Optical system for observing equipment having image vibration compensation system

An optical system for a binocular is provided with an objective optical system, an erecting system and an eyepiece. The objective optical system includes a first lens having positive refractive power, a second lens having negative refractive power and a third aspherical lens having positive refractive power. The third lens is capable of moving in a direction orthogonal to an optical axis of the objective optical system. The objective optical system satisfies the following conditions: EQU (1) D.sub.12 /f.sub.0 <0.16, where, PA1 D.sub.12 is a distance from the object side of the first lens and the image side of the second lens of the objective optical system, and PA1 f.sub.0 is the focal length of the objective optical system.

BACKGROUND OF THE INVENTION 
The present invention relates to an optical system for an observing 
equipment such as a binocular or a terrestrial telescope that has an image 
vibration compensation system. 
Recently, binoculars provided with image vibration compensation systems for 
preventing vibration of observed image due to hand-held shaking of a user 
have been developed. Japanese Laid Open Publication No. HEI 6-43365 
discloses an image vibration compensation system of a binocular that 
employs variable angle prism for each of telescopic optical systems of the 
binocular. FIG. 14 shows one example of the telescopic optical system that 
has the same arrangement of the optical components as the publication. The 
optical system includes an objective lens 1 that is a doublet, a variable 
angle prism 2 as a compensation element, an erecting system 3 and an 
eyepiece 4. When the optical system vibrates due to hand-held shaking of a 
user, the vertex angle of the variable angle prism 2 is controlled to 
stabilize the image. 
In such a construction, however, since the variable angle prism 2 is 
located in the convergent light, if the vertex angle of the prism is 
changed, coma occurs. FIG. 15A shows the axial coma when the vertex angle 
of the variable angle prism 2 has not yet changed. FIG. 15B shows the 
axial coma when the variable angle prism 2 is changed in order to 
compensate the inclination of the optical system which was inclined by 1 
degree. As shown in FIGS. 15A and 15B, the coma has been increased 
significantly when the vertex angle has been changed. Accordingly, the 
image viewed by a user is deteriorated due to the coma when the vertex 
angle of the variable angle prism 2 has been changed to compensate the 
vibration of the image. 
Another example of the image vibration compensation system for binoculars 
is disclosed in Japanese Laid Open Publication No. HEI 6-308431. The 
binocular in the publication employs a compensation device that is 
attached in front of the objective lenses of the binocular. Since the 
objective lens of the telescopic optical system has the largest diameter 
in the system, and the device is arranged in front of the objective 
lenses, the entire system becomes large in size. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide an optical 
system of an observing equipment having an image vibration compensation 
system, which is compact in size, and can be manufactured easily. 
For the above object, according to the present invention, there is provided 
an optical system of an observing equipment having an image vibration 
compensation system. The optical system includes: 
an objective optical system for forming an image of an object, the 
objective optical system including a first lens having positive refractive 
power, a second lens having negative refractive power and a third lens 
which has at least one aspherical surface and has a positive refractive 
power, the first, second and third lenses being arranged in this order 
from an object side, the third lens being movable in a direction 
orthogonal to an optical axis of the objective optical system; 
an erecting system for erecting the image formed by the objective optical 
system; and 
an observing optical system for observing the image erected by the erecting 
system, 
wherein condition (1) below is satisfied: 
EQU (1) D.sub.12 /f.sub.0 &lt;0.16, 
where, 
D.sub.12 is a distance between the object side surface of the first lens 
and the image side surface of the second lens, and 
f.sub.0 is a focal length of the objective optical system. 
With this construction, vibration of an image due to the hand-held shaking 
is compensated by the third lens (i.e., a compensation element). The third 
lens has at least one aspherical surface, and spherical aberration of the 
third lens can be well suppressed. Accordingly, in the optical system, 
coma can be well suppressed even when the element (i.e., the third lens) 
is moved to stabilize a position of an image. Further, the compensation 
element is a part of the objective optical system located at the image 
side in the objective optical system, the size of the compensation element 
becomes smaller than the conventional element which is located at the 
object side of the objective optical system. 
