Three-dimensional display apparatus, head-up display system, and mobile body
A three-dimensional display apparatus includes a display panel and an optical element. The display panel includes a display surface. The display surface extends in a first direction, extends in a second direction orthogonal to the first direction. The first direction corresponds to a parallax direction of user's eyes seeing an image. The display surface curves around a central axis extending in the second direction. The display surface includes subpixels arranged in a grid pattern in the first direction and the second direction within the display surface. The optical element is arranged along the display surface, and the optical element includes strip-shaped regions, each of which extends in a certain direction. The optical element is configured to define a beam direction of image light emitted from the subpixels. The display surface forms an arc in a cross-section that is orthogonal to the second direction. A position of an eye box, in the first direction, is set to a position within a distance r sin θ from the center of the arc. The r represents a diameter of the arc. The θ represents an angle formed by a linear line connecting between a first direction edge of the display panel and a center of the arc and a linear line connecting between a first direction center of the display panel and the center of the arc viewed in the second direction. The eye box is an acceptable range of a position of the user's eyes when the user sees the image.
1. A three-dimensional display apparatus comprising:
a display panel including a display surface that extends in a first direction, extends in a second direction orthogonal to the first direction, curves around a central axis extending in the second direction, and includes subpixels arranged in a grid pattern in the first direction and the second direction within the display surface, the first direction is corresponding to a parallax direction of a user's eyes of a user seeing an image; and
an optical element that is arranged along the display surface, and the optical element includes strip-shaped regions, each of which extends in a certain direction, and is configured to define a beam direction of image light emitted from the subpixels,
wherein the display surface forms an arc in a cross-section that is orthogonal to the second direction,
wherein a position of an eye box, in the first direction, is set to a position within a distance r sin θ from the center of the arc, where r represents a diameter of the arc and θ represents an angle formed by a linear line connecting between a first direction edge of the display panel and a center of the arc and a linear line connecting between a first direction center of the display panel and the center of the arc viewed in the second direction, and the eye box is an acceptable range of a position of the user's eyes when the user sees the image,
wherein the eye box is set to the position, in a third direction orthogonal to the first direction and the second direction, where a certain number or more of subpixels for displaying a subject eye image are included in the first direction in a visible region most remote in the first direction from the center of the display panel on the display surface, and
wherein, when L represents a length of the display panel in a first in-plane direction corresponding to the first direction of the display surface, n represents the number of subpixels that are continuously arranged in the first in-plane direction and display the subject eye image, and E represents an interocular distance between the user's eyes, a distance d of the eye box from the center of the display surface satisfies the following equation:
[
Equation
1
]
d
=
<
W
2
×
r
W
2
-
(
2
n
-
1
)
×
E
n
.
2. The three-dimensional display apparatus according to claim 1 ,
wherein the eye box is set to the position, in the third direction orthogonal to the first direction and the second direction, equal to or longer than a distance r−r cos θ toward the center of the arc from the center of the display panel.
3. The three-dimensional display apparatus according to claim 1 ,
wherein a curvature of the arc is located such that (n−1)-number or more subpixels displaying a subject eye image are included in a visible region that is most remote in the first direction from the first direction center of the display surface.
4. The three-dimensional display apparatus according to claim 3 ,
wherein the curvature of the arc satisfies:
E
-
E
1
<
E
/
n
,
E
1
=
E
11
+
E
12
,
[
Equation
2
]
E
11
:
1
2
E
=
r
tan
:
r
cos
2
sin
+
r
sin
θ
-
1
2
E
,
and
[
Equation
3
]
E
12
:
1
2
E
=
r
tan
θ
-
E
12
:
r
sin
θ
+
r
cos
2
θ
sin
θ
.
