Optical system for camera and camera apparatus

A compact optical system capable of providing a clear image of minimal distortion even at a wide field angle. The optical system is a decentered optical system (10). Curved surfaces (3 and 4) constituting the optical system include at least one rotationally asymmetric surface having no axis of rotational symmetry in nor out of the surface. To correct rotationally asymmetric aberrations due to decentration by the rotationally asymmetric surface, the following condition is satisfied: EQU -1000<FX/FXn<1000 (1-1) PA1 where FX is the focal length in the X-direction of the optical system, and FXn is the focal length in the X-direction of that portion of the rotationally asymmetric surface on which an axial principal ray strikes.

BACKGROUND OF THE INVENTION 
The present invention relates to an optical system and, more particularly, 
to a decentered optical system having power, which comprises a decentered 
reflecting surface. 
There has heretofore been known a compact reflecting decentered optical 
system as disclosed in Japanese Pat. Appln. Laid-Open (KOKAI) No. 
59-84201. This is an invention of a one-dimensional light-receiving lens 
comprising a cylindrical reflecting surface; therefore, two-dimensional 
imaging cannot be effected with the conventional optical system. Japanese 
Pat. Appln. Laid-Open (KOKAI) No. 62-144127 discloses an optical system 
wherein the identical cylindrical surface is used twice to effect 
reflection in order to reduce spherical aberration in the above-mentioned 
invention. Japanese Pat. Appln. Laid-Open (KOKAI) No. 62-205547 discloses 
the use of an aspherical reflecting surface as a reflecting surface, but 
makes no mention of the configuration of the reflecting surface. 
U.S. Pat. Nos. 3,810,221 and 3,836,931 both disclose an example in which a 
rotationally symmetric aspherical mirror and a lens system having a 
surface which has only one plane of symmetry are used to constitute a 
finder optical system of a reflex camera. In this example, however, the 
surface having only one plane of symmetry is utilized for the purpose of 
correcting the tilt of a virtual image for observation. 
Japanese Pat. Appln. Laid-Open (KOKAI) No. 1-257834 (U.S. Pat. No. 
5,274,406) discloses an example in which a surface having only one plane 
of symmetry is used for a reflecting mirror to correct image distortion in 
a back projection type television. In this example, however, a projection 
lens system is used for projection onto a screen, and the surface having 
only one plane of symmetry is used for correction of image distortion. 
Japanese Pat. Appln. Laid-Open (KOKAI) No. 7-333551 discloses an example of 
a back-coated mirror type decentered optical system using an anamorphic 
surface and a toric surface as an observation optical system. However, the 
decentered optical system is not sufficiently corrected for aberrations, 
including image distortion. 
None of the above-described prior art use a surface having only one plane 
of symmetry as a back-coated mirror to form a turn-back optical path. 
In the conventional rotationally symmetric optical systems, a transmitting 
rotationally symmetric lens having refracting power is assigned to exert 
the required refracting power. Therefore, many constituent elements are 
needed for aberration correction. In the conventional decentered optical 
systems, however, an imaged figure or the like is undesirably distorted 
and the correct shape cannot be recorded unless aberrations of the formed 
image are favorably corrected and, particularly, rotationally asymmetric 
distortion is favorably corrected. 
In a rotationally symmetric optical system comprising a refracting lens 
which is formed from a surface rotationally symmetric about an optical 
axis, a straight-line optical path is formed. Therefore, the whole optical 
system undesirably lengthens in the direction of the optical axis, 
resulting in an unfavorably large-sized apparatus. 
In view of the problems associated with the prior art, an object of the 
present invention is to provide a compact optical system capable of 
providing a clear image of minimal distortion even at a wide field angle. 
SUMMARY OF THE INVENTION 
To attain the above-described object, the present invention provides a 
decentered optical system including at least one curved surface with a 
rotationally asymmetric surface configuration having no axis of rotational 
symmetry in nor out of the surface, wherein rotationally asymmetric 
aberrations due to decentration are corrected by the rotationally 
asymmetric surface. 
According to a first aspect of the present invention, there is provided a 
decentered optical system including at least one rotationally asymmetric 
surface having no axis of rotational symmetry in nor out of the surface, 
wherein, assuming that a light ray emanating from the center of an object 
point and passing through the center of a pupil to reach the center of an 
image is defined as a principal ray, and that a Y-axis is taken in the 
decentration plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
X-axis direction are made to enter the optical system from the entrance 
side thereof, and the sine of an angle formed between the two rays as 
projected on the XZ-plane at the exit side of the optical system is 
denoted by NA'X, and further that a value obtained by dividing the 
distance d between the parallel rays by NA'X is denoted by FX, and the 
focal length in the X-axis direction of that portion of the rotationally 
asymmetric surface on which the axial principal ray strikes is denoted by 
FXn, the following condition is satisfied to correct rotationally 
asymmetric aberrations due to decentration by the rotationally asymmetric 
surface: 
EQU -1000&lt;FX/FXn&lt;1000 (1-1) 
According to a second aspect of the present invention, there is provided a 
decentered optical system including at least one rotationally asymmetric 
surface having no axis of rotational symmetry in nor out of the surface, 
wherein, assuming that a light ray emanating from the center of an object 
point and passing through the center of a pupil to reach the center of an 
image is defined as a principal ray, and that a Y-axis is taken in the 
decentration plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
Y-axis direction are made to enter the optical system from the entrance 
side thereof, and the sine of an angle formed between the two rays in the 
YZ-plane at the exit side of the optical system is denoted by NA'Y, and 
further that a value obtained by dividing the distance d between the 
parallel rays by NA'Y is denoted by FY, and the focal length in the Y-axis 
direction of that portion of the rotationally asymmetric surface on which 
the axial principal ray strikes is denoted by FYn, the following condition 
is satisfied to correct rotationally asymmetric aberrations due to 
decentration by the rotationally asymmetric surface: 
EQU -1000&lt;FY/FYn&lt;1000 (2-1) 
According to a third aspect of the present invention, there is provided a 
decentered optical system including at least one rotationally asymmetric 
surface having no axis of rotational symmetry in nor out of the surface, 
wherein, assuming that a light ray emanating from the center of an object 
point and passing through the center of a pupil to reach the center of an 
image is defined as a principal ray, and that a Y-axis is taken in the 
decentration plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
X-axis direction are made to enter the optical system from the entrance 
side thereof, and the sine of an angle formed between the two rays as 
projected on the XZ-plane at the exit side of the optical system is 
denoted by NA'X, and a value obtained by dividing the distance d between 
the parallel rays by NA'X is denoted by FX, and further that the principal 
ray and a light ray which is parallel to the principal ray at a slight 
distance d in the Y-axis direction are made to enter the optical system 
from the entrance side thereof, and the sine of an angle formed between 
the two rays in the YZ-plane at the exit side of the optical system is 
denoted by NA'Y, and a value obtained by dividing the distance d between 
the parallel rays by NA'Y is denoted by FY, the following condition is 
satisfied to correct rotationally asymmetric aberrations due to 
decentration by the rotationally asymmetric surface: 
EQU 0.01&lt;.vertline.FY/FX.vertline.&lt;100 (3-1) 
First of all, a coordinate system used in the following description will be 
explained. It is assumed that a light ray passing through the center of an 
object point and passing through the center of a stop to reach the center 
of an image plane is defined as an axial principal ray. It is also assumed 
that an optical axis defined by a straight line intersecting the first 
surface of the optical system is defined as a Z-axis, and that an axis 
perpendicularly intersecting the Z-axis in the decentration plane of each 
surface constituting the optical system is defined as a Y-axis, and 
further that an axis perpendicularly intersecting the optical axis and 
also perpendicularly intersecting the Y-axis is defined as an X-axis. 
Ray tracing will be described by forward ray tracing in which light rays 
are traced from the object toward the image plane. 
In general, a spherical lens system comprising only a spherical lens is 
arranged such that aberrations produced by spherical surfaces, such as 
spherical aberration, coma and curvature of field, are corrected with some 
surfaces by canceling the aberrations with each other, thereby reducing 
aberrations as a whole. On the other hand, aspherical surfaces and the 
like are used to favorably effect aberration correction with a minimal 
number of surfaces. The reason for this is to reduce various aberrations 
which would be produced by spherical surfaces. 
However, in a decentered optical system, rotationally asymmetric 
aberrations due to decentration cannot be corrected by a rotationally 
symmetric optical system. 
The arrangement and operation of the present invention will be described 
below. 
The basic arrangement of the present invention is as follows: A decentered 
optical system includes at least one curved surface with a rotationally 
asymmetric surface configuration having no axis of rotational symmetry in 
nor out of the surface, and rotationally asymmetric aberrations due to 
decentration are corrected by the rotationally asymmetric surface. 
When a rotationally symmetric optical system is decentered, rotationally 
asymmetric aberrations occur, and it is impossible to correct these 
aberrations only by the rotationally symmetric optical system. 
Rotationally asymmetric aberrations due to decentration include image 
distortion, curvature of field, and astigmatic and comatic aberrations, 
which occur even on the axis. FIG. 99 shows curvature of field produced by 
a decentered concave mirror M. FIG. 100 shows axial astigmatism produced 
by a decentered concave mirror M. FIG. 101 shows axial comatic aberration 
produced by a decentered concave mirror M. According to the present 
invention, a rotationally asymmetric surface is disposed in the optical 
system to correct such rotationally asymmetric aberrations due to 
decentration. 
Rotationally asymmetric aberrations produced by the decentered concave 
mirror M include rotationally asymmetric curvature of field such as that 
shown in FIG. 99. For example, when light rays from an infinitely distant 
object point are incident on the decentered concave mirror M, the light 
rays are reflected by the concave mirror M to form an image. In this case, 
the back focal length from that portion of the concave mirror M on which 
the light rays strike to the image surface is half the curvature of the 
portion on which the light rays strike. Consequently, an image surface 
tilted with respect to the axial principal ray is formed as shown in FIG. 
99. It has heretofore been impossible to correct such rotationally 
asymmetric curvature of field by a rotationally symmetric optical system. 
The tilted curvature of field can be corrected by forming the concave 
mirror M from a rotationally asymmetric surface, and, in this example, 
arranging it such that the curvature is made strong (refracting power is 
increased) in the positive Y-axis direction (the upward direction in the 
figure), whereas the curvature is made weak (refracting power is reduced) 
in the negative Y-axis direction. It is also possible to obtain a flat 
image surface with a minimal number of constituent surfaces by disposing a 
rotationally asymmetric surface having the same effect as that of the 
above-described arrangement in the optical system separately from the 
concave mirror M. 
Next, rotationally asymmetric astigmatism will be explained. A decentered 
concave mirror M produces astigmatism even for axial rays, as shown in 
FIG. 100, as in the case of the above. The astigmatism can be corrected by 
appropriately changing the curvature in the X-axis direction of the 
rotationally asymmetric surface as in the case of the above. 
Rotationally asymmetric coma will be explained below. A decentered concave 
mirror M produces coma even for axial rays, as shown in FIG. 101, as in 
the case of the above. The coma can be corrected by changing the tilt of 
the rotationally asymmetric surface according as the distance from the 
origin of the X-axis increases, and further appropriately changing the 
tilt of the surface according to the sign (positive or negative) of the 
Y-axis. 
As the above-described rotationally asymmetric surface, it is desirable to 
use a plane-symmetry three-dimensional surface characterized by having 
only one plane of symmetry. 
The term "three-dimensional surface" as used in the present invention means 
a surface which is defined by the following equation: 
##EQU1## 
where C.sub.m (m is an integer of 2 or higher) are coefficients. 
In general, the above-described three-dimensional surface does not have 
planes of symmetry in both the XZ- and YZ-planes. In the present 
invention, a three-dimensional surface having only one plane of symmetry 
parallel to the YZ-plane is obtained by making all terms with odd-numbered 
powers of x zero. For example, in the above defining equation (a), the 
coefficients of the terms C.sub.4, C.sub.6, C.sub.9, C.sub.11, C.sub.13, 
C.sub.15, C.sub.18, C.sub.20, C.sub.22, C.sub.24, C.sub.26, C.sub.28, 
C.sub.31, C.sub.33, C.sub.35, C.sub.37, . . . are set equal to zero. By 
doing so, it is possible to obtain a three-dimensional surface having only 
one plane of symmetry parallel to the YZ-plane. 
A three-dimensional surface having only one plane of symmetry parallel to 
the XZ-plane is obtained by making all terms with odd-numbered powers of y 
zero. For example, in the above defining equation (a), the coefficients of 
the terms C.sub.3, C.sub.6, C.sub.8, C.sub.10, C.sub.13, C.sub.15, 
C.sub.17, C.sub.19, C.sub.21, C.sub.24, C.sub.26, C.sub.28, C.sub.30, 
C.sub.32, C.sub.34, C.sub.36, . . . are set equal to zero. By doing so, it 
is possible to obtain a three-dimensional surface having only one plane of 
symmetry parallel to the XZ-plane. The use of a three-dimensional surface 
having such a plane of symmetry makes it possible to improve the 
productivity. 
Rotationally asymmetric aberrations due to decentration can be effectively 
corrected by using a three-dimensional surface having either a plane of 
symmetry parallel to the YZ-plane or a plane of symmetry parallel to the 
XZ-plane. 
It should be noted that the above defining equation is shown merely as an 
example, and that the feature of the present invention resides in that 
rotationally asymmetric aberrations due to decentration are corrected by a 
rotationally asymmetric surface having only one plane of symmetry. 
Therefore, the same advantageous effect can be obtained for any other 
defining equation. 
It is desirable that the plane of symmetry of the rotationally asymmetric 
surface should be disposed in a plane approximately coincident with the 
decentration plane, which is the direction of decentration of each surface 
constituting the optical system. 
If the rotationally asymmetric surface is a three-dimensional surface which 
is disposed in the decentered optical system and which has a plane of 
symmetry approximately coincident with the decentration plane of each 
decentered surface, both sides of the plane of symmetry can be made 
symmetric. This makes it possible to favorably effect aberration 
correction and to improve the productivity to a considerable extent. 
It is also desirable to use the rotationally asymmetric surface as a 
reflecting surface. 
If the above-described three-dimensional surface is formed as a reflecting 
surface, aberration correction can be made favorably. If a rotationally 
asymmetric surface is used as a reflecting surface, no chromatic 
aberration occurs in contrast to a case where it is used as a transmitting 
surface. Moreover, even if the tilt of the surface is small, the surface 
can bend light rays. Accordingly, the amount of other aberration produced 
by the surface is also small. In other words, when the same refracting 
power is to be obtained, the amount of aberration produced by a reflecting 
surface is smaller than by a refracting surface. 
In this case, it is desirable for the reflecting surface to be a surface 
having totally reflecting action or reflecting action. 
If the reflecting surface is a totally reflecting surface tilted with 
respect to light rays so that the light rays are incident thereon at an 
angle exceeding the critical angle, a high reflectivity can be obtained. 
The reflecting surface is preferably a reflecting surface having a thin 
film of a metal, e.g. aluminum or silver, formed thereon, or a reflecting 
surface formed from a dielectric multilayer film. In the case of a metal 
thin film having reflecting action, a high reflectivity can be readily 
obtained. The use of a dielectric reflecting film is advantageous in a 
case where a reflecting film having wavelength selectivity or minimal 
absorption is to be formed. 
The rotationally asymmetric surface having only one plane of symmetry can 
also be used as a back-coated mirror. 
By forming the above-described reflecting surface from a back-coated 
mirror, curvature of field can be reduced. The reason for this is as 
follows: When concave mirrors of the same focal length are to be formed 
from a back-coated mirror and a surface-coated mirror, respectively, the 
back-coated mirror can have a greater radius of curvature by an amount 
corresponding to the refractive index and thus produces a smaller amount 
of aberration, particularly curvature of field. 
Assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, and that a Y-axis is taken in the decentration 
plane of each surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
X-axis direction are made to enter the optical system from the entrance 
side thereof, and the sine of an angle formed between the two rays as 
projected on the XZ-plane at the exit side of the optical system is 
denoted by NA'X, and further that a value obtained by dividing the 
distance d between the parallel rays by NA'X is denoted by FX, and the 
focal length in the X-axis direction of that portion of the rotationally 
asymmetric surface on which the axial principal ray strikes is denoted by 
FXn, it is desirable to satisfy the following condition: 
EQU -1000&lt;FX/FXn&lt;1000 (1-1) 
The focal length of each surface of the optical system according to the 
present invention will be described. It is preferable from the viewpoint 
of aberration correction to satisfy the above condition (1-1) on the 
assumption that, as shown in FIG. 102, the direction of decentration of 
the optical system S is taken in the Y-axis direction, and that a light 
ray of height d in the YZ-plane which is parallel to the axial principal 
ray of the optical system S is made to enter the optical system S from the 
object side, and the sine of an angle formed between the parallel light 
and the axial principal ray as they are projected on the YZ-plane after 
exiting from the optical system S is denoted by NA'Y, and further that 
d/NA'Y is defined as a focal length FY in the Y-axis direction, and a 
focal length FX in the X-axis direction is similarly defined, and further 
that the focal length in the X-axis direction of that portion of a 
specific rotationally asymmetric surface A according to the present 
invention on which the axial principal ray strikes is denoted by FXn. 
If FX/FXn is not larger than the lower limit of the condition (1-1), i.e. 
-1000, or not smaller than the upper limit, i.e. 1000, the focal length of 
the rotationally asymmetric surface becomes excessively short on the 
negative side and the positive side, respectively, in comparison to the 
focal length FX of the entire optical system. Consequently, the refracting 
power of the rotationally asymmetric surface becomes excessively strong, 
and aberrations produced by the rotationally asymmetric surface cannot be 
corrected by another surface. 
It is even more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU -100&lt;FX/FXn&lt;100 (1-2) 
By satisfying the condition (1-2), rotationally asymmetric aberrations can 
be corrected even more favorably. 
It is still more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU -10&lt;FX/FXn&lt;10 (1-3) 
By satisfying the condition (1-3), rotationally asymmetric aberrations can 
be corrected even more favorably. 
Assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, and that a Y-axis is taken in the decentration 
plane of each surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
Y-axis direction are made to enter the optical system from the entrance 
side thereof, and the sine of an angle formed between the two rays in the 
YZ-plane at the exit side of the optical system is denoted by NA'Y, and 
further that a value obtained by dividing the distance d between the 
parallel rays by NA'Y is denoted by FY, and further the focal length in 
the Y-axis direction of that portion of the rotationally asymmetric 
surface on which the axial principal ray strikes is denoted by FYn, it is 
desirable to satisfy the following condition: 
EQU -1000&lt;FY/FYn&lt;1000 (2-1) 
If FY/FYn is not larger than the lower limit of the condition (2-1), i.e. 
-1000, or not smaller than the upper limit, i.e. 1000, the focal length of 
the rotationally asymmetric surface becomes excessively short on the 
negative side and the positive side, respectively, in comparison to the 
focal length FY of the entire optical system. Consequently, the refracting 
power of the rotationally asymmetric surface becomes excessively strong, 
and aberrations produced by the rotationally asymmetric surface cannot be 
corrected by another surface. 
It is even more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU -100&lt;FY/FYn&lt;100 (2-2) 
By satisfying the condition (2-2), rotationally asymmetric aberrations can 
be corrected even more favorably. 
It is still more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU -10&lt;FY/FYn&lt;10 (2-3) 
By satisfying the condition (2-3), rotationally asymmetric aberrations can 
be corrected even more favorably. 
It is preferable from the viewpoint of aberration correction to satisfy the 
following condition: 
EQU 0.01&lt;.vertline.FY/FX.vertline.&lt;100 (3-1) 
where FX and FY are the focal lengths of the entire optical system. 
If .vertline.FY/FX.vertline. is not larger than the lower limit of the 
condition (3-1), i.e. 0.01, or not smaller than the upper limit, i.e. 100, 
the focal lengths in the X- and Y-axis directions of the entire optical 
system become excessively different from each other. Consequently, it 
becomes difficult to correct image distortion favorably, and the image is 
undesirably distorted. 
It is even more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU 0.1&lt;.vertline.FY/FX.vertline.&lt;10 (3-2) 
By satisfying the condition (3-2), rotationally asymmetric aberrations can 
be corrected even more favorably. 
