Optical system and display apparatus
An optical system guides a light beam from an image display element to an exit pupil and includes, in order from an exit pupil side to an image display element side, a first transmissive reflective surface, a second transmissive reflective surface, and an optical element disposed closer to the exit pupil than the first transmissive reflective surface. The optical element includes, in order from the exit pupil side to the image display element side, a first optical element made of a first optical material and a second optical element made of a second optical material different from the first optical material. The first and second optical elements are cemented together, and a diffraction grating is formed on a cemented surface. The diffraction grating includes a grating surface and a grating wall surface, the grating surface having a convex shape facing the image display element side. A predetermined inequality is satisfied.
1 . An optical system configured to guide a light beam from an image display element to an exit pupil, the optical system comprising, in order from an exit pupil side to an image display element side:
a first transmissive reflective surface;
a second transmissive reflective surface; and
an optical element disposed closer to the exit pupil than the first transmissive reflective surface,
wherein the optical element includes, in order from the exit pupil side to the image display element side, a first optical element made of a first optical material and a second optical element made of a second optical material different from the first optical material,
wherein the first optical element and the second optical element are cemented together, and a diffraction grating is formed on a cemented surface of the first optical element and the second optical element,
wherein the diffraction grating includes a grating surface contributing to diffraction and a grating wall surface adjacent to the grating surface in a radial direction, the grating surface having a convex shape facing the image display element side, and
wherein the following inequalities are satisfied:
0.5
≤
d
1
≤
2
0
.
0
0.02
≤
d
2
≤
0
.
4
0
where d1 [mm] is a thickness of the first optical material in an optical axis direction,
and d2 [mm] is a thickness of the second optical material in the optical axis direction.
2 . The optical system according to claim 1 , wherein the first optical material is a thermoplastic resin.
3 . The optical system according to claim 1 , wherein the second optical material is a UV curable resin.
4 . The optical system according to claim 1 , wherein the following inequality is satisfied:
0
.
0
2
≤
❘
"\[LeftBracketingBar]"
n
1
-
n
2
❘
"\[RightBracketingBar]"
≤
0.2
where n1 is a refractive index of the first optical material for d-line, and n2 is a refractive index of the second optical material for the d-line.
5 . The optical system according to claim 1 , wherein the following inequality is satisfied:
5
≤
❘
"\[LeftBracketingBar]"
v
1
-
v
2
❘
"\[RightBracketingBar]"
where ν1 is an Abbe number based on d-line of the first optical material, and ν2 is an Abbe number based on the d-line of the second optical material.
6 . The optical system according to claim 1 , wherein the following inequalities are satisfied:
n
1
>
n
2
v
1
>
v
2
where n1 is a refractive index of the first optical material for d-line, n2 is a refractive index of the second optical material for the d-line, ν1 is an Abbe number based on the d-line of the first optical material, and ν2 is an Abbe number based on the d-line of the second optical material.
7 . The optical system according to claim 1 , wherein the following inequalities are satisfied:
25
≤
v
1
≤
6
0
18
≤
v
2
≤
4
0
where ν1 is an Abbe number based on d-line of the first optical material, and ν2 is an Abbe number based on the d-line of the second optical material.
8 . The optical system according to claim 1 , wherein the following inequality is satisfied:
0
.
0
0
1
≤
h
≤
0
.
0
2
0
where h [mm] is a grating height of the diffraction grating.
9 . The optical system according to claim 1 , wherein the following inequality is satisfied:
0
.
0
1
≤
P
min
where Pmin [mm] is a minimum grating pitch of the diffraction grating.
10 . The optical system according to claim 1 , wherein the following inequality is satisfied:
N
≤
1
0
0
0
where N is the number of annuli of the diffraction grating.
11 . The optical system according to claim 1 , wherein the first optical material has pencil hardness higher than 3H, and the second optical material has a pencil hardness lower than 3H.
12 . The optical system according to claim 1 , wherein an optical surface facing the exit pupil is made of acrylic resin.
13 . The optical system according to claim 1 , wherein a surface of the second optical material that faces the cemented surface is the first transmissive reflective surface.
14 . A display apparatus comprising:
the optical system according to claim 1 ; and
an image display element configured to display an image.