Objective of variable focal length

A variable focal length objective of which at least one of a pulrality of lens units is moved to vary the image magnification, wherein at least one of the plurality of lens units has at least one refractive index distribution type lens provided with a condition of N.sub.1 >0 as, taking the distance from the optical axis to a radial direction as h, the refractive index distribution is expressed by N(h)=N.sub.0 +N.sub.1 h.sup.2 +N.sub.2 h.sup.4 +N.sub.3 h.sup.6 +. . . (N.sub.0, N.sub.1, N.sub.2 . . . are constants), and satisfies the following conditions: ##EQU1## where fmax: the maximum focal length; PA0 fmin: the minimum focal length; PA0 Lmin: the optical total length when the total length is shortest; PA0 Y: the maximum image height; PA0 N.sub.1 *: the coefficient of h.sup.2 of the refractive index distribution type lens having a refractive index distribution of N.sub.1 >0; PA0 D*: the lens thickness of the refractive index distribution type lens having the refractive index distribution of N.sub.1 >0.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to variable focal length objectives, and more 
particularly to compact variable focal length objectives having refractive 
index distribution type lenses. 
2. Description of the Related Art 
Recently, the requirement of reducing the bulk and size of the variable 
focal length objective has been becoming more and more urgent, and there 
are various proposal for shortening the optical total length. 
But, in general, as the optical total length of the variable focal length 
objective shortens, the Petzval sum is caused to rapidly increase in the 
negative sense with the result of a large over-correction of the curvature 
of field. This aberration is very difficult to correct, giving rise to a 
fatal obstruction in attaining a desired decrease of the optical total 
length of the variable focal length objective. 
In order to achieve an advance in the compactness of the entire system of 
the variable focal length objective, for example, of the type comprising a 
plurality of lens units, of which the first and second counting from the 
front are positive and negative in power respectively and movable with the 
air separation therebetween being made variable for varying the focal 
length of the entire system, or of the type comprising, from front to 
rear, a positive first lens unit, a negative second lens unit, a positive 
or negative third lens unit and a positive fourth lens unit, the first to 
third lens units constituting a zoom section, and the fourth lens unit 
constituting a relay lens, in other words, the so-called 4-component type, 
or of the type comprising a plurality of lens units, of from front to 
rear, a positive first lens unit, a negative second lens unit and a third 
lens unit of strong positive power, whereby as the focal length of the 
entire system varies from the shortest to the longest, whilst the 
separation between the first and second lens units increases and the 
separation between the second and third lens units decreases, the third 
lens unit moves forward, there are the three conventional methods (1) by 
strengthening the power of each of the lens units which constitute the 
zoom section, (2) by decreasing the telephoto ratio of the relay lens, and 
(3) by employing the telephoto type in designing the third positive lens 
unit. However, the use of the first method (1) results in the production 
of a large negative value of the Petzval sum in the second lens unit as 
this lens unit usually as the variator has the strongest power. This 
implies that the curvature of field is extremely over-corrected. The 
second method (2), too, has a similar result, becuase the direction of 
decreasing the telephoto ratio of the relay lens coincides with the 
direction in which the Petzval sum is produced to a negative value. So, 
the use of this method unavoidably leads to over-correct the curvature of 
field. Also, the third method (3) is not useful from the similar reason. 
Further, if such Petzval sum is corrected by lowering the refractive index 
of the convex lens, or by using a positive lens of strong power in 
combination with a negative lens, very large spherical aberration or very 
large higher order aberrations is or are produced which cannot be well 
corrected. In such a manner, the requirement of reducing the bulk and size 
of the variable focal length objective is in contradiction to the 
requirement of correcting the Petzval sum, as far as the system of the 
lenses all of which are made of homogeneous material is concerned. This is 
valid not only in the above-mentioned types of variable focal length 
objectives, but also another types of variable focal length objectives in 
which as the first lens unit moves during zooming, the total length 
increases with increase in the focal length, or in which the fourth lens 
unit is made axially movable with zooming. 
Further, the 2-component zoom lenses comprising from front to rear a 
negative first lens unit and a positive second lens unit, are of no 
exception. 
That is, in the case of the 2-component zoom lenses, letting the focal 
lengths of the first and second lens units be denoted by f1 and f2 
respectively and the image magnification of the second lens unit by 
.beta.2, the focal length f of the entire system can be expressed by 
f=f1.times..beta.2, and the distance S2 between the object side position 
and the image side position of the second lens unit by 
S2=f2.times.(1-.beta.2).sup.2 /.beta.2. Therefore, even with the same 
image magnification of the second lens unit, the shorter the focal length 
of the second lens unit, the greater the reduction of the optical total 
length of the entire system can be made. It should be noted here that to 
allow for a reduction of the focal length of the second lens unit with 
maintenance of the air separation between the first and second lens units 
at the telephoto end to larger values than an acceptable minimum, the 
second lens unit must be designated to the telephoto type of power 
arrangement, and the tendency of the telephoto type must be so 
strengthened that the principal point is shifted enough forward. The use 
of this method in achieving the desired reduction of the total length 
results in the production of a large negative value of the Petzval sum. So 
the curvature of field is over-corrected. Also, the correction of the 
Petzval sum by lowering the refractive index of the convex lens, or by 
using a positive lens of strong power in combination with a negative lens 
of strong power, results in objectionable increase of the spherical 
aberration or the production of higher order aberrations, any of which is 
difficult to correct. 
