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Патент USA US3051063

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SEARCH ROOM
SR
350-423
OR
39051905?‘
Q/
Aug. 28, 1962
3,051,052
L. BERGSTEIN
VARIFOCAL LENS SYSTEM WITH FOUR POINTS OF
EXACT IMAGE SHIFT COMPENSATION
4 Sheets-Sheet 1
Filed Aug. 31, 1959
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INVENTOR:
L.BERGSTEIN_
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AGENT
Aug. 28, 1962
3,051,052
L. BERGSTEIN
VARIFOCAL LENS SYSTEM‘ WITH FOUR POINTS OF
EXACT IMAGE SHIFT COMPENSATION
4 Sheets-Sheet 2
Filed Aug. 31, 1959
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INVENTOR
L. BE RG STE IN
BY
AGENT
Aug. 28, 1962
|_. BERGSTEIN
.
3,051,052
VARIFOCAL LENS SYSTEM WITH FOUR POINTS, OF
EXACT IMAGE SHIFT COMPENSATION
Filed Aug. 51, 1959
4 Sheets-Sheet 3
mo
‘“
//
F/G.9
INVENTOR."
L. B ERG STEIN
Aug. 28, 1962
.
|_. BERGSTEIN
VARIF‘OCAL LENS SYSTEM WITH FOUR POINTS OF
EXACT IMAGE SHIFT COMPENSATION
Filed Aug. 31, 1959 '
3,051,052
4 Sheets-Sheet 4
9 00"
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INVENTOR:
L. BERGSTEIN
BY
AGENT
3,051,052
United States Patent 0 " IC€
Patented Aug. 28, 1962
2
1
3,051,052
VARIFOCAL LENS SYSTEM WITH FOUR POINTS
OF EXACT IMAGE SHIFT COMPENSATION
Leonard Bergstein, 1583 Lincoln Place, Brooklyn, N.Y.
Filed Aug. 31, 1959, Ser. No. 837,032
5 Claims. (Cl. 88-57)
My present invention relates to a varifocal lens system
system will remain unaffected if both the power of the
?rst element and its spacing from the next component are
so varied that the position of the secondary focal point
of the ?rst component remains unchanged; it follows that
the relative spacing of the ?rst and second components is
not a critical parameter and that the varifocal system Will
be fully determined if, in addition to the focal lengths
(or powers) and the relative spacings of the second, third
and fourth components, the distance between the second
of four components as described in my co-pending appli
cation Ser. No. 558,665, ?led January 12, 1956, now 10 component and the secondary focal point of the ?rst com
ponent is given. Thus the front (or ?rst) component may
abandoned, of which the present application is a continu
be either positively or negatively refracting so far as image
ation-in-part.
deviation suppression is concerned.
In my co-pending application Ser. No. 554,287, ?led
I have found further that a lens system as described
December 20, 1955, now Patent No. 2,906,177 issued
September 29, 1959, I have disclosed a general theory of .15 above and designed on the assumption of ?nite lens thick
ness and minimum image-plane displacement should have
varifocal systems enabling the designing of such systems
two movable components whose focal lengths have a ratio
with any number of components. In accordance with
ranging, for optimum results, between substantially 1.03
this theory, a system of n alternately stationary and mov
and 1.20. The more forwardly positioned movable com
able components (including a movable rear component)
can be arranged to have an overall focal length variable 20 ponent will have the greater focal length if the movable
components are positively refracting; otherwise, its focal
between two predetermined values upon a variation of the
length will be less than that of the movable rear compo
spacing between the stationary and the movable compo
nent of the varifocal system.
nents and to produce an image in a plane whose shift y
One (not necessarily controlling) advantage of using a
from a reference position will be Zero in n predetermined
positions of the movable components relative to the sta 25 front component of the same refractivity type as the third
tionary components. The displacement of the movable
set of components has been designated 2, ranging between
component is that the resulting equality between'the num
ber of positively and negatively refracting components
makes it possible to reduce Petzval’s sum Era/Nd to zero
two extreme values 1min and zmax. The ?rst value of z
(<p being the refractive power and Nd being the index of
for which y equals zero is designated 11 and may or may
not be equal to 2mm; the last value of z for which y is 30 refraction of each component) so as to correct for ?eld
curvature and astigmatism throughout the operative range
zero has been designated zn and may or may not be equal
to Zn“. The larger the value of n, the closer is the spac
of the system.