In the specific embodiment, at least one of the following conditions are 
satisfied. 
(2) .vertline..phi..sub.12 /.phi..sub.13 .vertline.&lt;0.4, 
EQU (3) 1.0 &lt;h.sub.i /h.sub.x &lt;1.4, 
where, 
.phi..sub.12 is a composite power of the first and second lenses, 
.phi..sub.13 is a composite power of the first, second and third lenses, 
h.sub.i (.noteq.0) is a height of a point where a paraxial axial ray 
intersects the object side surface of the first lens, and 
h.sub.x is a height of a point where the paraxial axial ray intersects the 
image side surface of the second lens. 
In the specification and claims, "the paraxial axial ray" is defined as a 
ray from an object point on an optical axis at infinity. 
Optionally, the third lens of the objective optical system may be a plastic 
lens. A plastic lens is light in weight which enables a driving mechanism 
to be made compact. Further, it is relatively easy to form the aspherical 
surface on the plastic lens.

DESCRIPTION OF THE EMBODIMENTS 
FIG. 1 shows a binocular 10 that employs a pair of telescopic optical 
systems. The binocular 10 employs an image vibration compensation system. 
FIG. 2 shows a front view of the binocular 10. The binocular 10 includes a 
center body 11 and a pair of grip portions 12 that are connected to the 
center body 11 at right and left side thereof, respectively. The grip 
portions 12 are rotatable with respect to the center body 12 in order to 
adjust a distance therebetween to fit a pupil distance of a user. A 
diopter adjusting dial 13 is attached to a rear portion (i.e., the lower 
portion in FIG. 1) of the center body 12. 
The binocular 10 is provided with right and left telescopic optical systems 
arranged side by side for right and left eyes of the user. Since the left 
telescopic optical system is symmetric to the right telescopic optical 
system, FIG. 1 shows elements included in the right telescopic optical 
system, and description is directed therefor. 
The telescopic optical system consists of an objective optical system OL 
for forming an image of an object, an erecting system PS for erecting the 
image, and an eyepiece EP as an observing optical system. 
The objective optical system OL, which is provided in the center body 11, 
includes: a first lens L1 having positive refractive power; a second lens 
L2 having negative refractive power; and an aspherical third lens L3 
having positive refractive power. The first to third lenses L1, L2 and L3 
are arranged in this order from an object side. It should be noted that at 
least one surface of the third lens L3 is formed to be an aspherical 
surface. The third lens L3 is a plastic lens, and in a first embodiment 
described later, an image side surface is formed as an aspherical surface. 
In second and third embodiments, the object side surface is formed as the 
aspherical surface. The third lens L3 is mounted on a driving mechanism 17 
that moves the third lens L3 in a direction orthogonal to an optical axis 
O of the objective optical system OL. 
The objective optical system OL forms an inverted image, and the inverted 
image is erected into proper orientation through the erecting system PS. 
The erecting system PS is provided with a first prism P1 and a second 
prism P2, which constitute type II Porro prism system. The first prism P1 
has two reflection surfaces for rotating the image by 90 degrees, and the 
second prism PS2 also has two reflection surfaces for further rotating the 
image by 90 degrees. 
The eyepiece EP has fourth through eighth lenses L4 through L8. The 
objective optical system OL and the first prism P1 is arranged in the 
center body 11, and the second prism P2 and the eyepiece EP are arranged 
in the grip portion 12. 
The grip portion 12 is rotatable, with respect to the center body 11, about 
the optical axis O of the objective optical system OL. The erecting system 
PS and the eyepiece EP are rotated together with the grip portion 12. The 
left and right grip portions rotate in the opposite directions, and the 
user can adjust the distance between the left and right eyepieces to 
correspond to the pupil distance of the user. 
In this specification, an x-axis direction and a y-axis direction are 
defined with respect to the binocular 10. The y-axis direction is defined 
as a direction which is orthogonal to a plane including the optical axes O 
of both the right and left telescopic optical systems. The x-axis 
direction is defined as a direction, which is parallel to a line on a 
plane orthogonal to the optical axis O, and is orthogonal to the y-axis 
direction. Thus, the x-axis and y-axis are orthogonal to each other, and 
both are orthogonal to the optical axis O. 