In such a manner, regardless of what type is employed in designing variable 
focal length objectives, attempts to a desired reduction of the total 
length of the entire system have been foiled without exception by the 
difficulty of well correcting the curvature of field. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide a variable focal length 
objective of greatly advanced compactness while still permitting good 
correction of field curvature to be achieved for high grade of imagery.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In the general embodiment of the invention, the variable focal length 
objective comprises a plurality of lens units, of which at least one unit 
is axially moved to vary the focal length of the entire system, wherein as 
the refractive index N and the height h from the optical axis are related 
by the equation: N(h)=N.sub.0 +N.sub.1 h.sup.2 +N.sub.2 h.sup.4 +N.sub.3 
h.sup.6 + . . . (N.sub.0, N.sub.1, N.sub.2 . . . are constants), at least 
one of the plurality of lens units is included with at least one 
refractive index distribution type lens having a feature of N.sub.1 &gt;0, 
and the following conditions are satisfied: 
##EQU2## 
where fmax: the longest focal length; 
fmin: the shortest focal length; 
Lmin: the optical total length at the minimum of the physical length; 
y: the maximum image height; 
N.sub.1 *: the coefficient of h.sup.2 of that lens of the refractive index 
distribution type which has a refractive index distrubtion of N.sub.1 &gt;0; 
D*: the lens thickness (the separation between the front and rear surface 
measured on the optical axis) of that lens of the refractive index 
distrubtion type which has the refractive index distribution of N.sub.1 &gt;0 
In the above-stated inequality (1), the left side term or Lmin/fmax is 
usually called the telephoto ratio of the variable focal length objective, 
and becomes a useful index to the degree of shortness of the physical 
length of the variable focal length objective. When the angular field 
increases, the difficulty of minimizing the telephoto ratio is, however, 
rapidly increased. If, in the ordinary or homogeneous lens system, 
Lmin/fmax does not satisfy the condition (1), the Petzval sum takes a 
negative value, or it becomes difficult to avoid an over-correction of the 
curvature of field. For note, when the optical total length exceeds the 
right side value of the inequality of condition (1), the objective is 
liable to be under-corrected for the field of curvature. 
Also, the captial sigma in the equality of condition (2) indicates that 
when two or more refractive index distribution type lenses of N.sub.1 &lt;0 
are used, their sum must be considered. 
When the refractive index distribution takes place in a direction 
perpendicular to the optical axis, or in the case of the so-called radial 
refractive index distribution type lens, the power the interior of that 
lens attributes to can be written approximately as -2N.sub.1 D. When 
N.sub.1 is positive, the interior of the lens has a negative power or a 
diverging action (negative gradient power). If, as the refractive index 
distribution type lens of negative gradient power is plural in number, the 
total sum of their internal powers in relation to the power of the entire 
system satisfies the condition (2), it becomes possible to achieve good 
correction of the Petzval sum. For note, if the condition (2) is violated, 
though the spherical aberration and coma can be advantageously corrected, 
no great advance to the fulfillment of both requirements of well 
correcting the Petzval sum or curvature of field and of shortening the 
optical total length can be achieved. 
It should be recognized that the inclusion of at least one refractive index 
distribution type lens which satisfies the above-stated conditions in at 
least one of the plurality of lens units sets forth a feature which is 
characteristic of the invention. It is, therefore, to be understood that 
the scope and spirit of the invention covers those objectives which 
further includes, for example, such a refractive index distribution type 
lens that the refractive index decreases as the radial distance from the 
optical axis increases, or that N.sub.1 &gt;0, that is, the gradient power is 
positive, or such a refractive index distribution type lens that the 
refractive index varies along the optical axis, or that is of the axial 
type, or both radial and axial types of refractive index distributive 
lenses, for an improved result is attained. 
It is also to be understood that the principle of the invention is 
applicable not only to the 2-component, 3-component and 4-component 
variable focal length objectives but also to any other zoom types, and 
further to other fields of lenses without limitation. 
For note, the refractive index distribution in the aforesaid axial type 
lens may be expressed by the following equation: 
EQU N(x)=N.sub.0 +N.sub.1 x+N.sub.2 x.sup.2 +N.sub.3 x.sup.3 + . . . (N.sub.0, 
N.sub.1, N.sub.3, . . . are constant) 
where x is the axial distance measured from the front vertex toward the 
rear. 
The present invention is next described in connection with specific 
embodiments thereof. 
FIG. 1(A) is a longitudinal section view illustrating the construction and 
arrangement of the lens units of the variable focal length objective 
according to the invention. FIG. 1(B) shows its aberrations in three 
operative positions. 
In FIG. 1(A), Ri (i=1, 2, 3 . . . ) represents the i-th surface counting 
from the front, Di (I=1, 2, 3 . . . ) the axial air separation or axial 
thickness between the i-th and (i+1)th surfaces counting from the front, 
and I the first lens unit, II the second lens unit, III the third lens 
unit, and IV the fourth lens unit. Also, in FIG. 1(B), the spherical 
aberration, astigmatism and distortion are shown in the focal length 
positions of f=100 mm, 200 mm and 304.5 mm. In the figure, d and g stand 
for d-line and g-line respectively, and S and M denote the sagittal 
surface and meridional surface respectively. For note, in the section 
view, the refractive index lens is depicted with hatching for the purpose 
of clear identification. 
