U.S. patent application number 09/810245 was filed with the patent office on 2001-08-16 for zoom lens system.
Invention is credited to Kohno, Tetsuo, Yagyu, Genta.
Application Number | 20010013980 09/810245 |
Document ID | / |
Family ID | 26338936 |
Filed Date | 2001-08-16 |
United States Patent
Application |
20010013980 |
Kind Code |
A1 |
Kohno, Tetsuo ; et
al. |
August 16, 2001 |
Zoom lens system
Abstract
A zoom lens system has, from the object side, a first lens unit,
a second lens unit and a third lens unit. The first lens unit has a
negative optical power as a whole. The second and third lens units
have a positive optical power as a whole. In the zoom lens system,
zooming is achieved by varying the distance between the first and
second lens units, and at least one of the lens elements is a
plastic lens element.
Inventors: |
Kohno, Tetsuo; (Osaka,
JP) ; Yagyu, Genta; (Osaka, JP) |
Correspondence
Address: |
Platon N. Mandros
BURNS, DOANE, SWECKER & MATHIS, L.L.P.
P.O. Box 1404
Alexandria
VA
22313-1404
US
|
Family ID: |
26338936 |
Appl. No.: |
09/810245 |
Filed: |
March 19, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09810245 |
Mar 19, 2001 |
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09468366 |
Dec 21, 1999 |
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6229655 |
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Current U.S.
Class: |
359/689 ;
359/676; 359/683; 359/684; 359/694 |
Current CPC
Class: |
G02B 15/143507 20190801;
G02B 15/177 20130101 |
Class at
Publication: |
359/689 ;
359/684; 359/683; 359/676; 359/694 |
International
Class: |
G02B 015/14 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 22, 1998 |
JP |
H10-363664 |
Jan 12, 1999 |
JP |
H11-005056 |
Claims
What is claimed is:
1. A zoom lens system comprising, in order from an object side: a
first lens unit; a second lens unit having a positive optical
power; and a third lens unit, wherein zooming is achieved by moving
at least two lens units so as to vary a distance between the first
and second lens units and a distance between the second and third
lens units, and wherein at least one of the lens elements included
in the lens units is a plastic lens element that fulfills the
following conditions: -0.8<Cp.times.(N'-N)/.phi.W<0.8
-0.45<M3/M2<0.90 (where .phi.T/.phi.W>1.6) where Cp
represents a curvature of the plastic lens element; .phi.W
represents an optical power of the entire zoom lens system at a
wide-angle end; N' represents a refractive index of an object-side
medium of an aspherical surface for d line; N represents a
refractive index of an image-side medium of an aspherical surface
for d line; M3 represents an amount of movement of the third lens
unit (where the direction pointing to the object side is negative
with respect to the wide-angle end); M2 represents an amount of
movement of the second lens unit; and .phi.T represents an optical
power of the entire zoom lens system at a telephoto end.
2. The zoom lens system of claim 1 wherein said first lens unit has
a negative optical power.
3. The zoom lens system of claim 1 wherein said second lens unit
includes a positive lens element and a negative lens element.
4. The zoom lens system of claim 1 wherein said third lens unit has
a positive optical power.
5. The zoom lens system of claim 1 wherein said plastic lens
element is contained in the first lens unit and fulfills the
following conditions: .vertline..phi.P/.phi.1.vertline.<1.20
0.20<.vertline..phi.1/.phi.W- .vertline.<0.70 where .phi.P
represents an optical power of the plastic lens element; .phi.1
represents an optical power of the first lens unit; and .phi.T
represents an optical power of the entire zoom lens system at a
telephoto end.
6. The zoom lens system of claim 5 wherein said first lens unit has
a negative optical power.
7. The zoom lens system of claim 6 wherein said first lens unit
includes a positive lens element and a negative lens element.
8. The zoom lens system of claim 5 wherein said third lens unit has
a positive optical power.
9. The zoom lens system of claim 1, wherein said plastic lens
element is included in the second lens unit and fulfills the
following conditions: .vertline..phi.P/.phi.2.vertline.<2.5
0.25<.phi.2/.phi.W<0.75 where .phi.P represents an optical
power of the plastic lens element; and .phi.2 represents an optical
power of the second lens unit.
10. The zoom lens system of claim 9 wherein said first lens unit
has a negative optical power.
11. The zoom lens system of claim 9 wherein said second lens unit
includes a positive lens element and a negative lens element.
12. The zoom lens system of claim 9 wherein said third lens unit
has a positive optical power.
13. The zoom lens system of claim 1 wherein said plastic lens
element is included in the third lens unit and fulfills the
following conditions: -0.30<M3/M2<0.90
.vertline..phi.P/.phi.3.vertline.<1.70
0.1<.phi.3/.phi.W<0.60 where .phi.P represents an optical
power of the plastic lens element; and .phi.3 represents an optical
power of the third lens unit.
14. The zoom lens system of claim 13 wherein said first lens unit
has a negative optical power.
15. The zoom lens system of claim 13 wherein said third lens unit
has a positive optical power.
16. The zoom lens system of claim 1, wherein at least one of the
lens elements included in the first lens unit and at least one of
the lens elements included in the second lens unit are plastic lens
elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
0.5<log(.beta.2T/.beta.2W)/log Z<2.2 where .phi.Pi represents
an optical power of an ith plastic lens element; hi represents a
height of incidence at which a paraxial ray enters an object-side
surface of the ith plastic lens element at a telephoto end,
assuming that initial values of a converted inclination .alpha.1
and a height h1, for paraxial tracing, are 0 and 1, respectively;
.beta.2W represents a lateral magnification of the second lens unit
at the wide-angle end; .beta.2T represents a lateral magnification
of the second lens unit at the telephoto end; Z represents a zoom
ratio; and log represents a natural logarithm.
17. The zoom lens system of claim 16 wherein said first lens unit
has a negative optical power.
18. The zoom lens system of claim 16 wherein said third lens unit
has a positive optical power.
19. The zoom lens system as claimed in claim 1, wherein at least
one of the lens elements included in the first lens unit and at
least one of the lens elements included in the third lens element
are plastic lens elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.ti- mes.hi<1.4
-1.2<log(.beta.3T/.beta.3W)/log Z<0.5 where .phi.Pi
represents an optical power of an ith plastic lens element; hi
represents a height of incidence at which a paraxial ray enters an
object-side surface of the ith plastic lens element at a telephoto
end, assuming that initial values of a converted inclination
.alpha.1 and a height h1, for paraxial tracing, are 0 and 1,
respectively; .beta.3W represents a lateral magnification of the
third lens unit at the wide-angle end; .beta.3T represents a
lateral magnification of the third lens unit at the telephoto end;
Z represents a zoom ratio; and log represents a natural
logarithm.
20. The zoom lens system of claim 19 wherein said first lens unit
has a negative optical power.
21. The zoom lens system of claim 19 wherein said second lens unit
includes a positive lens element and a negative lens element.
22. The zoom lens system of claim 19 wherein said third lens unit
has a positive optical power.
23. The zoom lens system of claim 1, wherein at least one of the
lens elements included in the second lens unit and at least one of
the lens elements included in the third lens unit are plastic lens
elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
0.75<log(.beta.3T/.beta.3W)/log(.beta.2T/.beta.2W)<0.65 where
.phi.Pi represents an optical power of an ith plastic lens element;
hi represents a height of incidence at which a paraxial ray enters
an object-side surface of the ith plastic lens element at a
telephoto end, assuming that initial values of a converted
inclination .alpha.1 and a height h1, for paraxial tracing, are 0
and 1, respectively; .beta.2W represents a lateral magnification of
the second lens unit at the wide-angle end; .beta.2T represents a
lateral magnification of the second lens unit at the telephoto end;
.beta.3W represents a lateral magnification of the third lens unit
at the wide-angle end; .beta.3T represents a lateral magnification
of the third lens unit at the telephoto end; and log represents a
natural logarithm.
24. The zoom lens system of claim 23 wherein said first lens unit
has a negative optical power.
25. The zoom lens system of claim 23 wherein said second lens unit
includes a positive lens element and a negative lens element.
26. The zoom lens system of claim 23 wherein said third lens unit
has a positive optical power.
27. The zoom lens system comprising, in order from an object side:
a first lens unit; a second lens unit having a positive optical
power; and a third lens unit, wherein zooming is achieved by
varying a distance between the first and second lens units and a
distance between the second and third lens units, and wherein at
least one of the lens elements included in the second lens unit is
a plastic lens element that fulfills the following conditions:
.vertline..phi.P/.phi.2.vertline.<2.5
0.25<.phi.2/.phi.W<0.75 where .phi.P represents an optical
power of the plastic lens element; .phi.2 represents an optical
power of the second lens unit; and .phi.W represents an optical
power of the entire zoom lens system at a wide-angle end.
28. A zoom lens system comprising, in order from an object side: a
first lens unit; a second lens unit having a positive optical
power; and a third lens unit, wherein zooming is achieved by moving
at least two lens units so as to vary a distance between the first
and second lens units and a distance between the second and third
lens units, and wherein at least one of the lens elements included
in the third lens unit is a plastic lens element that fulfill the
following conditions: -0.30<M3/M2<0.90
.vertline..phi.P/.phi.3.vertline.<1.70
0.1<.phi.3/.phi.W<0.60 where M3 represents an amount of
movement of the third lens unit (the direction pointing to the
object side is negative with respect to a wide-angle end); M2
represents an amount of movement of the second lens unit; .phi.P
represents an optical power of the plastic lens element; .phi.3
represents an optical power of the third lens unit; and .phi.W
represents an optical power of the entire zoom lens system at a
wide-angle end.
29. A zoom lens system comprising, in order from an object side: a
first lens unit; a second lens unit having a positive optical
power; and a third lens unit, wherein zooming is achieved by moving
at least two lens units so as to vary a distance between the first
and second lens units and a distance between the second and third
lens units, and wherein at least one of the lens elements included
in the first lens unit and at least one of the lens elements
included in the second lens unit are plastic lens element that
fulfills the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
0.5<log(.beta.2T/.beta.2W)/log Z<2.2 where .phi.Pi represents
an optical power of an ith plastic lens element; .phi.W represents
an optical power of the entire zoom lens system at a wide-angle
end; hi represents a height of incidence at which a paraxial ray
enters an object-side surface of the ith plastic lens element at a
telephoto end, assuming that initial values of a converted
inclination .alpha.1 and a height h1, for paraxial tracing, are 0
and 1, respectively; .beta.2W represents a lateral magnification of
the second lens unit at the wide-angle end; .beta.2T represents a
lateral magnification of the second lens unit at the telephoto end;
Z represents a zoom ratio; and log represents a natural
logarithm.
30. A zoom lens system comprising, in order from an object side: a
first lens unit; a second lens unit having a positive optical
power; and a third lens unit, wherein zooming is achieved by moving
at least two lens units so as to vary a distance between the first
and second lens units and a distance between the second and third
lens units, and wherein at least one of the lens elements included
in the first lens unit and at least one of the lens elements
included in the third lens unit are plastic lens element that
fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
-1.2<log(.beta.3T/.beta.3W)/log Z<0.5 where .phi.Pi
represents an optical power of an ith plastic lens element; .phi.W
represents an optical power of the entire zoom lens system at a
wide-angle end; hi represents a height of incidence at which a
paraxial ray enters an object-side surface of the ith plastic lens
element at a telephoto end, assuming that initial values of a
converted inclination .alpha.1 and a height h1, for paraxial
tracing, are 0 and 1, respectively; .beta.3W represents a lateral
magnification of the third lens unit at the wide-angle end;
.beta.3T represents a lateral magnification of the third lens unit
at the telephoto end; Z represents a zoom ratio; and log represents
a natural logarithm.
31. A zoom lens system comprising, in order from an object side: a
first lens unit; a second lens unit having a positive optical
power; and a third lens unit having a positive optical power,
wherein zooming is achieved by moving at least two lens units so as
to vary a distance between the first and second lens units and a
distance between the second and third lens units, and wherein at
least one of the lens elements included in the second lens unit and
at least one of the lens elements included in the third lens unit
are plastic lens elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
-0.75<log(.beta.3T/.beta.3W)/log(.beta.2T/.beta.2W)<0.65
where .phi.Pi represents an optical power of an ith plastic lens
element; .phi.W represents an optical power of the entire zoom lens
system at a wide-angle end; hi represents a height of incidence at
which a paraxial ray enters an object-side surface of the ith
plastic lens element at a telephoto end, assuming that initial
values of a converted inclination .alpha.1 and a height h1, for
paraxial tracing, are 0 and 1, respectively; .beta.2W represents a
lateral magnification of the second lens unit at the wide-angle
end; .beta.2T represents a lateral magnification of the second lens
unit at the telephoto end; .beta.3W represents a lateral
magnification of the third lens unit at the wide-angle end;
.beta.3T represents a lateral magnification of the third lens unit
at the telephoto end; and log represents a natural logarithm.
32. A digital camera comprising a zoom lens system, a low pass
filter and an image sensor, wherein said zoom lens system includes,
in order from the object side thereof: a first lens unit; a second
lens unit having a positive optical power; and a third lens unit,
wherein zooming is achieved by moving at least two lens units so as
to vary a distance between the first and second lens units and a
distance between the second and third lens units, and wherein at
least one of the lens elements included in the lens units is a
plastic lens element that fulfills the following conditions:
-0.8<Cp.times.(N'-N)/.phi.W<0.8 -0.45<M3/M2<0.90(where
.phi.T/.phi.W>1.6) where Cp represents a curvature of the
plastic lens element; .phi.W represents an optical power of the
entire zoom lens system at a wide-angle end; N' represents a
refractive index of an object-side medium of an aspherical surface
for d line; N represents a refractive index of an image-side medium
of an aspherical surface for d line; M3 represents an amount of
movement of the third lens unit (where the direction pointing to
the object side is negative with respect to the wide-angle end); M2
represents an amount of movement of the second lens unit; and
.phi.T represents an optical power of the entire zoom lens system
at a telephoto end.
33. The digital camera of claim 32, wherein said first lens unit
has a negative optical power.
34. The digital camera of claim 32, wherein said second lens unit
includes a positive lens element and a negative lens element.
35. The digital camera of claim 32, wherein said third lens unit
has a positive optical power.