It is still more desirable from the viewpoint of aberration correction to 
satisfy the following condition: 
EQU 0.5&lt;.vertline.FY/FX.vertline.&lt;2 (3-3) 
By satisfying the condition (3-3), rotationally asymmetric aberrations can 
be corrected even more favorably. 
The optical system according to the present invention may comprise only a 
first reflecting surface, wherein light rays are reflected by the first 
reflecting surface in a direction different from a direction in which the 
light rays are incident thereon. If the first reflecting surface is tilted 
with respect to the axial principal ray, aberrations due to decentration 
are produced when light rays are reflected at the surface. Rotationally 
asymmetric aberrations due to decentration can be satisfactorily corrected 
by forming the reflecting surface from a rotationally asymmetric surface. 
If the reflecting surface is not formed from a rotationally asymmetric 
surface, a large amount of rotationally asymmetric aberration is produced, 
and the resolution is degraded. Further, aberration correction can be made 
even more effectively by satisfying the above conditions (1-1) to (3-3). 
The optical system according to the present invention may comprise a first 
reflecting surface and a first transmitting surface, wherein light rays 
enter the optical system through the first transmitting surface and are 
reflected by the first reflecting surface to exit from the optical system 
through the first transmitting surface in a direction different from a 
direction in which the light rays are incident on the first transmitting 
surface. By adding one transmitting surface, the Petzval sum of the 
optical system can be reduced. In the case of transmitting and reflecting 
surfaces of positive power, Petzval curvatures cancel each other. 
Accordingly, power can be dispersed, and the Petzval sum can be reduced. 
Thus, it becomes possible to correct curvature of field. 
It is preferable from the viewpoint of favorably correcting field curvature 
that the first transmitting surface and the first reflecting surface 
should have powers of the same sign at their axial principal ray 
transmitting and reflecting regions. 
The optical system according to the present invention may comprise a first 
reflecting surface, a first transmitting surface, and a second 
transmitting surface, wherein light rays enter the optical system through 
the first transmitting surface and are reflected by the first reflecting 
surface to exit from the optical system through the second transmitting 
surface in a direction different from a direction in which the light rays 
are incident on the first transmitting surface. By dividing the 
above-described first transmitting surface into two surfaces, curvature of 
field can be corrected even more favorably. In a case where the first and 
second transmitting surfaces constitute a transmission lens, it is 
possible to suppress divergence of light rays at the first reflecting 
surface and hence possible to reduce the size of the first reflecting 
surface. If the optical system is arranged such that light rays travel 
successively through the first transmitting surface, the first reflecting 
surface, and the second transmitting surface, it is possible to form the 
first reflecting surface from a back-coated mirror. If the first 
reflecting surface is formed from a back-coated mirror, curvature of field 
can be corrected more favorably than in the case of a surface-coated 
mirror. If either or both of the first and second transmitting surfaces 
are given power different in sign from the power of the first reflecting 
surface, curvature of field can be corrected approximately completely. On 
the other hand, if the powers of the first and second transmitting 
surfaces are made approximately zero, favorable effects can be produced on 
chromatic aberrations. That is, the first reflecting surface produces no 
chromatic aberration in theory and hence need not correct chromatic 
aberration with another surface. Therefore, the powers of the first and 
second transmitting surfaces are made approximately zero so that no 
chromatic aberration is produced by these surfaces. This makes it possible 
to construct an optical system having minimal chromatic aberration as a 
whole. 
The optical system according to the present invention may comprise a first 
reflecting surface, a second reflecting surface, and a first transmitting 
surface, wherein light rays enter the optical system through the first 
transmitting surface and are reflected by the first reflecting surface and 
then reflected by the second reflecting surface to exit from the optical 
system through the first transmitting surface. If the optical system 
comprises a pair of first and second reflecting surfaces and a first 
transmitting surface, the optical axis can be folded by the two reflecting 
surfaces. This enables a reduction in the size of the optical system. 
Moreover, because reflection takes place an even number of times, an image 
can be formed without being reversed. Further, it is possible to vary the 
powers of the two reflecting surfaces. Accordingly, the principal point 
can be positioned in front of or behind the optical system by using a 
combination of a positive power and a negative power or a combination of a 
negative power and a positive power. This also makes it possible to 
produce favorable effects on the curvature of field. Furthermore, it is 
also possible to substantially eliminate field curvature by forming the 
two reflecting surfaces from back-coated mirrors. 
The optical system according to the present invention may comprise a first 
reflecting surface, a second reflecting surface, a first transmitting 
surface, and a second transmitting surface, wherein light rays enter the 
optical system through the first transmitting surface and are reflected by 
the first reflecting surface and then reflected by the second reflecting 
surface to exit from the optical system through the second transmitting 
surface. If the optical system comprises a pair of first and second 
reflecting surfaces, and a pair of first and second transmitting surfaces, 
the optical axis can be folded by the two reflecting surfaces, and thus 
the optical system can be constructed in a compact form, as stated above. 
Moreover, the presence of two transmitting surfaces makes it possible to 
produce even more favorable effects on the principal point position and 
field curvature. Furthermore, even more favorable aberration correcting 
performance can be obtained by forming the two reflecting surfaces from 
back-coated mirrors. 
In the above-described case, the optical system may be arranged such that 
the optical path has portions intersecting each other. If some portions of 
the optical path intersect each other, it is possible to construct the 
optical system in a compact form. The arrangement makes it possible to 
dispose the object and image planes approximately perpendicular to each 
other. Accordingly, the optical system and an imaging device or the like, 
which is disposed at the image-formation position, can be disposed 
approximately parallel to each other. Thus, an imaging optical system of 
low height, for example, can be constructed. 
In the above-described case, the optical system may be arranged such that 
the optical path has no portions intersecting each other. If no portions 
of the optical path intersect each other, a Z-shaped optical path can be 
formed. Consequently, the angle of decentration at each reflecting surface 
can be reduced, and the amount of aberration due to decentration can be 
reduced. Therefore, the arrangement is favorable from the viewpoint of 
correcting aberrations due to decentration. Further, the optical path from 
the object to the optical system and the optical path from the optical 
system to the image plane can be disposed approximately parallel to each 
other. In particular, when the optical system is used as an observation 
optical system or an ocular optical system, the direction for observation 
of an object and the direction for observation through the optical system 
are identical with each other. Accordingly, it is possible to make 
observation without feeling incongruous. 
In the above-described case, the first transmitting surface and second 
reflecting surface of the optical system may be the identical surface. If 
the first transmitting surface and the second reflecting surface are the 
identical surface, the number of surfaces to be formed is three. 
Accordingly, the productivity of the optical system improves. 
In the above-described case, the first reflecting surface and second 
transmitting surface of the optical system may be the identical surface. 
If the first reflecting surface and the second transmitting surface are 
the identical surface, the number of surfaces to be formed is three. 
Accordingly, the productivity of the optical system improves. 
The optical system according to the present invention may comprise a first 
reflecting surface, a second reflecting surface, a third reflecting 
surface, a first transmitting surface, and a second transmitting surface, 
wherein light rays enter the optical system through the first transmitting 
surface and are reflected successively by the first, second and third 
reflecting surfaces to exit from the optical system through the second 
transmitting surface in a direction different from a direction in which 
the light rays are incident on the first transmitting surface. If the 
optical system comprises three reflecting surfaces and two transmitting 
surfaces, the degree of freedom further increases, which is favorable from 
the viewpoint of aberration correction. 
In this case, the first transmitting surface and second reflecting surface 
of the optical system may be the identical surface. Alternatively, the 
first reflecting surface and the third reflecting surface may be the 
identical surface. Alternatively, the first transmitting surface and the 
third reflecting surface may be the identical surface. Alternatively, the 
second transmitting surface and the second reflecting surface may be the 
identical surface. By forming at least two surfaces from the identical 
surface configuration in this way, the productivity of the optical system 
improves. 
The optical system according to the present invention may comprise at least 
a first reflecting surface, a second reflecting surface, a third 
reflecting surface, a fourth reflecting surface, a first transmitting 
surface, and a second transmitting surface, wherein light rays enter the 
optical system through the first transmitting surface and are reflected 
successively by the first, second, third and fourth reflecting surfaces to 
exit from the optical system through the second transmitting surface in a 
direction different from a direction in which the light rays are incident 
on the first transmitting surface. If the optical system comprises four 
reflecting surfaces, and two transmitting surfaces, the degree of freedom 
further increases, which is favorable from the viewpoint of aberration 
correction. 
In this case, the first transmitting surface and second reflecting surface 
of the optical system may be the identical surface. The second 
transmitting surface and third reflecting surface of the optical system 
may be the identical surface. The first and third reflecting surfaces of 
the optical system may be the identical surface. The second and fourth 
reflecting surfaces of the optical system may be the identical surface. 
The first transmitting surface and second and fourth reflecting surfaces 
of the optical system may be the identical surface. The optical system may 
be arranged such that the first transmitting surface and the second 
reflecting surface are the identical surface, and that the first and third 
reflecting surface are the identical surface. The optical system may be 
arranged such that the first transmitting surface and the second 
reflecting surface are the identical surface, and that the second 
transmitting surface and the third reflecting surface are the identical 
surface. The optical system may be arranged such that the first and third 
reflecting surfaces are the identical surface, and that the second and 
fourth reflecting surfaces are the identical surface. The optical system 
may be arranged such that the second and fourth reflecting surfaces are 
the identical surface, and that the second transmitting surface and the 
third reflecting surface are the identical surface. The optical system may 
be arranged such that the first transmitting surface and the second and 
fourth reflecting surfaces are the identical surface, and that the second 
transmitting surface and the third reflecting surface are the identical 
surface. The optical system may be arranged such that the first 
transmitting surface and the second and fourth reflecting surfaces are the 
identical surface, and that the first and third reflecting surfaces are 
the identical surface. The optical system may be arranged such that the 
first transmitting surface and the second reflecting surface are the 
identical surface, and that the second transmitting surface and the first 
and third reflecting surfaces are the identical surface. The optical 
system may be arranged such that the second and fourth reflecting surfaces 
are the identical surface, and that the second transmitting surface and 
the first and third reflecting surfaces are the identical surface. 
Alternatively, the optical system may be arranged such that the first 
transmitting surface and the second and fourth reflecting surfaces are the 
identical surface, and that the second transmitting surface and the first 
and third reflecting surfaces are the identical surface. By forming at 
least two surfaces from the identical surface configuration in this way, 
the productivity of the optical system improves. 
The optical system according to the present invention may be produced by 
first machining a rotationally asymmetric surface and then machining a 
rotationally symmetric surface. If a rotationally asymmetric surface is 
first formed and then a rotationally symmetric surface is machined, 
positioning of each surface is facilitated, and the manufacturing accuracy 
improves. 
The optical system according to the present invention may be produced by 
cementing together an optical component having at least one rotationally 
asymmetric surface machined thereon and an optical component having 
another surface machined thereon. If a decentered optical system is 
produced by cementing together an optical component having a rotationally 
asymmetric surface formed thereon and an optical component having another 
surface machined thereon, the rotationally asymmetric surface is formed on 
a planar thin member by machining. Therefore, it is possible to avoid 
degradation of the machining accuracy due to distortion or the like of the 
optical component during machining. In a case where a rotationally 
asymmetric surface is produced by injection molding, the optical component 
is preferably as thin as possible. The thinner the optical component, the 
further the distortion of the resin after the injection molding can be 
reduced. 
When the optical system according to the present invention is arranged as 
an ocular optical system having a folded optical path, a reflecting 
surface constituting the folded optical path may have power. If an ocular 
optical system is constructed by using a folded optical path, it is 
possible to give power to a reflecting surface, and a transmission lens 
can be omitted. Moreover, the optical system can be constructed in a 
compact form by folding the optical path. It is also possible to give 
power to an inversion prism, which is even more desirable. 
When the optical system according to the present invention is arranged as 
an image-forming optical system having a folded optical path, a reflecting 
surface constituting the folded optical path may have power. If an 
image-forming optical system is constructed by using a folded optical 
path, it is possible to give power to a reflecting surface, and a 
transmission lens can be omitted. Moreover, the optical system can be 
constructed in a compact form by folding the optical path. It is also 
possible to give power to an inversion prism, which is even more 
desirable. 
An afocal optical system can be constructed of a combination of the 
above-described image-forming optical system having a folded optical path 
and an ocular optical system. For example, a prism optical system for 
obtaining an inverted image can be arranged as an image-forming optical 
system by giving power to it. Thus, the optical system can be constructed 
in a compact form. It is particularly preferable that an objective lens 
system of a real-image finder in a finder optical system of a camera or 
the like should be formed from an optical system having a rotationally 
asymmetric surface used in an inversion prism. By doing so, it is possible 
to reduce the size of the objective lens system and to simplify the 
structure thereof. 
The afocal optical system may be arranged to obtain an erect image by an 
even number of reflections. In particular, when a human being makes an 
observation, the ease of observation is markedly improved by providing an 
erect image. 
An afocal optical system can be constructed of a combination of an 
image-forming optical system and the above-described ocular optical system 
having a folded optical path. Such a combination makes it possible to 
reduce the size of an afocal optical system of short focal length in 
particular, which is complicated in arrangement. In the case of an ocular 
optical system having a focal length of 100 mm or less, the effect of 
reducing the size is even more remarkable. 
In this case also, the afocal optical system may be arranged to obtain an 
erect image by an even number of reflections. In particular, when a human 
being makes an observation, the ease of observation is markedly improved 
by providing an erect image. 
An afocal optical system can be constructed of a combination of the 
above-described image-forming optical system having a folded optical path 
and the above-described ocular optical system having a folded optical 
path. Such a combination makes it possible to construct an afocal optical 
system in an even more compact form. It is even more desirable to use a 
rotationally asymmetric surface for an inversion prism and to give power 
to the prism optical system, thereby simplifying the structure of an 
objective lens or an ocular lens or omitting it, and thus simplifying the 
structure of the optical system. 
In this case also, the afocal optical system may be arranged to obtain an 
erect image by an even number of reflections. In particular, when a human 
being makes an observation, the ease of observation is markedly improved 
by providing an erect image. 
The optical system according to the present invention may also be arranged 
as a camera optical system and provided as an optical device in a camera. 
Thus, it is possible to construct a camera optical system in a compact 
form. 
In this case, the camera optical system may be disposed in a real-image 
finder optical system of a camera, or in a virtual-image finder optical 
system of a camera. Thus, it is possible to provide a compact finder 
optical system of minimal aberration. It is preferable to use a 
rotationally asymmetric surface as a back-coated mirror and to form a 
reflecting surface of an inversion prism as a back-coated mirror. By doing 
so, it is possible to provide a finder optical system having a minimal 
number of components. 
The camera optical system may be disposed in an objective lens system or an 
ocular optical system of a finder optical system. Thus, the optical system 
can be constructed in a compact form. In particular, the ocular optical 
system is preferably formed by using a rotationally asymmetric reflecting 
surface. It is even more desirable to form a back-coated reflecting 
surface of the prism optical system from a rotationally asymmetric 
surface. By doing so, it is possible to construct an ocular optical system 
corrected for image distortion. If a rotationally asymmetric surface is 
used in the objective lens system, not only the image distortion but also 
chromatic aberrations can be favorably corrected. It is still more 
desirable to use a rotationally asymmetric surface as a back-coated 
mirror. By doing so, the amount of aberration produced can be reduced. 
In a case where the above-described camera optical system according to the 
present invention is disposed in an objective lens system of a finder 
optical system, the arrangement may be such that at least one lens whose 
refracting power is not zero is disposed on the object side of the 
objective lens system, and the camera optical system is disposed on the 
observation side of the lens. The arrangement may also be such that the 
camera optical system is disposed on the object side of the objective lens 
system, and at least one lens whose refracting power is not zero is 
disposed on the observation side of the camera optical system. 
Alternatively, the objective lens system may be arranged such that at 
least one lens whose refracting power is not zero is disposed on the 
object side, and the camera optical system is disposed on the observation 
side of the lens, and further at least one lens whose refracting power is 
not zero is disposed on the observation side of the camera optical system. 
The objective lens system may comprise two lens units, that is, the camera 
optical system, and a positive lens unit whose overall refracting power is 
greater than zero. The objective lens system may also comprise two lens 
units, that is, the camera optical system, and a negative lens unit whose 
overall refracting power is smaller than zero. 
That is, it is possible to improve the performance of the optical system by 
disposing another optical system on the object side of the objective lens 
system. By disposing an optical system on the object side of the objective 
lens system, it is possible to enlarge the entrance pupil diameter and 
field angle of light rays entering the camera optical system having a 
folded optical path according to the present invention. Thus, it is 
possible to construct a camera finder optical system having a reduced 
f-number or a widened field angle. In particular, it is preferable to 
dispose a positive optical system on the object side when it is intended 
to construct a finder optical system having a long focal length and a 
small f-number as a whole. If a negative optical system is disposed on the 
object side, an optical system of wide observation field angle can be 
effectively constructed. That is, by disposing a negative optical system 
on the object side, it is possible to converge light rays of wide field 
angle from an object which enter the camera optical system. Accordingly, 
it is possible to obtain a wide field angle without increasing the size of 
the prism optical system. In a case where a negative optical system is 
formed from a lens having a negative power, the negative lens produces 
image distortion and lateral chromatic aberration to a considerable 
extent. Therefore, it is preferable from the viewpoint of favorably 
correcting aberrations to arrange the camera optical system such that 
aberrations produced by the negative lens and aberrations produced by the 
prism optical system cancel each other. It is also preferable from the 
viewpoint of reducing image distortion produced by the negative lens that 
the radius of curvature of the negative lens on the prism optical system 
side should be smaller than the radius of curvature on the object side. If 
the negative lens is formed from a rotationally symmetric surface, the 
productivity of the lens improves. It is also possible to form the 
negative lens from a rotationally asymmetric surface. By doing so, image 
distortion can be corrected even more favorably. If the negative lens is 
produced in the form a diffraction optical element or a Fresnel lens, it 
is possible to obtain a thin lens. This is advantageous when it is desired 
to construct a compact optical system. 
If another optical system is disposed on the image side of the camera 
optical system having a folded optical path according to the present 
invention, the performance of the optical system can be improved. By 
disposing another optical system on the image side, it is possible to 
control the exit pupil position of light rays exiting from the camera 
optical system having a folded optical path and also possible to enlarge 
the field angle. In particular, when a positive optical system is disposed 
on the image side, it is possible to dispose the exit pupil far away from 
the imaging plane. If a negative optical system is disposed on the image 
side, the field angle can be effectively widened. 
If another optical system is disposed on each of the object and image sides 
of the camera optical system having a folded optical path according to the 
present invention, the performance of the optical system can be 
furthermore improved. In particular, it is preferable to dispose a 
positive optical system on the object system when it is intended to 
construct a telephoto type lens having a long focal length and a small 
f-number. If a negative optical system is disposed on the object side, an 
optical system having a wide observation field angle can be effectively 
constructed. Regarding an optical system disposed on the image side, when 
it is desired to dispose the exit pupil at a distant position, a positive 
optical system is preferably disposed on the image side, whereas, when it 
is desired to widen the field angle, a negative optical system is 
preferably disposed on the image side. 
If an optical system is constructed of at least two lens units, that is, 
the camera optical system having a folded optical path according to the 
present invention, and a positive optical system, aberration correction 
can be made effectively. In a case where the camera optical system having 
a folded optical path, which is combined with a positive optical system, 
is arranged to have a positive focal length, the aberration correcting 
action is shared between the two lens units, and the amount of aberration 
produced reduces. In a case where the camera optical system is arranged to 
have a negative focal length, the field angle can be widened by the 
negative lens unit. 
If an optical system is constructed of at least two lens units, that is, 
the camera optical system having a folded optical path according to the 
present invention, and a negative optical system, aberration correction 
can be made effectively. In a case where the camera optical system having 
a folded optical path, which is combined with a negative optical system, 
is arranged to have a positive focal length, the field angle can be 
widened by the negative lens unit. In a case where the camera optical 
system is arranged to have a negative focal length, the aberration 
correcting action is shared between the two lens units, and the amount of 
aberration produced reduces. 