5. A head-up display system comprising:
a three-dimensional display apparatus that includes:
a display panel including a display surface that extends in a first direction, extends in a second direction orthogonal to the first direction, curves around a central axis extending in the second direction, and includes subpixels arranged in a grid pattern in the first direction and the second direction within the display surface, the first direction is corresponding to a parallax direction of user's eyes seeing an image; and
an optical element that is arranged along the display surface and, the optical element includes strip-shaped regions, each of which extends in a certain direction, and is configured to define a beam direction of image light emitted from the subpixels,
wherein the display surface forms an arc in a cross-section that is orthogonal to the second direction,
wherein a position of an eye box, in the first direction, is set to a position within a distance r sin θ from the center of the arc, where r represents a diameter of the arc and θ represents an angle formed by a linear line connecting between a first direction edge of the display panel and a center of the arc and a linear line connecting between a first direction center of the display panel and the center of the arc viewed in the second direction, and the eye box is an acceptable range of a position of the user's eyes when the user sees the image,
wherein the eye box is set to the position, in a third direction orthogonal to the first direction and the second direction, where a certain number or more of subpixels for displaying a subject eye image are included in the first direction in a visible region most remote in the first direction from the center of the display panel on the display surface, and
wherein, when L represents a length of the display panel in a first in-plane direction corresponding to the first direction of the display surface, n represents the number of subpixels that are continuously arranged in the first in-plane direction and display the subject eye image, and E represents an interocular distance between the user's eyes, a distance d of the eye box from the center of the display surface satisfies the following equation:
[
Equation
1
]
d
=
<
W
2
×
r
W
2
-
(
2
n
-
1
)
×
E
n
.
6. The head-up display system according to claim 5 ,
wherein a curvature of the arc is located such that (n−1)-number or more subpixels displaying a subject eye image are included in a visible region that is most remote in the first direction from the first direction center of the display surface.
7. The head-up display system according to claim 6 ,
wherein the curvature of the arc satisfies:
E
-
E
1
<
E
/
n
,
E
1
=
E
11
+
E
12
,
[
Equation
2
]
E
11
:
1
2
E
=
r
tan
:
r
cos
2
sin
+
r
sin
θ
-
1
2
E
,
and
[
Equation
3
]
E
12
:
1
2
E
=
r
tan
θ
-
E
12
:
r
sin
θ
+
r
cos
2
θ
sin
θ
.
8. A mobile body comprising:
a head-up display system provided with a three-dimensional display apparatus that includes:
a display panel including a display surface that extends in a first direction, extends in a second direction orthogonal to the first direction, the display panel curves around a central axis extending in the second direction, and the display panel includes subpixels arranged in a grid pattern in the first direction and the second direction within the display surface, the first direction is corresponding to a parallax direction of user's eyes seeing an image; and
an optical element that is arranged along the display surface and, the optical element includes strip-shaped regions, each of which extends in a certain direction, and is configured to define a beam direction of image light emitted from the subpixels,
wherein the display surface forms an arc in a cross-section that is orthogonal to the second direction,
wherein a position of an eye box, in the first direction, is set to a position within a distance r sin θ from the center of the arc, where r represents a diameter of the arc and θ represents an angle formed by a linear line connecting between a first direction edge of the display panel and a center of the arc and a linear line connecting between a first direction center of the display panel and the center of the arc viewed in the second direction, and the eye box is an acceptable range of a position of the user's eyes when the user sees the image,
wherein the eye box is set to the position, in a third direction orthogonal to the first direction and the second direction, where a certain number or more of subpixels for displaying a subject eye image are included in the first direction in a visible region most remote in the first direction from the center of the display panel on the display surface, and
wherein, when L represents a length of the display panel in a first in-plane direction corresponding to the first direction of the display surface, n represents the number of subpixels that are continuously arranged in the first in-plane direction and display the subject eye image, and E represents an interocular distance between the user's eyes, a distance d of the eye box from the center of the display surface satisfies the following equation:
[
Equation
1
]
d
=
<
W
2
×
r
W
2
-
(
2
n
-
1
)
×
E
n
.
9. The mobile body according to claim 8 ,
wherein a curvature of the arc is located such that (n−1)-number or more subpixels displaying a subject eye image are included in a visible region that is most remote in the first direction from the first direction center of the display surface.
10. The mobile body according to claim 9 ,
wherein the curvature of the arc satisfies:
E
-
E
1
<
E
/
n
,
E
1
=
E
11
+
E
12
,
[
Equation
2
]
E
11
:
1
2
E
=
r
tan
:
r
cos
2
sin
+
r
sin
θ
-
1
2
E
,
and
[
Equation
3
]
E
12
:
1
2
E
=
r
tan
θ
-
E
12
:
r
sin
θ
+
r
cos
2
θ
sin
θ
.