36. The digital camera of claim 32, wherein said plastic lens
element is contained in the first lens unit and fulfills the
following conditions: .vertline..phi.P/.phi.1.vertline.<1.20
0.20<.vertline..phi.1/.phi.W- .vertline.<0.70 where .phi.P
represents an optical power of the plastic lens element; .phi.1
represents an optical power of the first lens unit; and .phi.T
represents an optical power of the entire zoom lens system at a
telephoto end.
37. The digital camera of claim 36, wherein said first lens unit
has a negative optical power.
38. The digital camera of claim 37, wherein said first lens unit
includes a positive lens element and a negative lens element.
39. The digital camera of claim 36, wherein said third lens unit
has a positive optical power.
40. The digital camera of claim 32, wherein said plastic lens
element is included in the second lens unit and fulfills the
following conditions: .vertline..phi.P/.phi.2.vertline.<2.5
0.25<.phi.2/.phi.W<0.75 where .phi.P represents an optical
power of the plastic lens element; and .phi.2 represents an optical
power of the second lens unit.
41. The digital camera of claim 40, wherein said first lens unit
has a negative optical power.
42. The digital camera of claim 40, wherein said second lens unit
includes a positive lens element and a negative lens element.
43. The digital camera of claim 40, wherein said third lens unit
has a positive optical power.
44. The zoom lens system of claim 32 wherein said plastic lens is
included in the third lens unit and fulfills the following
conditions: -0.30<M3/M2<0.90
.vertline..phi.P/.phi.3.vertline.<1.70 0.1<3/.phi.W<0.60
where .phi.P represents an optical power of the plastic lens
element; and .phi.3 represents an optical power of the third lens
unit.
45. The digital camera of claim 44, wherein said first lens unit
has a negative optical power.
46. The digital camera of claim 44, wherein said third lens unit
has a positive optical power.
47. The digital camera of claim 32, wherein at least one of the
lens elements included in the first lens unit and at least one of
the lens elements included in the second lens unit are plastic lens
elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
0.5<log(.beta.2T/.beta.2W)/log Z<2.2 where .phi.Pi represents
an optical power of an ith plastic lens element; hi represents a
height of incidence at which a paraxial ray enters an object-side
surface of the ith plastic lens element at a telephoto end,
assuming that initial values of a converted inclination .alpha.1
and a height h1, for paraxial tracing, are 0 and 1, respectively;
.beta.2W represents a lateral magnification of the second lens unit
at the wide-angle end; .beta.2T represents a lateral magnification
of the second lens unit at the telephoto end; Z represents a zoom
ratio; and log represents a natural logarithm.
48. The digital camera of claim 47, wherein said first lens unit
has a negative optical power.
49. The digital camera of claim 47, wherein said third lens unit
has a positive optical power.
50. The digital camera of claim 32, wherein at least one of the
lens elements included in the first lens unit and at least one of
the lens elements included in the third lens element are plastic
lens elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<- ;1.4
-1.2<log(.beta.3T/.beta.3W)/log Z<0.5 where .phi.Pi
represents an optical power of an ith plastic lens element; hi
represents a height of incidence at which a paraxial ray enters an
object-side surface of the ith plastic lens element at a telephoto
end, assuming that initial values of a converted inclination
.alpha.1 and a height h1, for paraxial tracing, are 0 and 1,
respectively; .beta.3W represents a lateral magnification of the
third lens unit at the wide-angle end; .beta.3T represents a
lateral magnification of the third lens unit at the telephoto end;
Z represents a zoom ratio; and log represents a natural
logarithm.
51. The digital camera of claim 50, wherein said first lens unit
has a negative optical power.
52. The digital camera of claim 50, wherein said second lens unit
includes a positive lens element and a negative lens element.
53. The digital camera of claim 50, wherein said third lens unit
has a positive optical power.
54. The digital camera of claim 32, wherein at least one of the
lens elements included in the second lens unit and at least one of
the lens elements included in the third lens unit are plastic lens
elements that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
-0.75<log(.beta.3T/.beta.3W)/log(.beta.2T/.beta.2W)<0.65
where .phi.Pi represents an optical power of an ith plastic lens
element; hi represents a height of incidence at which a paraxial
ray enters an object-side surface of the ith plastic lens element
at a telephoto end, assuming that initial values of a converted
inclination .alpha.1 and a height h1, for paraxial tracing, are 0
and 1, respectively; .beta.2W represents a lateral magnification of
the second lens unit at the wide-angle end; .beta.2T represents a
lateral magnification of the second lens unit at the telephoto end;
.beta.3W represents a lateral magnification of the third lens unit
at the wide-angle end; .beta.3T represents a lateral magnification
of the third lens unit at the telephoto end; and log represents a
natural logarithm.
55. The digital camera of claim 54, wherein said first lens unit
has a negative optical power.
56. The digital camera of claim 54, wherein said second lens unit
includes a positive lens element and a negative lens element.
57. The digital camera of claim 54, wherein said third lens unit
has a positive optical power.
Description
[0001] This disclosure is based on applications No. H10-363664
filed in Japan on Dec. 22, 1998 and No. H1 1-005056 filed in Japan
on Jan. 12, 1999, the entire contents of which are hereby
incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to a zoom lens system, and
more particularly to a compact and inexpensive zoom lens system
particularly suited for use in digital still cameras.
[0004] 2. Description of the Prior Art
[0005] In recent years, as personal computers become more
prevalent, digital still cameras that allow easy storage of image
data on a recording medium such as a floppy disk have been coming
into wider use. This trend has created an increasing demand for
more inexpensive digital still cameras. This in turn has created an
increasing demand for further cost reduction in imaging optical
systems. On the other hand, photoelectric conversion devices have
come to have an increasingly large number of pixels year by year,
which accordingly demands imaging optical systems that offer higher
and higher performance. To comply with such requirements, it is
necessary to produce a high-performance imaging optical system at
comparatively low cost.
[0006] To achieve this objective, for example, Japanese Laid-open
Patent Applications Nos. H1-183615 and H9-311273 propose optical
systems having a first lens unit of a negative-negative-positive
configuration and a second lens unit of a
positive-negative-positive configuration. Moreover, the optical
systems proposed in Japanese Laid-open Patent Applications Nos.
H7-113956, H6-300969, and H7-63991 have a second lens unit
including a doublet lens element formed by cementing together
negative lens elements; and the optical system proposed in Japanese
Laid-open Patent Application No. H5-93858 has a second lens unit
including a doublet lens element formed by cementing together, from
the object side, a positive lens element and a negative lens
element. If a doublet lens element is considered to be a single
lens element, it is assumed that those optical systems are each
composed of a first lens unit of a negative-negative-positive
configuration and a second lens unit of a
positive-negative-positive configuration.
[0007] Furthermore, Japanese Laid-open Patent Applications Nos.
H6-201993 and H1-191820 propose optical systems that are composed
of a first lens unit having a negative optical power, a second lens
unit having a positive optical power, and a third lens unit having
a positive optical power and employ a plastic lens element.
[0008] In the optical systems proposed in the above-mentioned
patent applications, however, there is still plenty of room for
improvement from the viewpoint of miniaturization, high
performance, and cost reduction.
SUMMARY OF THE INVENTION
[0009] An object of the present invention is to provide a compact,
high-resolution, and low-cost zoom lens system suitable, in
particular, for use in a digital still camera by arranging plastic
lens elements effectively in a two-unit zoom lens system of a
negative-positive configuration.
[0010] To achieve the above object, according to one aspect of the
present invention, a zoom lens system includes, from the object
side, a first lens unit and a second lens unit. The first lens unit
is composed of a negative, a negative, and a positive lens element
and has a negative optical power as a whole. The second lens unit
is composed of a positive, a negative, and a positive lens element
and has a positive optical power as a whole. In the zoom lens
system, zooming is achieved by varying the distance between the
first and second lens units, and at least one of those lens
elements is a plastic lens element.
[0011] According to another aspect of the present invention, a zoom
lens system includes, from the object side, a first lens unit
having a negative optical power and a second lens unit having a
positive optical power. In the zoom lens system, zooming is
achieved by varying the distance between the first and second lens
units, and at least a negative lens element and a positive lens
element of the lens elements included in the lens units are plastic
lens elements that fulfill the following condition:
-1.2<.phi.Pi/.phi.W.times.hi<1.2
[0012] where
[0013] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0014] .phi.Pi represents the optical power of the ith plastic lens
element; and
[0015] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination a 1 and the height h1, for paraxial tracing,
are 0 and 1, respectively.
[0016] According to another aspect of the present invention, an
image taking apparatus is composed of a zoom lens system, a
photoelectric conversion device, and an optical low-pass filter.
The photoelectric conversion device has a light sensing surface on
which an image is formed by the zoom lens system. The optical
low-pass filter is disposed on the object side of the photoelectric
conversion device. The zoom lens system is composed of, from the
object side, a first lens unit and a second lens unit. The first
lens unit is composed of a negative, a negative, and a positive
lens element, and has a negative optical power as a whole. The
second lens unit is composed of a positive, a negative, and a
positive lens element, and has a positive optical power as a whole.
In the zoom lens system, zooming is achieved by varying the
distance between the first and second lens units, and at least one
of those lens elements is a plastic lens element.
[0017] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit has a negative optical power. The second lens unit is composed
of at least a positive and a negative lens element, and has a
positive optical power. The third lens unit has a positive optical
power. In the zoom lens system, zooming is achieved by moving at
least two lens units so as to vary the distance between the first
and second lens units and the distance between the second and third
lens units, and at least one of the lens elements included in the
lens units is a plastic lens element that fulfills the following
conditions:
-0.8<Cp.times.(N'-N)/.phi.W<0.8
-0.45<M3/M2<0.90(where .phi.T/.phi.W>1.6)
[0018] where
[0019] Cp represents the curvature of the plastic lens element;
[0020] HW represents the optical power of the entire zoom lens
system at the wide-angle end;
[0021] N' represents the refractive index of the object-side medium
of the aspherical surface for the d line;
[0022] N represents the refractive index of the image-side medium
of the aspherical surface for the d line;
[0023] M3 represents the amount of movement of the third lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end);
[0024] M2 represents the amount of movement of the second lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end); and
[0025] .phi.T represents the optical power of the entire zoom lens
system at the telephoto end.
[0026] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit is composed of at least a positive and a negative lens
element, and has a negative optical power. The second and third
lens units have a positive optical power. In the zoom lens system,
zooming is achieved by moving at least two lens units so as to vary
the distance between the first and second lens units and the
distance between the second and third lens units, and at least one
of the lens elements included in the first lens unit is a plastic
lens element that fulfills the following conditions:
.vertline..phi.P/.phi.1.vertline.<1.20
0.20<.vertline..phi.1/.phi.W.vertline.<0.70
-0.45<M3/M2<0.90(where .phi.T/.phi.W>1.6)
[0027] where
[0028] .phi.P represents the optical power of the plastic lens
element;
[0029] .phi.1 represents the optical power of the first lens
unit;
[0030] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0031] M3 represents the amount of movement of the third lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end);
[0032] M2 represents the amount of movement of the second lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end); and
[0033] .phi.T represents the optical power of the entire zoom lens
system at the telephoto end.
[0034] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit has a negative optical power. The second lens unit is composed
of at least a positive and a negative lens element, and has a
positive optical power. The third lens unit has a positive optical
power. In the zoom lens system, zooming is achieved by varying the
distance between the first and second lens units and the distance
between the second and third lens units, and at least one of the
lens elements included in the second lens unit is a plastic lens
element that fulfills the following conditions:
.vertline..phi.P/.phi.2.vertline.<2.5
0.25<.phi.2/.phi.W<0.75
[0035] where
[0036] .phi.P represents the optical power of the plastic lens
element;
[0037] .phi.2 represents the optical power of the second lens unit;
and
[0038] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end.
[0039] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit has a negative optical power. The second and third lens units
have a positive optical power. In the zoom lens system, zooming is
achieved by moving at least two lens units so as to vary the
distance between the first and second lens units and the distance
between the second and third lens units, and at least one of the
lens elements included in the third lens unit is a plastic lens
element that fulfills the following conditions:
-0.30<M3/M2<0.90
.vertline..phi.P/.phi.3.vertline.<1.70
0.1<.phi.3/.phi.W<0.60
[0040] where
[0041] M3 represents the amount of movement of the third lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end);
[0042] M2 represents the amount of movement of the second lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end);
[0043] .phi.P represents the optical power of the plastic lens
element;
[0044] .phi.3 represents the optical power of the third lens unit;
and
[0045] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end.
[0046] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit has a negative optical power. The second and third lens units
have a positive optical power. In the zoom lens system, zooming is
achieved by moving at least two lens units so as to vary the
distance between the first and second lens units and the distance
between the second and third lens units, and at least one of the
lens elements included in the first lens unit and at least one of
the lens elements included in the second lens unit are plastic lens
elements that fulfill the following conditions:
-1.4<.phi.Pi/W.times.hi<1.4
0.5<log(.beta.2T/.beta.2W)/log Z<2.2
[0047] where
[0048] .phi.Pi represents the optical power of the ith plastic lens
element;
[0049] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0050] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination .alpha.1 and the height h1, for paraxial
tracing, are 0 and 1, respectively;
[0051] .beta.2W represents the lateral magnification of the second
lens unit at the wide-angle end;
[0052] .beta.2T represents the lateral magnification of the second
lens unit at the telephoto end;
[0053] Z represents the zoom ratio; and
[0054] log represents a natural logarithm (since the condition
defines a proportion, the base does not matter).
[0055] According to another aspect of the present invention, a zoom
lens system is composed of, from the object side, a first lens
unit, a second lens unit, and a third lens unit. The first lens
unit has a negative optical power. The second lens unit is composed
of at least a positive and a negative lens element, and has a
positive optical power. The third lens unit has a positive optical
power. In the zoom lens system, zooming is achieved by moving at
least two lens units so as to vary the distance between the first
and second lens units and the distance between the second and third
lens units, and at least one of the lens elements included in the
first lens unit and at least one of the lens elements included in
the third lens unit are plastic lens elements that fulfill the
following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
-1.2<log(.beta.3T/.beta.3W)/log Z<0.5
[0056] where
[0057] .phi.Pi represents the optical power of the ith plastic lens
element;
[0058] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0059] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination a 1 and the height h1, for paraxial tracing,
are 0 and 1, respectively;
[0060] .beta.3W represents the lateral magnification of the third
lens unit at the wide-angle end;
[0061] .beta.3T represents the lateral magnification of the third
lens unit at the telephoto end;
[0062] Z represents the zoom ratio; and
[0063] log represents a natural logarithm (since the condition
defines a proportion, the base does not matter).