If an objective lens system of a finder optical system is constructed of 
the camera optical system according to the present invention, and another 
lens unit, the magnification can be changed by varying the spacing between 
the two lens units. By arranging the camera optical system and another 
optical system such that the magnification is changed by varying the 
spacing therebetween, it is possible to construct a compact 
variable-magnification finder optical system. In general, a 
variable-magnification optical system is arranged such that the 
magnification is changed by varying the spacing between at least two lens 
units. If the camera optical system having a folded optical path according 
to the present invention is adopted for a variable-magnification optical 
system, it is possible to construct a compact variable-magnification 
finder optical system having a folded optical path. It is also possible to 
adjust the focus position by varying the spacing between the lens units. 
It is preferable that the spacing between the lens units should be varied 
by using a unit-spacing varying device that varies the spacing between the 
lens units by moving an optical system in the direction of the optical 
axis. 
An objective lens system of a finder optical system may be constructed of 
three lens units, that is, the camera optical system according to the 
present invention, a positive lens unit whose overall refracting power is 
greater than zero, and a negative lens unit whose overall refracting power 
is smaller than zero. 
In this case, the magnification can be changed by varying the spacing 
between the camera optical system according to the present invention and 
the positive lens unit and the spacing between the positive and negative 
lens units. By arranging an optical system such that the magnification is 
changed by varying the spacing between at least three lens units in total, 
it is possible to construct an optical compensation variable-magnification 
finder optical system. Thus, the number of moving lens units is minimized, 
and the way in which the lens units are moved is simplified. 
A real-image finder optical system, which has an objective lens system for 
forming an object image and an ocular optical system for observing the 
object image, may be arranged such that it has an indication-within-finder 
optical system which forms an indication image different from the object 
image to display photographic information or the like, and that the camera 
optical system according to the present invention is disposed in the 
indication-within-finder optical system. The use of the camera optical 
system according to the present invention makes it possible to construct a 
compact indication-within-finder optical system. 
It is also possible to construct an optical system having an objective lens 
system for forming an object image, an imaging device for receiving the 
object image, and a distance-measuring part for measuring a displacement 
between the imaging device and an object image formation position which 
changes with the object distance, wherein the camera optical system 
according to the present invention is provided as an optical device 
constituting the distance-measuring part. The use of the camera optical 
system according to the present invention makes it possible to construct a 
compact AF optical system. 
It is also possible to construct an optical system having an objective lens 
system for forming an object image, an imaging device for receiving the 
object image, and a photometer part for measuring an optimal value of an 
exposure to the imaging device which changes with the brightness of the 
object, wherein the camera optical system according to the present 
invention is provided as an optical device constituting the photometer 
part. The use of the camera optical system according to the present 
invention makes it possible to construct a compact AE optical system. 
It is also possible to construct an optical system having an objective lens 
system for forming an object image, an imaging device for receiving the 
object image, a date display part for displaying an information image, 
e.g. a date of photo shooting, and an information image forming optical 
system for forming the information image displayed by the date display 
part on the imaging device, wherein the camera optical system according to 
the present invention is provided as the information image forming optical 
system. The use of the camera optical system according to the present 
invention makes it possible to construct a compact date information image 
forming optical system. 
It is also possible to construct an optical system having an objective lens 
system for forming an object image, and a silver halide film provided as 
an imaging device for receiving the object image, wherein the camera 
optical system according to the present invention is provided as the 
objective lens system. By using the camera optical system according to the 
present invention as an objective lens system, it is possible to construct 
a compact imaging optical system for silver halide film. 
It is also possible to construct an optical system having an objective lens 
system for forming an object image, and an electronic imaging device 
provided as an imaging device for receiving the object image, wherein the 
camera optical system according to the present invention is provided as 
the objective lens system. By using the camera optical system according to 
the present invention as an objective lens system, it is possible to 
construct a compact optical system for an electronic camera. 
In a case where the camera optical system according to the present 
invention is used as an objective lens system, the objective lens system 
may have the camera optical system according to the present invention, and 
an antivibration optical system having the function of preventing 
formation of a blurred image, e.g. camera-shake, due to vibration. By 
combining an antivibration optical system with the camera optical system 
according to the present invention, it is possible to minimize the 
aggravation of aberrations when the antivibration function is made to 
work. This is particularly effective when an optical system according to 
the present invention comprises a back-coated mirror. The reason for this 
is that in theory a back-coated reflecting mirror requires a smaller 
curvature than a transmission lens system. That is, the antivibration 
function is realized by bending light rays through a variable-apical angle 
prism or the like having the function of bending light rays so that, even 
when the optical system is tilted, the light rays reach the previous image 
position. This, however, requires the optical system to be favorably 
corrected for aberrations with respect to as many angles of incident rays 
as possible. If an antivibration optical system is constructed by using a 
conventional transmission refracting lens system, because each surface 
constituting the optical system has a large curvature, aberrations are 
rapidly aggravated when light rays are deviated. In the case of an optical 
system having a reflecting surface formed from a back-coated mirror, 
because the curvature of the surface is small, variation of aberrations is 
minimized even if light rays are slightly deviated. 
In this case, the antivibration optical system may be formed from a 
wedge-shaped prism. 
The camera optical system provided in an objective lens system may be 
arranged such that the refracting power is variable. 
In this case, the camera optical system may have a first decentered optical 
system with a rotationally asymmetric curved surface whose refracting 
power varies in a first direction perpendicular to an optical axis, and a 
second decentered optical system with a rotationally asymmetric curved 
surface whose refracting power varies in a second direction perpendicular 
to both the optical axis and the first direction, so that the refracting 
power of the camera optical system is changed by moving the first 
decentered optical system in the first direction, and/or moving the second 
decentered optical system in the second direction. That is, at least two 
cylindrical optical elements each comprising a rotationally asymmetric 
surface are disposed in the XY-plane, which is approximately perpendicular 
to the optical axis, and the two optical elements are moved approximately 
rectilinearly in the X- and Y-axis directions, respectively. Each 
cylindrical optical element is arranged such that the curvatures in a 
direction perpendicularly intersecting the direction of movement at two 
ends thereof are different from each other. The optical element movable in 
the X-axis direction causes the power in the Y-axis direction to change by 
being moved in the X-axis direction, whereas the optical element movable 
in the Y-axis direction causes the power in the X-axis direction to change 
by being moved in the Y-axis direction. By simultaneously moving the at 
least two optical elements, the powers in the X- and Y-axis directions are 
changed. Thus, a variable-refracting power optical system can be 
constructed. In this case, the optical system is not a liquid crystal lens 
or the like in which the configuration of the optical system or the 
internal structure of the optical system is changeable. Therefore, it is 
possible to obtain stable refracting power varying effect which is not 
affected by temperature, gravity, etc. 
The optical system according to the present invention may be arranged as a 
converter lens. The use of the optical system according to the present 
invention makes it possible to construct a compact converter lens. 
The optical system according to the present invention may be disposed in an 
optical device provided in binoculars. By using the optical system 
according to the present invention in an optical system of binoculars, it 
is possible to construct compact binoculars. 
In this case, the optical system according to the present invention may be 
disposed in an objective lens system provided in binoculars. If a 
rotationally asymmetric surface is used in an objective lens system for 
binoculars, it is possible to favorably correct not only image distortion 
but also chromatic aberrations. It is preferable to use a rotationally 
asymmetric surface as a back-coated mirror. By doing so, it is possible to 
reduce aberrations produced in the objective lens system. 
The optical system according to the present invention may be disposed in an 
ocular lens system provided in binoculars. If an optical system in 
binoculars is constructed by using a folded optical path, and moreover a 
binocular afocal optical system is constructed by using an optical element 
with a reflecting surface having power, it is possible to construct the 
optical system in a compact form. In particular, it is desirable to form 
an ocular optical system from a rotationally asymmetric reflecting 
surface, and it is preferable to form a back-coated reflecting surface of 
a prism optical system from a rotationally asymmetric surface. By doing 
so, it is possible to construct an ocular optical system for binoculars 
which is corrected for image distortion. 
The optical system according to the present invention may be disposed in 
each of objective and ocular lens systems provided in binoculars. By using 
a rotationally asymmetric surface in each of objective and ocular lens 
systems constituting an optical system for binoculars, it is possible to 
provide a finder optical system which is compact and has minimal 
aberration. It is preferable to use the rotationally asymmetric surfaces 
as back-coated mirrors and to construct a reflecting surface of an 
inversion prism as a back-coated mirror. By doing so, it is possible to 
provide a binocular optical system having a minimal number of components. 
The optical system according to the present invention may be disposed at an 
entrance surface and/or an exit surface of an image rotator. A 
conventional image rotator does not particularly have power and is used in 
combination with an optical system having refracting power, e.g. an 
image-forming lens, which is provided separately from the image rotator. 
However, if an optical system is constructed by using a rotationally 
asymmetric surface according to the present invention, the image rotator 
itself can be given refracting power. Accordingly, it becomes possible to 
simplify the arrangement of an image-forming lens or the like or to omit 
the image-forming lens. 
The optical system according to the present invention may be disposed in an 
optical device provided in a microscope. By using the optical system 
according to the present invention in an optical device provided in a 
microscope, it is possible to provide a microscope which is compact and 
has minimal aberration. 
In this case, the optical system according to the present invention may be 
disposed in an objective optical system for a microscope. By constructing 
an objective optical system for a microscope using the optical system 
according to the present invention, it is possible to construct a 
microscope objective lens having minimal chromatic aberration in 
particular. A reflecting surface in the optical system according to the 
present invention produces no chromatic aberration in theory. Therefore, 
it is preferable to construct a microscope objective lens by using the 
optical system according to the present invention in which a strong 
refracting power can be given to the reflecting surface, which produces no 
chromatic aberration. 
In this case, the optical system according to the present invention may be 
disposed in an ocular optical system for a microscope. The use of the 
optical system according to the present invention makes it possible to 
provide a microscope ocular lens which is compact and has minimal 
aberration. In particular, by using a folded optical path, the size of the 
optical system can be reduced, and it is possible to construct an ocular 
lens having a high eye point. It is preferable to construct an ocular lens 
as a prism optical system by using a rotationally asymmetric surface as a 
back-coated mirror. By doing so, it is possible to provide an ocular 
optical system having a minimal number of components. 
The optical system according to the present invention may be disposed in an 
intermediate-image relay optical system for a microscope. The use of the 
optical system according to the present invention makes it possible to 
construct a microscope intermediate-image relay optical system which is 
compact and has minimal aberration. By giving power to a reflecting 
surface, it is possible to omit an optical path bending mirror or prism. 
The optical system according to the present invention may be disposed in an 
illumination system for a microscope. The use of the optical system 
according to the present invention makes it possible to construct a 
microscope illumination optical system which is compact and has minimal 
unevenness of illumination. If power is given to a reflecting surface, it 
becomes possible to omit an optical path bending mirror or prism. 
In this case, the optical system according to the present invention may be 
disposed in an incident-light illumination system for a microscope or in a 
transmission illumination system for a microscope. 
The optical system according to the present invention may be disposed in a 
multi-discussion lens barrel for a microscope. The use of the optical 
system according to the present invention makes it possible to construct a 
microscope multi-discussion lens barrel optical system which has a minimal 
number of components. If power is given to a reflecting surface, it 
becomes possible to omit an optical path bending mirror or prism. 
The optical system according to the present invention may be disposed in an 
optical system of an image-drawing device for a microscope. The use of the 
optical system according to the present invention makes it possible to 
construct an optical system of an image-drawing device for a microscope 
which has a minimal number of components. If power is given to a 
reflecting surface, it becomes possible to omit an optical path bending 
mirror or prism. 
The optical system according to the present invention may be disposed in an 
autofocus system for a microscope. The use of the optical system according 
to the present invention makes it possible to construct a microscope AF 
optical system which has a minimal number of components. If power is given 
to a reflecting surface, it becomes possible to omit an optical path 
bending mirror or prism. 
The optical system according to the present invention may be disposed in a 
projection optical system for an inverted microscope. The use of the 
optical system according to the present invention makes it possible to 
construct a projection optical system for an inverted microscope which has 
a minimal number of components. If power is given to a reflecting surface, 
it becomes possible to omit an optical path bending mirror or prism. 
The optical system according to the present invention may be disposed in an 
optical device provided in a binocular stereoscopic microscope having an 
optical axis for a right eye and an optical axis for a left eye. The use 
of the optical system according to the present invention makes it possible 
to provide a binocular stereoscopic microscope which is compact and has 
minimal aberration. If a binocular stereoscopic microscope, e.g. an 
operating microscope, is constructed by using the optical system according 
to the present invention, it is possible to correct rotationally 
asymmetric aberrations and hence possible to view a flat and clear 
observation image. 
In this case, in order to correct aberrations due to decentration which are 
produced by an objective lens system common to an optical axis for a right 
eye and an optical axis for a left eye, the optical system according to 
the present invention may be provided for each of the optical axes for 
right and left eyes. If a binocular stereoscopic microscope, e.g. an 
operating microscope, is constructed by using the optical system according 
to the present invention for each of the optical axes for right and left 
eyes, it is possible to correct rotationally asymmetric aberrations and 
hence possible to view a flat and clear observation image. 
The optical system according to the present invention may be provided in a 
variable-magnification optical system incorporated in a binocular 
stereoscopic microscope. If the optical system according to the present 
invention is disposed in the variable-magnification optical system, it is 
possible to produce aberration correcting effects during low power 
observation, when rotationally asymmetric aberrations are particularly 
likely to occur. It is preferable to dispose the optical system according 
to the present invention in an optical element on the object side of the 
variable-magnification optical system. By doing so, aberrations such as 
field curvature and image distortion can be favorably corrected during 
observation at low power. 
The optical system according to the present invention may be provided in an 
image-forming optical system incorporated in a binocular stereoscopic 
microscope. By using the optical system according to the present invention 
in the image-forming optical system, an ordinary observation mode and an 
observation mode corrected for rotationally asymmetric aberrations can be 
readily switched from one to another by replacing only the image-forming 
optical system. 
The optical system according to the present invention may be provided in an 
ocular optical system incorporated in a binocular stereoscopic microscope. 
The use of the optical system according to the present invention in the 
ocular optical system enables an improvement in the capability of 
correcting rotationally asymmetric aberrations; this is even more 
desirable. The reason for this is as follows: In an ocular optical system, 
an extra-axial principal ray passes at a position relatively higher than 
the optical axis. Therefore, an ocular optical system using the optical 
system according to the present invention exhibits a great capability of 
correcting off-axis rotationally asymmetric aberrations. 
In an arrangement wherein two optical (axes for right and left eyes) are 
tilted with respect to an object plane, and objective lens systems are 
provided for the two optical axes, the optical system according to the 
present invention may be provided for each of the optical axes for right 
and left eyes to correct aberrations produced by the two objective lens 
systems. If a binocular stereoscopic microscope is constructed by using 
the optical system according to the present invention, it is possible to 
correct rotationally asymmetric aberrations produced by objective lens 
systems provided on optical axes tilted with respect to an object plane, 
and hence possible to view a flat and clear observation image. 
In this case, the optical systems according to the present invention, which 
are provided for the right and left optical axes, may be disposed closest 
to the object on the right and left optical axes. If the optical systems 
according to the present invention are disposed closest to the object, 
when the magnification is changed by a variable-magnification optical 
system, aberrations vary with the observation object height. Accordingly, 
aberration variation during zooming reduces. 
In this case, the optical systems according to the present invention, which 
are provided for the right and left optical axes, may be disposed on the 
respective image sides of the right and left objective lens systems. By 
doing so, replacement of objective lens systems can be readily performed 
because the optical systems need not be removed when the objective lens 
systems are replaced. 
The optical system according to the present invention may be disposed in an 
optical device provided in an endoscope. If an optical system for an 
endoscope is constructed by using the optical system according to the 
present invention, a compact optical system can be formed because the 
optical path is folded. If another optical system of positive refracting 
power is disposed between the endoscope optical system and the image 
formation position, it is possible to dispose the pupil position in the 
optical system according to the present invention and to dispose the exit 
pupil at a distant position. Accordingly, it is possible to reduce the 
size of the prism optical system while maintaining telecentricity on the 
image side. If the optical element of positive refracting power is not 
provided, the telecentricity degrades, and the light-gathering efficiency 
reduces in a case where a CCD, for example, is used as an imaging device. 
In a case where an image guide is utilized, the light-gathering efficiency 
reduces, and it becomes impossible to observe a bright image unless an 
optical fiber bundle of large numerical aperture is used. 
In a case where the above-described positive optical system is formed from 
a lens of positive power, the positive lens produces image distortion and 
lateral chromatic aberration to a considerable extent. Therefore, it is 
preferable from the viewpoint of favorably correcting aberrations to 
arrange the system such that aberrations produced by the positive lens and 
aberrations produced by the prism optical system according to the present 
invention cancel each other. It is preferable from the viewpoint of 
reducing image distortion produced by the positive lens that the radius of 
curvature on the image-formation plane side of the positive lens should be 
smaller than the radius of curvature on the object side. Conversely, the 
positive lens may have a curvature on the object side thereof and a flat 
surface on the image-formation plane side and be integrated with an 
imaging device. By doing so, the productivity of the optical system can be 
improved. If the positive lens is formed from a rotationally symmetric 
surface, the productivity of the lens improves. It is also possible to 
form the positive lens from a rotationally asymmetric surface. In this 
case, it is possible to correct image distortion even more favorably. If 
the positive lens is produced in the form a diffraction optical element or 
a Fresnel lens, it is possible to obtain a thin lens. This is advantageous 
when it is desired to construct a compact optical system. 
In this case, the optical system according to the present invention may be 
applied to an endoscope using an imaging device. If an optical system for 
an endoscope is constructed by using the optical system according to the 
present invention and a two-dimensional imaging device, a compact 
endoscope can be obtained. The reason for this is that a two-dimensional 
imaging device comprises an electric board or the like which is thin and 
has a wide imaging area, and it is therefore preferable to dispose the 
two-dimensional imaging device at a tilt with respect to an optical axis 
of light rays from an object from the viewpoint of reducing the overall 
size of the apparatus. 
The optical system according to the present invention may be used in an 
endoscope objective optical system. By doing so, it is possible to reduce 
both the diameter and length of an objective optical system incorporated 
in a distal end part of an endoscope. Thus, it is possible to solve, 
particularly, the problem that the endoscope distal end part is likely to 
become undesirably thick. 
A protective transparent plate may be disposed on the object side of the 
optical system according to the present invention. By doing so, it becomes 
possible to facilitate removal of dust and water drops from the endoscope 
distal end part. It is preferable that the protective transparent plate be 
a transparent plane-parallel plate. 
An object-side surface of the optical system according to the present 
invention may be a plane surface. This makes it possible to facilitate 
removal of dust and water drops from the endoscope distal end part. 
An image-side surface of the optical system according to the present 
invention may be a plane surface. This makes it possible to accurately 
position a two-dimensional imaging device and the optical system according 
to the present invention with respect to each other. 
The image-side surface of the optical system according to the present 
invention may be placed in close contact with an imaging device. By doing 
so, the assembleability of optical components can be improved. 
An optical fiber bundle may be disposed at the image-formation plane of the 
optical system separately from the optical system. By doing so, 
replacement of the optical fiber bundle is facilitated. 
An optical fiber bundle may be placed in close contact with the image-side 
surface of the optical system according to the present invention. By doing 
so, it becomes possible to construct a compact endoscope objective optical 
system. 
The object-side surface of the optical system may be formed from a 
protective transparent plate. By doing so, it becomes possible to 
facilitate removal of dust and water drops from the endoscope distal end 
part. It is preferable that the protective transparent plate be a 
plane-parallel plate. 
The object-side surface of the optical system according to the present 
invention may be a plane surface. This makes it possible to facilitate 
removal of dust and water drops from the endoscope distal end part. 
A first surface in the distal end part of the endoscope may be made of 
glass or a crystalline material, e.g. sapphire. By doing so, the optical 
system in the endoscope distal end part becomes unlikely to be damaged. 
The first surface of the endoscope objective optical system may be recessed 
from the enclosure of the endoscope. By doing so, the distal end portion 
of the optical system is prevented from being damaged by contacting an 
object under observation. 
The first surface of the endoscope objective optical system may project 
from the enclosure of the endoscope. This makes it possible to readily 
remove water drops from the distal end part. 
The optical system according to the present invention may be disposed in a 
camera adapter for an endoscope to project an observation image onto an 
imaging device through the optical system. The use of a rotationally 
asymmetric surface makes it possible to construct the optical system in a 
compact form. It should be noted that a CCD, a film, etc. may be used as 
an imaging device. 