The variable focal length objective of FIG. 1 comprises, from front to 
rear, the positive first lens unit I which is held stationary during 
variation of the focal length, the negative second unit II which axially 
moves during variation of the focal length to contribute to the variation 
of the focal length, the positive third lens unit III which axially moves 
during variation of the focal length to compensate for the shift of an 
image plane, and the positive fourth lens unit IV which is held stationary 
during variation of the focal length, a radial refractive index 
distribution type lens of negative power gradient that satisfies the 
above-stated inequalities (1) and (2) being used in the negative second 
lens unit aII or the so-called variator. 
The refractive index distribution type lens is different from the ordinary 
lens of homogeneous material and gets even in its interior a converging or 
diverging action. For the refractive index distribution along the line 
perpendicular to the optical axis expressed by the above-described 
equation: N(h)=N.sub.0 +N.sub.1 h.sup.2 +N.sub.2 h.sup.4 + . . . , the 
interior of the lens has a power of -2N.sub.1 D. In this specific 
embodiment, the power of the interior of the refractive index distribution 
type lens accounts for 5/6 of the power of the variator consisting of the 
second lens unit II. 
Also, the refractive index distribution type lens has an ability to correct 
aberrations, and plays an excellent role particularly in correcting the 
Petzval sum. The Petzval sum P produced from the refractive index 
distribution type lens varies as a function of the power .phi. owing to 
the convergence or divergence of its interior material referred to the 
normalized focal length of the entire system to unity and the refractive 
index N.sub.0 at the base, or P=.phi./N.sub.0.sup.2, that is, in inverse 
proportion to the square of the value N.sub.0 of the refractive index, 
being smaller than that produced from the refracting surfaces thereof 
which can be expressed by P=.phi./N.sub.0. Therefore, whilst the 
homogeneous system of the same power arrangement as in the objective of 
this embodiment has its variator resulting in the production of the 
Petzval sum on the order of -1.25 to -1.3, it is in the variable focal 
length objective of the invention that the variator has its Petzval sum 
reduced to as small as -1.025. 
This fact implies that a possibility of further minimizing the optical 
total length of the entire system either by strengthening the power of the 
zoom section or by decreasing the telephoto ratio of the relay section is 
created without sacrificing the image quality. In the past, however, such 
an increase of the power of the zoom section or such a decrease of the 
telephoto ratio of the relay section for the purpose of shortening the 
total length resulted in a large increase of the Petzval sum in the 
negative sense. The impossibility of correcting it was the most serious 
problem. But, the employment of a lens unit whose Petzval sum has a 
reduced value in the negative sense as the variator consisting of the 
negative seconds lens unit II in the variable focal length objective leads 
to increase the possibility of shortening the optical total length of the 
entire system by the above-described method. This is reflected to the 
variable focal length objective of the invention in such a way that the 
telephoto ratio of the relay section which consists of the positive fourth 
lens unit is reduced so that for the optical total length of the entire 
system taken at a value of 254.8 mm, the ratio of the optical total length 
to the longest focal length of the entire system, or the telephoto ratio, 
is reduced to a very small value of 0.836. Further, the refractive index 
of the positive lens at the frontmost position in the relay section is 
made higher by a corresponding amount to the room created for correction 
of the Petzval sum to achieve good correction of spherical aberration. 
Meanwhile, the refractive index distribution type lens can be corrected for 
aberrations both at and inside the lens surfaces by controlling the 
refractive index distribution. So, the variator which would otherwise 
necessitate up to five lens elements as usual is enabled to be constructed 
by only one lens element and moreover in the form that both of its 
surfaces are weak in curvature. 
In order to correct the spherical aberration by bending the rays of light 
passing through the interior of the lens on account of the control of the 
refractive index distribution shape, it is an actual practice, for 
example, that if one puts N(h)=N.sub.0 +N.sub.1 h.sup.2 +N.sub.2 h.sup.4 
+N.sub.3 h.sup.6 + . . . in shaping the refractive index distribution as 
has been described above, what value of the coefficient N.sub.2 is 
appropriate is determined. 
In such a manner, the variable focal length objective of the invention is 
provided with at least one refractive index distribution type lens having 
the feature of N.sub.1 &gt;0 in the equation for the refractive index 
distribution, thereby it being made possible to achieve a much-desired 
reduction of the bulk and size while still permitting an improvement of 
the image quality. 
The variable focal length objective of the invention shown in FIG. 1 can be 
constructed in accordance with the numerical data given in Tables 1.1 to 
1.3 for the focal lengths of the entire system, f, the F-number, FNO, the 
image angles, 2.omega., the radii of curvature, R, the axial thicknesses 
or air separations, D, the refractive indices, N, and Abbe numbers, .nu., 
of the lens elements with the subscripts numbered consecutively from front 
to rear along with the coefficients N.sub.0, N.sub.1, N.sub.2 for the 
spectral d-line and g-line of the above-described equation for refractive 
index distribution. 
TABLE 1.1 
______________________________________ 
f = 100-304.5 FNO = 4.0 2.omega. = 34.34.degree.-11.6.degree. 
