Diffractive optical element, optical system, image pickup apparatus, and display apparatus
A diffractive optical element includes a diffractive area including annular sections concentrically arranged. At least one of the annular sections has a non-circular shape. A predetermined inequality is satisfied.
1 . A diffractive optical element comprising:
a diffractive area including annular sections concentrically arranged,
wherein at least one of the annular sections has a non-circular shape,
wherein the annular sections are rotationally symmetric and concentric, and
wherein the following inequalities are satisfied:
6
<
P
min
×
Rdc
/
Re
<
65
0.5
<
Rdc
/
Re
<
0.95
0.7
<
Rdc
/
RPm
<
1
.
5
0
where Rdc (mm) is a shortest one of distances from a center of the annular sections to an outer circumference of the diffractive area, Re (mm) is a radius of one of the annular sections which is farthest from the center, Pmin (μm) is a minimum value of an array pitch of the diffractive optical element, and RPm (mm) is a radius of the annulus having the minimum value Pmin.
2 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
0.8
<
1000
×
(
R
2
2
-
R
1
2
)
/
(
Re
×
Pmin
)
<
2
.
4
where R1 (mm) is a radius of a first annulus counted from the center, and R2 (mm) is a radius of a second annulus counted from the center.
3 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
0.4
<
fd
×
λ0
/
(
Re
×
P
min
)
<
1
.
2
0
where λ0 (μm) is a design wavelength of the diffractive optical element, and fd (mm) is a focal length on a diffractive surface.
4 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
0
.
0
5
<
Dm
/
Pmin
<
1.
where Dm (μm) is a grating height in an annulus having the minimum value Pmin.
5 . The diffractive optical element according to claim 1 , wherein annular ends are points where an outer peripheral area intersects with each annular section, where the annular sections have a non-circular shape, and wherein the following inequality is satisfied:
1.
5
<
P
o
u
t
m
/
Pmin
<
6
.
0
where Pout (μm) is an interval between adjacent annular ends among the annular sections in which the circumference is non-circular, and Pou tm (μm) is a minimum value of the interval Pout.
6 . The diffractive optical element according to claim 1 , wherein an outermost annulus in the diffractive optical element has the circumference that is non-circular, and the following inequality is satisfied:
3.
<
Lae
/
Re
<
6
.
0
where Lae (mm) is a length of an arc in the outermost annulus.
7 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
1
5
0
<
N
R
<
8
0
0
where NR is the number of annuli in the annular sections.
8 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
20
<
Ndc
<
300
where Ndc is the number of annuli having a radius larger than the shortest distance Rdc and smaller than the radius Re among the annular sections.
9 . The diffractive optical element according to claim 1 , wherein an optical material of the diffractive optical element includes a thermoplastic resin.
10 . The diffractive optical element according to claim 1 , wherein the diffractive optical element includes layers of a first diffraction grating made of a first material, and a second diffraction grating made of a second material different from the first material.
11 . The diffractive optical element according to claim 1 , wherein the diffractive optical element has an outer circumferential area in which no diffraction grating is formed outside an annulus having the radius Re.
12 . The diffractive optical element according to claim 1 , wherein the following inequality is satisfied:
-
5
.
0
<
(
Ψ
2
(
h
)
-
2
×
C
2
)
/
C
2
<
-
0
.
5
where h (mm) is a distance in a direction perpendicular to an optical axis in the diffractive optical element, an optical path difference function Ψ of a diffractive surface is Ψ(h)=C 2 h 2 +C 4 h 4 +C 6 h 6 . . . , Ψ2(h) is a second derivative value of the optical path difference function Ψ with respect to h, and Ci is a phase coefficient (i=2, 4, 6 . . . ).
13 . The diffractive optical element according to claim 1 , wherein the diffractive optical element has a gate portion, and
wherein in the diffractive area, a direction of a shortest length from the center and a direction of the gate portion are opposite to each other with respect to an annular rotation center.
14 . An optical system comprising the diffractive optical element according to claim 1 .
15 . An image pickup apparatus comprising:
the optical system according to claim 14 ; and
an image sensor configured to receive an optical image formed by the optical system.
16 . A display apparatus comprising:
a display element configured to display an image; and
the optical system according to claim 14 configured to guide light from the display element.