The driving mechanism 17 drives the third lens L3 in the x-axis and y-axis 
directions such that the image viewed by a user is stabilized even when a 
hand-held shaking is applied to the binocular. 
At the initial or neutral positions of the third lens L3, the optical axis 
of the third lens L3 is coincident with the optical axis O of the first 
and second lenses L1 and L2. 
When the object side of the binocular 10 moves, relatively to the eyepiece 
side, in the y-axis direction due to a hand-held shaking, the driving 
mechanism 17 moves the third lens in the y-axis direction so that a 
position of an image is maintained. Similarly, when the object side of the 
binocular 10 moves, relatively to the eyepiece side, in the x-axis 
direction due to the hand-held shaking, the driving mechanism 17 moves the 
third lens in the x-axis direction so that the image position is 
maintained. In this specification, the angle formed between the optical 
axes O before and after the binocular 10 has been moved in the y-axis 
direction is referred to as a tilt angle in the y-axis direction, and the 
angle formed between the optical axes O before and after the binocular 10 
has been moved in the x-axis direction is referred to as a tilt angle in 
the x-axis direction. It should be noted that the hand-held shaking 
applied to the binocular 10 can be represented by the tilt angle(s) in the 
x-axis and/or y-axis directions, and accordingly, trembling of the image 
due to the hand-held shaking can be compensated by moving the third lens 
in the x-axis and/or y-axis direction. 
FIG. 3 shows an example of the driving mechanism 17 for driving the third 
lens L3. 
The driving mechanism 17 includes a rectangular lens frame 18 that holds 
the third lenses L3 of both the telescopic optical systems at openings 
formed thereon, a first actuator 24 for linearly shifting the rectangular 
lens frame 18 in the y-axis direction and a second actuator 29 for 
linearly shifting the frame 18 in the x-axis direction. 
At longitudinal side ends of the lens frame 18, a pair of guide bars 21 and 
21 are provided. The guide bar 21 has a center bar 21a and edge bars 21b 
formed at both edges of the center bar 21a. Both of the edge bars 21b are 
perpendicular to the center bar 21a and are directed to the same 
direction. The guide bars 21 and 21 are arranged such that the center bars 
21a and 21a are parallel to the y-axis and that the tip ends of the edge 
bars 21b and 21b are faced to the rectangular lens frame 18. 
The center bars 21a and 21a of the guide bars 21 and 21 are slidably fitted 
in through-holes formed in a pair of supports 22 and 22 that are formed 
inside the body 101 of the binocular. 
The tip ends of the edge bars 21b of the one guide bars 21 are slidably 
inserted into holes 27a and 27a formed at one side end of the rectangular 
lens frame 18. The tip ends of the edge bars 21b of the other guide bars 
21 are slidably inserted into holes 27b and 27b formed at the opposite 
side end of the rectangular lens frame 18. 
With this structure, the lens frame 18 is movable in the y-axis direction 
and in the x-axis direction. 
The first and second actuator 24 and 29 are secured on the inner surface of 
the body 101 of the binocular. A plunger 24a of the first actuator 24 is 
capable of protruding/retracting in the y-axis direction. The plunger 24a 
abuts a projection 23 formed on the lens frame 18 between the pair of 
third lenses L3. Further, coil springs 26 and 26 are provided to the 
center bars 21a and 21a to bias the lens frame 18 in the upward direction 
in FIG. 3 with respect to the body 101 of the binocular. 
A plunger 29a of the second actuator 29 is capable of protruding/retracting 
in the x-axis direction. The plunger 29a abuts a projection 28 formed on 
the side of the lens frame 18. The coil springs 30 and 30 are provided to 
the edge bars 21b and 21b of the one guide bar 21 to bias the lens frame 
18 in the rightward direction in FIG. 3. 
When electrical power is applied to the first actuator 24 to make the 
plunger 24a protrude, the plunger 24a pushes the projection 23 to linearly 
move the rectangular lens frame 18 in the downward direction in FIG. 3. 