In this case, a plane glass plate may be provided in front of or behind the 
optical system according to the present invention. With such an 
arrangement, it is possible to prevent dust or other foreign matter from 
entering the optical system when the endoscope camera adapter optical 
system is detached or attached. 
It is possible to provide a device for varying the spacing between the 
optical system according to the present invention and another optical 
system or the image-formation plane. With such an arrangement, focusing 
can be performed. 
The arrangement may be such that the sum total of reflections taking place 
in the optical system according to the present invention and another 
optical system is an even number. Such an arrangement is preferable 
because an image can be formed without being reversed, and thus it is 
possible for an observer to make observation without feeling incongruous. 
The camera adapter for an endoscope may comprise an optical system in which 
the sum total of reflections is an odd number, and an electrically 
image-inverting circuit. In a case where the number of reflections in the 
optical system is an odd number, it is preferable to invert the image by 
electric processing because by doing so an observer can make observation 
without feeling incongruous. 
The camera adapter for an endoscope may have a semitransparent reflecting 
surface to divide an optical path into two. If the optical path is divided 
into two by a semitransparent reflecting surface, it is possible to have 
an observation optical path and a camera optical path and hence possible 
to perform photographing while making observation. 
The observation optical path for an observer may be approximately parallel 
to an optical axis of light rays entering the endoscope camera adapter 
from an observation optical system. It is preferable that the observation 
optical path should be approximately parallel to an optical axis of light 
rays entering the endoscope camera adapter from the observation optical 
system. The reason for this is that if the observation optical path is 
approximately parallel to the optical axis, the observation direction and 
the direction for controlling observation equipment such as an endoscope 
coincide with each other, thus allowing an observer to perform observation 
without feeling incongruous. 
Still other objects and advantages of the invention will in part be obvious 
and will in part be apparent from the specification. 
The invention accordingly comprises the features of construction, 
combinations of elements, and arrangement of parts which will be 
exemplified in the construction hereinafter set forth, and the scope of 
the invention will be indicated in the claims.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Examples of optical systems according to the present invention, together 
with examples of optical systems of various optical apparatuses using the 
optical systems according to the present invention, will be described 
below. 
Examples 1 to 5 and Examples 7 to 13 will be described, first. They are 
examples of representative optical systems involving constituent 
parameters according to the present invention. However, the present 
invention is not necessarily limited to these examples. It should be noted 
that Example 6 is concerned with a surface having reflecting action. 
In constituent parameters of Examples 1 to 5 (described later), a 
coordinate system is defined as follows: As shown in FIG. 1, the center of 
a pupil (aperture) 1 is defined as the origin of an optical system. An 
optical axis 2 is defined by a light ray emanating from the center of an 
object (not shown in the figure) and passing through the center of the 
aperture 1. A direction in which the light ray travels as far as a first 
surface of an optical system 10 along the optical axis 2 is defined as a 
direction of the Z-axis. A direction perpendicularly intersecting the 
Z-axis and passing through the origin in a plane where the optical axis 2 
is bent by the optical system 10 is defined as a direction of the Y-axis. 
A direction perpendicularly intersecting both the Z- and Y-axes and 
passing through the origin is defined as a direction of the X-axis. A 
direction extending toward the first surface of the optical system 10 from 
the object point is defined as a positive direction of the Z-axis. The X-, 
Y- and Z-axes constitute a right-handed orthogonal coordinate system. In 
the coordinate system, each surface separation is defined along the Z-axis 
direction. A position given by the surface separation becomes the origin 
of a new coordinate system defining the position of the subsequent 
surface. A displacement in the Y-axis direction of the vertex of the 
surface relative to the new origin is given as a displacement Y. An amount 
of rotation from the Z-axis direction of the center axis of an expression 
defining the surface is given as a tilt angle .THETA.. Similarly, the 
subsequent surface is defined with respect to the coordinate system 
defining the preceding surface. That is, according to a coordinate system 
newly defined after decentration of each surface, a surface separation 
between the surface and the subsequent surface is defined. It should be 
noted that, regarding the tilt angle, the counterclockwise direction is 
defined as a positive direction. 
In the constituent parameters of Examples 7 to 13 (described later), a 
coordinate system is defined as follows: As shown in FIG. 7, the surface 
No. 1 [containing a pupil (aperture) 1] of an optical system 10 is defined 
as the origin of the optical system. An optical axis 2 is defined by a 
light ray emanating from the center of an object (not shown in the figure) 
and passing through the center of the aperture 1. A direction in which the 
light ray travels as far as a first surface of the optical system 10 along 
the optical axis 2 is defined as a direction of the Z-axis. A direction 
perpendicularly intersecting the Z-axis and passing through the origin in 
a plane in which the optical axis 2 is bent by the optical system 10 is 
defined as a direction of the Y-axis. A direction perpendicularly 
intersecting both the Z- and Y-axes and passing through the origin is 
defined as a direction of the X-axis. A direction extending from the 
object point toward the first surface of the optical system is defined as 
a positive direction of the Z-axis. The X-, Y- and Z-axes constitute a 
right-handed orthogonal coordinate system. Regarding each surface for 
which displacements Y and Z and a tilt angle .THETA. are shown, the 
displacements Y and Z are each a displacement of the position of the 
vertex of the surface relative to the surface No. 1 [containing the pupil 
(aperture) 1] of the optical system, which is the origin of the optical 
system 10, and the tilt angle .THETA. is an amount of rotation of the 
center axis of an expression defining the surface from the Z-axis 
direction. It should be noted that, regarding the tilt angle, the 
counterclockwise direction is defined as a positive direction. Regarding 
each surface for which a surface separation is shown, the surface 
separation is an axial distance between the surface and the subsequent 
surface. 
Three-dimensional surfaces are polynomial surfaces expressed by the above 
equation (a). It should be noted that the Z-axis of the defining equation 
(a) is the axis of a three-dimensional surface. 
The non-rotationally symmetric aspherical configuration of each surface may 
be expressed in the coordinate system defining the surface as follows: 
##EQU2## 
where R.sub.y is the paraxial curvature radius of the surface in the 
YZ-plane (the plane of the figure); R.sub.x is the paraxial curvature 
radius in the XZ-plane; K.sub.x is the conical coefficient in the 
XZ-plane; K.sub.y is the conical coefficient in the YZ-plane; AR, BR, CR 
and DR are 4th-, 6th-, 8th- and 10th-order aspherical coefficients, 
respectively, which are rotationally symmetric with respect to the Z-axis; 
and AP, BP, CP and DP are 4th-, 6th-, 8th- and 10th-order aspherical 
coefficients, respectively, which are rotationally asymmetric with respect 
to the Z-axis. 
Coefficients concerning aspherical surfaces which are not shown in the 
constituent parameters (shown later) are zero. The refractive index of a 
medium lying between surfaces is expressed by the refractive index for the 
spectral d-line (wavelength: 587.56 nm). Lengths are given in millimeters. 
Three-dimensional surfaces may also be defined by Zernike polynomials. That 
is, the configuration of a three-dimensional surface may be defined by the 
following equation (c). The Z-axis of the defining equation (c) is the 
axis of Zernike polynomial. 
##EQU3## 
where D.sub.m (m is an integer of 2 or higher) are coefficients. 
Examples of other surfaces usable in the present invention include those 
which are given by the following defining equation: 
EQU Z=.SIGMA..SIGMA.C.sub.nm XY 
Assuming that k=7 (polynomial of degree 7), for example, the equation, when 
expanded, may be given by: 
##EQU4## 
EXAMPLE 1 
FIG. 1 is a sectional view of Example 1 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
refracting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered toric surface, and a second surface 4 
formed from a decentered spherical surface. Constituent parameters of this 
example will be shown later. In this example, imaging field angles are as 
follows: The horizontal field angle is 24.degree., and the vertical field 
angle is 16.7.degree.. The entrance pupil diameter is 2 millimeters. It 
should be noted that reference numeral 5 denotes an image plane. The same 
shall apply hereinafter. 
EXAMPLE 2 
FIG. 2 is a sectional view of Example 2 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
refracting decentered optical system 10 consisting essentially of a first 
surface 3 formed from an anamorphic surface, and a second surface 4 formed 
from a decentered spherical surface. Constituent parameters of this 
example will be shown later. In this example, imaging field angles are as 
follows: The horizontal field angle is 24.degree., and the vertical field 
angle is 16.7.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 3 
FIG. 3 is a sectional view of Example 3 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
refracting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a three-dimensional surface, and a second surface 4 
formed from a decentered spherical surface. Constituent parameters of this 
example will be shown later. In this example, imaging field angles are as 
follows: The horizontal field angle is 24.degree., and the vertical field 
angle is 16.7.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 4 
FIG. 4 is a sectional view of Example 4 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
refracting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional surface, and a second 
surface 4 formed from a decentered spherical surface. Constituent 
parameters of this example will be shown later. In this example, imaging 
field angles are as follows: The horizontal field angle is 24.degree., and 
the vertical field angle is 16.7.degree.. The entrance pupil diameter is 2 
millimeters. 
EXAMPLE 5 
FIG. 5 is a sectional view of Example 5 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional reflecting surface. 
Constituent parameters of this example will be shown later. In this 
example, imaging field angles are as follows: The horizontal field angle 
is 24.degree., and the vertical field angle is 16.7.degree.. The entrance 
pupil diameter is 2 millimeters. 
EXAMPLE 6 
This example is concerned with the structure of a surface having reflecting 
action, which may be applied in a case where a rotationally asymmetric 
surface according to the present invention is used as a reflecting 
surface, particularly as a back-coated mirror. As shown in FIGS. 6(a), 
6(b) and 6(c), examples of reflecting surfaces usable in the present 
invention include a structure in which, as shown in FIG. 6(a), a 
transparent member 11 made of a transparent material such as a glass or 
plastic material has an aluminum coating layer 12 provided on the surface 
thereof; a structure in which, as shown in FIG. 6(b), a transparent member 
11 has a silver coating layer 13 provided on the surface thereof; and a 
structure in which, as shown in FIG. 6(c), a transparent member 11 has an 
aluminum coating layer 12 partially provided on the surface thereof to 
form a semitransparent mirror. It is also possible to use a reflecting 
surface structure which is provided with an optical multilayer film so as 
to have a reflectivity of 100% or to form a semitransparent mirror. 
EXAMPLE 7 
FIG. 7 is a sectional view of Example 7 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional transmitting surface, 
a second surface 4 formed from a decentered three-dimensional reflecting 
surface, and a third surface 6 formed from a transmitting surface common 
to the first and third surfaces 3 and 6. Constituent parameters of this 
example will be shown later. In this example, imaging field angles are as 
follows: The horizontal field angle is 24.degree., and the vertical field 
angle is 16.7.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 8 
FIG. 8 is a sectional view of Example 8 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional transmitting surface, 
a second surface 4 formed from a decentered three-dimensional reflecting 
surface, and a third surface 6 formed from a decentered three-dimensional 
transmitting surface. Constituent parameters of this example will be shown 
later. In this example, imaging field angles are as follows: The 
horizontal field angle is 24.degree., and the vertical field angle is 
16.7.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 9 
FIG. 9 is a sectional view of Example 9 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional transmitting surface, 
a second surface 4 formed from a decentered three-dimensional reflecting 
surface, a third surface 6 formed from a decentered three-dimensional 
reflecting surface, and a fourth surface 7 formed from a decentered 
three-dimensional transmitting surface. Constituent parameters of this 
example will be shown later. In this example, imaging field angles are as 
follows: The horizontal field angle is 24.degree., and the vertical field 
angle is 16.7.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 10 
FIG. 10 is a sectional view of Example 10 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a three-dimensional transmitting surface, a second 
surface 4 formed from a decentered three-dimensional reflecting surface, a 
third surface 6 formed from a decentered three-dimensional reflecting 
surface, and a fourth surface 7 formed from a decentered three-dimensional 
transmitting surface. Constituent parameters of this example will be shown 
later. In this example, imaging field angles are as follows: The 
horizontal field angle is 40.degree., and the vertical field angle is 
30.degree.. The entrance pupil diameter is 2 millimeters. 
EXAMPLE 11 
FIG. 11 is a sectional view of Example 11 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional transmitting surface, 
a second surface 4 formed from a decentered three-dimensional reflecting 
surface, a third surface 6 which is a reflecting surface formed from a 
surface common to the first and third surfaces 3 and 6, and a fourth 
surface 7 formed from a decentered three-dimensional transmitting surface. 
Constituent parameters of this example will be shown later. In this 
example, imaging field angles are as follows: The horizontal field angle 
is 40.degree., and the vertical field angle is 30.degree.. The entrance 
pupil diameter is 10 millimeters. 
EXAMPLE 12 
FIG. 12 is a sectional view of Example 12 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a decentered three-dimensional transmitting surface, 
a second surface 4 formed from a decentered three-dimensional reflecting 
surface, a third surface 6 formed from a decentered three-dimensional 
reflecting surface, and a fourth surface 7 which is a transmitting surface 
formed from a surface common to the second and fourth surfaces 4 and 7. 
Constituent parameters of this example will be shown later. In this 
example, imaging field angles are as follows: The horizontal field angle 
is 40.degree., and the vertical field angle is 30.degree.. The entrance 
pupil diameter is 10 millimeters. 
EXAMPLE 13 
FIG. 13 is a sectional view of Example 13 taken by the YZ-plane containing 
the optical axis 2. The optical system according to this example is a 
reflecting decentered optical system 10 consisting essentially of a first 
surface 3 formed from a three-dimensional transmitting surface, a second 
surface 4 formed from a decentered three-dimensional reflecting surface, a 
third surface 6 formed from a plane reflecting surface, a fourth surface 7 
which is a reflecting surface formed from a surface common to the first 
and fourth surfaces 3 and 7, and a fifth surface 8 which is a transmitting 
surface formed from a surface common to the second and fifth surfaces 4 
and 8. Constituent parameters of this example will be shown later. In this 
example, imaging field angles are as follows: The horizontal field angle 
is 40.degree., and the vertical field angle is 30.degree.. The entrance 
pupil diameter is 10 millimeters. 
The constituent parameters of the above Examples 1 to 5 and 7 to 13 are as 
follows: 
__________________________________________________________________________ 
Refractive 
Surface 
Radius of Surface 
index Abbe's No. 
No. curvature separation 
(Displacement) 
(Tilt angle) 
__________________________________________________________________________ 
Example 1 
1 .infin.(pupil) 
5.000 
2 R.sub.y 88.44333 
3.000 1.51633 
64.15 
R.sub.x 95.45737 Y 0.000 .theta. 
-1.99.degree. 
3 -17.301 38.032 
Y 0.069 .theta. 
-1.77.degree. 
4 .infin.(image plane) 
Y 3.119 .theta. 
10.00.degree. 
CXn 0.01048 
CYn 0.01130 
FXn 184.8040 
FYn 184.8766 
FX 28.3607 
FY 27.8784 
FXn/FX 
6.51620 
FYn/FY 
6.63154 
FY/FX 
0.98299 
Example 2 
1 .infin.(pupil) 
2.273 
2 R.sub.y 96.003 
3.000 1.5163 64.15 
R.sub.x 95.457 Y 0.000 .theta. 
0.00.degree. 
K.sub.y 0 
K.sub.x 0 
AR -8.9601 .times. 10.sup.-5 
AP -4.4886 .times. 10.sup.-1 
3 -17.143 37.747 
Y 0.094 .theta. 
-2.42.degree. 
4 .infin.(image plane) 
Y 4.240 .theta. 
10.00.degree. 
CXn 0.01048 
CYn 0.01042 
FXn 184.8767 
FYn 185.9339 
FX 28.4495 
FY 28.1215 
FXn/FX 
6.49842 
FYn/FY 
6.61181 
FY/FX 
1.01745 
Example 3 
1 .infin.(pupil) 
5.000 
2 Three-dimensional surface(1) 
3.000 1.5163 64.15 
Y 0.000 .theta. 
0.00.degree. 
3 -11.903 37.119 
Y 0.000 .theta. 
-1.42.degree. 
4 .infin.(image plane) 
Y 1.436 .theta. 
10.00.degree. 
Three-dimensional surface(1) 
C.sub.5 
-1.6641 .times. 10.sup.-2 
C.sub.7 
-1.6675 .times. 10.sup.-2 
C.sub.10 
3.5664 .times. 10.sup.-4 
CXn -0.03335 
CYn -0.03328 
FXn -58.0733 
FYn -58.1955 
FX 35.5619 
FY 35.2237 
FXn/FX 
-1.63302 
FYn/FY 
-1.65217 
FY/FX 
0.99049 
Example 4 
1 .infin.(pupil) 
5.000 
2 Three-dimensional surface(1) 
3.000 1.5163 64.15 
Y 0.000 .theta. 
-2.57.degree. 
3 -15.349 36.155 
Y 0.089 .theta. 
-2.06.degree. 
4 .infin.(image plane) 
Y 3.615 .theta. 
10.00.degree. 
Three-dimensional surface(1) 
C.sub.5 
-6.2923 .times. 10.sup.-3 
C.sub.7 
-6.1230 .times. 10.sup.-4 
C.sub.10 
1.0315 .times. 10.sup.-4 
CXn -0.01225 
CYn -0.01258 
FXn -158.10170 
FYn -153.95436 
FX 35.67606 
FY 35.81662 
FXn/FX 
-4.43159 
FYn/FY 
-4.29841 
FY/FX 
1.00394 
Example 5 
1 .infin.(pupil) 
23.667 
2 Three-dimensional surface(1) 
-33.473 
Y 0.000 .theta. 
-20.00.degree. 
3 .infin.(display plane) 
Y 12.183 .theta. 
-29.79.degree. 
Three-dimensional surface(1) 
C.sub.5 
-6.6312 .times. 10.sup.-3 
C.sub.7 
-7.3816 .times. 10.sup.-3 
C.sub.8 
1.3051 .times. 10.sup.-4 
C.sub.10 
3.5104 .times. 10.sup.-4 
C.sub.12 
-1.7318 .times. 10.sup.-6 
C.sub.14 
1.4418 .times. 10.sup.-6 
C.sub.16 
1.0842 .times. 10.sup.-6 
C.sub.17 
-2.2182 .times. 10.sup.-6 
C.sub.19 
-1.3828 .times. 10.sup.-6 
C.sub.21 
-6.8971 .times. 10.sup.-6 
CXn -0.01476 
CYn -0.01326 
FXn -33.87534 
FYn -37.70739 
FX 35.52397 
FY 35.37319 
FXn/FX 
-0.95359 
FYn/FY 
-1.06599 
FY/FX 
0.99576 
Example 7 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5163 64.15 
Y 0.000 .theta. 
-17.45.degree. 
Z 17.611 
3 Three-dimensional surface(2) 
1.5163 64.15 
Y -0.529 .theta. 
-20.00.degree. 
Z 22.611 
4 Three-dimensional surface(1) 
Y 0.000 .theta. 
-17.45.degree. 
Z 17.611 
5 .infin.(image plane) 
Y 24.425 .theta. 
-47.96.degree. 
Z -7.952 
Three-dimensional surface(1) 
C.sub.5 
1.8423 .times. 10.sup.-2 
C.sub.7 
3.2520 .times. 10.sup.-2 
Three-dimensional surface(2) 
C.sub.5 
2.3788 .times. 10.sup.-3 
C.sub.7 
7.6150 .times. 10.sup.-3 
Three-dimensional surface(2) 
CXn 0.01523 
CYn 0.00476 
FXn 21.65092 
FYn 69.27385 
FX 28.80566 
FY 28.36382 
FXn/FX 
0.75162 
FYn/FY 
2.44233 
FY/FX 
0.98466 
Example 8 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5163 64.15 
Y 0.000 .theta. 
-11.28.degree. 
Z 1.758 
3 Three-dimensional surface(2) 
1.5163 64.15 
Y -1.816 .theta. 
-20.00.degree. 
Z 28.620 
4 Three-dimensional surface(3) 
Y 17.796 .theta. 
-28.72.degree. 
Z 1.758 
5 .infin.(image plane) 
Y 41.948 .theta. 
-49.40.degree. 