[0064] According to still another aspect of the present invention,
a zoom lens system is composed of, from the object side, a first
lens unit, a second lens unit, and a third lens unit. The first
lens unit has a negative optical power. The second lens unit is
composed of at least a positive and a negative lens element, and
has a positive optical power. The third lens unit has a positive
optical power. In the zoom lens system, zooming is achieved by
moving at least two lens units so as to vary the distance between
the first and second lens units and the distance between the second
and third lens units, and at least one of the lens elements
included in the second lens unit and at least one of the lens
elements included in the third lens unit are plastic lens elements
that fulfill the following conditions:
-1.4<.phi.Pi/.phi.W.times.hi<1.4
-0.75<log(.beta.3T/.beta.3W)/log(.beta.2T/.beta.2W)<0.65
[0065] where
[0066] .phi.Pi represents the optical power of the ith plastic lens
element;
[0067] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0068] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination .alpha.1 and the height h1, for paraxial
tracing, are 0 and 1, respectively;
[0069] .beta.2W represents the lateral magnification of the second
lens unit at the wide-angle end;
[0070] .beta.2T represents the lateral magnification of the second
lens unit at the telephoto end;
[0071] .beta.3W represents the lateral magnification of the third
lens unit at the wide-angle end;
[0072] .beta.3T represents the lateral magnification of the third
lens unit at the telephoto end; and
[0073] log represents a natural logarithm (since the condition
defines a proportion, the base does not matter).
BRIEF DESCRIPTION OF THE DRAWINGS
[0074] The objects and features of this invention will become clear
from the following description, taken in conjunction with the
preferred embodiments with reference to the accompanied drawings in
which:
[0075] FIG. 1 is a lens arrangement diagram of the zoom lens system
of a first embodiment (Example 1) of the present invention;
[0076] FIG. 2 is a lens arrangement diagram of the zoom lens system
of a second embodiment (Example 2) of the present invention;
[0077] FIG. 3 is a lens arrangement diagram of the zoom lens system
of a third embodiment (Example 3) of the present invention;
[0078] FIG. 4 is a lens arrangement diagram of the zoom lens system
of a fourth embodiment (Example 4) of the present invention;
[0079] FIG. 5 is a lens arrangement diagram of the zoom lens system
of a fifth embodiment (Example 5) of the present invention;
[0080] FIGS. 6A to 6I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 1;
[0081] FIGS. 7A to 7I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 2;
[0082] FIGS. 8A to 8I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 3;
[0083] FIGS. 9A to 9I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 4;
[0084] FIGS. 10A to 10I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 5;
[0085] FIG. 11 is a lens arrangement diagram of the zoom lens
system of a sixth embodiment (Example 6) of the present
invention;
[0086] FIG. 12 is a lens arrangement diagram of the zoom lens
system of a seventh embodiment (Example 7) of the present
invention;
[0087] FIG. 13 is a lens arrangement diagram of the zoom lens
system of an eighth embodiment (Example 8) of the present
invention;
[0088] FIG. 14 is a lens arrangement diagram of the zoom lens
system of a ninth embodiment (Example 9) of the present
invention;
[0089] FIG. 15 is a lens arrangement diagram of the zoom lens
system of a tenth embodiment (Example 10) of the present
invention;
[0090] FIG. 16 is a lens arrangement diagram of the zoom lens
system of an eleventh embodiment (Example 11) of the present
invention;
[0091] FIG. 17 is a lens arrangement diagram of the zoom lens
system of a twelfth embodiment (Example 12) of the present
invention;
[0092] FIG. 18 is a lens arrangement diagram of the zoom lens
system of a thirteenth embodiment (Example 13) of the present
invention;
[0093] FIG. 19 is a lens arrangement diagram of the zoom lens
system of a fourteenth embodiment (Example 14) of the present
invention;
[0094] FIGS. 20A to 20I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 6;
[0095] FIGS. 21A to 21I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 7;
[0096] FIGS. 22A to 22I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 8;
[0097] FIGS. 23A to 23I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 9;
[0098] FIGS. 24A to 24I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 10;
[0099] FIGS. 25A to 25I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 11;
[0100] FIGS. 26A to 26I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 12;
[0101] FIGS. 27A to 27I are graphic representations of the
aberrations observed -in an infinite-distance shooting condition in
the zoom lens system of the Example 13;
[0102] FIGS. 28A to 28I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of the Example 14;
[0103] FIG. 29 is a lens arrangement diagram of the zoom lens
system of a fifteenth embodiment (Example 15) of the present
invention;
[0104] FIGS. 30A to 30I are graphic representations of the
aberrations observed in an infinite-distance shooting condition in
the zoom lens system of Example 15; and
[0105] FIG. 31 is a schematic illustration of the optical
components of a digital camera.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0106] Embodiments 1 to 5
[0107] Hereinafter, zoom lens systems embodying the present
invention will be described with reference to the drawings. FIGS. 1
to 5 are lens arrangement diagrams of the zoom lens systems of a
first, a second, a third, a fourth, and a fifth embodiment,
respectively. In each diagram, the left-hand side corresponds to
the object side, and the right-hand side corresponds to the image
side. Note that, in each diagram, arrows schematically indicate the
movement of the lens units during zooming from the wide-angle end
to the telephoto end. Moreover, each diagram shows the lens
arrangement of the zoom lens system during zooming, as observed at
the wide-angle end. As shown in these diagrams, the zoom lens
systems of the embodiments are each built as a two-unit zoom lens
system of a negative-positive configuration that is composed of,
from the object side, a first lens unit Gr1 and a second lens unit
Gr2. Both the first and second lens units (Gr1 and Gr2) are movably
disposed in the zoom lens system.
[0108] The first lens unit Gr1 is composed of, from the object
side, a negative lens element, a negative lens element, and a
positive lens element and has a negative optical power as a whole.
The second lens unit Gr2 is composed of an aperture stop S, a
positive lens element, a negative lens element, and a positive lens
element and has a positive optical power as a whole. In the zoom
lens system, the first to sixth lens elements counted from the
object side are represented as G1 to G6, respectively. Note that a
flat plate disposed at the image-side end of the zoom lens system
is a low-pass filter LPF. As illustrated in FIG. 31, within a
digital camera the low-pass filter LPP is disposed between the zoom
lens system ZLS and a photoelectric image sensor is having a
light-sensing surface on which an image is formed by the zoom lens
system.
[0109] As shown in FIG. 1, in the first embodiment, the second and
sixth lens elements (G2 and G6) counted from the object side
(hatched in the figure) are plastic lens elements. As shown in FIG.
2, in the second embodiment, the second, third, fifth, and sixth
lens elements (G2, G3, G5, and G6) counted from the object side
(hatched in the figure) are plastic lens elements.
[0110] Moreover, as shown in FIG. 3, in the third embodiment, the
second, fifth, and sixth lens elements (G2, G5, and G6) counted
from the object side (hatched in the figure) are plastic lens
elements. As shown in FIG. 4, in the fourth embodiment, the third
and fifth lens elements (G3 and G5) counted from the object side
(hatched in the figure) are plastic lens elements. Lastly, as shown
in FIG. 5, in the fifth embodiment, the second and sixth lens
elements (G2 and G6) counted from the object side (hatched in the
figure) are plastic lens elements.
[0111] The conditions to be preferably fulfilled by an optical
system will be described below. It is preferable that the zoom lens
systems of the embodiments fulfill Condition (1) below.
0.25<.vertline..phi.1/.phi.W51 <0.80 (1)
[0112] where
[0113] .phi.1 represents the optical power of the first lens unit;
and
[0114] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end.
[0115] Condition (1) defines, in the form of the optical power of
the first lens unit, the condition to be fulfilled to achieve
proper correction of aberrations and keep the size of the zoom lens
system appropriate. If the value of Condition (1) is equal to or
less than its lower limit, the optical power of the first lens unit
is so weak that aberrations can be corrected properly, but
simultaneously the total length, as well as the diameter of the
front-end lens unit, of the zoom lens system becomes unduly large.
In contrast, if the value of Condition (1) is equal to or greater
than its upper limit, the optical power of the first lens unit is
so strong that the total length of the zoom lens system is
successfully minimized, but simultaneously the inclination of the
image plane toward the over side becomes unduly large. In addition,
barrel-shaped distortion becomes unduly large at the wide-angle
end.
[0116] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (2) below.
0.35<.phi.2/.phi.W<0.75 (2)
[0117] where
[0118] .phi.2 represents the optical power of the second lens
unit.
[0119] Condition (2) defines, in the form of the optical power of
the second lens unit, the condition to be fulfilled to achieve, as
in Condition (1), proper correction of aberrations and keep the
size of the zoom lens system appropriate. If the value of Condition
(2) is equal to or less than its lower limit, the optical power of
the second lens unit is so weak that aberrations can be corrected
properly, but simultaneously the total length, as well as the
diameter of the front-end lens unit, of the zoom lens system
becomes unduly large. In contrast, if the value of Condition (2) is
equal to or greater than its upper limit, the optical power of the
second lens unit is so strong that the total length of the zoom
lens system is successfully minimized, but simultaneously spherical
aberration appears notably on the under side.
[0120] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (3) below.
-1.2<.phi.Pi/.phi.W.times.hi<1.2 (3)
[0121] where
[0122] .phi.Pi represents the optical power of the ith plastic lens
element; and
[0123] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination .alpha.1 and the height h1, for paraxial
tracing, are 0 and 1, respectively.
[0124] Condition (3) defines, in the form of the sum of the degrees
in which the individual plastic lens elements, by their temperature
variation, affect the back focal distance, the condition to be
fulfilled to suppress variation in the back focal distance
resulting from temperature variation. When a plurality of plastic
lens elements are used, it is preferable that positively-powered
and negatively-powered lens elements be combined in such a way that
the degree in which they affect the back focal distance are
canceled out by one another. If the value of Condition (3) is equal
to or less than its lower limit, the variation in the back focal
distance caused by temperature variation in the negatively-powered
plastic lens element becomes unduly great. In contrast, if the
value of Condition (3) is equal to or greater than its upper limit,
the variation in the back focal distance caused by temperature
variation in the positively-powered plastic lens element becomes
unduly great. Thus, in either case, the zoom lens system needs to
be provided with a mechanism that corrects the back focal distance
in accordance with temperature variation.
[0125] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (4) below.
.vertline..phi.P/.phi.1.vertline.<1.35 (4)
[0126] where
[0127] .phi.P represents the optical power of the plastic lens
element.
[0128] Condition (4) defines, in the form of the optical power of
the plastic lens element included in the first lens unit, the
condition to be fulfilled to keep the variation of aberrations
resulting from temperature variation within an appropriate range.
If the value of Condition (4) is equal to or greater than its upper
limit curvature of field, in particular, the curvature of field on
the wide-angle side varies too greatly with temperature.
[0129] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (5) below.
.vertline..phi.P/.phi.2.vertline.<2.15 (5)
[0130] Condition (5) defines, in the form of the optical power of
the plastic lens element included in the second lens unit, the
condition to be fulfilled to keep, as in Condition (4), the
variation of aberrations resulting from temperature variation
within an appropriate range. If the value of Condition (5) is equal
to or greater than its upper limit, spherical aberration, in
particular, the spherical aberration on the telephoto side, varies
too greatly with temperature.
[0131] No lower limit is given for Conditions (4) and (5). This is
because, as the value of either of the conditions decreases, the
optical power of the plastic lens element becomes weaker, and this
is desirable in terms of suppression of the variation of
aberrations resulting from temperature variation. This, however,
has no effect on correction of aberrations under normal
temperature, and accordingly makes the use of plastic lenses
meaningless. To avoid this, where the plastic lens element fulfills
Condition (6) below, it is essential to use an aspherical
surface.
0.ltoreq..vertline..phi.P/.phi.A.vertline.<0.45 (6)
[0132] where
[0133] .phi.A represents the optical power of the lens unit
including the plastic lens element.
[0134] Note however that this is not to discourage providing an
aspherical surface on the lens surface of a plastic lens element
having an optical power that makes the value of Condition (6) equal
to or greater than its upper limit.
[0135] As described above, if an aspherical surface is used, it is
preferable that the following conditions be fulfilled. First, where
an aspherical surface is used in the first lens unit, it is
preferable that Condition (7) below be fulfilled.
-0.85<(.vertline.X.vertline.-.vertline.X.sub.0.vertline.)/{C.sub.0(N'-N-
)f1}<-0.05 (7)
[0136] where
[0137] C.sub.0 represents the curvature of the reference spherical
surface of the aspherical surface;
[0138] N represents the refractive index of the image-side medium
of the aspherical surface for the d line;
[0139] N' represents the refractive index of the object-side medium
of the aspherical surface for the d line;
[0140] X represents the deviation of the aspherical surface along
the optical axis at the height in a direction perpendicular to the
optical axis (the direction pointing to the object side is
negative);
[0141] X.sub.0 represents the deviation of the reference spherical
surface of the aspherical surface along the optical axis at the
height in a direction perpendicular to the optical axis (the
direction pointing to the object side is negative); and
[0142] f1 represents the focal length of the first lens unit.
[0143] Condition (7) defines the surface shape of the aspherical
surface and assumes that the aspherical surface is so shaped as to
weaken the optical power of the first lens unit. Fulfillment of
Condition (7) makes it possible to achieve proper correction of the
distortion and the image plane on the wide-angle side, in
particular. If the value of Condition (7) is equal to or less than
its lower limit, positive distortion becomes unduly large on the
wide-angle side, in particular, in a close-shooting condition, and
simultaneously the inclination of the image plane toward the over
side becomes unduly large. In contrast, if the value of Condition
(7) is equal to or greater than its upper limit, negative
distortion becomes unduly large on the wide-angle side, in
particular, in a close-shooting condition, and simultaneously the
inclination of the image plane toward the under side becomes unduly
large. Note that, in a case where the first lens unit includes a
plurality of aspherical surfaces, at least one of those aspherical
surfaces needs to fulfill Condition (7) above; that is, the other
aspherical surfaces do not necessarily have to fulfill Condition
(7) above, if that is advantageous for the correction of other
aberrations.
[0144] In a case where an aspherical surface is used in the second
lens unit, it is preferable that Condition (8) below be
fulfilled.
-0.95<(.vertline.X.vertline.-.vertline.X.sub.0.vertline.)/{C.sub.0(N'-N-
)f2}<-0.05 (8)
[0145] where
[0146] f2 represents the focal length of the second lens unit.