When the electrical power for retracting the plunger 24a is applied to the 
actuator 24, due to force of the coil springs 26, the projection 23 is 
kept contacting the plunger 24a, i.e., the lens frame 18 moves in the 
upward direction in FIG. 3. 
In the same manner, when the electrical power is applied to the second 
actuator 29 to make the plunger 29a protrude, the projection 28 is pushed 
to linearly move the rectangular lens frame 18 in the leftward direction 
in FIG. 3. When the electrical power for retracting the plunger 29a is 
applied, the lens frame 18 moves in the rightward direction in FIG. 3 due 
to force of the coil springs 30 and 30. 
When the third lens L3 is moved in the y-axis direction, the image in the 
user view moves in the vertical (up/down) direction. Accordingly, by 
controlling the first actuator 24, the vertical movement of the image due 
to the vertical hand-held shaking can be compensated, while by controlling 
the second actuator 29, the horizontal movement of the image due to the 
horizontal hand-held shaking can be compensated. 
Further, the driving mechanism 17 is provided with an x-direction position 
sensor 221 and a y-direction position sensor 227 that are also secured to 
the body 101 of the binocular. The position sensor may be an optical 
sensor having a light emitting element and a position sensitive device 
(PSD). 
As shown in FIG. 4, the first and second actuators 24 and 29 are controlled 
by a controller 233 through drivers 222 and 228, respectively. The 
controller 233 controls the drivers 222 and 228 based on the signals from 
a vertical hand-held shaking sensor 150V, a horizontal hand-held shaking 
sensor 150H, the x-direction position sensor 221, and the y-direction 
position sensor 227. 
The controller 233 calculates amount of movements of the binocular in the 
vertical and horizontal directions due to the hand-held shaking, and 
controls the drivers 222 and 228 to drive the first and second actuators 
24 and 29 by an amount corresponding to the amount of movement of the 
image due to the hand-held shaking. Specifically, the controller 233 
determines a target position to which the lens frame 18 is to be 
positioned for canceling change of the position of the image due to the 
hand-held shaking based on the amount of movement detected by the 
hand-held shaking sensors 150V and 150H. Then, the controller 233 controls 
the driver to move the lens frame 18 to the calculated target position 
with monitoring the position detected by the position sensors 221 and 227. 
As the above control is continuously executed, the controller 233 
continuously updates the target position, and accordingly, trembling of 
the images due to the hand-held shaking is compensated. 
According to the embodiment, the telescopic optical system satisfies 
condition (1): 
EQU (1) D.sub.12 /f.sub.0 &lt;0.16, 
where, 
D.sub.12 is a distance from the object side surface of the first lens and 
the image side surface of the second lens of the objective optical system, 
and 
f.sub.0 is the focal length of the objective optical system. 
Condition (1) defines a range of a distance between the first and second 
lenses L1 and L2 of the objective optical system OL as compared with the 
focal length of the objective optical system OL. If condition (1) is 
satisfied, tilting sensitivity and decentering sensitivity are 
sufficiently small, which allows easy (less accurate) manufacturing and 
assembling of a lens. If the ratio is larger than the upper limit, tilting 
and/or decentering sensitivity must be suppressed, and therefore the 
accurate manufacturing and assembling are required, which increases cost 
of the binocular. 
According to the embodiment, it is preferable that the telescopic optical 
system further satisfies at least one of conditions (2) and (3): 
EQU .vertline..phi..sub.12 /.phi..sub.13 .vertline.&lt;0.4 
EQU (3) 1.0&lt;h.sub.i /h.sub.x &lt;1.4 
where, 
.phi..sub.12 is a composite power of the first and second lenses of the 
objective optical system, 
.phi..sub.13 is a composite power of the first, second and third lenses of 
the objective optical system, 
h.sub.i (.noteq.0) is a height of a point where a paraxial axial ray 
intersects the object side surface of the first lens, and 
h.sub.x is a height of a point where the paraxial axial ray intersects the 
image side surface of the second lens. 