Axial thick- 
Radius of ness or air 
Refractive Abbe 
curvature separation index number 
______________________________________ 
R1 = 210.378 
D1 = 3.90 N1 = 1.80518 .nu.1 = 25.4 
R2 = 95.402 
D2 = 9.40 N2 = 1.61272 .nu.2 = 58.7 
R3 = -4243.836 
D3 = 0.14 
R4 = 135.346 
D4 = 6.68 N3 = 1.61272 .nu.3 = 58.7 
R5 = -2643.187 
D5 = Vari- 
able 
R6 = -279.005 
D6 = 10.53 N4 = N4 (h) 
R7 = 258.188 
D7 = Vari- 
able 
R8 = 133.470 
D8 = 8.08 N5 = 1.51633 .nu.5 = 64.1 
R9 = -46.653 
D9 = 2.09 N6 = 1.75520 .nu.6 = 27.5 
R10 = -84.501 
D10 = Vari- 
able 
R11 = 49.541 
D11 = 6.27 N7 = 1.71300 .nu.7 = 55.2 
R12 = 1079.685 
D12 = 1.11 
R13 = -380.726 
D13 = 2.78 N8 = 1.80518 .nu.8 = 25.4 
R14 = 271.435 
D14 = 64.41 
R15 = -25.406 
D15 = 2.78 N9 = 1.76200 .nu.9 = 40.1 
R16 = -72.472 
D16 = 0.28 
R17 = 227.126 
D17 = 5.01 N10 = 1.59551 
.nu.10 = 30.5 
R18 = -75.129 
______________________________________ 
TABLE 1.2 
______________________________________ 
Di 100 200 304.5 
______________________________________ 
D5 2.7787 47.8801 63.3781 
D7 51.0469 26.2032 0.2132 
D10 23.2531 2.9954 13.4873 
______________________________________ 
TABLE 1.3 
______________________________________ 
Ni 
(h) .lambda. 
N.sub.0 N.sub.1 N.sub.2 N.sub.4 
______________________________________ 
N4 d 1.47069 8.0759.times.10.sup.-4 
-3.1382.times.10.sup.-7 
8.9457.times.10.sup.-11 
(h) g 1.47925 8.0465.times.10.sup.-4 
-3.1744.times.10.sup.-7 
9.5646.times.10.sup.-11 
______________________________________ 
FIG. 2(A) is a longitudinal section view illustrating the construction and 
arrangements of the lens elements of another specific variable focal 
length objective of the invention, and FIG. 2(B) shows its spherical 
aberration, astigmatism and distortion in the focal length positions of 
f=100 mm, 200 mm and 286 mm. 
This or second objective is of the similar type to that of the first one, 
comprising, from front to rear, a positive first lens unit I which is held 
stationary during zooming, a negative second lens unit II which axially 
moves with zooming to contribute to the variation of the focal length of 
the entire system, a positive third lens unit III which axially moves to 
compensate for the shift of an image plane during zooming, and a positive 
fourth lens unit IV which is held stationary during zooming, the fourth 
lens unit IV, or the so-called relay section, being divided into two parts 
of which the front part includes a frontmost lens of convex form which is 
a radial type refractive index distributive lens having a positive 
gradient power followed after a very short separation by a doublet 
consisting of a front lens of convex form which is a radial type 
refractive index distributive lens having a negative gradient power and a 
rear lens of homogeneous material, and the rear parts includes a rearmost 
lens of meniscus form which is a radial type refractive index distributive 
lens having a negative gradient power. 
Whilst a decrease of the telephoto ratio of the conventional relay section 
for the purpose of shortening the total length of the variable focal 
length objective has resulted in deterioration of the Petzval sum to the 
negative direction with a rapid increase of the curvature of field in the 
direction to over-correction which could not be well corrected by any 
design of the other lens unit, it is in the objective of the invention 
that use is made of the radial type refractive index distributive lens 
having the negative gradient power in the rear part of the relay section 
or the positive fourth lens unit IV so that the interior of that lens 
because of its having a diverging effect contributes to an increase in the 
negative power of the rear part, thereby the telephoto ratio of the relay 
section is decreased. Since the Petzval sum produced from the refractive 
index distribution type lens is small, curvature of field is hardly 
produced. The use of the two refractive index distribution type lenses in 
the front part of the relay section provides a possibility of achieving a 
further reduction of the total length of the entire system, while 
nevertheless permitting good correction of not only the curvature of 
field, but also spherical aberration, coma and astigmatism to be 
performed. 
The numerical data in accordance with which the second specific objective 
of the invention can be constructed are given in Tables 2.1 to 2.3. 
TABLE 2.1 
______________________________________ 
f = 100-286 FNO = 4.0 2.omega. = 33.5.degree.-12.degree. 
