Optical: systems and elements – Prism – With reflecting surface
Reexamination Certificate
2000-03-31
2001-04-24
Spyrou, Cassandra (Department: 2872)
Optical: systems and elements
Prism
With reflecting surface
C359S431000
Reexamination Certificate
active
06222688
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to decentered optical systems and, more particularly, to a compact decentered optical system in which at least three reflecting surfaces having an image-forming power required for image formation are decentered.
Hitherto, an optical system in which a rotationally asymmetric curved surface having no plane of symmetry, e.g. a free-form surface, is three-dimensionally decentered has been proposed by the present applicant in Japanese Patent Application Unexamined Publication (KOKAI) No. 10-186237.
In the conventional three-dimensionally decentered optical system as disclosed in Japanese Patent Application Unexamined Publication (KOKAI) No. 10-186237, when a reflecting surface is formed by using a back coating mirror, the center points in the effective areas of the entrance, reflecting and exit surfaces of a prism or some points thereof are in one plane. Therefore, it is impossible to freely lay out large reflecting and transmitting surfaces owing to the interference between the effective apertures of the surfaces.
SUMMARY OF THE INVENTION
In view of the above-described problems associated with the prior art, an object of the present invention is to provide a fast and compact decentered optical system corrected for aberrations due to three-dimensional decentration by three-dimensionally disposing a rotationally asymmetric surface having no plane of symmetry.
To attain the above-described object, the present invention provides a decentered optical system including at least one optical surface that is a rotationally asymmetric curved surface having no plane of symmetry and having a positive power. The decentered optical system has an entrance surface, at least three reflecting surfaces, and an exit surface. At least one of intersections between an optical axis and the entrance surface, the reflecting surfaces and the exit surface is not in a plane where the other intersections are present.
In this case, it is desirable that the space lying between the entrance surface, the at least three reflecting surfaces and the exit surface should be filled with a medium having a refractive index larger than 1.
The function of the present invention will be described below.
According to the present invention, a rotationally asymmetric surface is formed from a curved surface having no plane of symmetry. Therefore, it is possible to correct rotationally asymmetric aberrations having no plane of symmetry that are produced by a three-dimensionally decentered optical system. Thus, it is possible to provide a decentered prism optical system or the like which is compact and has minimal aberrations and which is suitable for use as an image-forming optical system of an electronic camera or as an ocular optical system used in a head-mounted image observation apparatus.
The arrangement and operation of the present invention will be described below more specifically.
The basic decentered optical system according to the present invention is characterized by including at least one optical surface that is a rotationally asymmetric curved surface having no plane of symmetry and having a positive power.
In a case where the decentered optical system is used, for example, as an ocular optical system of a head-mounted image display apparatus, or as an image-forming optical system of a camera, an endoscope, etc., it is necessary in order to eliminate a dead space and minimize the overall size of the apparatus to dispose an image display device or an image-formation plane and each optical surface constituting the decentered optical system such that the constituent elements are accommodated in the apparatus in as compact a form as possible. Consequently, the optical system must inevitably be decentered three-dimensionally, and this causes rotationally asymmetric aberrations to occur. It is impossible to correct the rotationally asymmetric aberrations by only a rotationally symmetric optical system. The best surface configuration for correcting the rotationally asymmetric aberrations due to three-dimensional decentration is a rotationally asymmetric surface. Therefore, in the decentered optical system according to the present invention, a rotationally asymmetric surface having no plane of symmetry and having a positive power is disposed in the optical system to effect image formation and to correct the rotationally asymmetric aberrations.
A free-form surface used in the present invention as a rotationally asymmetric surface having no plane of symmetry is defined by the following equation. The Z-axis of the defining equation is the axis of the free-form surface.
Z
=
cr
2
/
[
1
+
{
1
-
(
1
+
k
)
c
2
r
2
}
]
+
∑
j
=
2
66
C
j
X
m
Y
n
(
a
)
In Eq. (a), the first term is a spherical surface term, and the second term is a free-form surface term.