Condition (2) defines a range of a ratio of the composite power of the 
first and second lenses L1 and L2 with respect to the composite power of 
the objective optical system OL. The smaller the ratio is, the easier the 
aberration correction is. That is, if condition (2) is satisfied, 
aberrations can easily be corrected. If the ratio is larger than the upper 
limit, a spherical aberration and coma cannot be corrected sufficiently. 
Condition (3) defines a range of a ratio of the ray height h.sub.i on the 
object side surface of the first lens with respect to the ray height 
h.sub.x on the image side surface of the second lens. If condition (3) is 
satisfied, aberration is easily corrected. If the ratio is smaller than 
the lower limit, the first lens L1 should have a negative refractive 
power, which requires a larger diameter of the second and third lenses L2 
and L3. If the ratio is larger than the upper limit, the difference 
between the ray heights h.sub.i and h.sub.x becomes too large and the 
spherical aberration and chromatic aberration cannot be compensated 
sufficiently. 
[Numerical Embodiments] 
Hereafter, numerical embodiments of the telescopic optical systems will be 
described with reference to FIGS. 5 through 13. 
[First Embodiment] 
FIG. 5 shows a telescopic optical system according to a first embodiment 
and the numerical construction thereof is described in TABLE 1. The prisms 
P1 and P2 of the erecting system PS are shown as plane parallel plates in 
FIG. 5. 
In TABLE 1, r (mm) denotes a radius of curvature of a surface (the values 
at the vertex for aspherical surfaces), d (mm) denotes a distance between 
the surfaces along the optical axis, n denotes a refractive index at a 
wavelength of 588 nm and .nu.d denotes an Abbe number. 
TABLE 1 
______________________________________ 
Surface 
Number r d n vd 
______________________________________ 
#1 60.633 3.990 1.51633 
64.1 
#2 -85.349 1.420 
#3 -79.717 3.000 1.60342 
38.0 
#4 108.664 22.540 
#5 62.900 4.000 1.49176 
57.4 
#6 -252.509 20.000 
#7 INFINITY 34.000 1.56883 
56.3 
#8 INFINITY 2.000 
#9 INFINITY 32.000 1.56883 
56.3 
#10 INFINITY 7.710 
#11 -25.818 4.000 1.49176 
57.4 
#12 154.980 14.560 
#13 23.936 6.770 1.49176 
57.4 
#14 -10.075 0.700 
#15 -11.190 2.000 1.58547 
29.9 
#16 25.294 0.200 
#17 24.157 6.200 1.49176 
57.4 
#18 -15.260 0.500 
#19 22.703 3.500 1.60311 
60.7 
#20 -75.123 -- 
______________________________________ 
The image side surface #6 of the third lens L3 is an aspherical surface. 
Further, surfaces #12 and #14 are also aspherical surfaces. 
An aspherical surface is expressed by the following equation: 
##EQU1## 
where, X(h) is a SAG, that is, a distance of a curve from a tangential 
plane at a point on the surface where the height from the optical axis is 
h. C is a curvature (1/r) of the vertex of the surface, K is a conic 
constant, A.sub.4, A.sub.6, A.sub.8 and A.sub.10 are aspherical surface 
coefficients of fourth, sixth, eighth and tenth orders. The constant K and 
coefficients A.sub.4 and A.sub.6 are indicated in TABLE 2. In the 
embodiments, coefficients A.sub.8 and A.sub.10 are equal to zero. 
TABLE 2 
______________________________________ 
6th surface 12th surface 14th surface 
______________________________________ 
K = 0.00000 K = 0.00000 K = -1.00000 
A.sub.4 = 0.49600 .times. 10.sup.-6 
A.sub.4 = 0.70600 .times. 10.sup.-5 
A.sub.4 = 0.46000 .times. 10.sup.-5 
A.sub.6 = 0.00000 
A.sub.6 = -0.45400 .times. 10.sup.-6 
A.sub.6 = 0.00000 
______________________________________ 
FIGS. 6A through 6D show third order aberrations of the telescopic optical 
system according to the first embodiment: 
FIG. 6A shows spherical aberrations at d-line (588 nm), g-line (436 nm) and 
c-line (656 nm); 
FIG. 6B shows a lateral chromatic aberration at the same wavelengths as in 
FIG. 6A; 
FIG. 6C shows an astigmatism (S: Sagittal, M: Meridional); and 
FIG. 6D shows distortion. 