Z -27.025 
Three-dimensional surface(1) 
C.sub.5 
-2.9815 .times. 10.sup.-3 
C.sub.7 
5.8788 .times. 10.sup.-3 
C.sub.10 
-1.9434 .times. 10.sup.-4 
Three-dimensional surface(2) 
C.sub.5 
-5.6421 .times. 10.sup.-3 
C.sub.7 
3.0794 .times. 10.sup.-3 
C.sub.10 
-6.3954 .times. 10.sup.-5 
Three-dimensional surface(3) 
C.sub.5 
2.7620 .times. 10.sup.-3 
C.sub.7 
3.3894 .times. 10.sup.-2 
C.sub.10 
2.5637 .times. 10.sup.-5 
Three-dimensional surface(2) 
CXn 0.00616 
CYn -0.01128 
FXn 53.52979 
FYn -29.23258 
FX 33.52330 
FY 34.95281 
FXn/FX 
1.59679 
FYn/FY 
-0.83634 
FY/FX 
1.04264 
Example 9 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5163 64.15 
Y 0.000 .theta. 
0.00.degree. 
Z 10.000 
3 Three-dimensional surface(2) 
1.5163 64.15 
Y 0.000 .theta. 
-45.00.degree. 
Z 20.000 
4 Three-dimensional surface(3) 
1.5163 64.15 
Y 10.000 .theta. 
45.00.degree. 
Z 20.000 
5 Three-dimensional surface(4) 
Y 10.000 .theta. 
0.00.degree. 
Z 10.000 
6 .infin.(image plane) 
Y 10.000 .theta. 
-13.68.degree. 
Z -10.000 
Three-dimensional surface(1) 
C.sub.5 
-2.5583 .times. 10.sup.-3 
C.sub.7 
-1.1629 .times. 10.sup.-3 
C.sub.8 
3.6340 .times. 10.sup.-4 
C.sub.10 
0 C.sub.12 
3.2535 .times. 10.sup.-5 
C.sub.14 
3.1012 .times. 10.sup.-5 
C.sub.16 
8.2196 .times. 10.sup.-5 
Three-dimensional surface(2) 
C.sub.5 
-2.5807 .times. 10.sup.-3 
C.sub.7 
-5.9100 .times. 10.sup.-3 
C.sub.8 
-7.4253 .times. 10.sup.-6 
C.sub.10 
3.3196 .times. 10.sup.-5 
C.sub.12 
3.2466 .times. 10.sup.-7 
C.sub.14 
-3.5149 .times. 10.sup.-7 
C.sub.16 
1.9988 .times. 10.sup.-5 
Three-dimensional surface(3) 
C.sub.5 
-2.9513 .times. 10.sup.-3 
C.sub.7 
-4.5073 .times. 10.sup.-3 
C.sub.8 
-1.0598 .times. 10.sup.-4 
C.sub.10 
-1.0663x .times. 10.sup.-5 
C.sub.12 
-2.8568 .times. 10.sup.-6 
C.sub.14 
7.7238 .times. 10.sup.-7 
C.sub.16 
-9.1435 .times. 10.sup.-6 
Three-dimensional surface(4) 
C.sub.5 
-1.9093 .times. 10.sup.-2 
C.sub.7 
-1.9783 .times. 10.sup.-2 
C.sub.8 
-7.3494 .times. 10.sup.-4 
C.sub.10 
0 C.sub.12 
-9.6786 .times. 10.sup.-5 
C.sub.14 
-5.5417 .times. 10.sup.-5 
C.sub.16 
-4.5951 .times. 10.sup.-6 
Three-dimensional surface 
(1) (2) (3) (4) 
CXn -0.00233 
-0.01182 
-0.00901 
-0.03957 
CYn -0.00512 
-0.00516 
-0.00590 
-0.03819 
FXn -831.2214 
27.8970 36.5975 -48.9448 
PYn -378.2706 
63.9037 55.8887 -50.7134 
FX 33.59086 
FY 31.39717 
FXn/FX 
-24.7455 
0.8305 1.0895 -1.4571 
FYn/FY 
-12.0479 
2.0353 1.7801 -1.6152 
FY/FX 0.9347 
Example 10 
1 Three-dimensional surface(1) 
1.5163 64.15 
2 Three-dimensional surface(2) 
1.5163 64.15 
Y 0.000 .theta. 
-22.50.degree. 
Z 26.000 
3 Three-dimensional surface(3) 
1.5163 64.15 
Y 14.000 .theta. 
-67.50.degree. 
Z 12.000 
4 Three-dimensional surface(4) 
2.000 Y -10.000 .theta. 
90.00.degree. 
Z 10.000 
5 .infin.(image plane) 
Three-dimensional surface(1) 
C.sub.5 
1.3733 .times. 10.sup.-2 
C.sub.7 
1.8225 .times. 10.sup.-2 
C.sub.8 
-9.4288 .times. 10.sup.-5 
C.sub.10 
-1.3336 .times. 10.sup.-4 
Three-dimensional surface(2) 
C.sub.5 
-7.9366 .times. 10.sup.-4 
C.sub.7 
-1.1721 .times. 10.sup.-3 
C.sub.8 
-2.5491 .times. 10.sup.-5 
C.sub.10 
-5.6154 .times. 10.sup.-5 
Three-dimensional surface(3) 
C.sub.5 
2.8039 .times. 10.sup.-3 
C.sub.7 
-8.7180 .times. 10.sup.-4 
C.sub.8 
-7.6318 .times. 10.sup.-5 
C.sub.10 
-1.4966 .times. 10.sup.-4 
Three-dimensional surface(4) 
C.sub.5 
8.4385 .times. 10.sup.-3 
C.sub.7 
-6.4925 .times. 10.sup.-3 
C.sub.8 
-2.7582 .times. 10.sup.-4 
C.sub.10 
3.1268 .times. 10.sup.-4 
Three-dimensional surface 
(1) (2) (3) (4) 
CXn 0.03645 -0.00234 
-0.00174 
-0.01299 
CYn 0.02747 -0.00159 
0.00561 0.01688 
FXn 53.13432 
140.9160 
-189.5078 
-149.0951 
FYn 70.50404 
207.3859 
58.7778 114.7361 
FX 49.19207 
FY 34.94060 
FXn/FX 
1.0801 2.8646 -3.8524 -3.03087 
FYn/FY 
2.0178 5.9354 1.6822 3.28374 
FY/FX 0.7102 
__________________________________________________________________________ 
Surface 
Radius of Surface 
Refractive 
No. curvature separation 
index Abbe's No. 
__________________________________________________________________________ 
Example 11 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5163 64.15 
Y -22.988 .theta. 
-8.98.degree. 
Z 50.530 
3 Three-dimensional surface(2) 
1.5163 64.15 
Y -1.449 .theta. 
17.73.degree. 
Z 76.977 
4 Three-dimensional surface(1) 
1.5163 64.15 
Y -22.988 .theta. 
-8.98.degree. 
Z 50.530 
5 Three-dimensional surface(3) 
Y -48.948 .theta. 
-78.43.degree. 
Z 67.306 
6 .infin.(image plane) 
Y -58.973 .theta. 
-45.00.degree. 
Z 77.331 
Three-dimensional surface(1) 
C.sub.5 
6.7120 .times. 10.sup.-4 
C.sub.7 
-1.1797 .times. 10.sup.-4 
C.sub.8 
0 
C.sub.10 
2.1250 .times. 10.sup.-5 
Three-dimensional surface(2) 
C.sub.5 
-2.0716 .times. 10.sup.-3 
C.sub.7 
-3.2040 .times. 10.sup.-3 
C.sub.8 
0 
C.sub.10 
1.8112 .times. 10.sup.-5 
Three-dimensional surface(3) 
C.sub.5 
1.3932 .times. 10.sup.-3 
C.sub.7 
1.2275 .times. 10.sup.-2 
C.sub.8 
0 
C.sub.10 
6.8065 .times. 10.sup.-5 
Three-dimensional surface 
(1) (2) (t) (3) 
CXn 0.00076 -0.00641 
-0.00024 
0.02455 
CYn 0.00134 -0.00414 
0.00134 0.00279 
FXn 2548.34984 
51.44205 
1373.93135 
-78.8898 
FYn 1445.3327 
79.6482 -246.07726 
-777.80959 
FX 66.22517 
FY 50.40322 
FXn/FX 
38.4801 0.7768 20.7464 -3.03087 
FYn/FY 
28.6754 1.5802 1.6822 3.28374 
FY/FX 0.7102 
Example 12 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5163 64.15 
Y 0.000 .theta. 
4.56.degree. 
Z 48.036 
3 Three-dimensional surface(2) 
1.5163 64.15 
Y 0.781 .theta. 
54.56.degree. 
Z 76.770 
4 Three-dimensional surface(3) 
1.5163 64.15 
Y -28.138 .theta. 
83.15 
Z 85.930 
5 Three-dimensional surface(2) 
Y 0.781 .theta. 
54.56.degree. 
Z 76.770 
6 .infin.(image plane) 
Y 14.258 .theta. 
50.00.degree. 
Z 111.028 
Three-dimensional surface(1) 
C.sub.5 
6.1734 .times. 10.sup.-3 
C.sub.7 
9.9567 .times. 10.sup.-3 
C.sub.8 
2.2653 .times. 10.sup.-5 
Three-dimensional surface(2) 
C.sub.5 
9.6423 .times. 10.sup.-4 
C.sub.7 
3.0939 .times. 10.sup.-3 
C.sub.8 
4.2479 .times. 10.sup.-6 
C.sub.10 
1.8481 .times. 10.sup.-5 
Three-dimensional surface(3) 
C.sub.5 
3.8994 .times. 10.sup.-3 
C.sub.7 
4.1772 .times. 10.sup.-3 
C.sub.8 
-4.2157 .times. 10.sup.-6 
C.sub.10 
1.7324 .times. 10.sup.-6 
Three-dimensional surface 
(1) (2) (3) (2) 
CXn 0.01991 0.00619 0.00835 0.00534 
CYn 0.01235 0.00193 0.00780 0.00134 
FXn 97.2750 -53.2704 
39.4902 -362.6865 
FYn 156.8215 
-170.8516 
42.2748 -1445.3327 
FX 55.61735 
FY 45.53734 
FXn/FX 
1.7490 -0.9578 0.7100 -6.52110 
FYn/FY 
3.4438 -3.7519 0.9284 -31.7395 
FY/FX 0.81876 
Example 13 
1 .infin.(pupil) 
2 Three-dimensional surface(1) 
1.5254 56.25 
Z 4.230 
3 Three-dimensional surface(2) 
1.5254 56.25 
Y 0.000 .theta. 
-53.34.degree. 
Z 14.245 
4 .infin. 1.5254 56.25 
Y 47.807 .theta. 
57.45.degree. 
Z 28.564 
5 Three-dimensional surface(1) 
1.5254 56.25 
Y 0.000 .theta. 
0.00.degree. 
Z 4.230 
6 Three-dimensional surface(2) 
Y 0.000 .theta. 
-53.34.degree. 
Z 14.245 
7 .infin.(image plane) 
Y 0.000 .theta. 
-19.11.degree. 
Z 26.296 
Three-dimensional surface(1) 
C.sub.5 
1.0924 .times. 10.sup.-3 
C.sub.7 
7.2551 .times. 10.sup.-3 
C.sub.8 
-1.1681 .times. 10.sup.-5 
C.sub.10 
1.0202 .times. 10.sup.-5 
C.sub.12 
1.0606 .times. 10.sup.-5 
C.sub.14 
-8.1164 .times. 10.sup.-7 
C.sub.16 
-5.8312 .times. 10.sup.-7 
C.sub.17 
-9.2779 .times. 10.sup.-9 
C.sub.19 
1.0029 .times. 10.sup.-8 
C.sub.21 
2.5790 .times. 10.sup.-8 
Three-dimensional surface(2) 
C.sub.5 
-6.7102 .times. 10.sup.-4 
C.sub.7 
3.6136 .times. 10.sup.-4 
C.sub.8 
-1.3035 .times. 10.sup.-5 
C.sub.10 
-5.9967 .times. 10.sup.-6 
C.sub.12 
2.8639 .times. 10.sup.-7 
C.sub.14 
1.1362 .times. 10.sup.-6 
C.sub.16 
1.4776 .times. 10.sup.-7 
C.sub.17 
3.7664 .times. 10.sup.-9 
C.sub.19 
-3.4413 .times. 10.sup.-8 
C.sub.21 
-2.3892 .times. 10.sup.-7 
Three-dimensional surface 
(1) (2) (1) (2) 
CXn 0.01451 0.00070 0.01421 0.00075 
CYn 0.00218 -0.00134 
0.00586 -0.00171 
FXn 133.4766 
-471.0622 
23.2050 -2582.3278 
FYn 888.4155 
246.0773 
56.2702 1132.5999 
FX 34.36426 
FY 31.49606 
FXn/FX 
3.8842 13.7079 0.6753 75.1457 
FYn/FY 
28.2072 7.8130 1.7866 35.9601 
FY/FX 0.9165 
__________________________________________________________________________ 
The following is a description of examples concerning the arrangement of 
surfaces of a decentered optical system according to the present invention 
which has at least one rotationally asymmetric surface that satisfies at 
least one of the above-described conditions (1-1) to (3-3). In the 
following description, the object plane and the image plane are relative 
to each other; it will be apparent that the object and image planes may be 
replaced by each other to use the optical path reversely. 
EXAMPLE 14 
As shown in FIG. 14, a decentered optical system 10 according to this 
example comprises, in order in which incident light rays from an object 
pass, a first transmitting surface T1, a first reflecting surface R1, a 
second reflecting surface R2, a third reflecting surface R3, a fourth 
reflecting surface R4, and a second transmitting surface T2. The light 
rays enter the optical system through the first transmitting surface T1 
and are reflected successively by the first reflecting surface R1, the 
second reflecting surface R2, the third reflecting surface R3, and the 
fourth reflecting surface R4. The reflected light rays exit from the 
optical system through the second transmitting surface T2 in a direction 
different from a direction in which the light rays are incident on the 
first transmitting surface T1 to reach the image plane. The image plane 
may be replaced by the object plane to use the optical path reversely. 
EXAMPLE 15 
As shown in FIG. 15, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1 and the second reflecting surface R2 are the 
identical surface. 
EXAMPLE 16 
As shown in FIG. 16, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the second 
transmitting surface T2 and the third reflecting surface R3 are the 
identical surface. 
EXAMPLE 17 
As shown in FIG. 17, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
reflecting surface R1 and the third reflecting surface R3 are the 
identical surface. 
EXAMPLE 18 
As shown in FIG. 18, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the second 
reflecting surface R2 and fourth reflecting surface R4 are the identical 
surface. 
EXAMPLE 19 
As shown in FIG. 19, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1, the second reflecting surface R2, and the fourth 
reflecting surface R4 are the identical surface. 
EXAMPLE 20 
As shown in FIG. 20, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1 and the second reflecting surface R2 are the 
identical surface, and the first reflecting surface R1 and the third 
reflecting surface R3 are the identical surface. 
EXAMPLE 21 
As shown in FIG. 21, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1 and the second reflecting surface R2 are the 
identical surface, and the second transmitting surface T2 and the third 
reflecting surface R3 are the identical surface. 
EXAMPLE 22 
As shown in FIG. 22, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
reflecting surface R1 and the third reflecting surface R3 are the 
identical surface, and the second reflecting surface R2 and the fourth 
reflecting surface R4 are the identical surface. 
EXAMPLE 23 
As shown in FIG. 23, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the second 
reflecting surface R2 and the fourth reflecting surface R4 are the 
identical surface, and the second transmitting surface T2 and the third 
reflecting surface R3 are the identical surface. 
EXAMPLE 24 
As shown in FIG. 24, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1, the second reflecting surface R2, and the fourth 
reflecting surface R4 are the identical surface, and the second 
transmitting surface T2 and the third reflecting surface R3 are the 
identical surface. 
EXAMPLE 25 
As shown in FIG. 25, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1, the second reflecting surface R2, and the fourth 
reflecting surface R4 are the identical surface, and the first reflecting 
surface R1 and the third reflecting surface R3 are the identical surface. 
EXAMPLE 26 
As shown in FIG. 26, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1 and the second reflecting surface R2 are the 
identical surface, and the second transmitting surface T2, the first 
reflecting surface R1 and the third reflecting surface R3 are the 
identical surface. 
EXAMPLE 27 
As shown in FIG. 27, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the second 
reflecting surface R2 and the fourth reflecting surface R4 are the 
identical surface, and the second transmitting surface T2, the first 
reflecting surface R1, and the third reflecting surface R3 are the 
identical surface. 
EXAMPLE 28 
As shown in FIG. 28, a decentered optical system 10 according to this 
example is the same as that shown in FIG. 14 except that the first 
transmitting surface T1, the second reflecting surface R2, and the fourth 
reflecting surface R4 are the identical surface, and the second 
transmitting surface T2, the first reflecting surface R1, and the third 
reflecting surface R3 are the identical surface. 
EXAMPLE 29 
This example relates to a machining method usable in a case where a 
decentered optical system according to the present invention consists 
essentially of a rotationally asymmetric surface and a rotationally 
symmetric surface. As shown in FIG. 29, a decentered optical system 10 
according to this example comprises, in order in which incident light rays 
from an object pass, a first transmitting surface T1, a first reflecting 
surface R1, a second reflecting surface R2, and a second transmitting 
surface T2. The light rays enter the optical system through the first 
transmitting surface T1 and are reflected successively by the first 
reflecting surface R1 and the second reflecting surface R2. The reflected 
light rays exit from the optical system through the second transmitting 
surface T2 in a direction different from a direction in which the light 
rays are incident on the first transmitting surface T1 to reach an image 
plane. The second transmitting surface T2 and the first reflecting surface 
R1 are the identical surface. In a case where the first transmitting 
surface T1 is a rotationally symmetric surface, and the first reflecting 
surface R1 and the second reflecting surface R2 are rotationally 
asymmetric surfaces, first the rotationally asymmetric surfaces R1 and R2 
are machined, and thereafter, the rotationally symmetric surface T1 is 
machined. Such a machining sequence facilitates positioning of each 
surface, and the manufacturing accuracy improves. 
EXAMPLE 30 
This example relates to a method of producing a decentered optical system 
according to the present invention in such a manner that the decentered 
optical system is divided into portions including a rotationally 
asymmetric surface and some other portions, and that each portion is first 
machined, and thereafter, the machined portions are cemented together to 
form a decentered optical system. As shown in FIG. 30, the decentered 
optical system 10 comprises a first transmitting surface T1, a first 
reflecting surface R1, a second reflecting surface R2, and a second 
transmitting surface T2 as in the case of FIG. 10. Light rays enter the 
optical system through the first transmitting surface T1 and are reflected 
successively by the first reflecting surface R1 and the second reflecting 
surface R2. The reflected light rays exit from the optical system through 
the second transmitting surface T2 in a direction different from a 
direction in which the light rays are incident on the first transmitting 
surface T1 to reach an image plane. In a case where the first transmitting 
surface T1 is a rotationally symmetric surface, while the first reflecting 
surface R1 and the second reflecting surface R2 are rotationally 
asymmetric surfaces, and the second transmitting surface T2 is a 
rotationally symmetric surface, the optical system is divided into a first 
portion 14 including the first reflecting surface R1, a second portion 15 
including the second reflecting surface R2, and a third portion 16 
including both the first transmitting surface T1 and the second 
transmitting surface T2. After surfaces of each portion have been 
machined, the three portions 14, 15 and 16 are cemented together to 
produce the decentered optical system 10. With such a production method, 
rotationally asymmetric surfaces are formed by machining plane thin 
members. Accordingly, it is possible to avoid degradation of the machining 
accuracy due to distortion or the like of components during machining. It 
should be noted that in a case where a rotationally asymmetric surface is 
produced by injection molding, the optical component is preferably as thin 
as possible. The thinner the optical component, the further the distortion 
of the resin after the injection molding can be reduced. 
EXAMPLE 31 
As shown in FIG. 31, this example relates to an ocular optical system 
having a folded optical path including a reflecting surface M, wherein the 
reflecting surface M is formed from a rotationally asymmetric surface so 
as to have power. By doing so, it is possible to omit a transmission lens 
in the ocular optical system. Moreover, the folded optical path enables 
the ocular optical system to be constructed in a compact form. It should 
be noted that an inversion prism in an ocular optical system can also be 
given power by the same way as the above. 