Axial thick- 
Radius of ness or air 
Refractive Abbe 
curvature separation index number 
______________________________________ 
R1 = 195.068 
D1 = 3.76 N1 = 1.80518 .nu.1 = 25.4 
R2 = 93.266 
D2 = 9.40 N2 = 1.61272 .nu.2 = 58.7 
R3 = 58340.891 
D3 = 0.14 
R4 = 131.571 
D4 = 6.69 N3 = 1.61272 .nu.3 = 58.7 
R5 = 221519.437 
D5 = Vari- 
able 
R6 = 714.405 
D6 = 2.09 N4 = 1.71300 .nu.4 = 53.8 
R7 = 55.496 
D7 = 5.88 
R8 = -62.772 
D8 = 1.95 N5 = 1.71300 .nu.5 = 53.8 
R9 = 62.789 
D9 = 4.74 N6 = 1.84666 .nu.6 = 23.9 
R10 = -1831.869 
D10 = Vari- 
able 
R11 = 148.046 
D11 = 8.08 N7 = 1.51633 .nu. 7 = 64.1 
R12 = -44.817 
D12 = 1.95 N8 = 1.75520 .nu.8 = 27.5 
R13 = -79.338 
D13 = Vari- 
able 
R14 = 62.624 
D14 = 5.74 N9 = N9 (h) 
R15 = 7841.012 
D15 = 0.14 
R16 = 38.557 
D16 = 13.28 
N10 = N10 (h) 
R17 = -82.341 
D17 = 2.09 N11 = 1.92286 
.nu.11 = 20.9 
R18 = 149.496 
D18 = 27.21 
R19 = 137.780 
D19 = 5.57 N12 = 1.53256 
.nu.12 = 45.9 
R20 = -37.470 
D20 = 3.16 
R21 = -26.092 
D21 = 10.12 
R22 = -38.926 N13 = N13 (h) 
______________________________________ 
TABLE 2.2 
______________________________________ 
Di 100 200 286 
______________________________________ 
D5 2.3926 47.5055 61.0879 
D10 47.1435 22.2934 0.9012 
D13 23.2591 2.9962 10.8061 
______________________________________ 
TABLE 2.3 
__________________________________________________________________________ 
Ni (h) 
.lambda. 
N.sub.0 
N.sub.1 N.sub.2 N.sub.3 
__________________________________________________________________________ 
N9 (h) 
d 1.53113 
-1.40101 .times. 10.sup.-4 
5.15986 .times. 10.sup.-8 
1.44289 .times. 10.sup.-10 
g 1.54160 
-7.60684 .times. 10.sup.-5 
5.39739 .times. 10.sup.-8 
4.32743 .times. 10.sup.-10 
N10 (h) 
d 1.51633 
1.35945 .times. 10.sup.-4 
-6.07396 .times. 10.sup.-8 
-1.28137 .times. 10.sup.-10 
g 1.52621 
8.57620 .times. 10.sup.-5 
-7.83396 .times. 10.sup.-8 
-4.10306 .times. 10.sup.-10 
N13 (h) 
d 1.53633 
1.51842 .times. 10.sup.-3 
1.06359 .times. 10.sup.-7 
2.58554 .times. 10.sup.-10 
g 1.52621 
1.55218 .times. 10.sup.-3 
1.25181 .times. 10.sup.-7 
1.43805 .times. 10.sup.-10 
__________________________________________________________________________ 
FIG. 3(A) is a longitudinal section view of the construction and 
arrangement of the lens elements of still another specific variable focal 
length objective of the invention, and FIG. 3(B) shows the spherical 
aberration, astigmatism and distortion of the objective of FIG. 3(A) in 
three different focal length positions of f=100 mm, 160 mm and 250 mm. 
This or third objective of the invention comprises, from front to rear, a 
positive first lens unit I which axially moves during zooming, a negative 
second lens unit II which axially moves with zooming to contribute to 
variation of the focal length of the entire system, and a positive third 
lens unit III which is held stationary during zooming. The negative second 
lens unit II is constructed by only one radial type refractive index 
distributive lens. The positive third lens unit III is divided into two 
parts of which the front part comprises, from front to rear, a positive 
lens in the form of a radial type refractive index distributive lens 
having a negative gradient power, followed by a very small spacing by a 
doublet consisting of a positive front lens which is an axial type 
refractive index distributive lens in which the refractive index decreases 
as the distance from the front vertex increases, and a homogeneous rear 
lens, and the rear part includes a negative frontmost lens which is a 
radial type refractive index distributive lens having a negative gradient 
power. 
The use of the radial type refractive index distributive lens of the 
negative gradient power in the negative second lens unit II enables the 
Petzval sum to be decreased, and is advantageous for correcting the 
spherical aberration in the telephoto end. For example, under the 
condition of the same power arrangement, while the negative second lens 
unit II which would otherwise be made up of homogeneous material alone 
produces a Petzval sum of about -1.45 to -1.6 referred to the normalized 
focal length of the entire system to 1, it is in the invention that 
because of being constructed with the radial type refractive index 
distributive lens, it produces a very small Petzval sum of -0.96. 
Since, in such a manner, the Petzval sum produced from the negative second 
lens unit II can be reduced, because the telephoto ratio of the relay 
section consisting of the positive third lens unit III can be decreased, 
it is made possible to achieve a remarkable reduction of the optical total 
length of the entire system. Also, due to the small Petzval sum of the 
negative second lens unit II, the positive third lens unit III or the 
relay section is allowed to be constructed in the form of the telephoto 
type, contributing to a decrease of the total length, and further since 
the positive third lens unit III, too, is constructed with inclusion of 
such refractive index distribution type lenses as has been described 
above, the tendency to the telephoto type is much more strengthened, 
thereby the telephoto ratio of the relay section is reduced to so small a 
value that the optical total length can be extremely shortened. Also, of 
the two negative lenses in the rear part of the positive third lens unit 
III which is stationary during zooming, the front negative lens has the 
radial type refractive index distribution having the negative gradient 
power, assisting in strengthening the negative power of the rear part, 
because its interior has a diverging effect. At this time, the Petzval sum 
ascribable to the interior is smaller than that ascribable to the 
refracting surfaces. Therefore, the over-correction of the curvature of 
field is weakened. Also, by controlling the refracting surfaces and the 
shape of the refractive index distribution, astigmatism is corrected. 