The vertical axis in FIG. 6A represents a diameter of an eye ring, and the 
vertical axes in FIGS. 6B through 6D respectively represent an angle B 
formed between the exit ray from the eyepiece and the optical axis. Unit 
of the horizontal axis is "mm" in each of FIGS. 6A through 6C, and is 
"percent" in FIG. 6D. 
FIG. 7A is a graph showing the axial coma of the telescopic optical system 
of the first embodiment when the third lens is not decentered, and FIG. 7B 
is a graph showing the axial coma where the third lens is decentered to 
stabilize the image when the tilt angle due to the hand-held shaking is 1 
degree. According to the first embodiment, coma can be made smaller, even 
when the third lens L3 is decentered, than the conventional compensation 
system using a variable angle prism. 
[Second Embodiment] 
FIG. 8 shows an optical system according to a second embodiment. The 
numerical construction of the second embodiment is indicated in TABLE 3. 
TABLE 3 
______________________________________ 
Surface 
Number r d n vd 
______________________________________ 
#1 35.933 4.500 1.51633 
64.1 
#2 -90.773 8.000 
#3 -50.707 3.000 1.60342 
38.0 
#4 49.852 20.680 
#5 71.184 4.000 1.52580 
57.4 
#6 -124.599 19.500 
#7 INFINITY 34.000 1.56883 
56.3 
#8 INFINITY 2.000 
#9 INFINITY 32.000 1.56883 
56.3 
#10 INFINITY 5.000 
#11 -10.527 3.500 1.49176 
57.4 
#12 -13.446 12.730 
#13 23.936 6.770 1.49176 
57.4 
#14 -10.075 0.700 
#15 -11.190 2.000 1.58547 
29.9 
#16 25.294 0.200 
#17 24.157 6.200 1.49176 
57.4 
#18 -15.260 0.500 
#19 22.703 3.500 1.60311 
60.7 
#20 -75.123 -- 
______________________________________ 
The object side surface #5 of the third lens L3 is an aspherical surface. 
Further, the surfaces #12 and #14 are also aspherical surfaces. The 
constant K and coefficients A.sub.4 and A.sub.6 are indicated in TABLE 4. 
The coefficients A.sub.8 and A.sub.10 are equal to zero. 
TABLE 4 
______________________________________ 
5th surface 12th surface 14th surface 
______________________________________ 
K = 0.00000 K = 0.00000 K = -1.00000 
A.sub.4 = -0.92860 .times. 10.sup.-6 
A.sub.4 = -0.11680 .times. 10.sup.-3 
A.sub.4 = -0.46000 .times. 10.sup.-5 
A.sub.6 = 0.00000 
A.sub.6 = -0.14640 .times. 10.sup.-6 
A.sub.6 = 0.00000 
______________________________________ 
FIGS. 9A through 9D show third order aberrations of the telescopic optical 
system according to the second embodiment. 
FIG. 10A is a graph showing the axial coma of the telescopic optical system 
of the second embodiment when the third lens is not decentered. FIG. 10B 
is a graph showing the axial coma when the third lens is decentered to 
stabilize the image when the tilt angle is 1 degree. In the second 
embodiment, coma can be made smaller, even when the third lens L3 is 
decentered, than the conventional compensation system using a variable 
angle prism. 
[Third Embodiment] 
FIG. 11 shows an optical system according to a third embodiment, and the 
numerical construction thereof is indicated in TABLE 5. 