Similarly, as shown in FIG. 32, in the case of an ocular optical system 
having a folded optical path including two reflecting surfaces M1 and M2, 
at least one reflecting surface M1 can be formed from a rotationally 
asymmetric surface so as to have power. 
EXAMPLE 32 
As shown in FIG. 33, this example relates to an image-forming optical 
system having a folded optical path including a reflecting surface M3, 
wherein the reflecting surface M3 is formed from a rotationally asymmetric 
surface so as to have power. By doing so, it is possible to omit a 
transmission lens in the image-forming optical system. Moreover, the 
folded optical path enables the image-forming optical system to be 
constructed in a compact form. It should be noted that an inversion prism 
in an image-forming optical system can also be given power by the same way 
as the above. 
Similarly, as shown in FIG. 34, in the case of an image-forming optical 
system having a folded optical path including two reflecting surfaces M4 
and M5, at least one reflecting surface M4 can be formed from a 
rotationally asymmetric surface so as to have power. 
EXAMPLE 33 
In this example, as shown in FIG. 35, an image-forming optical system such 
as that shown in FIG. 34 is used as an objective optical system, and this 
is combined with an ocular optical system 17 consisting essentially of an 
ordinary transmission lens to form an afocal optical system for a 
telescope, a real-image finder, etc. If an objective optical system is 
formed by giving power to a prism optical system for obtaining an inverted 
image, for example, it is possible to construct a compact optical system. 
If an objective lens of a real-image finder for a camera is constructed of 
an optical system in which a rotationally asymmetric surface is used in an 
inversion prism, it is possible to obtain a compact camera finder having a 
simple structure. It should be noted that an erect image can be obtained 
by an even number of reflections, as shown in FIG. 35. 
EXAMPLE 34 
In this example, as shown in FIG. 36, an ocular optical system such as that 
shown in FIG. 32 is combined with an image-forming optical system 18 
consisting essentially of an ordinary transmission lens, which is used as 
an objective optical system, to form an afocal optical system for a 
telescope, a real-image finder, etc. Thus, it becomes possible to reduce 
the size of an afocal optical system of short focal length in particular, 
which is complicated in arrangement, to thereby obtain a compact optical 
system. The effect of reducing the size is particularly remarkable in an 
ocular optical system having a focal length of 100 millimeters or less. It 
should be noted that an erect image can be obtained by even number of 
reflections, as shown in FIG. 36. 
EXAMPLE 35 
In this example, as shown in FIG. 37, an image-forming optical system such 
as that shown in FIG. 34 is used as an objective optical system, and this 
is combined with an ocular optical system such as that shown in FIG. 32 to 
form an afocal optical system for a telescope, a real-image finder, etc. 
The combination makes it possible to achieve a further reduction in the 
size of the afocal optical system. It should be noted that if a 
rotationally asymmetric surface is used in an inversion prism, and thus 
the prism optical system is given power, it is possible to simplify the 
structure of an objective lens or an ocular lens or to omit it. In this 
case also, the afocal optical system may be arranged to obtain an erect 
image by an even number of reflections. 
The following is a description of examples of optical systems for various 
optical apparatuses which use decentered optical systems having at least 
one rotationally asymmetric surface that satisfies at least one of the 
conditions (1-1) to (3-3) according to the present invention. 
EXAMPLE 36 
In this example, as shown in the perspective view of FIG. 38, a decentered 
optical system according to the present invention is used as an ocular 
optical system of a finder 19 in a camera 21 comprising a finder 19, a 
taking lens 20, and an imaging device (not shown) such as a photographic 
film or a CCD. As shown in FIG. 39, the finder according to this example 
uses as an objective optical system an image-forming optical system 18 
consisting essentially of an ordinary transmission lens, and further uses 
as an ocular optical system 27 a decentered optical system according to 
the present invention which comprises a first transmitting surface T1, a 
first reflecting surface R1, a second reflecting surface R2, and a second 
transmitting surface T2, wherein the first reflecting surface R1 is a 
rotationally asymmetric surface. In this example, an image plane formed by 
the image-forming optical system 18 lies between the first transmitting 
surface T1 and first reflecting surface R1 of the ocular optical system 
27. 
EXAMPLE 37 
In this example, a decentered optical system according to the present 
invention is used as the objective optical system of the finder 19 in the 
camera 21 shown in FIG. 38. As shown in FIG. 40, the finder according to 
this example uses as an objective (image-forming) optical system 28 a 
decentered optical system according to the present invention which 
comprises a first transmitting surface T1, a first reflecting surface R1, 
a second reflecting surface R2, and a second transmitting surface T2, 
wherein the first reflecting surface R1 is a rotationally asymmetric 
surface. The finder further uses an ordinary transmission lens as an 
ocular optical system 17. In this example, an image plane formed by the 
image-forming optical system 28 is coincident with the second transmitting 
surface T2. 
EXAMPLE 38 
In this example, a decentered optical system according to the present 
invention is used as the whole of the optical system of the finder 19 in 
the camera 21 shown in FIG. 38. As shown in FIG. 41, the finder according 
to this example has an objective (image-forming) optical system 28 and an 
ocular optical system 27, which are integrally formed from a transparent 
member. The finder comprises a first transmitting surface T1, a first 
reflecting surface R1, a second reflecting surface R2, and a second 
transmitting surface T2. The first transmitting surface T1 and the first 
reflecting surface R1 constitute the image-forming optical system 28, and 
the second reflecting surface R2 and the second transmitting surface T2 
constitute the ocular optical system 27. At least one of the four surfaces 
T1, R1, R2 and T2 is formed from a rotationally asymmetric surface. 
EXAMPLE 39 
In this example, a decentered optical system according to the present 
invention is used as an ocular optical system of an optical system for 
each eye, which is provided in binoculars 23 such as that shown in the 
perspective view of FIG. 42. As shown in FIG. 43, the binocular optical 
system according to this example uses as an objective optical system an 
image-forming optical system 18 consisting essentially of an ordinary 
transmission lens. The binocular optical system further uses as an ocular 
optical system 27 a decentered optical system according to the present 
invention which comprises a first transmitting surface T1, a first 
reflecting surface R1, a second reflecting surface R2, and a second 
transmitting surface T2, wherein the first reflecting surface R1 and the 
second transmitting surface T2 are the identical surface, and the first 
reflecting surface R1 is a rotationally asymmetric surface. In this 
example, an image plane formed by the image-forming optical system 18 lies 
between the first transmitting surface T1 and first reflecting surface R1 
of the ocular optical system 27. 
EXAMPLE 40 
In this example, a decentered optical system according to the present 
invention is used as an objective optical system of an optical system for 
each eye, which is provided in the binoculars 23 shown in FIG. 42. As 
shown in FIG. 44, the binocular optical system according to this example 
uses as an objective (image-forming) optical system 28 a decentered 
optical system according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and the first reflecting surface R1 is a rotationally 
asymmetric surface. The binocular optical system further uses an ocular 
optical system 17 consisting essentially of an ordinary transmission lens. 
In this example, an image plane formed by the image-forming optical system 
28 is approximately coincident with the second transmitting surface T2. 
EXAMPLE 41 
In this example, a decentered optical system according to the present 
invention is used as the whole of an optical system for each eye, which is 
provided in the binoculars 23 shown in FIG. 42. As shown in FIG. 45, the 
optical system for a single eye according to this example has an objective 
(image-forming) optical system 28 and an ocular optical system 27, which 
are integrally formed from a transparent member. The optical system 
comprises a first transmitting surface T1, a first reflecting surface R1, 
a second reflecting surface R2, and a second transmitting surface T2. The 
first transmitting surface T1 and the first reflecting surface R1 
constitute the image-forming optical system 28, and the second reflecting 
surface R2 and the second transmitting surface T2 constitute the ocular 
optical system 27. All the four surfaces T1, R1, R2 and T2 are formed from 
rotationally asymmetric surfaces. 
EXAMPLE 42 
This example relates to a virtual-image finder having a virtual-image 
afocal optical system as a finder 19 of a camera 21 such as that shown in 
the perspective view of FIG. 38. As shown in FIG. 46, the finder optical 
system in this example is formed from a virtual-image afocal optical 
system 29 comprising a first transmitting surface T1, a first reflecting 
surface R1, a second reflecting surface R2, and a second transmitting 
surface T2, wherein the first reflecting surface R1 and the second 
transmitting surface T2 are the identical surface, and both the first and 
second reflecting surfaces R1 and R2 are rotationally asymmetric surfaces, 
and wherein the first reflecting surface R1 assumes to be a principal 
surface having a positive power, and the second reflecting surface R2 
assumes to be a principal surface having a negative power. 
EXAMPLE 43 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 47, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes an ordinary lens system 24 disposed on the object 
side of the decentered optical system 10. 
EXAMPLE 44 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 48, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes an ordinary lens system 24 disposed on the image 
side of the decentered optical system 10. 
EXAMPLE 45 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 49, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes an ordinary lens system 24.sub.1 disposed on the 
object side of the decentered optical system 10, and an ordinary lens 
system 24.sub.2 disposed on the image side of the decentered optical 
system 10. 
EXAMPLE 46 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 50, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes an ordinary positive lens unit 25 disposed on the 
object or image side (on the object side in the case of the illustrated 
example) of the decentered optical system 10. 
EXAMPLE 47 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 51, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes an ordinary negative lens unit 26 disposed on the 
object or image side (on the object side in the case of the illustrated 
example) of the decentered optical system 10. 
EXAMPLE 48 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 52, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes two or more lens units 30 and 31 (two in the case 
of the illustrated example) disposed on either or both of the object and 
image sides (on the object side in the case of the illustrated example) of 
the decentered optical system 10. With this arrangement, the magnification 
is changed by varying the spacing between the lens units 30 and 31 and the 
spacing between the lens units 30 and 31 on the one hand and the 
decentered optical system 10 on the other. In this case, the image plane, 
generally, moves according as the magnification changes. 
EXAMPLE 49 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 53, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes a lens unit disposed on the object or image side 
(on the object side in the case of the illustrated example) of the 
decentered optical system 10. One of the two lens units is arranged to be 
a negative lens unit (the object-side lens unit in the case of the 
illustrated example) 32, and the other lens unit is arranged to be a 
positive lens unit (the lens unit on the object side of the decentered 
optical system 10 in the case of the illustrated example) 33. With this 
arrangement, the magnification is changed by varying the spacing between 
the two lens units 32 and 33. In this case, the image plane can be fixed. 
EXAMPLE 50 
This example relates to a taking lens 20 of a camera 21 such as that shown 
in the perspective view of FIG. 38. As shown in FIG. 54, a photographic 
optical system according to this example includes a decentered optical 
system 10 according to the present invention which comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The photographic optical 
system further includes two lens units disposed on either the object or 
image side (on the object side in the case of the illustrated example) or 
on both the object and image sides, respectively, of the decentered 
optical system 10, thereby constructing the optical system of a total of 
three lens units 34, 35 and 36. With this arrangement, the magnification 
is changed by varying the spacing between the two lens units 34 and 35 and 
the spacing between the lens units 35 and 36. In this case, the image 
plane can be fixed. 
EXAMPLE 51 
In this example, a decentered optical system 10 according to the present 
invention is used as a part of an antivibration optical system used in an 
objective lens system of a camera or the like, as shown in FIG. 55. In the 
illustrated example, the decentered optical system 10 shown in FIG. 34, 
which consists essentially of two reflecting surfaces M4 and M5 to form a 
folded optical path, is used as an objective lens disposed on the image 
side of a variable-apical angle prism 37 constituting a principal part of 
the antivibration optical system. 
EXAMPLE 52 
In this example, a decentered optical system according to the present 
invention is used as a lens constituting a variable-refracting power 
optical system which is used, for example, in an objective lens system of 
a camera or the like. As shown in FIG. 56, an optical system according to 
this example has a first decentered optical system 38 having a 
rotationally asymmetric curved surface whose refracting power varies in a 
direction of X-axis perpendicular to an optical axis lying perpendicular 
to the plane of the figure, and a second decentered optical system 39 
having a rotationally asymmetric curved surface whose refracting power 
varies in a direction of Y-axis perpendicular to both the optical axis and 
the X-axis. Thus, the refracting power of the composite optical system can 
be changed by moving the first decentered optical system 38 along the 
X-axis and also moving the second decentered optical system 39 along the 
Y-axis. In the arrangement shown in FIG. 56, the entrance-side surface of 
the first decentered optical system 38 is a rotationally asymmetric curved 
surface in which the radius of curvature in the Y-axis direction decreases 
along the X-axis, and the exit-side surface of the second decentered 
optical system 39 is a rotationally asymmetric curved surface in which the 
radius of curvature in the X-axis direction increases along the Y-axis. 
EXAMPLE 53 
In this example, a decentered optical system according to the present 
invention is used as a part of an indication-within-finder optical system 
in a camera. As shown in FIG. 57, a single-lens reflex camera consists 
essentially of a taking lens 40, a quick return mirror 41, a penta prism 
42, an ocular lens 43, and a photographic film (not shown). A decentered 
optical system 10 according to the present invention is used to display, 
within the finder of the single-lens reflex camera, data, e.g. an exposure 
value, displayed on a display part 44. The decentered optical system 10 
comprises three surfaces as shown in FIG. 11, wherein the first 
transmitting surface and the second reflecting surface are formed from a 
single surface common to the two surfaces, and reflection takes place 
twice. Light form an object displayed on the display part 44 passes 
successively through the decentered optical system 10, the penta prism 42, 
and the ocular lens 43 to display, within the field of view or at the 
periphery of the visual field, an enlarged image of the object displayed 
on the display part 44. 
EXAMPLE 54 
In this example, a decentered optical system according to the present 
invention is used as a part of an autofocus (AF) optical system in a 
camera. As shown in FIG. 58, a single-lens reflex camera consists 
essentially of a taking lens 40, a quick return mirror 41, a penta prism 
42, an ocular lens 43, and a photographic film (not shown). Light from an 
object which enters the single-lens reflex camera through the taking lens 
40 passes through the quick return mirror 41 to reach an AF 
distance-measuring part 45 through a decentered optical system 10 
according to the present invention. The decentered optical system 10 
comprises three surfaces as shown in FIG. 11, wherein the first 
transmitting surface and the second reflecting surface are formed from a 
single surface common to the two surfaces, and reflection takes place 
twice. 
EXAMPLE 55 
In this example, a decentered optical system according to the present 
invention is used as a part of an automatic exposure control (AE) optical 
system in a camera. As shown in FIG. 59, a single-lens reflex camera 
consists essentially of a taking lens 40, a quick return mirror 41, a 
penta prism 42, an ocular lens 43, and a photographic film (not shown). 
Light from an object which enters the single-lens reflex camera through 
the taking lens 40 reaches the penta prism 42 via the quick return mirror 
41. A part of the light is led to a decentered optical system 10 according 
to the present invention through a reflecting surface of the penta prism 
42 and reaches an AE measuring part 46. The decentered optical system 10 
comprises three surfaces as shown in FIG. 11, wherein the first 
transmitting surface and the second reflecting surface are formed from a 
single surface common to the two surfaces, and reflection takes place 
twice. 
EXAMPLE 56 
In this example, a decentered optical system according to the present 
invention is used as an optical system for imprinting data, e.g. a date, 
in a camera. As shown in FIG. 60, a single-lens reflex camera consists 
essentially of a taking lens 40, a quick return mirror 41, a penta prism 
42, an ocular lens 43, and a photographic film 47. Data, e.g. a date, 
displayed on a date display part 48 in the single-lens reflex camera is 
imaged in a peripheral portion of the film 47 by a decentered optical 
system 10 according to the present invention. The decentered optical 
system 10 comprises three surfaces as shown in FIG. 11, wherein the first 
transmitting surface and the second reflecting surface are formed from a 
single surface common to the two surfaces, and reflection takes place 
twice. 
EXAMPLE 57 
In this example, as shown in FIG. 61, a decentered optical system 10 
according to the present invention is used as a converter lens 49 which is 
mounted in front of or behind a taking lens 40 (in front of the lens 40 in 
the illustrated example) in a camera of the like to change the focal 
length of the lens 40. In the illustrated example, a refracting decentered 
optical system such as those shown in FIGS. 1 to 4 is used. 
EXAMPLE 58 
This example relates to a camera wherein, as shown in FIG. 62, a silver 
halide film 47 is disposed at the image plane of the photographic optical 
system shown in FIG. 47, which uses the decentered optical system 10 
according to the present invention. 
EXAMPLE 59 
This example relates to a camera wherein, as shown in FIG. 63, an imaging 
device 50 is disposed at the image plane of the photographic optical 
system shown in FIG. 47, which uses the decentered optical system 10 
according to the present invention. 
EXAMPLE 60 
In this example, as shown in FIG. 64, a decentered optical system 10 
according to the present invention is used as an optical system for 
observation. The decentered optical system 10 comprises a first 
transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein the 
first reflecting surface R1 and the second transmitting surface T2 are the 
identical surface, and both the first and second reflecting surfaces R1 
and R2 are rotationally asymmetric surfaces. The optical path is reversed 
to observe, with an eye, an enlarged image of an object 51 disposed in 
front of the second transmitting surface T2 through the decentered optical 
system 10. 
EXAMPLE 61 
In this example, as shown in FIG. 65, a decentered optical system 10 
according to the present invention is arranged in the form of an image 
rotator 52. The decentered optical system 10 has a dove prism-like shape 
and comprises a first transmitting surface T1, a first reflecting surface 
R1, and a second transmitting surface T2, wherein all the three surfaces 
are formed from rotationally asymmetric surfaces. The image rotator can be 
provided with image-formation properties or the like. 
EXAMPLE 62 
In this example, as shown in FIG. 66, a decentered optical system 10 
according to the present invention is used as an objective lens 53 of a 
microscope which consists essentially of an objective lens 53 and an 
ocular lens 54 to observe an enlarged image of a specimen on a specimen 
plane 55. In the illustrated example, the decentered optical system 10 
comprises a penta prism including at least one rotationally asymmetric 
surface having power. 
EXAMPLE 63 
In this example, as shown in FIG. 67, a decentered optical system 10 
according to the present invention is used as an ocular lens 54 of a 
microscope consisting essentially of an objective lens 53 and an ocular 
lens 54 to observe an enlarged image of a specimen on a specimen plane 55. 
In the illustrated example, the decentered optical system 10 comprises a 
penta prism including at least one rotationally asymmetric surface having 
power. 
EXAMPLE 64 
In this example, as shown in FIG. 68, a decentered optical system 10 
according to the present invention is used as a relay lens 56 of a 
microscope consisting essentially of an objective lens 53, a relay lens 56 
for relaying an intermediate image, and an ocular lens 54 to observe an 
enlarged image of a specimen on a specimen plane 55. In the illustrated 
example, the decentered optical system 10 comprises a penta prism 
including at least one rotationally asymmetric surface having power. 
EXAMPLE 65 
In this example, as shown in FIG. 69, a decentered optical system 10 
according to the present invention which consists essentially of a single 
reflecting surface is used as a reflecting mirror 58 for converting a 
divergent bundle of rays from a light source 57 into a convergent bundle 
of rays in an illumination optical system for a microscope. 
EXAMPLE 66 
In this example, as shown in FIG. 70, a rotationally asymmetric surface 
according to the present invention is applied to a beam-splitting surface, 
a reflecting surface, etc. of a beam-splitting system 59 in an 
incident-light illumination optical system for a microscope consisting 
essentially of a light source 57 and a beam-splitting system 59, wherein a 
bundle of light rays from the light source 57 is reflected by the 
beam-splitting system 59, and the reflected ray bundle is directed onto a 
specimen plane 55 by an objective lens 53, and then light reflected and 
scattered by a specimen on the specimen plane 55 is made to enter an 
ocular lens (not shown) through the objective lens 53 and the 
beam-splitting system 59. It should be noted that, in the illustrated 
example, a rotationally asymmetric surface according to the present 
invention is also used as a reflecting mirror 58 for converting a 
divergent bundle of rays from the light source 57 into a convergent bundle 
of rays. 
EXAMPLE 67 
In this example, as shown in FIG. 71, a rotationally asymmetric surface 
according to the present invention is applied to reflecting surfaces, etc. 
of a penta prism constituting an optical deflection system 60 in a 
transmission illumination system for a microscope which consists 
essentially of a light source 57 and an optical deflection system 60 to 
illuminate a specimen plane 55 from below it. It should be noted that, in 
the illustrated example, a rotationally asymmetric surface according to 
the present invention is also used as a reflecting mirror 58 for 
converting a divergent bundle of rays from the light source 57 into a 
convergent bundle of rays. 
