Virtual image display apparatus with curved surface having both positive and negative curvature and functioning as both reflection surface and refraction surface

1. A virtual image display apparatus comprising:

a light guide member which includes two or more non-axisymmetric curved surfaces and is a part of an optical system, an intermediate image being formed inside the light guide member, wherein at least one of the two or more non-axisymmetric curved surfaces of the light guide member comprises an opposite-sign curvature curved surface which includes at least one opposite-sign curvature point different in sign of curvature depending on direction such that the opposite-sign curvature curved surface has a positive or negative curvature in an x-direction from a point on the opposite-sign curvature curved surface and the opposite-sign curvature curved surface has a negative or positive curvature, respectively, in a y-direction from the point on the opposite-sign curvature curved surface, the opposite-sign curvature curved surface is a surface at a light incidence side of the light guide member and functions as a reflection surface for video light and also functions as a refraction surface for the video light, wherein the light guide member comprises:

a first surface;

a second surface;

a third surface arranged to face the first surface; and

a video element which generates the video light, wherein the video light is reflected by the third surface, is reflected by the first surface, is reflected by the second surface, is transmitted through the first surface, and reaches an observation side.

2. The virtual image display apparatus according to claim 1 ,

wherein the light guide member causes the video light and external light to be visually recognized, and

when an external scene is visually recognized through the first surface and the third surface, diopter is substantially 0.

3. The virtual image display apparatus according to claim 1 ,

wherein, in the light guide member, the opposite-sign curvature curved surface is located between the first surface and the third surface when following a plurality of surfaces constituting the light guide member around the light guide member.

4. The virtual image display apparatus according to claim 1 ,

wherein, for each surface in the light guide member, when an expression of a surface shape is expanded as a polynomial in terms of orthogonal coordinates x and y extending in a tangential direction with the origin of each surface as a reference, and the surface shape is specified as z, and

in terms of the expression of the opposite-sign curvature curved surface, when a quadratic differential value in an x direction of z at the origin is a and a quadratic differential value in a y direction of z at the origin is b, the relationship a<0<b or b<0<a is established.

5. The virtual image display apparatus according to claim 4 ,

wherein, for the quadratic differential value of the opposite-sign curvature curved surface in the light guide member, 1×10 −3 <|a−b| is satisfied.

6. The virtual image display apparatus according to claim 1 ,

wherein, when an expression of a surface shape is expanded as a polynomial in terms of orthogonal coordinates x and y extending in a tangential direction from the origin with the origin of each surface constituting the optical system as a reference, and the coefficient of a term x m ·y n of a polynomial expression representing a k-th surface is Ak m,n , the following conditions of (1) to (3):

−10 −1 <A 1 0,2 +A 1 2,0 <10 −2 and −10 −1 <A 3 0,2 +A 3 2,0 <10 −2   (1)

| A 1 2,0 −A 1 0,2 |<10 −1 and | A 3 2,0 −A 3 0,2 |<10 −1   (2)

| A 1 2,0 −A 3 2,0 |<10 −2 and | A 1 0,2 −A 3 0,2 |<10 −2   (3)

are satisfied.

7. The virtual image display apparatus according to claim 1 ,

wherein a half mirror is formed on the second surface, the video light is provided to an observer, a light transmission member is arranged integrally outside the second surface, diopter to external light is substantially set to 0, and external light and video light are provided to the observer in an overlapping manner.

8. The virtual image display apparatus according to claim 1 , further comprising:

a projection lens which makes video light from the video element enter the light guide member,

wherein at least a part of the light guide member and the projection lens constitute a relay optical system which forms the intermediate image.

9. The virtual image display apparatus according to claim 8 ,

wherein the projection lens is constituted by an axisymmetric lens and includes at least one aspheric surface.

10. The virtual image display apparatus according to claim 8 ,

wherein the projection lens includes at least one non-axisymmetric aspheric surface.

11. The virtual image display apparatus according to claim 1 ,

wherein the optical system including the light guide member covers a part in front of the eyes of the observer, and a portion where the front of the eyes is not covered is provided.

12. The virtual image display apparatus according to claim 1 ,

wherein the video element has a signal light forming portion which emits signal light modulated corresponding to an image, and a scanning optical system which scans signal light entering from the signal light forming portion to emit signal light as scanning light.

13. The virtual image display apparatus according to claim 1 , wherein the first and third surfaces are non-axisymmetric curved surfaces.

14. A virtual image display apparatus comprising:

a light guide member configured to form an intermediate image and comprising:

a first surface;

a third surface arranged with the first surface so that the first and third surfaces face each other, wherein the light guide member has an opposite-sign curvature curved surface which includes different curvatures depending on direction such that the opposite-sign curvature curved surface has a positive or negative curvature in an x-direction from a point on the opposite-sign curvature curved surface and the opposite-sign curvature curved surface has a negative or positive curvature, respectively, in a y-direction from the point on the opposite-sign curvature curved surface, the opposite-sign curvature curved surface is a surface at a light incidence side of the light guide member and functions as a reflection surface for video light and also functions as a refraction surface for the video light; and

a video element which generates the video light, wherein the video light is reflected by the third surface, is reflected by the first surface, is reflected by a second surface, is transmitted through the first surface, and then reaches an observation side.

15. A method of displaying an image, the method comprising:

providing a light guide member having two or more non-axisymmetric curved surfaces, the light guide member comprising:

a first surface;

a second surface; and

a third surface arranged to face the first surface, wherein the light guide member is a part of an optical system and is configured to form an intermediate image inside the light guide member, and wherein the light guide member has an opposite-sign curvature curved surface which includes at least one opposite-sign curvature point different in sign of curvature depending on direction such that the opposite-sign curvature curved surface has a positive or negative curvature in an x-direction from a point on the opposite-sign curvature curved surface and the opposite-sign curvature curved surface has a negative or positive curvature, respectively, in a y-direction from the point on the opposite-sign curvature curved surface, the opposite-sign curvature curved surface is a surface at a light incidence side of the light guide member and functions as a reflection surface for video light and also functions as a refraction surface for the video light;

generating the video light from a video element; and

directing the video light to the light guide member so that: (1) the video light is totally reflected by the third surface, (2) is totally reflected by the first surface, (3) is reflected by the second surface, (4) is transmitted through the first surface, and (5) then reaches an observation side.

16. The method of claim 15 , wherein the directing comprises directing the video light to the light guide member so that the video light:

(1) is reflected by the third surface,

(2) is reflected by the first surface after being reflected from the third surface,

(3) is reflected by the second surface after being reflected from the first surface,

(4) is transmitted through the first surface after being reflected from the second surface, and

(5) reaches an observation side from the second surface.

17. The virtual image display apparatus according to claim 1 ,

wherein the x direction corresponds to a first direction, and in the y direction corresponding to a second direction orthogonal to the first direction.

18. The virtual image display apparatus according to claim 17 ,

wherein the first direction is a horizontal direction defined by a direction of alignment of eyes along the face.

19. The virtual image display apparatus according to claim 1 , wherein:

the opposite-sign curvature curved surface includes different curvatures located at the light incidence side of light guide member and depending on direction, and

the x- and y-directions are orthogonal to each other.