Ocular optical system and head mounted display
An ocular optical system including a Fresnel lens having a plurality of Fresnel zones formed on a lens surface on an observation object side, the plurality of Fresnel zones being arranged concentrically side by side along an aspherical surface having a shape which is rotationally symmetric with respect to a central axis of the Fresnel lens, the ocular optical system satisfying the conditional expression 0<PAE1/PAC1≤0.50, where PAE1 represents an average pitch in a radial direction of Fresnel zones formed in a portion having a radius of 15 mm or more from the central axis of the Fresnel lens, and PAC1 represents an average pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens excluding a first Fresnel zone.
1. An ocular optical system comprising:
a Fresnel lens including a plurality of Fresnel zones formed on a lens surface on an observation object side, wherein
the plurality of Fresnel zones are arranged concentrically side by side along an aspherical surface having a shape which is rotationally symmetric with respect to a central axis of the Fresnel lens, and satisfy the following conditional expression:
0< PAE 1/ PAC 1≤0.50,
where
PAE1 represents an average pitch in a radial direction of Fresnel zones formed in a portion having a radius of 15 mm or more from the central axis of the Fresnel lens out of the plurality of Fresnel zones, and
PAC1 represents an average pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens excluding a first Fresnel zone located on a most central axis side of the Fresnel lens out of the plurality of Fresnel zones,
wherein
the aspherical surface is expressed by using the following expression:
[
Expression
1
]
Z
d
=
y
2
/
R
d
1
+
1
-
(
1
+
k
d
)
y
2
/
R
d
2
+
∑
i
=
2
10
A
2
i
×
y
2
i
where
Z d represents a sag amount of the aspherical surface at a distance y from the central axis of the Fresnel lens,
R d represents a radius of curvature of a reference spherical surface,
k d represents a conic constant, and
A 2i represents a (2×i)-order aspherical coefficient, and
the following expression is satisfied:
k d ≤−5.0.
2. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
0< PAE 2/ PAC 1≤0.55,
where
PAE2 represents an average pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm to 22.5 mm from the central axis of the Fresnel lens out of the plurality of Fresnel zones.
3. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
0< PAE 3/ PAC 1≤0.60,
where
PAE3 represents an average pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm to 20 mm from the central axis of the Fresnel lens out of the plurality of Fresnel zones.
4. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
PAC 1≥1.0 [mm].
5. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
PMX 1/ PMN 1≥10.0,
where
PMX1 represents a maximum pitch in the radial direction of the plurality of Fresnel zones, and
PMN1 represents a minimum pitch in the radial direction of the plurality of Fresnel zones.
6. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
1< PMX 2/ PMN 2≤7.5,
where
PMX2 represents a maximum pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens out of the plurality of Fresnel zones, and
PMN2 represents a minimum pitch in the radial direction of the Fresnel zones formed in the portion having the radius of 15 mm or less from the central axis of the Fresnel lens out of the plurality of Fresnel zones.
7. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
1< PMX 3/ PMN 3≤2.5,
where
PMX3 represents a maximum pitch in the radial direction of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens excluding the first Fresnel zone out of the plurality of Fresnel zones, and
PMN3 represents a minimum pitch in the radial direction of the Fresnel zones formed in the portion having the radius of 15 mm or less from the central axis of the Fresnel lens excluding the first Fresnel zone out of the plurality of Fresnel zones.
8. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
QE 1/ QC 1≥2.0,
where
QE1 represents the number of Fresnel zones formed in a portion having a radius of 15 mm to 22.5 mm from the central axis of the Fresnel lens out of the plurality of Fresnel zones, and
QC1 represents the number of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens excluding the first Fresnel zone out of the plurality of Fresnel zones.
9. The ocular optical system according to claim 1 , wherein
the following conditional expression is satisfied:
QE 2/ QC 1≥1.0,
where
QE2 represents the number of Fresnel zones formed in a portion having a radius of 15 mm to 20 mm from the central axis of the Fresnel lens out of the plurality of Fresnel zones, and
QC1 represents the number of Fresnel zones formed in a portion having a radius of 15 mm or less from the central axis of the Fresnel lens excluding the first Fresnel zone out of the plurality of Fresnel zones.
10. The ocular optical system according to claim 1 , wherein
wall surface portions of the plurality of Fresnel zones are provided with light-shielding members.
11. The ocular optical system according to claim 1 , wherein
an outer diameter of the Fresnel lens is 45 mm to 70 mm.
12. A head mounted display comprising:
an image display part capable of displaying an image; and
an ocular optical system for observing an image displayed on the image display part, wherein the ocular optical system is the ocular optical system according to claim 1 .