Moreover, the front part, too, is included with the positive lens in the 
form of the radial type refractive index distributive lens having a gentle 
negative gradient power at the frontmost position thereof to allow for an 
increase of the power of the refracting surfaces of that positive lens 
with increase in the under-correction of the curvature of field. This 
enables the over-correction of the curvature of field to be corrected. 
Also, because as the bi-convex lens of the cemented doublet in the front 
part of the positive third lens unit III use is made of the axial type 
refractive index distributive lens in which the refractive index becomes 
progressively lower as the axial distance from the front vertex increases, 
for such a refractive index distribution takes another form at the front 
or convex surface in which the refractive index becomes progressively 
lower as the height from the optical axis increases, an effect of 
correcting spherical aberration and coma is produced, as the rays of light 
are less reflected than when the lens of homogeneous material is used. 
Thus, the field curvature which would otherwise tend to be over-corrected 
when the relay section is formed to a strong telephoto type, can be 
corrected to a minimum, and it becomes possible to well correct spherical 
aberration, coma and astigmatism. And, the index to the portability, or 
the ratio of the physical length when set in the casing therefor (at the 
wide angle end) to the longest focal length, or the so-called telephoto 
ratio can be taken at a very small value of 0.645. 
The third specific objective of the invention can be constructed in 
accordance with the lens data, the lens separations during zooming, and 
the refractive index distribution coefficients of the used refractive 
index distribution type lenses given in Tables 3.1 to 3.3. 
TABLE 3.1 
______________________________________ 
f = 100-250 FNO = 4.5 2.omega. = 31.degree.-12.7.degree. 
Axial thick- 
Radius of ness or air Refractive Abbe 
curvature separation index number 
______________________________________ 
R1 = 106.084 
D1 = 3.32 N1 = 1.80518 
.nu.1 = 25.4 
R2 = 58.076 
D2 = 11.88 N2 = 1.62374 
.nu.2 = 47.1 
R3 = -489.144 
D3 = Vari- 
able 
R4 = 1045.216 
D4 = 11.68 N3 = N3 (h) 
R5 = -273.849 
D5 = Vari- 
able 
R6 = 323.215 
D6 = 6.60 N4 = N4 (h) 
R7 = -74.986 
D7 = 0.13 
R8 = 30.128 
D8 = 6.72 N5 = N5 (x) 
R9 = -73.105 
D9 = 1.92 N6 = 1.72151 
.nu.6 = 29.2 
R10 = 397.026 
D10 = 28.66 
R11 = -55.865 
D11 = 2.19 N7 = N7 (h) 
R12 = -62.834 
D12 = 16.63 
R13 = -26.147 
D13 = 2.55 N8 = 1.51728 
.nu.8 = 69.6 
R14 = -66.609 
______________________________________ 
TABLE 3.2 
______________________________________ 
Di 100 160 250 
______________________________________ 
D3 0.7249 47.4124 75.4248 
D5 19.6360 12.7996 2.5449 
______________________________________ 
TABLE 3.3 
__________________________________________________________________________ 
Ni (h) 
.lambda. 
N.sub.0 
N.sub.1 N.sub.2 N.sub.3 N.sub.4 
__________________________________________________________________________ 
N3 (h) 
d 1.51633 
1.20582 .times. 10.sup.-3 
2.17677 .times. 10.sup.-7 
8.81288 .times. 10.sup.-11 
3.44547 .times. 10.sup.-14 
g 1.52621 
1.20921 .times. 10.sup.-3 
2.15365 .times. 10.sup.-7 
1.35241 .times. 10.sup.-11 
-3.86704 .times. 10.sup.-13 
N4 (h) 
d 1.62041 
1.31092 .times. 10.sup.-4 
1.83723 .times. 10.sup.-7 
2.97786 .times. 10.sup.-10 
3.60954 .times. 10.sup.-13 
g 1.63316 
1.59485 .times. 10.sup.-4 
2.54635 .times. 10.sup.-7 
2.17559 .times. 10.sup.-10 
6.92295 .times. 10.sup.-13 
N5 (h) 
d 1.63854 
-8.10577 .times. 10.sup.-3 
3.54976 .times. 10.sup.-4 
-4.23447 .times. 10.sup.-5 
g 1.65292 
-7.85935 .times. 10.sup.-3 
3.67316 .times. 10.sup.-4 
-6.08825 .times. 10.sup.-5 
N7 (h) 
d 1.51633 
6.19898 .times. 10.sup.-4 
2.48844 .times. 10.sup.-6 
4.66251 .times. 10.sup.-9 
1.04867 .times. 10.sup.-12 
g 1.52621 
5.73366 .times. 10.sup.-4 
2.60420 .times. 10.sup.-6 
2.63683 .times. 10.sup.-9 
1.17387 .times. 10.sup.-11 
__________________________________________________________________________ 
FIG. 4(A) is a longitudinal section view of the construction and 
arrangement of the lens elements of a further specific variable focal 
length objective of the invention, and FIG. 4(B) shows the spherical 
aberration, astigmatism and distortion of the objective of FIG. 4(A) in 
three different focal length positions of f=100 mm, 170 mm and 281 mm. 
This objective comprises from front to rear a positive first lens unit I 
which axially moves during zooming, a negative second lens unit II which 
axially moves during zooming, a positive third lens unit III which axially 
moves during zooming, and a negative fourth lens unit IV which is held 
stationary during zooming, whereby as zooming from the wide angle end to 
the telephoto end, the positive first lens unit I and positive third lens 
unit III are moved forward, and the negative second lens unit II is moved 
rearward to vary the focal length the entire system, and the third lens 
counting from front in the positive third lens unit III consists of a 
radial type refractive index distributive lens having a negative gradient 
power. 