[0147] Condition (8) defines the surface shape of the aspherical
surface and assumes that the aspherical surface is so shaped as to
weaken the optical power of the second lens unit. Fulfillment of
Condition (8) makes it possible to achieve proper correction of
spherical aberration, in particular. If the value of Condition (8)
is equal to or less than its lower limit, in particular, spherical
aberration appears notably on the over side at the telephoto end.
In contrast, if the value of Condition (8) is equal to or greater
than its upper limit, spherical aberration appears notably on the
under side at the telephoto end. Note that, in a case where the
second lens unit includes a plurality of aspherical surfaces, at
least one of those aspherical surfaces needs to fulfill Condition
(8) above; that is, the other aspherical surfaces do not
necessarily have to fulfill Condition (8) above, if that is
advantageous for the correction of other aberrations.
[0148] Embodiments 6 to 15
[0149] FIGS. 11 to 19 and 29 are lens arrangement diagrams of the
zoom lens systems of a sixth, a seventh, an eighth, a ninth, a
tenth, an eleventh, a twelfth, a thirteenth, a fourteenth and a
fifteenth embodiment, respectively. In each diagram, the left-hand
side corresponds to the object side, and the right-hand side
corresponds to the image side. In addition, in each diagram, arrows
schematically indicate the movement of the lens units during
zooming from the wide-angle end to the telephoto end. Note that
arrows with a broken line indicate that the lens unit is kept in a
fixed position during zooming. Moreover, each diagram shows the
lens arrangement of the zoom lens system during zooming, as
observed at the wide-angle end. As shown in these diagrams, the
zoom lens systems of the embodiments are each built as a three-unit
zoom lens system of a negative-positive-positive configuration that
is composed of, from the object side, a first lens unit Gr1, a
second lens unit Gr2, and a third lens unit Gr3. In this zoom lens
system, at least two lens units are moved during zooming.
[0150] The first lens unit Gr1 has a negative optical power as a
whole. The second and third lens units (Gr2 and Gr3) have a
positive optical power as a whole. In the zoom lens system, the
first to eighth lens elements counted from the object side are
represented as G1 to G8, respectively. The lens units provided in
the zoom lens system of each embodiment are each realized by the
use of a plurality of lens elements out of those lens elements G1
to G8. The second lens unit Gr2 includes an aperture stop S. Note
that a flat plate disposed at the image-side end of the zoom lens
system is a low-pass filter LPF.
[0151] As shown in FIG. 11, in the sixth embodiment, the second and
sixth lens elements (G2 and G6) counted from the object side
(hatched in the figure) are plastic lens elements. Moreover, as
shown in FIG. 12, in the seventh embodiment, the second and seventh
lens elements (G2 and G7) counted from the object side (hatched in
the figure) are plastic lens elements.
[0152] As shown in FIG. 13, in the eighth embodiment, the first and
seventh lens elements (G1 and G7) counted from the object side
(hatched in the figure) are plastic lens elements. Moreover, as
shown in FIG. 14, in the ninth embodiment, the second and fifth
lens elements (G2 and G5) counted from the object side (hatched in
the figure) are plastic lens elements. Furthermore, as shown in
FIG. 15, in the tenth embodiment, the first and seventh lens
elements (G1 and G7) counted from the object side (hatched in the
figure) are plastic lens elements.
[0153] As shown in FIG. 16, in the eleventh embodiment, the second
and fifth lens elements (G2 and G5) counted from the object side
(hatched in the figure) are plastic lens elements. Moreover, as
shown in FIG. 17, in the twelfth embodiment, the second, fifth,
sixth, and seventh lens elements (G2, G5, G6, and G7) counted from
the object side (hatched in the figure) are plastic lens
elements.
[0154] As shown in FIG. 18, in the thirteenth embodiment, the
second, fifth, sixth, seventh, and eighth lens elements (G2, G5,
G6, G7, and G8) counted from the object side (hatched in the
figure) are plastic lens elements. As shown in FIG. 19, in the
fourteenth embodiment, the second, sixth, and seventh lens elements
(G2, G6, and G7) counted from the object side (hatched in the
figure) are plastic lens elements. Referring to FIG. 29, in the
fifteenth embodiment, the first and fifth lens elements (G1 and G5)
are plastic lens elements.
[0155] The conditions to be preferably fulfilled by an optical
system will be described below. It is preferable that the zoom lens
systems of the sixth to fifteenth embodiments fulfill Condition (9)
below.
-0.8<Cp.times.(N'-N)/.phi.W<0.8 (9)
[0156] where
[0157] Cp represents the curvature of the plastic lens element;
[0158] .phi.W represents the optical power of the entire zoom lens
system at the wide-angle end;
[0159] N' represents the refractive index of the object-side medium
of the aspherical surface for the d line; and
[0160] N represents the refractive index of the image-side medium
of the aspherical surface for the d line.
[0161] Condition (9) defines the optical power of the lens surface
of the plastic lens element. If the optical power of the lens
surface is too strong, the surface shape varies with temperature,
with the result that various aberrations become unduly large. If
the value of Condition (9) is equal to or less than its lower
limit, the negative optical power is too strong. In contrast, if
the value of Condition (9) is equal to or greater than its upper
limit, the positive optical power is too strong. As a result, in
the plastic lens element provided in the first lens unit, curvature
of field varies too greatly with temperature, in particular; in the
plastic lens element provided in the second lens unit, spherical
aberration varies too greatly with temperature, in particular; and,
in the plastic lens element provided in the third lens unit,
spherical aberration and the coma aberration in marginal rays vary
greatly with temperature, in particular.
[0162] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (10) below.
-0.45<M3/M2<0.90 (10)
[0163] where
[0164] M3 represents the amount of movement of the third lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end); and
[0165] M2 represents the amount of movement of the second lens unit
(the direction pointing to the object side is negative with respect
to the wide-angle end).
[0166] Condition (10) defines, in the form of the ratio of the
amount of movement of the second lens unit to that of the third
lens unit, the condition to be fulfilled to keep the amount of
movement of the second and third lens units in appropriate ranges
in order to achieve zooming efficiently. Thus, in an optical system
in which a sufficient zoom ratio needs to be secured, fulfillment
of Condition (10) is effective. Moreover, it is more preferable
that the following condition be additionally fulfilled.
.phi.T/.phi.W>1.6
[0167] where
[0168] .phi.T represents the optical power of the entire zoom lens
system at the telephoto end.
[0169] If the value of Condition (10) is equal to or less than its
lower limit, the responsibility of the third lens unit for zooming
is so heavy that spherical aberration and the coma aberration in
marginal rays vary too greatly with zooming. In contrast, if the
value of Condition (10) is equal to or greater than its upper
limit, the amount of the movement of the second lens unit is so
large that the diameter of the front-end lens unit needs to be
unduly large in order to secure sufficient amount of peripheral
light on the wide-angle side, and simultaneously, the
responsibility of the second lens unit for zooming is so heavy that
spherical aberration varies too greatly with zooming.
[0170] Moreover, where a plastic lens element is used in the third
lens unit, the ability of the third lens unit to correct
aberrations tends to be insufficient. To avoid this, it is
preferable to make the range of Condition (10) narrower so as to
obtain the following condition:
-0.30<M3/M2<0.90 (10)
[0171] In a case where a plastic lens element is used in the first
lens unit, it is preferable that Condition (11) below be
fulfilled.
.vertline..phi.P/.phi.1).phi.1.vertline.<1.20 (11)
[0172] where
[0173] .phi.P represents the optical power of the plastic lens
element; and
[0174] .phi.1 represents the optical power of the first lens
unit.
[0175] Condition (11) defines, in the form of the ratio of the
optical power of the first lens unit to that of the plastic lens
element included in the first lens unit, the condition to be
fulfilled to keep the variation of aberrations resulting from
temperature variation within an appropriate range. If the value of
Condition (11) is equal to or greater than its upper limit,
curvature of field, in particular, the curvature of field on the
wide-angle side, varies too greatly with temperature. Moreover, to
correct the aberrations that occur in the first lens unit, it is
preferable to use at least a positive and a negative lens
element.
[0176] In a case where a plastic lens element is used in the second
lens unit, it is preferable that Condition (12) below be
fulfilled.
.vertline..phi.P/.phi.2.vertline.<2.5 (12)
[0177] where
[0178] .phi.2 represents the optical power of the second lens
unit.
[0179] Condition (12) defines, in the form of the ratio of the
optical power of the second lens unit to that of the plastic lens
element included in the second lens unit, the condition to be
fulfilled to keep the variation of aberrations resulting from
temperature variation within an appropriate range. If the value of
Condition (12) is equal to or greater than its upper limit,
spherical aberration, in particular, the spherical aberration on
the telephoto side, varies too greatly with temperature. Moreover,
to correct the aberrations that occur in the second lens unit, it
is preferable to use at least a positive and a negative lens
element.
[0180] In a case where a plastic lens element is used in the third
lens unit, it is preferable that Condition (13) below be
fulfilled.
.vertline..phi.P/.phi.3.vertline.<1.70 (13)
[0181] where
[0182] .phi.3 represents the optical power of the third lens
unit.
[0183] Condition (13) defines, in the form of the ratio of the
optical power of the third lens unit to that of the plastic lens
element included in the third lens unit, the condition to be
fulfilled to keep the variation of aberrations resulting from
temperature variation within an appropriate range. If the value of
Condition (13) is equal to or greater than its upper limit,
spherical aberration and the coma aberration in marginal rays vary
too greatly with temperature. Moreover, to correct the aberrations
that occur in the third lens unit, it is preferable to use at least
a positive and a negative lens element.
[0184] No lower limit is given for Conditions (11) to (13). This is
because, as the value of either of the conditions decreases, the
optical power of the plastic lens element becomes weaker, and this
is desirable in terms of suppression of the variation of
aberrations resulting from temperature variation. This, however,
has no effect on correction of aberrations under normal
temperature, and accordingly makes the use of plastic lenses
meaningless. To avoid this, where the plastic lens element fulfills
Condition (14) below, it is essential to use an aspherical
surface.
0.ltoreq..vertline..phi.P/.phi.A.vertline.<0.45 (14)
[0185] where
[0186] .phi.A represents the optical power of the lens unit
including the plastic lens element.
[0187] Note however that this is not to discourage providing an
aspherical surface on the lens surface of a plastic lens element
having an optical power that makes the value of Condition (14)
equal to or greater than its upper limit.
[0188] As described above, if an aspherical surface is used, it is
preferable that the following conditions be fulfilled. First, where
an aspherical surface is provided on the lens surface of the
plastic lens element of the first lens unit, it is preferable that
Condition (15) below be fulfilled.
-1.10<(.vertline.X.vertline.-.vertline.X.sub.0.vertline.)/{C.sub.0(N'-N-
).phi.1}<-0.10 (15)
[0189] where
[0190] C.sub.0 represents the curvature of the reference spherical
surface of the aspherical surface;
[0191] N represents the refractive index of the image-side medium
of the aspherical surface for the d line;
[0192] N' represents the refractive index of the object-side medium
of the aspherical surface for the d line;
[0193] X represents the deviation of the aspherical surface along
the optical axis at the height in a direction perpendicular to the
optical axis (the direction pointing to the object side is
negative);
[0194] X.sub.0 represents the deviation of the reference spherical
surface of the aspherical surface along the optical axis at the
height in a direction perpendicular to the optical axis (the
direction pointing to the object side is negative); and
[0195] f1 represents the focal length of the first lens unit.
[0196] If the value of Condition (15) is equal to or less than its
lower limit, positive distortion becomes unduly large on the
wide-angle side, in particular, in a close-shooting condition, and
simultaneously the inclination of the image plane toward the over
side becomes unduly large. In contrast, if the value of Condition
(15) is equal to or greater than its upper limit, it is impossible
to make efficient use of the aspherical surface, which makes the
use of an aspherical surface meaningless. As a result, the negative
distortion on the wide-angle side, in particular, in a
close-shooting condition, and the inclination of the image plane
toward the under side are undercorrected. Note that, in a case
where the first lens unit includes a plurality of aspherical
surfaces, at least one of those aspherical surfaces needs to
fulfill Condition (15) above; that is, the other aspherical
surfaces do not necessarily have to fulfill Condition (15) above,
if that is advantageous for the correction of other
aberrations.
[0197] In a case where an aspherical surface is provided on the
lens surface of the plastic lens element of the second lens unit,
it is preferable that Condition (16) below be fulfilled.
-0.35<(.vertline.X.vertline.-.vertline.X.sub.0.vertline.)/{C.sub.0(N'-N-
)f2}<-0.03 (16)
[0198] where
[0199] f2 represents the focal length of the second lens unit.
[0200] Condition (16) assumes that the aspherical surface is so
shaped as to weaken the positive optical power of the second lens
unit. Fulfillment of Condition (16) makes it possible to achieve
proper correction of spherical aberration, in particular. If the
value of Condition (16) is equal to or less than its lower limit,
in particular, spherical aberration appears notably on the over
side at the telephoto end. In contrast, if the value of Condition
(16) is equal to or greater than its upper limit, it is impossible
to make efficient use of the aspherical surface, which makes the
use of an aspherical surface meaningless. As a result, spherical
aberration is undercorrected on the telephoto side, in particular.
Note that, in a case where the second lens unit includes a
plurality of aspherical surfaces, at least one of those aspherical
surfaces needs to fulfill Condition (16) above; that is, the other
aspherical surfaces do not necessarily have to fulfill Condition
(16) above, if that is advantageous for the correction of other
aberrations.
[0201] In a case where an aspherical surface is provided on the
lens surface of the plastic lens element of the third lens unit, it
is preferable that Condition (17) below be fulfilled.
-0.70<(.vertline.X.vertline.-.vertline.X.sub.0.vertline.)/{C.sub.0(N'-N-
)f3}<-0.01 (17)
[0202] where
[0203] f3 represents the focal length of the third lens unit.
[0204] Condition (17) assumes that the aspherical surface is so
shaped as to weaken the positive optical power of the third lens
unit. Fulfillment of Condition (17) makes it possible to achieve
proper correction of spherical aberration and the coma aberration
in marginal rays. If the value of Condition (17) is equal to or
less than its lower limit, spherical aberration appears notably on
the over side, and simultaneously the coma aberration in marginal
rays becomes unduly large. In contrast, if the value of Condition
(17) is equal to or greater than its upper limit, it is impossible
to make efficient use of the aspherical surface, which makes the
use of an aspherical surface meaningless. As a result, spherical
aberration and the coma aberration in marginal rays are
undercorrected. Note that, in a case where the third lens unit
includes a plurality of aspherical surfaces, at least one of those
aspherical surfaces needs to fulfill Condition (17) above; that is,
the other aspherical surfaces do not necessarily have to fulfill
Condition (17) above, if that is advantageous for the correction of
other aberrations.