EXAMPLE 68 
In this example, as shown in FIG. 72, a decentered optical system 10 
according to the present invention is applied to a multi-discussion 
microscope. In the multi-discussion microscope, a bundle of light rays 
from an objective lens 53 is divided into two ray bundles by a 
beam-splitting system 59. One ray bundle is led directly to one ocular 
lens 54 to enable a main microscopic examiner to perform observation. The 
other ray bundle divided by the beam-splitting system 59 is led to another 
ocular lens 54 through an optical deflection system 60 to enable a 
sub-microscopic examiner to perform observation. The beam-splitting system 
59 and the optical deflection system 60 are each constructed of a 
decentered optical system 10 according to the present invention. 
EXAMPLE 69 
In this example, as shown in FIG. 73, a decentered optical system 10 
according to the present invention is applied to an image-drawing device 
for a microscope, in which an image of a sample on a specimen plane 55 
which is observed through an objective lens 53 and an image which is being 
drawn on an image-drawing plane 61 are combined together by a 
beam-splitting system 59 so as to be capable of being simultaneously 
observed through an ocular lens 54. A decentered optical system 10 
according to the present invention is used as an optical deflection system 
60 disposed in the image-drawing optical path. In the illustrated example, 
the decentered optical system 10 comprises a penta prism including at 
least one rotationally asymmetric surface having power. 
EXAMPLE 70 
As shown in FIG. 74, this example relates to an optical system of an 
autofocus microscope consisting essentially of an objective lens 53, an 
optical deflection reflecting prism 62, and an ocular lens 54, wherein a 
decentered optical system 10 according to the present invention is pasted 
on a reflecting surface of the optical deflection reflecting prism 62, and 
a bundle of light rays from a sample on a specimen plane 55 is made to 
enter a focus detector 63 through the decentered optical system 10, 
thereby performing automatic focusing. The decentered optical system 10 
comprises three surfaces as shown in FIG. 11, wherein the first 
transmitting surface and the second reflecting surface are formed from a 
single surface common to the two surfaces, and reflection takes place 
twice. 
EXAMPLE 71 
In this example, as shown in FIG. 75, a decentered optical system 10 
according to the present invention is used in an inverted microscope 
designed to observe a specimen plane 55 from below it. A decentered 
optical system 10 according to the present invention is used to constitute 
each of optical deflection systems 60 for leading a bundle of light rays 
from an objective lens 53 to an ocular lens 54. In the illustrated 
example, either of the decentered optical systems 10 comprises a penta 
prism including at least one rotationally asymmetric surface having power. 
EXAMPLE 72 
The following is a description of examples in which a decentered optical 
system according to the present invention is applied to an endoscope. In 
the following description, the term "endoscope" means an endoscope 64 
using an image guide optical fiber bundle and a relay lens system as shown 
in FIG. 76, and a video endoscope 71 such as that shown in FIG. 77, unless 
otherwise specified. The endoscope 64 shown in FIG. 76 has an insert part 
65 containing an image-forming optical system and illumination optical 
system (not shown), a camera 66, a monitor 67, and a light source unit 68. 
The image-forming optical system, together with a light guide for applying 
light in the direction of the visual field of the image-forming optical 
system, is incorporated in a distal end portion 69 of the insert part 65. 
In the insert part 65, a relay lens system, which is an image and pupil 
transfer optical system, is provided subsequently to the image-forming 
optical system. An ocular optical system (not shown) is disposed in the 
proximal portion of the endoscope 64. The camera 66, which serves as an 
imaging device, can be attached to the proximal portion of the endoscope 
64 at a position subsequent to the ocular optical system. Illuminating 
light from the light source unit 68 is supplied through a light guide 
cable 70 and passed through the proximal portion, the insert part 65, and 
the distal end portion 69 to illuminate an area in the direction of the 
visual field. 
The video endoscope 71 shown in FIG. 77 contains an image-forming optical 
system and an illumination optical system. The video endoscope 71 is 
associated with a light source unit 72 for supplying illuminating light, a 
video processor 73 for executing processing of signals associated with the 
video endoscope 71, a monitor 74 for displaying video signals outputted 
from the video processor 73, a VTR deck 75 and video disk 76 connected to 
the video processor 73 to record video signals and so forth, and a video 
printer 77 for printing out video signals in the form of images. The video 
endoscope 71 has an insert part 78 with a distal end portion 79. An 
image-forming optical system, an imaging device, and a light guide for 
applying light in the direction of the visual field are incorporated in 
the distal end portion 79. 
FIGS. 78(a), 78(b) and 78(c) show some examples in which a decentered 
optical system 10 having a rotationally asymmetric surface according to 
the present invention is used in the objective optical systems provided in 
the distal end portions of these endoscopes. FIG. 78(a) shows the distal 
end portion of a side-viewing video endoscope. A decentered optical system 
10 according to the present invention is disposed behind a lens 80 also 
serving as a protective glass. The decentered optical system 10 comprises 
a first transmitting surface T1, a first reflecting surface R1, a second 
reflecting surface R2, and a second transmitting surface T2, wherein at 
least one of the four surfaces is formed from a rotationally asymmetric 
surface. The optical axis is deflected through approximately 90.degree. by 
the decentered optical system 10, and a two-dimensional imaging device 81 
is disposed at the image plane of the decentered optical system 10. It is, 
of course, possible to dispose an end face of an optical fiber bundle in 
place of the two-dimensional imaging device 81 to thereby construct an 
endoscope such as that shown in FIG. 76. 
FIG. 78(b) shows the distal end portion of an endoscope using an optical 
fiber bundle 82 for guiding an endoscopic image. This endoscope is 
arranged to enable observation of an object in a diagonally forward 
direction. A decentered optical system 10 according to the present 
invention is disposed behind a lens 80 also serving as a protective glass. 
The decentered optical system 10 comprises a first transmitting surface 
T1, a first reflecting surface R1, a second reflecting surface R2, and a 
second transmitting surface T2, wherein the first transmitting surface T1 
and the second reflecting surface R2 are the identical surface, and at 
least one of the four surfaces is formed from a rotationally asymmetric 
surface. The optical axis is deflected through several tens of degrees by 
the decentered optical system 10, and an end face of an optical fiber 
bundle 82 is disposed at the image plane of the decentered optical system 
10. 
FIG. 78(c) shows the distal end portion of a direct-view video endoscope in 
which a decentered optical system 10 according to the present invention, 
such as that shown in FIG. 12, is disposed. The decentered optical system 
10 comprises a first transmitting surface T1, a first reflecting surface 
R1, a second reflecting surface R2, and a second transmitting surface T2, 
wherein at least one of the four surfaces is formed from a rotationally 
asymmetric surface. A two-dimensional imaging device 81 is disposed at an 
image plane tilted with respect to the optical axis. 
EXAMPLE 73 
As shown in FIGS. 79(a) and 79(b), this example relates to arrangements 
similar to those shown in FIGS. 78(a) and 78(b), wherein a transparent 
protective plate 83 is disposed on the entrance side of the decentered 
optical system 10 in place of the lens 80, which also serves as a 
protective glass [it should, however, be noted that in FIG. 79(b) a 
two-dimensional imaging device 81 is disposed at the image plane of the 
decentered optical system 10]. 
EXAMPLE 74 
As shown in FIGS. 80(a) and 80(b), this example relates to arrangements 
similar to those shown in FIGS. 78(a) and 78(b), wherein the first 
transmitting surface T1 on the entrance side of the decentered optical 
system 10 is a plane surface, and the lens 80, which also serves as a 
protective glass, is omitted [in FIGS. 80(a) and 80(b), a two-dimensional 
imaging device 81 or optical fiber bundle 82 disposed at the image plane 
is not shown]. 
EXAMPLE 75 
As shown in FIGS. 81(a) and 81(b), this example relates to arrangements 
similar to those shown in FIGS. 79(a) and 79(b), wherein the second 
transmitting surface T2 on the exit side of the decentered optical system 
10 is a plane surface. 
EXAMPLE 76 
As shown in FIGS. 82(a) and 82(b), this example relates to arrangements 
similar to those shown in FIGS. 81(a) and 81(b), wherein the image plane 
of the decentered optical system 10 is made coincident with the plane 
surface T2 on the exit side of the decentered optical system 10, and a 
two-dimensional imaging device 81 is placed in close contact with the 
surface T2. 
EXAMPLE 77 
As shown in FIGS. 83(a) and 83(b), this example relates to arrangements 
similar to those shown in FIGS. 81(a) and 81(b), wherein the second 
transmitting surface T2 on the exit side of the decentered optical system 
10 is a plane surface. The arrangements differ from those shown in FIGS. 
81(a) and 81(b) in that one end of an optical fiber bundle 82 is disposed 
at the image plane of the decentered optical system 10 in place of the 
two-dimensional imaging device 81. 
EXAMPLE 78 
As shown in FIGS. 84(a) and 84(b), this example relates to arrangements 
similar to those shown in FIGS. 82(a) and 82(b), wherein the image plane 
of the decentered optical system 10 is made coincident with the plane 
surface T2 on the exit side of the decentered optical system 10. In this 
example, one end of an optical fiber bundle 82 is disposed in place of the 
two-dimensional imaging device 81. 
EXAMPLE 79 
As shown in FIGS. 85(a) and 85(b), this example relates to arrangements 
similar to those shown in FIGS. 80(a) and 80(b), wherein the first 
transmitting surface T1 on the entrance side of the decentered optical 
system 10 is a plane surface, and the lens 80, which also serves as a 
protective glass, is omitted. In this example, one end of an optical fiber 
bundle 82 is disposed at the image plane of the decentered optical system 
10. 
EXAMPLE 80 
In this example, a crystalline material, e.g. sapphire, is used as the 
protective plate 83 disposed on the entrance side of the decentered 
optical system 10 in the arrangements shown in FIGS. 81(a), 81(b) and so 
forth. 
EXAMPLE 81 
As shown in FIGS. 86(a) and 86(b), this example relates to arrangements 
similar to those shown in FIGS. 79(a) and 79(b), wherein the first surface 
of the endoscope objective optical system (in this case, the front surface 
of the transparent protective plate 83) is recessed inward from the 
enclosure of the distal end of the endoscope. In other examples also, the 
first surface of the endoscope objective optical system may be similarly 
recessed inward from the enclosure of the endoscope distal end. 
EXAMPLE 82 
As shown in FIGS. 87(a) and 87(b), this example relates to arrangements 
similar to those shown in FIGS. 79(a) and 79(b), wherein the first surface 
of the endoscope objective optical system (in this case, the front surface 
of the transparent protective plate 83) projects outward from the 
enclosure of the distal end of the endoscope. In other examples also, the 
first surface of the endoscope objective optical system may similarly 
project outward from the enclosure of the endoscope distal end. 
EXAMPLE 83 
In this example, a decentered optical system 10 according to the present 
invention is disposed to correct decentration aberrations produced by an 
objective optical system of a binocular stereoscopic microscope. FIG. 88 
shows an optical system of a microscope which consists essentially of a 
single objective optical system 84 common to two optical systems for left 
and right eyes, and a combination of a variable-magnification optical 
system 85, an image-forming optical system 86, and an ocular optical 
system 87, which is disposed on each of optical axes for left and right 
eyes, whereby an object disposed on a common object plane 88 can be 
stereoscopically observed. In this example, decentered optical systems 10 
according to the present invention are disposed between the objective 
optical system 84 and the left and right variable-magnification optical 
systems 85, respectively, to correct decentration aberrations produced 
owing to the fact that the optical axes for left and right eyes are 
shifted rightwardly and leftwardly with respect to the optical axis of the 
objective optical system 84. As the decentered optical systems 10 in this 
example, refracting decentered optical systems such as those shown for 
example in FIGS. 1 to 4 are used. It is, of course, possible to use other 
types of decentered optical system having a reflecting surface. 
EXAMPLE 84 
In this example, as shown in FIG. 89, a decentered optical system 10 
according to the present invention is used to constitute any of a 
plurality of lens units (a first lens unit of a total of three lens units 
in the illustrated example) constituting each of left and right 
variable-magnification optical systems 85 in a binocular stereoscopic 
microscope such as that shown in FIG. 88 to correct decentration 
aberrations produced owing to the fact that the optical axes for left and 
right eyes are shifted rightwardly and leftwardly with respect to the 
optical axis of the objective optical system 84. As the decentered optical 
systems 10 in this example, refracting decentered optical systems such as 
those shown for example in FIGS. 1 to 4 are used. It is, of course, 
possible to use other types of decentered optical system having a 
reflecting surface. 
EXAMPLE 85 
In this example, as shown in FIG. 90, a decentered optical system 10 
according to the present invention is used to constitute each of left and 
right image-forming optical systems 86 in a binocular stereoscopic 
microscope such as that shown in FIG. 88 to correct decentration 
aberrations produced owing to the fact that the optical axes for left and 
right eyes are shifted rightwardly and leftwardly with respect to the 
optical axis of the objective optical system 84. As the decentered optical 
systems 10 in this example, refracting decentered optical systems such as 
those shown for example in FIGS. 1 to 4 are used. It is, of course, 
possible to use other types of decentered optical system having a 
reflecting surface. 
EXAMPLE 86 
In this example, as shown in FIG. 91, a decentered optical system 10 
according to the present invention is used to constitute each of left and 
right ocular optical systems 87 in a binocular stereoscopic microscope 
such as that shown in FIG. 88 to correct decentration aberrations produced 
owing to the fact that the optical axes for left and right eyes are 
shifted rightwardly and leftwardly with respect to the optical axis of the 
objective optical system 84. As the decentered optical systems 10 in this 
example, refracting decentered optical systems such as those shown for 
example in FIGS. 1 to 4 are used. It is, of course, possible to use other 
types of decentered optical system having a reflecting surface. 
EXAMPLE 87 
In this example, as shown in FIG. 92, a decentered optical system 10 
according to the present invention is applied to a binocular stereoscopic 
microscope having objective optical systems 89 for optical axes for left 
and right eyes, respectively, which form an angle with a common object 
plane 88. A decentered optical system 10 according to the present 
invention is disposed on the object side of each of the objective optical 
systems 89 to correct decentration aberrations produced owing to the fact 
that the left and right objective optical systems 89 are tilted with 
respect to the object plane 88. As the decentered optical systems 10 in 
this example, refracting decentered optical systems such as those shown 
for example in FIGS. 1 to 4 are used. It is, of course, possible to use 
other types of decentered optical system having a reflecting surface. 
EXAMPLE 88 
In this example, as shown in FIG. 93, a decentered optical system 10 
according to the present invention is used to constitute an objective lens 
90 constituting a part or the whole of each of left and right objective 
optical systems 89 in a binocular stereoscopic microscope arranged as 
shown in FIG. 92 to correct decentration aberrations produced owing to the 
fact that the left and right objective optical systems 89 are tilted with 
respect to the object plane 88. As the decentered optical systems 10 in 
this example, refracting decentered optical systems such as those shown 
for example in FIGS. 1 to 4 are used. It is, of course, possible to use 
other types of decentered optical system having a reflecting surface. 
EXAMPLE 89 
In this example, as shown in FIG. 94, a decentered optical system 10 
according to the present invention is used to constitute each of left and 
right ocular optical systems 87 in a binocular stereoscopic microscope 
arranged as shown in FIG. 92 to correct decentration aberrations produced 
owing to the fact that the left and right objective optical systems 89 are 
tilted with respect to the object plane 88. As the decentered optical 
systems 10 in this example, refracting decentered optical systems such as 
those shown for example in FIGS. 1 to 4 are used. It is, of course, 
possible to use other types of decentered optical system having a 
reflecting surface. 
EXAMPLE 90 
In this example, a decentered optical system 10 according to the present 
invention is used in an optical system of an endoscope camera adapter 
which is attached to an ocular lens part of an endoscope, e.g. a soft 
endoscope, which has an ocular lens to project an endoscopic image onto an 
imaging device. As shown in FIG. 95, an endoscope has an observation 
optical system 91, and a camera adapter 92 is attached to the observation 
side of the observation optical system 91. In the camera adapter 92, a 
decentered optical system 10 according to the present invention, which is 
arranged in the form of a penta prism including at least one rotationally 
asymmetric surface having power, is disposed, and a two-dimensional 
imaging device 93 is disposed at the image plane of the decentered optical 
system 10. 
EXAMPLE 91 
In this example, as shown in FIG. 96, a plane-parallel plate 94 which 
serves as a protective glass is provided on the entrance side of a 
decentered optical system 10 in an endoscope camera adapter 92 arranged as 
shown in FIG. 95. 
EXAMPLE 92 
In this example, as shown in FIG. 97, an endoscope camera adapter 92 
arranged as shown in FIG. 95 is provided with a mechanism for adjusting 
the spacing between an image-forming decentered optical system 10 and a 
two-dimensional imaging device 93, thereby enabling focus adjustment. 
EXAMPLE 93 
In this example, as shown in FIG. 98, an endoscope camera adapter 92 
arranged as shown in FIG. 95 is modified such that the first reflecting 
surface of a penta prism, which constitutes the decentered optical system 
10, is formed as an optical path splitting surface 95, e.g. a half-mirror, 
thereby enabling an endoscopic image to be directly observed 
simultaneously with imaging by the two-dimensional imaging device 93. In 
this example, an optical axis and power correcting optical element 96 is 
pasted on the optical path splitting surface 95, thereby making the 
observation direction approximately parallel to the optical axis of light 
rays entering the camera adapter 92 from the observation optical system 
91. 
In the foregoing, a description has been given of basic examples of 
decentered optical systems according to the present invention, examples 
relating to the arrangement of surfaces, and examples of application of 
the decentered optical systems to various optical elements and optical 
apparatuses. However, it should be noted that the present invention is not 
necessarily limited to these examples, and that various modifications may 
be imparted thereto. 
The above-described optical systems according to the present invention may 
be arranged, for example, as follows: 
[1] A decentered optical system comprising at least one rotationally 
asymmetric surface having no axis of rotational symmetry in nor out of the 
surface, wherein rotationally asymmetric aberrations due to decentration 
are corrected by the rotationally asymmetric surface. 
[2] The optical system as set forth in [1], wherein the rotationally 
asymmetric surface is a plane-symmetry three-dimensional surface 
characterized by having only one plane of symmetry. 
[3] The optical system as set forth in [2], wherein the plane of symmetry 
of said rotationally asymmetric surface is disposed in a plane 
approximately coincident with a decentration plane, which is a direction 
of decentration of each surface constituting the optical system. 
[4] The optical system as set forth in any one of [1] to [3], wherein said 
rotationally asymmetric surface is used as a reflecting surface. 
[5] The optical system as set forth in [4], wherein said reflecting surface 
is a surface having totally reflecting action or reflecting action. 
[6] The optical system as set forth in [2] or [3, wherein said rotationally 
asymmetric surface having only one plane of symmetry is used as a 
back-coated mirror. 
[7] The optical system as set forth in any one of [1] to [6], wherein, 
assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, said rotationally asymmetric surface is tilted 
with respect to said principal ray. 