In the zoom type as such, the strenghtening of the power of each of the 
lens unit leads to shorten the optical total length of the entire system. 
Another conventional method for shortening the optical total length of the 
entire system is to construct the positive third lens unit III in the form 
of the telephoto type, and strengthen the tendency to the telephoto type 
to make up such a power arrangement that the principal point is brought 
ahead with the result that the interval between the principal points of 
the negative second and positive third lens units is reduced. As has been 
described above, these conventional methods had a drawback that as the 
Petzval sum took a negative large value, over-correction of curvature of 
field resulted. 
In this specific embodiment, as the negative third lens of the positive 
third lens unit III use is made of a refractive index distribution type 
lens having the negative gradient power which satisfies the above-stated 
inequalities (1) and (2), thereby, despite the employment of such a power 
arrangement as described above, it is made possible to minimize the 
deterioration of the Petzval sum in the direction to a negative value. 
Thus, a shortening of the optical total length can be achieved. 
Further, the thus-created room for correction of the Petzval sum is partly 
reflected to allow for use of a glass of high refractive index in the 
positive lens of the positive third lens unit with an advantage of 
correcting spherical aberration and astigmatism. As a result, a variable 
focal length objective of high grade imagery becomes possible to realize. 
The specific objective of the invention shown in FIG. 4 can be constructed 
in accordance with the numerical data given in Tables 4.1 to 4.3 below. 
TABLE 4.1 
______________________________________ 
f = 100-281 FNO = 3.5-4.7 2.omega. = 62.degree.-24.degree. 
Axial thick- 
Radius of ness or air 
Refractive Abbe 
curvature separation index number 
______________________________________ 
R1 = 610.082 
D1 = 6.19 N1 = 1.80518 .nu.1 = 25.4 
R2 = 173.207 
D2 = 21.62 N2 = 1.60311 .nu.2 = 60.7 
R3 = -349.023 
D3 = 0.33 
R4 = 101.647 
D4 = 11.00 N3 = 1.60311 .nu.3 = 60.7 
R5 = 239.823 
D5 = Vari- 
able 
R6 = 1163.134 
D6 = 3.30 N4 = 1.80400 .nu.4 = 46.6 
R7 = 46.748 
D7 = 14.33 
R8 = -111.152 
D8 = 3.16 N5 = 1.83481 .nu.5 = 42.7 
R9 = 309.530 
D9 = 0.63 
R10 = 93.107 
D10 = 12.38 
N6 = 1.80518 .nu.6 = 25.4 
R11 = -97.659 
D11 = 2.17 
R12 = -67.211 
D12 = 3.16 N7 = 1.80400 .nu.7 = 46.6 
R13 = -287.590 
D13 = Vari- 
able 
R14 = 0.0 D14 = 2.75 
R15 = 66.587 
D15 = 11.00 
N8 = 1.77250 .nu.8 = 49.6 
R16 = -604.172 
D16 = 0.28 
R17 = 83.030 
D17 = 6.88 N9 = 1.62299 .nu.9 = 58.2 
R18 = 166.746 
D18 = 5.68 N10 (h) 
R19 = 215.782 
D19 = 15.32 
R20 = 78.172 
D20 = 5.64 
R21 = -205.827 
D21 = 6.88 N11 = 1.67000 
.nu.11 = 51.6 
R22 = -66.821 
D22 = Vari- 
able 
R23 = 0.0 D23 = Vari- 
able 
R24 = -54.766 
D24 = 3.03 N12 = 1.80400 
.nu.12 = 46.6 
R25 = -561.478 
D25 = 11.55 
N13 = 1.63930 
.nu.13 = 44.9 
R26 = -53.306 
______________________________________ 
TABLE 4.2 
______________________________________ 
f 
Di 100 170 281 
______________________________________ 
D5 5.86 31.53 53.61 
D13 51.09 25.42 3.34 
D22 2.60 8.11 22.96 
D23 13.20 29.79 37.03 
______________________________________ 
TABLE 4.3 
__________________________________________________________________________ 
Ni (h) 
.lambda. 
N.sub.0 
N.sub.1 N.sub.2 N.sub.3 N.sub.4 
__________________________________________________________________________ 
N10 (h) 
d 1.75520 
1.69830 .times. 10.sup.-4 
6.66923 .times. 10.sup.-8 
9.09760 .times. 10.sup.-14 
6.82251 .times. 10.sup.-15 
g 1.79132 
1.86492 .times. 10.sup.-4 
6.90556 .times. 10.sup.-8 
-1.68010 .times. 10.sup.-12 
1.04054 .times. 10.sup.-14 
__________________________________________________________________________ 
FIG. 5(A) is a longitudinal section view of the construction and 
arrangement of the lens elements of another specific variable focal length 
objective of the invention and FIG. 5(B) shows the spherical aberration, 
astigmatism and distortion of the objective of FIG. 5(A) in three 
different focal length positions of f=100 mm, 140 mm and 200 mm. 