TABLE 5 
______________________________________ 
Surface 
Number r d n vd 
______________________________________ 
#1 36.900 4.500 1.51633 
64.1 
#2 -72.950 8.410 
#3 -42.418 3.000 1.60342 
38.0 
#4 64.700 14.290 
#5 109.125 4.000 1.49176 
57.4 
#6 -139.150 21.010 
#7 INFINITY 34.000 1.56883 
56.3 
#8 INFINITY 2.000 
#9 INFINITY 32.000 1.56883 
56.3 
#10 INFINITY 6.170 
#11 14.400 3.500 1.49176 
57.4 
#12 11.153 15.500 
#13 23.936 6.770 1.49176 
57.4 
#14 -10.075 0.700 
#15 -11.190 2.000 1.58547 
29.9 
#16 25.294 0.200 
#17 24.157 6.200 1.49176 
57.4 
#18 -15.260 0.500 
#19 22.703 3.500 1.60311 
60.7 
#20 -75.123 -- 
______________________________________ 
The object side surface #5 of the third lens L3 is an aspherical surface. 
Further, surfaces #12 and #14 are also aspherical surfaces. The constant K 
and coefficients A.sub.4 and A.sub.6 are indicated in TABLE 6. The 
coefficients A.sub.8 and A.sub.10 are equal to zero. 
TABLE 6 
______________________________________ 
5th surface 12th surface 14th surface 
______________________________________ 
K = 0.00000 K = 0.00000 K = -1.00000 
A.sub.4 = 0.52830 .times. 10.sup.-6 
A.sub.4 = 0.30330 .times. 10.sup.-4 
A.sub.4 = -0.46000 .times. 10.sup.-5 
A.sub.6 = 0.00000 
A.sub.6 = -0.44950 .times. 10.sup.-6 
A.sub.6 = 0.00000 
______________________________________ 
FIGS. 12A through 12D show third order aberrations of the telescopic 
optical system according to the third embodiment. 
FIG. 13A is a graph showing the axial coma of the telescopic optical system 
of the third embodiment when the third lens is not decentered, and FIG. 
13B is a graph showing the axial coma when the third lens is decentered to 
stabilize the image when the tilt angle is 1 degree. In the third 
embodiment, coma can be made smaller, even when the third lens L3 is 
decentered, than the conventional compensation system using a variable 
angle prism. 
TABLE 7 shows the values of the first to third embodiments for conditions 
(1) to (4). 
TABLE 7 
______________________________________ 
First Second Third 
Embodiment 
Embodiment 
Embodiment 
______________________________________ 
Condition (1) 
D.sub.12 / f.sub.o 
0.09 0.15 0.13 
Condition (2) 
.vertline..phi..sub.12 / .phi..sub.13 .vertline. 
0.18 0.09 0.30 
Condition (3) 
h.sub.i / h.sub.x 
1.06 1.28 1.30 
______________________________________ 
Condition (3) 
EQU h.sub.i /h.sub.x 1.06 1.28 1.30 
TABLE 8 
______________________________________ 
Ex. 1 Ex. 2 Ex. 3 
______________________________________ 
f0 93.588 103.744 120.448 
f1 69.301 50.467 48.131 
f2 -75.750 -41.197 -42.016 
f3 102.830 86.770 125.036 
f12 514.216 1145.882 402.265 
.phi.12 0.002 0.001 0.002 
.phi.13 0.011 0.010 0.008 
hi 1.000 1.000 1.000 
hmax 0.944 0.780 0.766 
______________________________________ 
Each of the embodiments satisfies conditions (1), (2) and (3), and is 
suitable to the telescopic optical system of a binocular having an image 
vibration compensation system. 
It should be noted that, in the embodiments, the erected images are 
observed through the eyepiece EP. The invention is not limited to this 
particular structure, and is applicable to an observing equipment in which 
imaging devices (e.g., a CCD: a Charge Coupled Device) and an imaging 
lenses are used in place of, or in association with the eyepiece EP. 
Further, in the above embodiments, the image vibration compensation system 
is designed for compensating trembling of the image due to both the 
vertical and horizontal hand-held shakings. However, the system may be 
designed for compensating the hand-held shaking in one of these two 
directions according to uses. 
The present invention is directed the optical system of an observing 
equipment that includes hand-held shaking sensors, sensors for detecting 
the position of the compensation lenses. However, the details of the 
hand-held shaking sensors and/or position detection sensors do not form 
part of the invention. These are provided to assist in understanding of 
the invention, and any types of suitable hand-held shaking sensors and/or 
position detecting sensors could be employed to control the driving 
mechanism for the compensation lenses.