[0205] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (18) below.
0.20<.vertline..phi.1/.phi.W.vertline.<0.70 (18)
[0206] Condition (18) defines, in the form of the optical power of
the first lens unit, the condition to be fulfilled to achieve
proper correction of aberrations and keep the size of the zoom lens
system appropriate. If the value of Condition (18) is equal to or
less than its lower limit, the optical power of the first lens unit
is so weak that aberrations can be corrected properly, but
simultaneously the total length, as well as the diameter of the
front-end lens unit, of the zoom lens system becomes unduly large.
In contrast, if the value of Condition (18) is equal to or greater
than its upper limit, the optical power of the first lens unit is
so strong that aberrations become unduly large, in particular, the
inclination of the image plane toward the over side becomes unduly
large, and simultaneously barrel-shaped distortion becomes unduly
large on the wide-angle side. In this case, the use of a plastic
lens element, which offers a relatively low refractive index and a
strictly restricted range of dispersion, makes it difficult to
correct aberrations properly and thus requires more lens elements
in the zoom lens system.
[0207] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (19) below.
0.25<.phi.2/.phi.W<0.75 (19)
[0208] Condition (19) defines, in the form of the optical power of
the second lens unit, the condition to be fulfilled to achieve
proper correction of aberrations and keep the size of the zoom lens
system appropriate. If the value of Condition (19) is equal to or
less than its lower limit, the optical power of the second lens
unit is so weak that aberrations can be corrected properly, but
simultaneously the total length, as well as the diameter of the
front-end lens unit, of the zoom lens system becomes unduly large.
In contrast, if the value of Condition (19) is equal to or greater
than its upper limit, the optical power of the second lens unit is
so strong that aberrations become unduly large, in particular,
spherical aberration appears notably on the under side. In this
case, the use of a plastic lens element, which offers a relatively
low refractive index and a strictly restricted range of dispersion,
makes it difficult to correct aberrations properly and thus
requires more lens elements in the zoom lens system.
[0209] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (20) below.
0.1<.phi.3/.phi.W<0.60 (20)
[0210] Condition (20) defines, in the form of the optical power of
the third lens unit, the condition to be fulfilled to achieve
proper correction of aberrations and keep the size of the zoom lens
system appropriate. If the value of Condition (20) is equal to or
less than its lower limit, the optical power of the third lens unit
is so weak that aberrations can be corrected properly, but
simultaneously the total length, as well as the diameter of the
front-end lens unit, of the zoom lens system becomes unduly large.
In contrast, if the value of Condition (20) is equal to or greater
than its upper limit, the optical power of the third lens unit is
so strong that aberrations become unduly large, in particular,
spherical aberration appears notably on the under side. In this
case, the use of a plastic lens element, which offers a relatively
low refractive index and a strictly restricted range of dispersion,
makes it difficult to correct aberrations properly and thus
requires more lens elements in the zoom lens system.
[0211] Moreover, if the values of Conditions (18) to (20) are equal
to or greater than their upper limits, the optical power of the
plastic lens element tends to be unduly strong. Thus, it is
preferable that Conditions (11) and (18); (12) and (19); and (13)
and (20) be fulfilled at the same time, respectively.
[0212] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (21) below.
-1.4<.phi.Pi/.phi.W.times.hi<1.4 (21)
[0213] where
[0214] .phi.Pi represents the optical power of the ith plastic lens
element; and
[0215] hi represents the height of incidence at which a paraxial
ray enters the object-side surface of the ith plastic lens element
at the telephoto end, assuming that the initial values of the
converted inclination al and the height h1, for paraxial tracing,
are 0 and 1, respectively.
[0216] Condition (21) defines, in the form of the sum of the
degrees in which the individual plastic lens elements, by their
temperature variation, affect the back focal distance, the
condition to be fulfilled to suppress variation in the back focal
distance resulting from temperature variation. When a plurality of
plastic lens elements are used, it is preferable that
positively-powered and negatively-powered lens elements be combined
in such a way that the degree in which they affect the back focal
distance are canceled out by one another. If the value of Condition
(21) is equal to or less than its lower limit, the variation in the
back focal distance caused by temperature variation in the
negatively-powered plastic lens element becomes unduly great. In
contrast, if the value of Condition (21) is equal to or greater
than its upper limit, the variation in the back focal distance
caused by temperature variation in the positively-powered plastic
lens element becomes unduly great. Thus, in either case, the zoom
lens system needs to be provided with a mechanism that corrects the
back focal distance in accordance with temperature variation.
[0217] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (22) below.
0.5<log(.beta.2T/.beta.2W)/log Z<2.2 (22)
[0218] where
[0219] .beta.2W represents the lateral magnification of the second
lens unit at the wide-angle end;
[0220] .beta.2T represents the lateral magnification of the second
lens unit at the telephoto end;
[0221] Z represents the zoom ratio; and
[0222] log represents a natural logarithm (since the condition
defines a proportion, the base does not matter).
[0223] In a zoom lens system of the types like those of the present
invention, the responsibility of the second lens unit for zooming
is heavier than that of any other lens unit. The heavier the
responsibility for zooming, the larger the aberrations that
accompany zooming. Thus, in order to achieve proper correction of
aberrations, it is preferable to distribute the responsibility for
zooming among a plurality of lens units. Condition (22) defines the
responsibility for zooming of the second lens unit, to which the
heaviest responsibility for zooming is distributed in a zoom lens
system of the types like those of the present invention.
[0224] If the value of Condition (22) is equal to or less than its
lower limit, the responsibility of the second lens unit for zooming
is so light that the aberrations occurring in the second lens unit
can be corrected properly. This, however, affects the
responsibility of the other lens units for correcting aberrations,
and thus requires more lens elements in those other lens units,
with the result that the entire optical system needs to have an
unduly large size. In contrast, if the value of Condition (22) is
equal to or greater than its upper limit, the responsibility of the
second lens unit for zooming is so heavy that spherical aberration
varies too greatly with zooming, in particular.
[0225] It is preferable that the zoom lens systems of the
embodiments fulfill Condition (23) below.
-1.2<log(.beta.3T/.beta.3W)/log Z<0.5 (23)
[0226] where
[0227] .beta.3W represents the lateral magnification of the third
lens unit at the wide-angle end; and
[0228] .beta.3T represents the lateral magnification of the third
lens unit at the telephoto end.
[0229] Condition (23) defines the responsibility of the third lens
unit for zooming. If the value of Condition (23) is negative, the
third lens unit reduces its magnification during zooming. This is
disadvantageous from the viewpoint of zooming. In this case,
however, by moving the third lens unit during zooming, it is
possible to correct the aberrations occurring in the other lens
units during zooming. If the value of Condition (23) is equal to or
less than its lower limit, the third lens unit reduces its
magnification at an unduly high rate during zooming, and thus the
resulting loss in magnification needs to be compensated by the
other lens units. This requires an unduly large number of lens
elements in those other lens units and thus makes the entire
optical system unduly long. In contrast, if the value of Condition
(23) is equal to or greater than its upper limit, the
responsibility of the third lens unit for zooming is so heavy that
spherical aberration and coma aberration vary too greatly with
zooming.
[0230] Moreover, it is preferable that the zoom lens systems of the
embodiments fulfill Condition (24) below.
-0.75<log(.beta.3T/B3W)/log(.beta.2T/.beta.2W)<0.65 (24)
[0231] Condition (24) defines the preferable ratio of the
responsibility of the second lens unit for zooming to the
responsibility of the third lens unit for zooming. If the value of
Condition (24) is equal to or less than its lower limit, the third
lens unit reduces its magnification, and thus the responsibility of
the second lens unit for zooming is excessively heavy. As a result,
spherical aberration varies too greatly with zooming. In contrast,
if the value of Condition (24) is equal to or greater than its
upper limit, the responsibility of the third lens unit for zooming
is so heavy that spherical aberration and coma aberration vary too
greatly with zooming.
[0232] Hereinafter, examples of zoom lens systems embodying the
present invention will be presented with reference to their
construction data, graphic representations of aberrations, and
other data. Tables 1 to 5 list the construction data of Examples 1
to 5, which respectively correspond to the first to fifth
embodiments described above and have lens arrangements as shown in
FIGS. 1 to 5. Tables 6 to 15 list the construction data of Examples
6 to 15, which respectively correspond to the sixth to fifteenth
embodiments described above and have lens arrangements as shown in
FIGS. 11 to 19 and 29.
[0233] In the construction data of each example, ri (i =1, 2, 3, .
. . ) represents the ith surface counted from the object side and
its radius of curvature, di (i=1, 2, 3, . . . ) represents the ith
axial distance counted from the object side, and Ni (i=1, 2, 3, . .
. ) and ni (i=1, 2, 3, . . . ) respectively represent the
refractive index for the d line and the Abbe number of the ith lens
element counted from the object side. The values listed for the
focal length f and the F number FNO of the, entire zoom lens system
in Examples 1 to 5; the distance between the first and second lens
units; and the distance between the second lens unit and the
low-pass filter LPF are the values at, from left, the wide-angle
end (W), the middle-focal-length position (M), and the telephoto
end (T).
[0234] Moreover, the values listed for the focal length f and the F
number FNO of the entire zoom lens system in Examples 6 to 15; the
distance between the first and second lens units; the distance
between the second and third lens units; and the distance between
the third lens unit and the low-pass filter LPF are the values at,
from left, the wide-angle end (W), the middle-focal-length position
(M), and the telephoto end (T). Note that, in all of Examples, a
surface whose radius of curvature ri is marked with an asterisk (*)
is an aspherical surface, whose surface shape is defined by the
following formulae.
X=X.sub.0+.SIGMA.SA.sub.iY.sup.i (a)
X.sub.0=CY.sup.2/{1+(1-.epsilon.C.sup.2Y.sup.2).sup.1/2} (b)
[0235] where
[0236] X represents the displacement from the reference surface in
the optical axis direction;
[0237] Y represents the height in a direction perpendicular to the
optical axis;
[0238] C represents the paraxial curvature;
[0239] .epsilon. represents the quadric surface parameter; and
[0240] A.sub.i represents the aspherical coefficient of the ith
order.
[0241] FIGS. 6A to 6I, 7A to 7I, 8A to 8I, 9A to 9I, and 10A to 10I
show the aberrations observed in the infinite-distance shooting
condition in Examples 1 to 5, respectively. Of these diagrams,
FIGS. 6A to 6C, 7A to 7C, 8A to 8C, 9A to 9C, and 10A to 10C show
the aberrations observed at the wide-angle end [W]; FIGS. 6D to 6F,
7D to 7F, 8D to 8F, 9D to 9F, and 10D to 10F show the aberrations
observed at the middle focal length [M]; and FIGS. 6G to 6I, 7G to
7I, 8G to 8I, 9G to 9I, and 10G to 10I show the aberrations
observed at the telephoto end [T]. In the spherical aberration
diagrams, the solid line (d) represents the d line and the broken
line (SC) represents the sine condition. In the astigmatism
diagrams, the solid line (DS) and the broken line (DM) represent
the astigmatism on the sagittal plane and on the meridional plane,
respectively. In Examples 1 to 5, Conditions (1) to (5) mentioned
above are fulfilled.
[0242] FIGS. 20A to 20I, 21A to 21I, 22A to 22I, 23A to 23I, 24A to
24I, 25A to 25I, 26A to 26I, 27A to 27I, 28A to 28I, and 30A to 30I
show the aberrations observed in the infinite-distance shooting
condition in Examples 6 to 15, respectively. Of these diagrams,
FIGS. 20A to 20C, 21A to 21C, 22A to 22C, 23A to 23C, 24A to 24C,
25A to 25C, 26A to 26C, 27A to 27C, 28A to 28C, and 30A to 30C show
the aberrations observed at the wide-angle end [W]; FIGS. 20D to
20F, 21D to 21F, 22D to 22F, 23D to 23F, 24D to 24F, 25D to 25F,
26D to 26F, 27D to 27F, 28D to 28F, and 30D and 30F show the
aberrations observed at the middle focal length [M]; and FIGS. 20G
to 20I, 21G to 21I, 22G to 22I, 23G to 23I, 24G to 24I, 25G to 25I,
26G to 26I, 27G to 27I, 28G to 28I, and 30G to 30I show the
aberrations observed at the telephoto end [T]. In the spherical
aberration diagrams, the solid line (d) represents the d line and
the broken line (SC) represents the sine condition. In the
astigmatism diagrams, the solid line (DS) and the broken line (DM)
represent the astigmatism on the sagittal plane and on the
meridional plane, respectively. In Examples 6 to 15, the conditions
mentioned above are fulfilled.
[0243] The variables used in Conditions (1) to (5) in Examples 1 to
5 are listed in Table 16.
[0244] The values corresponding to Conditions (1) to (5) in
Examples 1 to 5 are listed in Table 17.
[0245] The values corresponding to Conditions (9) to (13) and (18)
to (24) in Examples 6 to 15 are listed in Table 18.
[0246] The values corresponding to Conditions (7) and (8) to be
fulfilled by the aspherical surface in Examples 1 to 5 are listed
in Table 19. Note that Y represents the maximum height of the
optical path on the aspherical surface.
[0247] The values corresponding to Conditions (15) to (17) to be
fulfilled by the aspherical surface in Examples 6 to 15 are listed
in Table 20. Note that Y represents the maximum height of the
optical path on the aspherical surface.