The objective of FIG. 5(A) comprises, from front to rear, negative first 
and positive second lens units I and II which axially move during zooming 
to vary the focal length of the entire system while compensating for the 
image shift, and a negative third lens unit III which is held stationary 
during zooming, the positive second lens unit II comprising, from front to 
rear, a radial type refractive index distributive lens having a positive 
gradient power and a radial type refractive index distributive lens having 
a negative gradient power. As the negative third lens unit III is 
introduced for the purpose of shortening the optical total length, this 
variable focal length objective may be considered to be an expanded form 
of the 2-component zoom lens. 
In order to shorten the total length of such a type as this variable focal 
length objective, the positive second lens unit II may, similarly to the 
case of the 2-component zoom lens, be made the telephoto type. That is, 
even if the image magnification of the positive second lens unit II is the 
same, the shorter the focal length of the positive second lens unit II, 
the smaller the optical total length of the entire system can be made. In 
order to shorten the focal length of the positive second lens unit II 
while preserving the acceptable minimum separation between the positive 
first lens unit I and negative second lens unit II, said lens unit may be 
formed to the telephoto type, and the tendency to the telephoto type may 
be strengthened to make up a power arrangement such that the principal 
point is shifted forward. But, when the shortening of the total length is 
attempted by this method, the Petzval sum is increased largely in the 
negative sense. 
However, the positive rear lens of the positive second lens unit II of the 
variable focal length objective of the invention is the refractive index 
distribution type lens having the negative gradient power. For this 
reason, the negative power of the rear part of the positive second lens 
unit II is made strenghtened, and the tendency of the positive second lens 
unit II is made strengthened to achieve a shortening of the total length. 
Also, since a smaller Petzval sum than from the refracting surfaces is 
produced, the over-correction of the curvature of field is diminished. 
Further, correction of distortion in the wide angle end, and astigmatism 
in the wide angle and telephoto ends is performed. Also, with the rays of 
light passing through the interior of the lens, an over-correction of 
spherical aberration results in balance with the under-correction of 
spherical aberration of the front part of the positive second lens unit 
II. 
The positive front lens of the positive second lens unit II has a radial 
type refractive index distribution having a positive gradient power, and 
has an effect of over-correcting spherical aberration at the front surface 
thereof when it usually produces large spherical aberration. Therefore, it 
is made possible to achieve a variable focal length objective well 
corrected for aberrations in the entire focal length range and having its 
lens back made long enough to preserve the necessary value. 
The objective of the invention shown in FIG. 5 can be constructed in 
accordance with the numerical data given in Tables 5.1 to 5.3 below. 
TABLE 5.1 
______________________________________ 
f = 100-200 FNO = 3.5-4.5 2.omega. = 63.44.degree.-34.35.degree. 
Axial thick- 
Radius of ness or air Refractive Abbe 
curvature separation index number 
______________________________________ 
R1 = 79.442 
D1 = 4.27 N1 = 1.69680 
.nu.1 = 55.5 
R2 = 45.721 
D2 = 25.58 
R3 = -223.812 
D3 = 3.72 N2 = 1.69680 
.nu.2 = 55.5 
R4 = 458.898 
D4 = 1.10 
R5 = 69.535 
D5 = 7.35 N3 = 1.75520 
.nu.3 = 27.5 
R6 = 98.647 
D6 = Variable 
R7 = 63.894 
D7 = 19.38 N4 = N4 (h) 
R8 = 182.790 
D8 = 22.76 
R9 = 253.153 
D9 = 7.28 N5 = N5 (h) 
R10 = -3226.156 
D10 = Variable 
R11 = 1408.323 
D11 = 4.13 N6 = 1.48749 
.nu.6 = 70.2 
R12 = 264.158 
______________________________________ 
TABLE 5.2 
______________________________________ 
Di 100 140 200 
______________________________________ 
D6 77.0198 39.0995 10.6593 
D10 4.9553 27.9256 62.3810 
______________________________________ 
TABLE 5.3 
__________________________________________________________________________ 
Ni (h) 
.lambda. 
N.sub.0 
N.sub.1 N.sub.2 N.sub.3 N.sub.4 
__________________________________________________________________________ 
N4 (h) 
d 1.63854 
-1.59742 .times. 10.sup.-4 
-6.11417 .times. 10.sup.-8 
-2.20806 .times. 10.sup.-11 
-1.40928 .times. 10.sup.-14 
g 1.65292 
-1.57014 .times. 10.sup.-4 
-6.20127 .times. 10.sup.-8 
-1.15164 .times. 10.sup.-11 
-2.18006 .times. 10.sup.-14 
N5 (h) 
d 1.58313 
3.53334 .times. 10.sup.-4 
3.46552 .times. 10.sup.-7 
2.07317 .times. 10.sup.-10 
1.51309 .times. 10.sup.-13 
g 1.59529 
3.59411 .times. 10.sup.-4 
3.8565 .times. 10.sup.-7 
4.5463 .times. 10.sup.-12 
4.54978 .times. 10.sup.-13 
__________________________________________________________________________ 
As has been described above, the present invention is to provide a variable 
focal length objective which enables good correction of curvature of field 
and the valuable decrease of the optical total length to be achieved at 
the same time by using one or more refractive index distribution type lens 
or lenses under the prescribed conditions. Further, since the Petzval sum 
produced has a small negative value, there is no need for surfaces of 
strong curvature or steep power arrangement when the Petzval sum is 
corrected, so that as higher order aberrations are hardly increased, a 
desired increase in the relative aperture becomes possible to achieve, and 
the aberrations are maintained stable during zooming.