In the spherical surface term:
c: the curvature at the vertex
k: a conic constant r={square root over ( )} (X
2
+Y
2
)
The free-form surface term is given by
∑
j
=
2
66
C
j
X
m
Y
n
=
C
2
X
+
C
3
Y
+
C
4
X
2
+
C
5
XY
+
C
6
Y
2
+
C
7
X
3
+
C
8
X
2
Y
+
C
9
XY
2
+
C
10
Y
3
+
C
11
X
4
+
C
12
X
3
Y
+
C
13
X
2
Y
2
+
C
14
XY
3
+
C
15
Y
4
+
C
16
X
5
+
C
17
X
4
Y
+
C
18
X
3
Y
2
+
C
19
X
2
Y
3
+
C
20
XY
4
+
C
21
Y
5
+
C
22
X
6
+
C
23
X
5
Y
+
C
24
X
4
Y
2
+
C
25
X
3
Y
3
+
C
26
X
2
Y
4
+
C
27
XY
5
+
C
28
Y
6
+
C
29
X
7
+
C
30
X
6
Y
+
C
31
X
5
Y
2
+
C
32
X
4
Y
3
+
C
33
X
3
Y
4
+
C
34
X
2
Y
5
+
C
35
XY
6
+
C
36
Y
7
…
where C
j
(j is an integer of 2 or higher) are coefficients.
In general, the above-described free-form surface does not have planes of symmetry in both the XZ- and YZ-planes. However, a free-form surface having only one plane of symmetry parallel to the YZ-plane is obtained by making all terms of odd-numbered degrees with respect to X zero. A free-form surface having only one plane of symmetry parallel to the XZ-plane is obtained by making all terms of odd-numbered degrees with respect to Y zero. Therefore, at least one of free-form surfaces used in the present invention is a free-form surface in which at least one of the terms of odd-numbered degrees with respect to X is not zero and at least one of the terms of odd-numbered degrees with respect to Y is not zero.
The above-described free-form surface as a rotationally asymmetric surface having no plane of symmetry may also be defined by Zernike polynomials. That is, the configuration of the free-form surface may be defined by the following equation (b). The Z-axis of the defining equation (b) is the axis of Zernike polynomial.
x
=
R
×
cos
(
A
)
y
=
R
×
sin
(
A
)
z
=
D
2
+
D
3
R
cos
(
A
)
+
D
4
R
sin
(
A
)
+
D
5
R
2
cos
(
2
A
)
+
D
6
(
R
2
-
1
)
+
D
7
R
2
sin
(
2
A
)
+
D
8
R
3
cos
(
3
A
)
+
D
9
(
3
R
3
-
2
R
)
cos
(
A
)
+
D
10
(
3
R
3
-
2
R
)
sin
(
A
)
+
D
11
R
3
sin
(
3
A
)
+
D
12
R
4
cos
(
4
A
)
+
D
13
(
4
R
4
-
3
R
2
)
cos
(
2
A
)
+
D
14
(
6
R
4
-
6
R
2
+
1
)
+
D
15
(
4
R
4
-
3
R
2
)
sin
(
2
A
)
+
D
16
R
4
sin
(
4
A
)
+
D
17
R
5
cos
(
5
A
)
+
D
18
(
5
R
5
-
4
R
3
)
cos
(
3
A
)
+
D
19
(
10
R
5
-
12
R
3
+
3
R
)
cos
(
A
)
+
D
20
(
10
R
5
-
12
R
3
+
3
R
)
sin
(
A
)
+
D
21
(
5
R
5
-
4
R
3
)
sin
(
3
A
)
+
D
22
R
5
sin
(
5
A
)
+
D
23
R
6
cos
&it
Nagata Tetsuo
Togino Takayoshi
Olympus Optical Co,. Ltd.
Pillsbury & Winthrop LLP
Robinson Mark A.
Spyrou Cassandra
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