1TABLE 1 Construction Data of Example 1 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.96 mm 3.24 mm
3.6 mm (F numbers) Radius of Axial Refractive Abbe Curvature
Distance Index (Nd) Number (d) r1 = 11.333 d1 = 0.779 N1 = 1.85000
.nu.1 = 40.04 r2 = 6.007 d2 = 1.940 r3* = 17.418 d3 = 1.400 N2 =
1.52510 .nu.2 = 56.38 r4 = 6.396 d4 = 1.895 r5 = 7.432 d5 = 1.763
N3 = 1.84666 .nu.3 = 23.82 r6 = 10.246 d6 = 13.009 6.374 1.500 r7 =
.infin. (Aperture Stop) d7 = 1.500 r8 = 5.989 d8 = 1.829 N4 =
1.75450 .nu.4 = 51.57 r9 = -125.715 d9 = 1.268 r10 = -12.153 d10 =
0.635 N5 = 1.75000 .nu.5 = 25.14 r11 = 9.023 d11 = 0.447 r12* =
13.010 d12 = 2.293 N6 = 1.52510 .nu.6 = 56.38 r13 = -6.778 d13 =
1.000 2.559 4.786 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.21447 .times. 10.sup.-3 A6 =
0.50169 .times. 10.sup.-5 A8 = 0.14584 .times. 10.sup.-6
[Aspherical Coefficients of 12th Surface (r12)] .epsilon. = 0.10000
.times. 10 A4 = -0.20572 .times. 10.sup.-2 A6 = -0.42994 .times.
10.sup.-5 A8 = -0.32617 .times. 10.sup.-5
[0248]
2TABLE 2 Construction Data of Example 2 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.96 mm 3.24 mm
3.6 mm (F numbers) Radius of Axial Refractive Abbe Curvature
Distance Index (Nd) Number (d) r1 = 14.260 d1 = 0.650 N1 = 1.53359
.nu.1 = 64.66 r2 = 6.334 d2 = 2.341 r3* = 24.115 d3 = 1.400 N2 =
1.52510 .nu.2 = 56.38 r4 = 5.871 d4 = 1.561 r5 = 6.894 d5 = 2.091
N3 = 1.58340 .nu.3 = 30.23 r6 = 13.124 d6 = 14.102 6.837 1.500 r7 =
.infin. (Aperture Stop) d7 = 1.500 r8 = 5.164 d8 = 2.262 N4 =
1.61555 .nu.4 = 57.97 r9 = -9.593 d9 = 0.479 r10* = -5.666 d10 =
1.472 N5 = 1.58340 .nu.5 = 30.23 r11 = 9.833 d11 = 0.604 r12* =
22.822 d12 = 1.943 N6 = 1.52510 .nu.6 = 56.38 r13 = -8.802 d13 =
1.000 2.422 4.454 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.16907 .times. 10.sup.-3 A6 =
0.35415 .times. 10.sup.-5 A8 = 0.80238 .times. 10.sup.-7
[Aspherical Coefficients of 10th Surface (r10)] .epsilon. = 0.10000
.times. 10 A4 = 0.79103 .times. 10.sup.-3 A6 = 0.24186 .times.
10.sup.-4 A8 = 0.30525 .times. 10.sup.-5 [Aspherical Coefficients
of 12th Surface (r12)] .epsilon. = 0.10000 .times. 10 A4 = -0.25573
.times. 10.sup.-2 A6 = -0.15034 .times. 10.sup.-5 A8 = -0.18614
.times. 10.sup.-4
[0249]
3TABLE 3 Construction Data of Example 3 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.96 mm 3.24 mm
3.6 mm (F numbers) Radius of Axial Refractive Abbe Curvature
Distance Index (Nd) Number (d) r1 = 11.551 d1 = 1.213 N1 = 1.75450
.nu.1 = 51.57 r2 = 6.152 d2 = 2.230 r3* = 21.819 d3 = 1.400 N2 =
1.52510 .nu.2 = 56.38 r4 = 6.113 d4 = 1.835 r5 = 7.256 d5 = 2.216
N3 = 1.69961 .nu.3 = 26.60 r6 = 11.287 d6 = 13.126 6.424 1.500 r7 =
.infin. (Aperture Stop) d7 = 1.500 r8 = 5.207 d8 = 2.259 N4 =
1.61213 .nu.4 = 58.19 r9 = -9.240 d9 = 0.467 r10* = -5.774 d10 =
1.430 N5 = 1.58340 .nu.5 = 30.23 r11 = 9.548 d11 = 0.601 r12* =
22.409 d12 = 1.984 N6 = 1.52510 .nu.6 = 56.38 r13 = -8.485 d13 =
1.000 2.495 4.630 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.19262 .times. 10.sup.-3 A6 =
0.34894 .times. 10.sup.-5 A8 = 0.12515 .times. 10.sup.-6
[Aspherical Coefficients of 10th Surface (r10)] .epsilon. = 0.10000
.times. 10 A4 = 0.43913 .times. 10.sup.-3 A6 = 0.33312 .times.
10.sup.-4 A8 = 0.24577 .times. 10.sup.-5 [Aspherical Coefficients
of 12th Surface (r12)] .epsilon. = 0.10000 .times. 10 A4 = -0.22305
.times. 10.sup.-2 A6 = -0.11486 .times. 10.sup.-4 A8 = -0.15332
.times. 10.sup.-4
[0250]
4TABLE 4 Construction Data of Example 4 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.9 mm 3.25 mm
3.6 mm (F numbers) Radius of Axial Refractive Abbe Curvature
Distance Index (Nd) Number (d) r1 = 13.912 d1 = 1.500 N1 = 1.75450
.nu.1 = 51.57 r2 = 6.626 d2 = 2.111 r3 = 25.350 d3 = 1.000 N2 =
1.75450 .nu.2 = 51.57 r4 = 7.001 d4 = 0.893 r5* = 14.283 d5 = 4.843
N3 = 1.58340 .nu.3 = 30.23 r6* = -45.283 d6 = 15.765 7.542 1.500 r7
= .infin. (Aperture Stop) d7 = 1.500 r8 = 5.964 d8 = 4.216 N4 =
1.65656 .nu.4 = 55.63 r9 = -7.373 d9 = 0.208 r10 = -6.131 d10 =
1.300 N5 = 1.58340 .nu.5 = 30.23 r11* = 9.768 d11 = 2.852 r12 =
-77.516 d12 = 1.708 N6 = 1.52200 .nu.6 = 65.93 r13 = -8.818 d13 =
1.000 2.668 5.052 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 5th Surface (r5)]
.epsilon. = 0.10000 .times. 10 A4 = 0.90348 .times. 10.sup.-4 A6 =
0.13458 .times. 10.sup.-5 A8 = 0.14476 .times. 10.sup.-6
[Aspherical Coefficients of 6th Surface (r6)] .epsilon. = 0.10000
.times. 10 A4 = -0.32219 .times. 10.sup.-3 A6 = -0.25483 .times.
10.sup.-5 A8 = -0.86784 .times. 10.sup.-7 [Aspherical Coefficients
of 11th Surface (r11)] .epsilon. = 0.10000 .times. 10 A4 = 0.20489
.times. 10.sup.-2 A6 = 0.27321 .times. 10.sup.-4 A8 = 0.40971
.times. 10.sup.-5 A10 = -0.20451 .times. 10.sup.-6
[0251]
5TABLE 5 Construction Data of Example 5 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 3.18 mm 3.55 mm
4.08 mm (F numbers) Radius of Axial Refractive Abbe Curvature
Distance Index (Nd) Number (d) r1 = 10.456 d1= 2.128 N1 = 1.85000
.nu.1 = 40.04 r2 = 3.870 d2 = 2.166 r3* = 16.226 d3 = 1.400 N2 =
1.52510 .nu.2 = 56.38 r4 = 6.827 d4 = 1.322 r5 = 8.144 d5 = 1.514
N3 = 1.83350 .nu.3 = 21.00 r6 = 13.791 d6 = 8.994 4.674 1.500 r7 =
.infin. (Aperture Stop) d7 = 1.500 r8 = 5.950 d8 = 1.897 N4 =
1.74989 .nu.4 = 51.73 r9 = -43.969 d9 = 1.242 r10 = -11.144 d10 =
0.753 N5 = 1.84714 .nu.5 = 25.28 r11 = 10.245 d11 = 0.400 r12* =
12.590 d12 = 2.297 N6 = 1.52510 .nu.6 = 56.38 r13 = -6.634 d13 =
1.000 3.314 6.620 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.13045 .times. 10.sup.-2 A6 =
0.11643 .times. 10.sup.-4 A8 = 0.51406 .times. 10.sup.-5
[Aspherical Coefficients of 12th Surface (r12)] .epsilon. = 0.10000
.times. 10 A4 = -0.22747 .times. 10.sup.-2 A6 = -0.36716 .times.
10.sup.-5 A8 = -0.32887 .times. 10.sup.-6
[0252]
6TABLE 6 Construction Data of Example 6 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.74 3.11 3.60 (F
numbers) Radius of Axial Refractive Abbe Curvature Distance Index
(Nd) Number (d) r1 = 13.380 d1 = 0.650 N1 = 1.75450 .nu.1 = 51.57
r2 = 5.890 d2 = 1.499 r3* = 12.328 d3 = 1.400 N2 = 1.52510 .nu.2 =
56.38 r4 = 5.632 d4 = 1.632 r5 = 7.068 d5 = 1.753 N3 = 1.84777
.nu.3 = 27.54 r6 = 10.246 d6 = 10.406 5.264 1.500 r7 = .infin.
(Aperture Stop) d7 = 1.500 r8 = 5.643 d8 = 1.901 N4 = 1.79073 .nu.4
= 46.15 r9 = -74.805 d9 = 0.921 r10 = -12.842 d10 = 0.600 N5 =
1.72145 .nu.5 = 25.50 r11 = 5.928 d11 = 0.400 r12* = 11.144 d12 =
2.170 N6 = 1.52510 .nu.6 = 56.38 r13 = -9.099 d13 = 1.000 3.519
7.154 r14 = 11.107 d14 = 3.164 N7 = 1.51680 .nu.7 = 64.20 r15 =
56.703 d15 = 0.796 r16 = .infin. d16 = 3.400 N8 = 1.54426 .nu.8 =
69.60 r17 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.38905 .times. 10.sup.-3 A6 =
0.24379 .times. 10.sup.-5 A8 = 0.38282 .times. 10.sup.-6
[Aspherical Coefficients of 12th Surface (r12)] .epsilon. = 0.10000
.times. 10 A4 = -0.13386 .times. 10.sup.-2 A6 = -0.11975 .times.
10.sup.-4 A8 = -0.53773 .times. 10.sup.-5
[0253]
7TABLE 7 Construction Data of Example 7 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.73 3.10 3.60 (F
numbers) Radius of Axial Refractive Abbe Curvature Distance Index
(Nd) Number (d) r1 = 14.718 d1 = 0.650 N1 = 1.75450 .nu.1 = 51.57
r2 = 6.639 d2 = 1.307 r3* = 11.594 d3 = 1.400 N2 = 1.52510 .nu.2 =
56.38 r4 = 5.294 d4 = 1.465 r5 = 6.937 d5 = 1.858 N3 = 1.84759
.nu.3 = 26.85 r6 = 10.034 d6 = 10.621 5.340 1.500 r7 = .infin.
(Aperture Stop) d7 = 1.500 r8 = 6.969 d8 = 2.905 N4 = 1.85000 .nu.4
= 40.04 r9 = -11.743 d9 = 0.210 r10 = -8.399 d10 = 1.855 N5 =
1.72131 .nu.5 = 25.51 r11 = 5.522 d11 = 0.400 r12 = 11.032 d12 =
2.012 N6 = 1.75450 .nu.6 = 51.57 r13 = -21.657 d13 = 1.000 3.398
6.919 r14* = 8.536 d14 = 3.241 N7 = 1.52510 .nu.7 = 56.38 r15 =
29.006 d15 = 0.676 r16 = .infin. d16 = 3.400 N8 = 1.54426 .nu.8 =
69.60 r17 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.35342 .times. 10.sup.-3 A6 =
0.71258 .times. 10.sup.-6 A8 = 0.33647 .times. 10.sup.-6
[Aspherical Coefficients of 14th Surface (r14)] .epsilon. = 0.10000
.times. 10 A4 = -0.23473 .times. 10.sup.-3 A6 = 0.43912 .times.
10.sup.-5 A8 = 0.10409 .times. 10.sup.-6
[0254]
8TABLE 8 Construction Data of Example 8 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of the Entire Optical System) FNO = 2.75 3.10 3.60 (F
numbers) Radius of Axial Refractive Abbe Curvature Distance Index
(Nd) Number (d) r1* = 14.652 d1 = 1.200 N1 = 1.58340 .nu.1 = 30.23
r2 = 8.289 d2 = 1.623 r3 = 26.068 d3 = 0.900 N2 = 1.79271 .nu.2 =
45.90 r4 = 5.496 d4 = 1.179 r5 = 7.356 d5 = 1.921 N3 = 1.84666
.nu.3 = 23.82 r6 = 15.373 d6 = 10.224 5.176 1.500 r7 = .infin.
(Aperture Stop) d7 = 1.500 r8 = 7.124 d8 = 3.411 N4 = 1.85000 .nu.4
= 40.04 r9 = -11.538 d9 = 0.154 r10 = -8.339 d10 = 1.713 N5 =
1.72418 .nu.5 = 25.37 r11 = 5.686 d11 = 0.401 r12 = 10.731 d12 =
2.078 N6 = 1.75450 .nu.6 = 51.57 r13 = -18.326 d13 = 1.000 3.307
6.708 r14* = 8.148 d14 = 3.002 N7 = 1.52510 .nu.7 = 56.38 r15 =
16.995 d15 = 0.795 r16 = .infin. d16 = 3.400 N8 = 1.54426 .nu.8 =
69.60 r17 = .infin. [Aspherical Coefficients of 1st Surface (r1)]
.epsilon. = 0.10000 .times. 10 A4 = 0.15951 .times. 10.sup.-3 A6 =
0.14779 .times. 10.sup.-6 A8 = 0.56026 .times. 10.sup.-7
[Aspherical Coefficients of 14th Surface (r14)] .epsilon. = 0.10000
.times. 10 A4 = -0.27776 .times. 10.sup.-3 A6 = 0.23365 .times.
10.sup.-5 A8 = 0.19731 .times. 10.sup.-6
[0255]
9TABLE 9 Construction Data of Example 9 f = 5.4 mm 7.5 mm 10.5 mm
(Focal Length of tile Entire Optical System) FNO = 2.73 3.10 3.60
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1 = 52.355 d1 = 1.100 N1 = 1.72677 .nu.1 =
52.55 r2 = 6.927 d2 = 3.324 r3* = 23.902 d3 = 1.940 N2 = 1.58340
.nu.2 = 30.23 r4 = -100.448 d4 = 14.827 7.138 1.500 r5 = .infin.