[8] The optical system as set forth in any one of [1] to [7], wherein, 
assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, and that a Y-axis is taken in the decentration 
plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that said principal ray and a light ray 
which is parallel to said principal ray at a slight distance d in the 
X-axis direction are made to enter said optical system from an entrance 
side thereof, and the sine of an angle formed between said two rays as 
projected on the XZ-plane at an exit side of said optical system is 
denoted by NA'X, and further that a value obtained by dividing the 
distance d between said parallel rays by the NA'X is denoted by FX, and 
the focal length in the X-axis direction of that portion of said 
rotationally asymmetric surface on which the axial principal ray strikes 
is denoted by FXn, the following condition is satisfied: 
EQU -1000&lt;FX/FXn&lt;1000 (1-1) 
[9] The optical system as set forth in [8], wherein said FX and FXn satisfy 
the following condition: 
EQU -100&lt;FX/FXn&lt;100 (1-2) 
[10] The optical system as set forth in [8], wherein said FX and FXn 
satisfy the following condition: 
EQU -10&lt;FX/FXn&lt;10 (1-3) 
[11] The optical system as set forth in any one of [1] to [10], wherein, 
assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, and that a Y-axis is taken in the decentration 
plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
Y-axis direction are made to enter said optical system from the entrance 
surface side thereof, and the sine of an angle formed between said two 
rays in the YZ-plane at the exit side of said optical system is denoted by 
NA'Y, and further that a value obtained by dividing the distance d between 
said parallel rays by the NA'Y is denoted by FY, and the focal length in 
the Y-axis direction of that portion of said rotationally asymmetric 
surface on which the axial principal ray strikes is denoted by FYn, the 
following condition is satisfied: 
EQU -1000&lt;FY/FYn&lt;1000 (2-1) 
[12] The optical system as set forth in [11], wherein said FY and FYn 
satisfy the following condition: 
EQU -100&lt;FY/FYn&lt;100 (2-2) 
[13] The optical system as set forth in [11], wherein said FY and FYn 
satisfy the following condition: 
EQU -10&lt;FY/FYn&lt;10 (2-3) 
[14] The optical system as set forth in any one of [1] to [13], wherein, 
assuming that a light ray emanating from the center of an object point and 
passing through the center of a pupil to reach the center of an image is 
defined as a principal ray, and that a Y-axis is taken in the decentration 
plane of the surface, and an X-axis is taken in a direction 
perpendicularly intersecting the Y-axis, and further an axis constituting 
an orthogonal coordinate system in combination with the X- and Y-axes is 
defined as a Z-axis, and further that the principal ray and a light ray 
which is parallel to the principal ray at a slight distance d in the 
X-axis direction are made to enter said optical system from an entrance 
side thereof, and the sine of an angle formed between said two rays as 
projected on the XZ-plane at an exit side of said optical system is 
denoted by NA'X, and a value obtained by dividing the distance d between 
said parallel rays by the NA'X is denoted by FX, and further that the 
principal ray and a light ray which is parallel to the principal ray at a 
slight distance d away from it in the Y-axis direction are made to enter 
said optical system from the entrance side thereof, and the sine of an 
angle formed between said two rays in the YZ-plane at the exit side of 
said optical system is denoted by NA'Y, and a value obtained by dividing 
the distance d between said parallel rays by the NA'Y is denoted by FY, 
the following condition is satisfied: 
EQU 0.01&lt;.vertline.FY/FX.vertline.&lt;100 (3-1) 
[15] The optical system as set forth in [14], wherein said FX and FY 
satisfy the following condition: 
EQU 0.1&lt;.vertline.FY/FX.vertline.&lt;10 (3-2) 
[16] The optical system as set forth in [14], wherein said FX and FY 
satisfy the following condition: 
EQU 0.5&lt;.vertline.FY/FX.vertline.&lt;2 (3-3) 
[17] The optical system as set forth in any one of [1] to [16], which 
comprises only a first reflecting surface, wherein light rays are 
reflected by the first reflecting surface in a direction different from a 
direction in which the light rays are incident thereon. 
[18] The optical system as set forth in any one of [1] to [16], which 
comprises a first reflecting surface and a first transmitting surface, 
wherein light rays enter the optical system through the first transmitting 
surface and are reflected by the first reflecting surface to exit from the 
optical system through the first transmitting surface in a direction 
different from a direction in which the light rays are incident on the 
first transmitting surface. 
[19] The optical system as set forth in any one of [1] to [16], which 
comprises a first reflecting surface, a first transmitting surface, and a 
second transmitting surface, wherein light rays enter the optical system 
through the first transmitting surface and are reflected by the first 
reflecting surface to exit from the optical system through the second 
transmitting surface in a direction different from a direction in which 
the light rays are incident on the first transmitting surface. 
[20] The optical system as set forth in any one of [1] to [16], which 
comprises a first reflecting surface, a second reflecting surface, and a 
first transmitting surface, wherein light rays enter the optical system 
through the first transmitting surface and are reflected by the first 
reflecting surface and then reflected by the second reflecting surface to 
exit from the optical system through the first transmitting surface. 
[21] The optical system as set forth in any one of [1] to [16], which 
comprises a first reflecting surface, a second reflecting surface, a first 
transmitting surface, and a second transmitting surface, wherein light 
rays enter the optical system through the first transmitting surface and 
are reflected by the first reflecting surface and then reflected by the 
second reflecting surface to exit from the optical system through the 
second transmitting surface. 
[22] The optical system as set forth in [21], wherein an optical path of 
the optical system has portions intersecting each other. 
[23] The optical system as set forth in [21], wherein an optical path of 
the optical system has no portions intersecting each other. 
[24] The optical system as set forth in [21], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface. 
[25] The optical system as set forth in [21], wherein the first reflecting 
surface and the second transmitting surface are the identical surface. 
[26] The optical system as set forth in any one of [1] to [16], which 
comprises a first reflecting surface, a second reflecting surface, a third 
reflecting surface, a first transmitting surface, and a second 
transmitting surface, wherein light rays enter the optical system through 
the first transmitting surface and are reflected successively by the 
first, second and third reflecting surfaces to exit from the optical 
system through the second transmitting surface in a direction different 
from a direction in which the light rays are incident on the first 
transmitting surface. 
[27] The optical system as set forth in [26], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface. 
[28] The optical system as set forth in [26], wherein the first reflecting 
surface and the third reflecting surface are the identical surface. 
[29] The optical system as set forth in [26], wherein the first 
transmitting surface and the third reflecting surface are the identical 
surface. 
[30] The optical system as set forth in [26], wherein the second 
transmitting surface and the second reflecting surface are the identical 
surface. 
[31] The optical system as set forth in any one of [1] to [16], which 
comprises at least a first reflecting surface, a second reflecting 
surface, a third reflecting surface, a fourth reflecting surface, a first 
transmitting surface, and a second transmitting surface, wherein light 
rays enter the optical system through the first transmitting surface and 
are reflected successively by the first, second, third and fourth 
reflecting surfaces to exit from the optical system through the second 
transmitting surface in a direction different from a direction in which 
the light rays are incident on the first transmitting surface. 
[32] The optical system as set forth in [31], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface. 
[33] The optical system as set forth in [31], wherein the second 
transmitting surface and the third reflecting surface are the identical 
surface. 
[34] The optical system as set forth in [31], wherein the first reflecting 
surface and the third reflecting surface are the identical surface. 
[35] The optical system as set forth in [31], wherein the second reflecting 
surface and the fourth reflecting surface are the identical surface. 
[36] The optical system as set forth in [31], wherein the first 
transmitting surface, the second reflecting surface, and the fourth 
reflecting surface are the identical surface. 
[37 ] The optical system as set forth in [31], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface, and wherein the first reflecting surface and the third reflecting 
surface are the identical surface. 
[38] The optical system as set forth in [31], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface, and wherein the second transmitting surface and the third 
reflecting surface are the identical surface. 
[39] The optical system as set forth in [31], wherein the first reflecting 
surface and the third reflecting surface are the identical surface, and 
wherein the second reflecting surface and the fourth reflecting surface 
are the identical surface. 
[40] The optical system as set forth in [31], wherein the second reflecting 
surface and the fourth reflecting surface are the identical surface, and 
wherein the second transmitting surface and the third reflecting surface 
are the identical surface. 
[41] The optical system as set forth in [31], wherein the first 
transmitting surface, the second reflecting surface, and the fourth 
reflecting surface are the identical surface, and wherein the second 
transmitting surface and the third reflecting surface are the identical 
surface. 
[42] The optical system as set forth in [31], wherein the first 
transmitting surface, the second reflecting surface, and the fourth 
reflecting surface are the identical surface, and wherein the first 
reflecting surface and the third reflecting surface are the identical 
surface. 
[43] The optical system as set forth in [31], wherein the first 
transmitting surface and the second reflecting surface are the identical 
surface, and wherein the second transmitting surface, the first reflecting 
surface, and the third reflecting surface are the identical surface. 
[44] The optical system as set forth in [31], wherein the second reflecting 
surface and the fourth reflecting surface are the identical surface, and 
wherein the second transmitting surface, the first reflecting surface, and 
the third reflecting surface are the identical surface. 
[45] The optical system as set forth in [31], wherein the first 
transmitting surface, the second reflecting surface, and the fourth 
reflecting surface are the identical surface, and wherein the second 
transmitting surface, the first reflecting surface, and the third 
reflecting surface are the identical surface. 
[46] The optical system as set forth in any one of [1] to [45], wherein a 
rotationally asymmetric surface is first machined, and then a rotationally 
symmetric surface is machined. 
[47] The optical system as set forth in any one of [1] to [45], which is 
produced by cementing together an optical component having at least one 
rotationally asymmetric surface machined thereon and an optical component 
having another surface machined thereon. 
[48] The optical system as set forth in any one of [1] to [47], which is 
arranged as an ocular optical system having a folded optical path, wherein 
a reflecting surface constituting said folded optical path has power. 
[49] The optical system as set forth in any one of [1] to [47], which is 
arranged as an image-forming optical system having a folded optical path, 
wherein a reflecting surface constituting said folded optical path has 
power. 
[50] An optical system which is formed as an afocal optical system from a 
combination of the image-forming optical system of [49] and an ocular 
optical system. 
[51] The optical system as set forth in [50], wherein said afocal optical 
system is arranged to obtain an erect image by an even number of 
reflections. 
[52] An optical system which is formed as an afocal optical system from a 
combination of an image-forming optical system and the ocular optical 
system of [48]. 
[53] The optical system as set forth in [52], wherein said afocal optical 
system is arranged to obtain an erect image by an even number of 
reflections. 
[54] An optical system which is formed as an afocal optical system from a 
combination of the image-forming optical system of [49] and the ocular 
optical system of [48]. 
[55] The optical system as set forth in [54], wherein said afocal optical 
system is arranged to obtain an erect image by an even number of 
reflections. 
[56] The optical system as set forth in any one of [1] to [55], which is 
arranged as a camera optical system and provided as optical means in a 
camera. 
[57] The optical system as set forth in [56], wherein said camera optical 
system is disposed in a real-image finder optical system of a camera. 
[58] The optical system as set forth in [56], wherein said camera optical 
system is disposed in a virtual-image finder optical system of a camera. 
[59] The optical system as set forth in [57] or [58], wherein said camera 
optical system is disposed in an objective lens system of a finder optical 
system. 
[60] The optical system as set forth in [57] or [58], wherein said camera 
optical system is disposed in an ocular optical system of a finder optical 
system. 
[61] The optical system as set forth in [59], wherein at least one lens 
whose refracting power is not zero is disposed on the object side of the 
objective lens system of said camera finder optical system, and said 
camera optical system is disposed on the observation side of the lens. 
[62] The optical system as set forth in [59], wherein said camera optical 
system is disposed on the object side of the objective lens system of said 
camera finder optical system, and at least one lens whose refracting power 
is not zero is disposed on the observation side of said camera optical 
system. 
[63] The optical system as set forth in [59], wherein the objective lens 
system of said camera finder optical system has: at least one lens whose 
refracting power is not zero, said lens being disposed on the object side; 
said camera optical system disposed on the observation side of said lens; 
and at least one lens whose refracting power is not zero, said lens being 
disposed on the observation side of said camera optical system. 
[64] The optical system as set forth in [59], wherein the objective lens 
system of said camera finder optical system comprises two lens units, that 
is, said camera optical system, and a positive lens unit whose overall 
refracting power is greater than zero. 
[65] The optical system as set forth in [59], wherein the objective lens 
system of said camera finder optical system comprises two lens units, that 
is, said camera optical system, and a negative lens unit whose overall 
refracting power is smaller than zero. 
[66] The optical system as set forth in [64] or [65], wherein said 
objective lens system changes a magnification by varying a spacing between 
said camera optical system and said lens unit. 
[67] The optical system as set forth in [59], wherein said objective lens 
system comprises three lens units, that is, said camera optical system, a 
positive lens unit whose overall refracting power is greater than zero, 
and a negative lens unit whose overall refracting power is smaller than 
zero. 
[68] The optical system as set forth in [67]. wherein said objective lens 
system changes a magnification by varying a spacing between said camera 
optical system and said positive lens unit and a spacing between said 
positive lens unit and said negative lens unit. 
[69] The optical system as set forth in [56], wherein said camera optical 
system is disposed in an indication-within-finder optical system of a 
real-image finder optical system having an objective lens system for 
forming an object image, and an ocular optical system for observing said 
object image, said indication-within-finder optical system being arranged 
to form an indication image different from said object image to display 
photographic information or the like. 
[70] The optical system as set forth in [56], which has an objective lens 
system for forming an object image, imaging means for receiving the object 
image, and a distance-measuring part for measuring a displacement between 
said imaging means and an object image formation position which changes 
with the object distance, wherein said camera optical system is provided 
as optical means constituting said distance-measuring part. 
[71] The optical system as set forth in [56], which has an objective lens 
system for forming an object image, imaging means for receiving the object 
image, and a photometer part for measuring an optimal value of an exposure 
to said imaging means which changes with the brightness of the object, 
wherein said camera optical system is provided as optical means 
constituting said photometer part. 
[72] The optical system as set forth in [56], which has an objective lens 
system for forming an object image, imaging means for receiving the object 
image, a date display part for displaying an information image, e.g. a 
date of photo shooting, and an information image forming optical system 
for forming on said imaging means the information image displayed by said 
date display part, wherein said camera optical system is provided as said 
information image forming optical system. 
[73] The optical system as set forth in [56], which has an objective lens 
system for forming an object image, and a silver halide film provided as 
imaging means for receiving the object image, wherein said camera optical 
system is provided as said objective lens system. 
[74] The optical system as set forth in [56], which has an objective lens 
system for forming an object image, and an electronic imaging device 
provided as imaging means for receiving the object image, wherein said 
camera optical system is provided as said objective lens system. 
[75] The optical system as set forth in [73] or [74], wherein said 
objective lens system has said camera optical system, and an antivibration 
optical system having the function of preventing formation of a blurred 
image, e.g. camera-shake, due to vibration. 
[76] The optical system as set forth in [75], wherein said antivibration 
optical system is formed from a wedge-shaped prism. 
[77] The optical system as set forth in [73] or [74], wherein said camera 
optical system provided in said objective lens system is arranged such 
that refracting power is variable. 
[78] The optical system as set forth in [77], wherein said camera optical 
system has a first decentered optical system with a rotationally 
asymmetric curved surface whose refracting power varies in a first 
direction perpendicular to an optical axis, and a second decentered 
optical system with a rotationally asymmetric curved surface whose 
refracting power varies in a second direction perpendicular to both the 
optical axis and the first direction, so that refracting power of said 
camera optical system is changed by moving said first decentered optical 
system in said first direction, and/or moving said second decentered 
optical system in said second direction. 
[79] The optical system as set forth in any one of [1] to [55], which is 
arranged as a converter lens. 
[80] The optical system as set forth in any one of [1] to [55], which is 
disposed in optical means provided in binoculars. 
[81] The optical system as set forth in [80], which is disposed in an 
objective lens system provided in binoculars. 
[82] The optical system as set forth in [80], which is disposed in an 
ocular lens system provided in binoculars. 
[83] The optical system as set forth in [80], which is disposed in each of 
an objective lens system and ocular lens system provided in binoculars. 
[84] The optical system as set forth in any one of [1] to [55], which is 
disposed at an entrance surface and/or an exit surface of an image 
rotator. 
[85] The optical system as set forth in any one of [1] to [55], which is 
disposed in optical means provided in a microscope. 
[86] The optical system as set forth in [85], which is disposed in an 
objective optical system for a microscope. 
[87] The optical system as set forth in [85], which is disposed in an 
ocular optical system for a microscope. 
[88] The optical system as set forth in [85], which is disposed in an 
intermediate-image relay optical system for a microscope. 
[89] The optical system as set forth in [85], which is disposed in an 
illumination system for a microscope. 
[90] The optical system as set forth in [89], which is disposed in an 
incident-light illumination system for a microscope. 
[91] The optical system as set forth in [89], which is disposed in a 
transmission illumination system for a microscope. 
[92] The optical system as set forth in [85], which is disposed in a 
multi-discussion lens barrel for a microscope. 
[93] The optical system as set forth in [85], which is disposed in an 
optical system of an image-drawing device for a microscope. 
[94] The optical system as set forth in [85], which is disposed in an 
autofocus system for a microscope. 
[95] The optical system as set forth in [85], which is disposed in a 
projection optical system for an inverted microscope. 
[96] The optical system as set forth in any one of [1] to [55], which is 
disposed in optical means provided in a binocular stereoscopic microscope 
having an optical axis for a right eye and an optical axis for a left eye. 
[97] The optical system as set forth in [96], wherein said binocular 
stereoscopic microscope has an objective lens system common to said 
optical axes for right and left eyes, said optical system being provided 
for each of said optical axes for right and left eyes in order to correct 
aberrations due to decentration which are produced by said objective lens 
system. 
[98] The optical system as set forth in [97], which is provided in a 
variable-magnification optical system. 
[99] The optical system as set forth in [97], which is provided in an 
image-forming optical system. 
[100] The optical system as set forth in [97], which is provided in an 
ocular optical system. 
[101] The optical system as set forth in [96], wherein said optical axes 
for right and left eyes are tilted with respect to an object plane, and 
two objective lens systems are provided for said two optical axes, 
respectively, said optical system being provided for each of said optical 
axes for right and left eyes to correct aberrations produced by said two 
objective lens systems. 
[102] The optical system as set forth in [101], which is disposed closest 
to the object side on each of said right and left optical axes. 
[103] The optical system as set forth in [101], which is disposed on the 
image side of each of said right and left objective lens systems. 
[104] The optical system as set forth in any one of [1] to [55], which is 
disposed in optical means provided in an endoscope. 
[105] The optical system as set forth in [104], wherein said endoscope uses 
an imaging device. 
[106] The optical system as set forth in [104], which is used in an 
endoscope objective optical system. 
[107] The optical system as set forth in [106], wherein a protective 
transparent plate is disposed on the object side of said optical system. 
[108] The optical system as set forth in [106], wherein an object-side 
surface of said optical system is a plane surface. 
[109] The optical system as set forth in [106], wherein an image-side 
surface of said optical system is a plane surface. 
[110] The optical system as set forth in [109], wherein the image-side 
surface of said optical system is placed in close contact with an imaging 
device. 
[111] The optical system as set forth in [104], wherein an optical fiber 
bundle is disposed at an image-formation plane of said optical system 
separately from said optical system. 
[112] The optical system as set forth in [104], wherein an optical fiber 
bundle is placed in close contact with an image-side surface of said 
optical system. 
[113] The optical system as set forth in [111], wherein an object-side 
surface of said optical system is formed from a protective transparent 
plate. 
[114] The optical system as set forth in [111], wherein an object-side 
surface of said optical system is a plane surface. 
[115] The optical system as set forth in [104], wherein a first surface in 
a distal end part of the endoscope is made of glass or a crystalline 
material, e.g. sapphire. 
[116] The optical system as set forth in [104], wherein a first surface of 
the endoscope objective optical system is recessed from an enclosure of 
the endoscope. 
[117] The optical system as set forth in [104], wherein a first surface of 
the endoscope objective optical system projects from an enclosure of the 
endoscope. 
[118] The optical system as set forth in any one of [1] to [55], which is 
disposed in a camera adapter for an endoscope to project an observation 
image onto an imaging device through said optical system. 
[119] The optical system as set forth in [118], wherein a plane glass plate 
is provided in front of or behind said optical system. 
[120] The optical system as set forth in [118], which has means for varying 
a spacing between said optical system and another optical system or an 
image-formation plane. 
[121] The optical system as set forth in [118], wherein a sum total of 
reflections taking place in said optical system and another optical system 
is an even number. 
[122] The optical system as set forth in [118], wherein said camera adapter 
for an endoscope comprises an optical system in which a sum total of 
reflections is an odd number, and an electrically image-inverting circuit. 
[123] The optical system as set forth in [118], wherein said camera adapter 
for an endoscope has a semitransparent reflecting surface to divide an 
optical path into two. 
[124] The optical system as set forth in [118], wherein an observation 
optical path for an observer is approximately parallel to an optical axis 
of light rays entering said endoscope camera adapter from an observation 
optical system. 
As will be clear from the foregoing description, the present invention 
provides an optical system which is compact and has minimal aberrations in 
comparison to rotationally symmetric transmission optical systems.