surfaces in the optical system, which performs at least one transmission and two reflections in the order in which the light rays emitted from the image display element pass, The optical system according to [8] above, which includes a fifth surface forming a reflecting surface, a fourth surface forming a reflecting surface, and a first surface forming a transmitting surface.

[0146]

As is apparent from the above description, according to the optical system of the present invention, in the optical system having the rotationally asymmetric optical surface in which the center of the outer shape of the optical surface does not coincide with the center of the surface shape, Since the point where the surface shape is symmetric with respect to the two directions orthogonal to the optical surface actually exists on the optical surface, the positioning of the optical surface with respect to the measuring machine is performed without depending on approximation. Since the point can be used as a reference, accurate surface shape measurement can be performed.

[Brief description of the drawings]

FIG. 1 is a sectional view of a first embodiment of an eyepiece optical system according to the present invention.

FIG. 2 is a sectional view of a second embodiment of the eyepiece optical system according to the present invention.

FIG. 3 is a sectional view of Example 3 of the eyepiece optical system according to the present invention.

FIG. 4 is a sectional view of Example 4 of the eyepiece optical system according to the present invention.

FIG. 5 is a sectional view of Example 5 of the eyepiece optical system according to the present invention.

FIG. 6 is a sectional view of Example 6 of the eyepiece optical system according to the present invention.

FIG. 7 is a sectional view of Example 7 of the eyepiece optical system according to the present invention.

FIG. 8 is a sectional view of an eyepiece optical system according to Example 8 of the present invention.

FIG. 9 is a sectional view of Example 9 of the eyepiece optical system according to the present invention.

FIG. 10 is a sectional view of Example 10 of the eyepiece optical system according to the present invention.

FIG. 11 is a sectional view of Embodiment 11 of the eyepiece optical system according to the present invention.

FIG. 12 is a sectional view of Embodiment 12 of the eyepiece optical system according to the present invention.

FIG. 13 is a sectional view of Embodiment 13 of the eyepiece optical system according to the present invention.

FIG. 14 is a sectional view of Embodiment 14 of the eyepiece optical system according to the present invention.

FIG. 15 is a sectional view of Embodiment 15 of the eyepiece optical system according to the present invention.

FIG. 16 is a sectional view of Embodiment 16 of the eyepiece optical system according to the present invention.

FIG. 17 is a sectional view of Embodiment 17 of the eyepiece optical system according to the present invention.

FIG. 18 is a sectional view of Embodiment 18 of the eyepiece optical system according to the present invention.

FIG. 19 is a sectional view of Embodiment 19 of the eyepiece optical system according to the present invention.

FIG. 20 is a sectional view of Example 20 of the eyepiece optical system according to the present invention.

21 is a sectional view of Embodiment 21 of the eyepiece optical system according to the present invention. FIG.

FIG. 22 is a diagram showing how distortion is generated by a rotationally asymmetric optical surface that is arranged to be inclined with respect to the optical axis.

FIG. 23 is a diagram showing how distortion is corrected by arranging a rotationally asymmetric optical surface that is tilted with respect to the optical axis so as to be displaced with respect to the optical axis.

FIG. 24 is a diagram showing an example of a surface shape in which a plurality of points having symmetrical surface shapes with respect to two orthogonal directions are present.

FIG. 25 is a side view of an example of a head- or face-mounted image display device using the optical system according to the present invention as an eyepiece optical system.

FIG. 26 is a diagram for defining the position of the center of the surface shape with respect to the outer diameter of the optical surface.

[Explanation of symbols]

1 ... Observer pupil position 2 ... Observer visual axis 3 ... First surface of optical system 4 ... Second surface of optical system 5 ... Third surface of optical system 6 ... Fourth surface of optical system 7 ... First surface of optical system 5 surfaces 8 ... Image display element 9 ... First reflecting mirror 10 ... Second reflecting mirror 11 ... Concave mirror 12 ... Optical element having positive refractive power 13 ... Anamorphic surface axis 14 ... Surface shape center 21 ... Eyepiece optical system 22 ... Image display element 31 ... Rotationally asymmetric optical surface 32 ... Optical axis of optical system 33 ... Center of surface shape 41 ... Point where surface shape is symmetrical with respect to two orthogonal directions 51 ... Optical Cross section of system 52 ... Both ends of cross section of optical surface 53 ... Center of surface shape

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Koichi Takahashi 2-43-2 Hatagaya, Shibuya-ku, Tokyo Olympus Optical Co., Ltd.

Claims (3)

[Claims] 1. An optical system having a rotationally asymmetric surface shape, arranged at an angle with respect to the optical axis, and having at least one optical surface in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape. In the above optical system, there is a point on the optical surface where the surface shape is symmetric with respect to two directions orthogonal to each other in at least an arbitrary area on the optical surface. 2. An optical surface having a rotationally asymmetric surface shape having at least one symmetric surface, arranged obliquely with respect to the optical axis, and having a center of a surface determined by the outer shape and a center of the surface shape not coincident with each other. In an optical system having at least one surface, when the shape of the optical surface cut at the symmetry plane is represented by any of the following mathematical expressions, at least one maximum point or minimum point of the mathematical expression exists in the optical surface. An optical system characterized by that. However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
CY is a Y-axis direction curvature, ak is a conic coefficient, and ac (n) is an aspherical surface coefficient. However, Z is the amount of deviation from the Y coordinate axis taken arbitrarily,
C _0n is a coefficient of each term. 3. An optical system having a rotationally asymmetric surface shape, arranged at an angle with respect to the optical axis, and having at least one optical surface in which the center of the surface determined by the outer shape does not coincide with the center of the surface shape. 2. The optical system according to claim 1, wherein the surface shape is an anamorphic surface or a toric surface, and the origin of the surface shape is in the optical surface.