(Aperture Stop) d5 = 1.500 r6 = 5.036 d6 = 3.339 N3 = 1.77742 .nu.3
= 47.95 r7 = -12.586 d7 = 0.234 r8 = -10.396 d8 = 0.800 N4 =
1.79850 .nu.4 = 22.60 r9 = 16.524 d9 = 0.740 r10 = -7.142 d10 =
1.200 N5 = 1.58340 .nu.5 = 30.23 r11* = -26.834 d11 = 1.000 2.921
5.663 r12 = 15.086 d12 = 2.096 N6 = 1.48749 .nu.6 = 70.44 r13 =
-14.941 d13 = 0.500 r14 = .infin. d14 = 3.400 N7 = 1.54426 .nu.7 =
69.60 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.24908 .times. 10.sup.-3 A6 =
-0.62198 .times. 10.sup.-7 A8 = 0.10295 .times. 10.sup.-6
[Aspherical Coefficients of 11th Surface (r11)] .epsilon. = 0.10000
.times. 10 A4 = 0.39625 .times. 10.sup.-2 A6 = 0.16585 .times.
10.sup.-3 A8 = 0.13563 .times. 10.sup.-4
[0256]
10TABLE 10 Construction Data of Example 10 f = 5.4 mm 7.5 mm 10.5
mm (Focal Length of the Entire Optical System) FNO = 2.75 3.11 3.60
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1* = 17.928 d1 = 1.200 N1 = 1.58340 .nu.1 =
30.23 r2 = 9.608 d2 = 1.325 r3 = 19.410 d3 = 0.900 N2 = 1.80280
.nu.2 = 44.68 r4 = 5.204 d4 = 1.288 r5 = 7.294 d5 = 1.940 N3 =
1.84666 .nu.3 = 23.82 r6 = 14.586 d6 = 10.102 5.348 1.500 r7 =
.infin. (Aperture Stop) d7 = 1.500 r8 = 6.594 d8 = 4.206 N4 =
1.81063 .nu.4 = 43.80 r9 = -10.411 d9 = 0.208 r10 = -7.270 d10 =
0.600 N5= 1.70098 .nu.5 = 26.53 r11 = 5.447 d11 = 0.504 r12 =
10.684 d12 = 2.062 N6 = 1.75450 .nu.6 = 51.57 r13 = -20.769 d13 =
1.000 3.880 6.996 r14* = 6.351 d14 = 2.209 N7 = 1.52510 .nu.7 =
56.38 r15 = 12.184 d15 = 1.055 0.800 1.067 r16 = .infin. d16 =
3.400 N8 = 1.54426 .nu.8 = 69.60 r17 = .infin. [Aspherical
Coefficients of 1st Surface (r1)] .epsilon. = 0.10000 .times. 10 A4
= 0.19398 .times. 10.sup.-3 A6 = 0.47895 .times. 10.sup.-6 A8 =
0.46069 .times. 10.sup.-7 [Aspherical Coefficients of 14th Surface
(r14)] .epsilon. = 0.10000 .times. 10 A4 = -0.37579 .times.
10.sup.-3 A6 = -0.11089 .times. 10.sup.-5 A8 = 0.87379 .times.
10.sup.-7
[0257]
11TABLE 11 Construction Data of Example 11 f = 5.4 mm 7.5 mm 10.5
mm (Focal Length of the Entire Optical System) FNO = 2.97 3.27 3.60
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1 = -112.214 d1 = 1.200 N1 = 1.63347 .nu.1 =
56.87 r2 = 7.682 d2 = 1.473 r3* = 17.799 d3 = 2.175 N2 = 1.58340
.nu.2 = 30.23 r4 = 274.206 d4 = 16.482 8.078 1.500 r5 =
.infin.(Aperture Stop) d5 = 1.500 r6 = 5.066 d6 = 2.164 N3 =
1.84746 .nu.4 = 40.25 r7 = -15.255 d7 = 0.208 r8 = -13.752 d8 =
0.800 N4 = 1.79850 .nu.5 = 22.60 r9 = 7.640 d9 = 0.352 r10* = 8.419
d10 = 1.200 N5 = 1.58340 .nu.6 = 30.23 r11 = 4.700 d11 = 1.000
1.802 2.808 r12 = 40.534 d12 = 2.262 N6 = 1.51838 .nu.7 = 66.35 r13
* = -6.756 d13 = 1.131 2.007 3.472 r14 = .infin. d14 = 3.400 N7 =
1.54426 .nu.8 = 69.60 r15 = .infin. [Aspherical Coefficients of 3rd
Surface (r3)] .epsilon. = 0.10000 .times. 10 A4 = 0.24372 .times.
10.sup.-3 A6 = -0.10309 .times. 10.sup.-6 A8 = 0.84837 .times.
10.sup.-7 [Aspherical Coefficients of 10th Surface (r10)] .epsilon.
= 0.10000 .times. 10 A4 = -0.35107 .times. 10.sup.-2 A6 = -0.17279
.times. 10.sup.-3 A8 = -0.80824 .times. 10.sup.-5 [Aspherical
Coefficients of 13th Surface (r13)] .epsilon. = 0.10000 .times. 10
A4 = 0.11613 .times. 10.sup.-3 A6 = -0.34635 .times. 10.sup.-4 A8 =
0.66386 .times. 10.sup.-6
[0258]
12TABLE 12 Construction Data of Example 12 f = 5.4 mm 8.0 mm 12.0
mm (Focal Length of the Entire Optical System) FNO = 2.55 2.95 3.60
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1 = 64.355 d1 = 0.650 N1 = 1.48749 .nu.1 =
70.44 r2 = 9.616 d2 = 1.136 r3* = 15.072 d3 = 1.400 N2 = 1.52510
.nu.2 = 56.38 r4 = 6.352 d4 = 1.939 r5 = 8.584 d5 = 2.060 N3 =
1.84877 .nu.3 = 32.01 r6 = 12.547 d6 = 15.531 7.207 1.500 r7 =
.infin.Aperture Stop) d7 = 1.500 r8 = 5.666 d8 = 3.346 N4 = 1.75450
.nu.4 = 51.57 r9 = -8.847 d9 = 0.100 r10 = -7.390 d10 = 0.600 N5 =
1.58340 .nu.5 = 30.23 r11 = 4.818 d11 = 0.400 r12* = 6.048 d12 =
2.459 N6 = 1.52510 .nu.6 = 56.38 r13 = 9.906 d13 = 1.000 3.334
6.995 r14 = 11.941 d14 = 1.979 N7 = 1.52510 .nu.7 = 56.38 r15* =
-29.235 d15 = 0.500 r16 = .infin. d16 = 3.400 N8 = 1.54426 .nu.8 =
69.60 r17 = .infin. [Aspherical Coefficients of 3rd Surface (r3)]
.epsilon. = 0.10000 .times. 10 A4 = 0.17978 .times. 10.sup.-3 A6 =
-0.30828 .times. 10.sup.-6 A8 = 0.71904 .times. 10.sup.-7
[Aspherical Coefficients of 12th Surface (r12)] .epsilon. 0.10000
.times. 10 A4 = -0.18066 .times. 10.sup.-2 A6 = -0.54257 .times.
10.sup.-4 A8 = -0.76508 .times. 10.sup.-5 [Aspherical Coefficients
of 15th Surface (r15)] .epsilon. = 0.10000 .times. 10 A4 = 0.29756
.times. 10.sup.-3 A6 = -0.62953 .times. 10.sup.-5 A8 = -0.77785
.times. 10.sup.-7
[0259]
13TABLE 13 Construction Data of Example 13 f = 5.4 mm 8.8 mm 14.0mm
(Focal Length of the Entire Optical System) FNO = 2.34 2.84 3.60 (F
numbers) Radius of Axial Refractive Abbe Curvature Distance Index
(Nd) Number (d) r1 = 25.623 d1 = 0.650 N1 = 1.48749 .nu.1 = 70.44
r2 = 9.290 d2 = 1.626 r3* = 19.577 d3 = 1.400 N2 = 1.52510 .nu.2 =
56.38 r4 = 5.973 d4 = 2.273 r5 = 7.949 d5 = 2.008 N3 = 1.84807
.nu.3 = 28.75 r6 = 10.541 d6 = 16.801 7.154 1.500 r7 =
.infin.(Aperture Stop) d7 = 1.500 r8 = 5.107 d8 = 2.743 N4 =
1.64626 .nu.4 = 56.17 r9 = -9.178 d9 = 0.100 r10 = -8.533 d10 =
0.600 N5 = 1.58340 .nu.5 = 30.23 r11 = 7.962 d11 = 0.849 r12* =
7.572 d12 = 1.401 N6 = 1.52510 .nu.6 = 56.38 r13 = 8.290 d13 =
1.000 4.278 9.371 r14* = 9.062 d14 = 1.423 N7 = 1.58340 .nu.7 =
30.23 r15 = 6.924 d15 = 0.747 r16 = 11.941 d16 = 1.979 N8 = 1.52510
.nu.8 = 56.38 r17* = -29.488 d17 = 0.500 r18 = .infin. d18 = 3.400
N9 = 1.54426 .nu.9 = 69.60 r19 = .infin. [Aspherical Coefficients
of 3rd Surface (r3)] .epsilon. = 0.10000 .times. 10 A4 = 0.16055
.times. 10.sup.-3 A6 = 0.48397 .times. 10.sup.-7 A8 = 0.67121
.times. 10.sup.-7 [Aspherical Coefficients of 12th Surface (r12)]
.epsilon. = 0.10000 .times. 10 A4 = -0.25048 .times. 10.sup.-2 A6 =
-0.87701 .times. 10.sup.-4 A8 = -0.12082 .times. 10.sup.-4
[Aspherical Coefficients of 14th Surface (r14)] .epsilon. = 0.10000
.times. 10 A4 = -0.52484 .times. 10.sup.31 3 A6 = 0.58442 .times.
10.sup.-5 A8 = 0.87159 .times. 10.sup.-8 [Aspherical Coefficients
of 17th Surface (r17)] .epsilon. = 0.10000 .times. 10 A4 = -0.91828
.times. 10.sup.-3 A6 = -0.59033 .times. 10.sup.-5 A8 = 0.27335
.times. 10.sup.-6
[0260]
14TABLE 14 Construction Data of Example 14 f = 5.4 mm 7.5 mm 13.5
mm (Focal Length of the Entire Optical System) FNO = 2.08 2.48 3.60
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1 = 14.018 d1 = 0.650 N1 = 1.74388 .nu.1 =
51.93 r2 = 6.286 d2 = 1.790 r3* = 17.191 d3 = 1.400 N2 = 1.52510
.nu.2 = 56.38 r4 = 5.770 d4 = 0.907 r5 = 6.726 d5 = 1.953 N3 =
1.84666 .nu.3 = 23.82 r6 = 10.531 d6 = 9.731 5.843 1.500 r7 =
.infin.(Aperture Stop) d7 = 1.500 r8 = 6.489 d8 = 1.774 N4 =
1.85000 .nu.4 = 40.04 r9 = 52.968 d9 = 0.665 r10 = -31.304 d10 =
0.600 N5 = 1.77185 .nu.5 = 23.46 r11 = 6.642 d11 = 0.400 r12* =
11.190 d12 = 2.101 N6 = 1.52510 .nu.6 = 56.38 r13 = -9.334 d13 =
1.000 5.310 15.247 r14 = -10.861 d14 = 1.200 N7 = 1.58340 .nu.7 =
30.23 r15* = 16.708 d15 = 0.100 r16 = 12.354 d16 = 2.934 N8 =
1.84353 .nu.8 = 40.59 r17 = -10.876 d17 = 2.914 2.385 0.717 r18 =
.infin. d18 = 3.400 N9 = 1.54426 .nu.9 = 69.60 r19 = .infin.
[Aspherical Coefficients of 3rd Surface (r3)] .epsilon. = 0.10000
.times. 10 A4 = 0.28799 .times. 10.sup.-3 A6 = 0.40089 .times.
10.sup.-5 A8 = 0.14823 .times. 10.sup.-6 [Aspherical Coefficients
of 12th Surface (r12)] .epsilon. = 0.10000 .times. 10 A4 = -0.62816
.times. 10.sup.-3 A6 = -0.22891 .times. 10.sup.-4 A8 = 0.42945
.times. 10.sup.-6 [Aspherical Coefficients of 15th Surface (r15)]
.epsilon. = 0.10000 .times. 10 A4 = 0.60130 .times. 10.sup.-3 A6 =
-0.42374 .times. 10.sup.-5 A8 = 0.11268 .times. 10.sup.-7
[0261]
15TABLE 15 Construction Data of Example 15 f = 5.4 mm 8.4 mm 15.6
mm (Focal Length of the Entire Optical System) FNO = 2.57 3.04 4.20
(F numbers) Radius of Axial Refractive Abbe Curvature Distance
Index (Nd) Number (d) r1 = 34.564 d1 = 1.600 N1 = 1.52510 .nu.1 =
56.38 r2 = 7.185 d2 = 3.500 r3* = 10.666 d3 = 2.344 N2 = 1.75000
.nu.2 = 25.14 r4 = 17.516 d4 = 22.572 11.179 1.713 r5 = .infin. d5
= 1.500 r6 = 8.000 d6 = 2.941 N3 = 1.80420 .nu.3 = 46.50 r7 =
-8.598 d7 = 0.010 N4 = 1.51400 .nu.4 = 42.83 r8 = -8.598 d8 = 0.600
N5 = 1.70055 .nu.5 = 30.11 r9 = 8.182 d9 = 0.200 r10* = 5.244 d10 =
3.249 N6 = 1.52510 .nu.6 = 56.38 r11* = 6.000 d11 = 2.740 5.844
13.277 r12 = 21.195 d12 = 2.000 N7 = 1.48749 .nu.7 = 70.44 r13 =
-16.672 d13 = 1.086 r14 = .infin. d14 = 3.400 N8 = 1.51680 .nu.8 =
64.20 r15 = .infin. [Aspherical Coefficients of 3rd Surface (r1)]
.epsilon. = 0.10000 .times. 10 A4 = 0.43400 .times. 10.sup.-3 A6 =
-0.55461 .times. 10.sup.-5 A8 = 0.27915 .times. 10.sup.-7
[Aspherical Coefficients of 12th Surface (r2)] .epsilon. = 0.10000
.times. 10 A4 = 0.26861 .times. 10.sup.-3 A6 = 0.25040 .times.
10.sup.-5 A8 = 0.23353 .times. 10.sup.-6 [Aspherical Coefficients
of 15th Surface (r10)] .epsilon. = 0.10000 .times. 10 A4 = -0.30306
.times. 10.sup.-3 A6 = -0.13415 .times. 10.sup.-4 A8 = -0.19911
.times. 10.sup.-5 [Aspherical Coefficients of 15th Surface (r11]
.epsilon. = 0.10000 .times. 10 A4 = 0.19342 .times. 10.sup.-2 A6 =
0.59893 .times. 10.sup.-4 A8 = -0.42081 .times. 10.sup.-5
[0262]
16TABLE 16 The variables used in Conditions (1) to (5) in Examples
1 to 5 .phi.1 .phi.2 .phi.W Example 1 0.076171 0.102604 0.185185
.phi.Pi hi .phi.Pi/.phi.W .times. hi Sum Example 1 G2: -0.04968
1.088763 -0.292107 G6: 0.11313 1.264821 0.7726821 0.480575 .phi.1
.phi.2 .phi.W Example 2 0.069512 0.102665 0.185162 .phi.Pi hi
.phi.Pi/.phi.W .times. hi Sum Example 2 G2: -0.06587 1.090648
-0.387944 G3: 0.045137 1.299594 0.3167591 G5: -0.16797 1.270288
-1.152222 G6: 0.080916 1.2079 0.5277862 -0.69562 .phi.1 .phi.2
.phi.W Example 3 0.07421 0.104252 0.185186 .phi.Pi hi
.phi.Pi/.phi.W .times. hi Sum Example 3 G2: -0.05994 1.070319
-0.346422 G3: -0.16771 1.288669 -1.167062 G5: 0.083429 1.23342
0.555676 -0.95781 .phi.1 .phi.2 Example 4 0.070779 0.089085
0.185184 .phi.Pi hi .phi.Pi/.phi.W .times. hi Sum Example 4 G3:
0.05212 1.068396 0.3006979 G5: -0.15954 1.348671 -1.161906 -0.86121
.phi.1 .phi.2 .phi.W Example 5 0.115 0.104369 0.185185 .phi.Pi hi
.phi.Pi/.phi.W .times. hi Sum Example 5 G2: -0.04227 1.161585
-0.265113 G6: 0.11589 1.553375 0.9721086 0.706996
[0263]
17TABLE 17 The values corresponding to Conditions (1) to (5) in
Examples 1 to 5 .vertline..phi.1/.phi.2.vertline. .phi.2/.phi.W
.vertline..phi.P/.phi.1.vertline. .vertline..phi.P/.phi.2.v-
ertline. .phi.Pi/.phi.W .times. hi Example 1 0.41 0.55 G2: 0.65 G6:
1.10 0.48 Example 2 0.38 0.55 G2: 0.95 G5: 1.64 -0.70 G3: 0.65 G6:
0.79 Example 3 0.40 0.56 G2: 0.81 G5: 1.61 -0.96 G6: 0.80 Example 4
0.38 0.48 G3: 0.74 G5: 1.79 -0.86 Example 5 0.62 0.56 G2: 0.37 G6:
1.11 0.71
[0264]
18TABLE 18 The values corresponding to Conditions (9) to (13) and
(18) to (2.phi.in Examples 6 to 15
.vertline..phi.P/.phi.W.vertline. .vertline..phi.P/.phi.1.vertli-
ne. .vertline..phi.P/.phi.2.vertline.
.vertline..phi.P/.phi.3.vertline. M3/M2 Example 6 G2: 0.25 0.63
0.00 G6: 0.55 1.10 Example 7 G2: 0.27 0.72 0.00 G7: 0.25 1.00
Example 8 G1: 0.15 0.39 0.00 G7: 0.20 1.00 Example 9 G2: 0.16 0.59
0.00 G5: 0.32 0.68 Example 10 G1: 0.14 0.38 0.00 G7: 0.24 0.47 1.00
Example 11 G2: 0.17 0.57 0.56 G5: 0.26 0.65 Example 12 G2: 0.24
0.86 0.00 G5: 1.10 2.27 G6: 0.22 0.46 G7: 0.33 1.00 Example 13 G2:
0.32 0.97 0.00 G5: 0.78 1.64 G6: 0.05 0.11 G7: 0.08 0.35 G8: 0.33
1.40 Example 14 G2: 0.31271 0.79 -0.18 G6: 0.5375 1.19 G7: 0.48626
1.38 log(.beta.2T/.beta.2W)/logZ log(.beta.3T/.beta.3W)/- logZ
Example 6 G2: 1.00 0.00 Example 7 G2: 1.00 0.00 Example 8 G1: 1.00
0.00 Example 9 G2: 0.99 0.01 Example 10 G1: 1.00 0.00 Example 11
G2: 1.87 -0.87 Example 12 G2: 0.99 0.01 Example 13 G2: 1.00 0.00
Example 14 G2: 0.75 0.25
log(.beta.3T/.beta.3W)/log(.beta.2T/.beta.2W) Example 6 G2: 0.00
Example 7 G2: 0.00 Example 8 G1: 0.00 Example 9 G2: 0.01 Example 10
G1: 0.00 Example 11 G2: -0.46 Example 12 G2: 0.01 Example 13 G2:
0.00 Example 14 G2: 0.34 .andgate.P/ 0W .times. h .phi.Pi/.phi.W
.times. hi Example 6 G2: -0.27 G6: 0.66 0.39 Example 7 G2: -0.28
G7: 0.17 -0.12 Example 8 G1: -0.15 G7: 0.14 -0.01 Example 9 G2:
0.21 G5: -0.30 -0.09 Example 10 G1: -0.14 G7: 0.16 0.02 Example 11
G2: 0.19 G5: -0.26 -0.08 Example 12 G2: -0.26 G5: -1.20 G6: 0.23
G7: 0.16 -1.06 Example 13 G2: -0.33 G5: -0.93 G6: 0.06 G7: -0.04
G8: 0.14 -1.10 Example 14 G2: -0.34 G6: 0.68 G7: -0.25 0.09
.vertline..phi.1/.phi.W.vertline. .phi.2/.phi.W .phi.3/.phi.W
Example 6 G2: 0.40 0.50 0.21 Example 7 G2: 0.37 0.50 0.25 Example 8
G1: 0.40 0.52 0.20 Example 9 G2: 0.27 0.47 0.34 Example 10 G1: 0.38
0.51 0.24 Example 11 G2: 0.29 0.40 0.48 Example 12 G2: 0.29 0.48
0.33 Example 13 G2: 0.33 0.47 0.23 Example 14 G2: 0.39 0.45 0.35 Cp
.times. (N'-N)/.phi.W Object side Image side Example 6 G2: 0.23
-0.50 G6: 0.25 0.31 Example 7 G2: 0.25 -0.54 G7: 0.33 -0.10 Example
8 G1: 0.22 -0.38 G7: 0.35 -0.17 Example 9 G2: 0.13 0.031 G5: -0.44
0.12 Example 10 G1: 0.18 -0.33 G7: 0.45 -0.23 Example 11 G2: 0.18
-0.01 G5: 0.37 -0.67 Example 12 G2: 0.19 -0.45 G5: -0.43 -0.65 G6:
0.47 -0.29 G7: 0.24 0.10 Example 13 G2: 0.15 -0.48 G5: -0.37 -0.40
G6: 0.37 -0.34 G7: 0.35 -0.46 G8: 0.24 0.10 Example 14 G2: 0.17
-0.49 G6: 0.25 0.30 G7: -0.29 -0.19
[0265]
19TABLE 19 The values corresponding to Conditions (7) and (8) in
Examples 1 to 5 Example 1 [3rd Surface (r3)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0- (N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00037 0.40Y -0.00634 0.60Y
-0.03585 0.80Y -0.13341 1.00Y -0.40394 [12th Surface (r12)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y -0.00000 0.20Y -0.00037 0.40Y -0.00598 0.60Y
-0.03057 0.80Y -0.09885 1.00Y -0.25219 Example 2 [3rd Surface (r3)]
Height (.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00051 0.40Y -0.00870 0.60Y
-0.04931 0.80Y -0.18376 1.00Y -0.55608 [10th Surface (r10)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y 0.00000 0.20Y 0.00005 0.40Y 0.00077 0.60Y
0.00408 0.80Y 0.01399 1.00Y 0.03852 [12th Surface (r12)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y 0.00000 0.20Y -0.00072 0.40Y -0.01169 0.60Y
-0.06096 0.80Y -0.20787 1.00Y -0.58532 Example 3 [3rd Surface (r3)]
Height (.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00050 0.40Y -0.00851 0.60Y
-0.04778 0.80Y -0.17765 1.00Y -0.54143 [10th Surface (r10)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y -0.00000 0.20Y 0.00003 0.40Y 0.00046 0.60Y
0.00259 0.80Y 0.00945 1.00Y 0.02790 [12th Surface (r12)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y 0.00000 0.20Y -0.00065 0.40Y -0.01058 0.60Y
-0.05546 0.80Y -0.19007 1.00Y -0.53702 Example 4 [5th Surface (r5)]
Height (.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00008 0.40Y -0.00129 0.60Y
-0.00719 0.80Y -0.02684 1.00Y -0.08390 [6th Surface (r6)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00066 0.40Y -0.01070 0.60Y
-0.05580 0.80Y -0.18492 1.00Y -0.48426 [11th Surface (r11)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y -0.00000 0.20Y -0.00017 0.40Y -0.00282 0.60Y
-0.01457 0.80Y -0.04772 1.00Y -0.12247 Example 5 [3rd Surface (r3)]
Height (.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00058 0.40Y -0.00938 0.60Y
-0.04968 0.80Y -0.17281 1.00Y -0.49672 [12th Surface (n12)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y 0.00000 0.20Y -0.00039 0.40Y -0.00630 0.60Y
-0.03215 0.80Y -0.10366 1.00Y -0.26303 The values corresponding to
Conditions (15) and (17) in Examples 6 to 15 Example 6 [3rd Surface
(r3)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00036 0.40Y -0.00585 0.60Y -0.03124 0.80Y -0.10983 1.00Y
-0.31946 [12th Surface (r12)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f2} 0.00Y 0.00000
0.20Y -0.00016 0.40Y -0.00266 0.60Y -0.01382 0.80Y -0.04620 1.00Y
-0.12441 Example 7 [3rd Surface (r3)] Height (.vertline.X.vertline.
- .vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00040 0.40Y -0.00645 0.60Y -0.03442 0.80Y -0.12249 1.00Y
-0.36724 [14th Surface (r14)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f3} 0.00Y 0.00000
0.20Y -0.00005 0.40Y -0.00072 0.60Y -0.00343 0.80Y -0.00979 1.00Y
-0.02004 Example 8 [1st Surface (r1)] Height (.vertline.X.vertline.
- .vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00047 0.40Y -0.00762 0.60Y -0.04017 0.80Y -0.13975 1.00Y
-0.40512 [14th Surface (r14)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f3} 0.00Y 0.00000
0.20Y -0.00007 0.40Y -0.00103 0.60Y -0.00497 0.80Y -0.01421 1.00Y
-0.02846 Example 9 [3rd Surface (r3)] Height (.vertline.X.vertline.
- .vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00034 0.40Y -0.00549 0.60Y -0.02824 0.80Y -0.09332 1.00Y
-0.24896 [11th Surface (r11)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f2} 0.00Y 0.00000
0.20Y -0.00086 0.40Y -0.01414 0.60Y -0.07574 0.80Y -0.26114 1.00Y
-0.14147 Example 10 [1st Surface (r1)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00077 0.40Y -0.01256 0.60Y
-0.06639 0.80Y -0.22928 1.00Y -0.65070 [14th Surface (r14)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f3} 0.00Y 0.00000 0.20Y -0.00008 0.40Y -0.00129 0.60Y
-0.00655 0.80Y -0.02065 1.00Y -0.04955 Example 11 [3rd Surface
(r3)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00041 0.40Y -0.00663 0.60Y -0.03428 0.80Y -0.11465 1.00Y
-0.31309 [10th Surface (r10)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f2} 0.00Y 0.00000
0.20Y -0.00016 0.40Y -0.00260 0.60Y -0.01388 0.80Y -0.04736 1.00Y
-0.12790 Example 12 [3rd Surface (r3)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f1} 0.00Y -0.00000 0.20Y -0.00058 0.40Y -0.00940 0.60Y
-0.04961 0.80Y -0.17667 1.00Y -0.53893 [12th Surface (r12)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f2} 0.00Y 0.00000 0.20Y -0.00011 0.40Y -0.00182 0.60Y
-0.00969 0.80Y -0.03330 1.00Y -0.09218 [15th Surface (r15)] Height
(.vertline.X.vertline. - .vertline.X0.vertline.)/{C0(N'-N)
.multidot. f3} 0.00Y 0.00000 0.20Y -0.00033 0.40Y -0.00502 0.60Y
-0.02364 0.80Y -0.06629 1.00Y -0.13286 Example 13 [3rd Surface
(r3)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00082 0.40Y -0.01333 0.60Y -0.07171 0.80Y -0.26196 1.00Y
-0.82010 [12th Surface (r12)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f2} 0.00Y 0.00000
0.20Y -0.00020 0.40Y -0.00328 0.60Y -0.01759 0.80Y -0.06132 1.00Y
-0.17301 [14th Surface (r14)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f3} 0.00Y 0.00000
0.20Y -0.00020 0.40Y -0.00311 0.60Y -0.01525 0.80Y -0.04605 1.00Y
-0.10564 [17th Surface (r17)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f3} 0.00Y 0.00000
0.20Y 0.00068 0.40Y 0.01090 0.60Y 0.05583 0.80Y 0.17801 1.00Y
0.43402 Example 14 [3rd Surface (r3)] Height (.vertline.X.vertline.
- .vertline.X0.vertline.)/{C0(N'-N) .multidot. f1} 0.00Y -0.00000
0.20Y -0.00048 0.40Y -0.00802 0.60Y -0.04370 0.80Y -0.15559 1.00Y
-0.44995 [12th Surface (r12)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f2} 0.00Y 0.00000
0.20Y -0.00007 0.40Y -0.00110 0.60Y -0.00579 0.80Y -0.01922 1.00Y
-0.04962 [15th Surface (r15)] Height (.vertline.X.vertline. -
.vertline.X0.vertline.)/{C0(N'-N) .multidot. f3} 0.00Y 0.00000
0.20Y -0.00067 0.40Y -0.01051 0.60Y -0.05178 0.80Y -0.15744 1.00Y
-0.36553
* * * * *