_
A
The lens combination having collective movable com
ponents along with a negative front component will give
becomes between the points Z1 and zn, whereby the peaks
of the image deviation y approach zero as the number of 35 a real, inverted image and will thus be usable as a photo
graphic, motion-picture or television objective, whereas
components is increased. Naturally, this number must
the presence of a positively refracting front component in
be held within limits dictated by physical as well as eco—
such system will produce a real, upright image. With
nomic considerations.
ing of the zeros of the curve y(z) and the ?atter this curve
Four-component varifocal lens systems have hitherto
been designed and the characteristic values of their com
ponents calculated on the assumption that the lenses were
in?nitely thin. Systems designed on the basis of this
assumption have the disadvantage that the three peaks of
the image-plane shift between the zeroes differ consider
ably from one another. Another disadvantage is that, a
when ?nite lens thickness is taken into account, the dis
placement z of the movable components is found to be
dispersive movable components the image will be virtual.
if a supplemental lens member or group is ?xedly posi
tioned behind the fourth (or last movable) component
of either type of varifocal system according to this inven
tion in such manner that the primary focal plane of the
supplemental system coincides with the substantially sta
tionary image plane of the varifocal group, the entire lens
assembly becomes an afocal system with variable mag
ni?cation. If the two planes do not coincide, the result
ing combination will have the same optical properties as
considerably less than the theoretical value of z, thereby
the varifocal four-component front group, yet with a.
cutting off a portion of the curve y(z) and one or another
of the zeroes, so as again to result in a large increase of 50 modi?ed focal length and back-focal distance. Such a
focal combination may be provided with an appropriate
the image-plane shift. To avoid this disadvantage, such
diaphragm in order to act as a photographic objective.
systems are designed to be larger (and, therefore, more
The supplemental system may also be used to derive a
expensive) than the theoretical requirements warrant.
real image from a virtual image produced by the varifocal
The general object of my present invention is to provide
a compact four-component varifocal system having the 55 front group.
De?nite relationships have been found to exist between
smallest possible image deviation.
the location of the points of full compensation Z1, Z2, Z3,
Another object of this invention is to provide a four
Z4 and the focal lengths f3, f0, )3; of the second, third and
component varifocal system which is corrected for spher
fourth lens components, respectively, as well as between
ical and chromatic aberrations, coma, astigmatism and
?eld curvature throughout its operative range.
60 the spacings of the various lens components. It will be
convenient to describe these relationships with reference
I have found, in accordance with this invention, that a
four-component varifocal system adapted to satisfy the
foregoing objects is one in which the second, third and
fourth components (counting the stationary component
nearest the object as the ?rst) are alternately refracting 65
(i.e., respectively, either positively, negatively and posi—
tively, or negatively, positively and negatively) and where
to a varifocal coef?cient K de?ned as
fmax —fmin
Rf_ 1
thaws... °r R.+1
where the varifocal range R; is equal to fmax/fmm; )‘mx
is the maximum overall focal length and fmm is the mini
mum overall focal length of the system.
in these three components are so dimensioned that no
In such a system, having a stationary front component,
real image will exist therebetween. As disclosed in my
above-identi?ed patent (wherein, however, the lens com 70 a movable second component behind the ?rst component,
a stationary third component behind the second compo
ponents are counted in ascending order from the image
nent and a movable fourth component on the image side
plane), the position of the image plane of the varifocal
3,051,052
4
3
11A and 1B but with the simple lenses thereof replaced
by compound lenses or lens combinations;
of the varifocal lens group,'l have found that the image
deviation y may be represented as a fourth-order poly
FIG. 7 is a table relating to the system of FIGS. 6A
nomial of z according to the relationship
and 6B;
FIG. 8 is a graph showing the image-plane deviation
in a system embodying my invention; and
(1)
FIGS. 9 and 10 are graphs showing further character—
istics of a lens system according to my invention.
The system of FIGS. 1A and 18, adapted to be used
as
an objective in a photographic camera, comprises a dis
10
mined values Z1, 22, 23, zr of a variable z representing
where the system has an image distance x, measured be
'
tween the image plane and the secondary focal point of
the fourth component, equal to x°+z for four predeter
the axial displacement of the movable components rela
tive to a reference position, x0 being a constant equal to
b3
and where zl is assumed to be Zero.
The coefficients
a1, a2, a3 and b1, b2, b3 are functions of the parameters
of the system; thus,
The values of b1, b2, b3, and 01 are given in terms of the
principal focal lengths f4, f3, f2 of the fourth, third and
second components, respectively, and of the interfocal
spacings (13,4 to all; of all the components, measured
from the secondary focal point of any lower-order com
ponent to the primary focal point of the nearest higher
order component, by the expressions
.
persive ?xed front component A, a collective movable
front component B, a dispersive ?xed rear component C,
and a collective movable rear component D.
Movable
components B, D are ganged for displacement in unison
by means of a rigid link G. A diaphragm DP is assumed
to have been positioned behind the assembly A—D,
which may be considered as a varifocal attachment,
followed by a further ?xed, collective lens member E.
The provision of such member E is, however, not essen
tial, especially in the case of a system whose front com
ponent A is negatively refracting, as in the system under
consideration, since in such case a real, inverted image
will be produced beyond the rear component D. Al
though all of the members A through E have been shown
diagrammatically as simple lens elements, the same are
also representative of compound lenses and lens combina
tions, e.g. as shown more particularly in FIGS. 6A
and 6B.
The only independently variable parameter in the sys
tem of FIGS. 1A and 1B, for the purpose of varying its
focal length, is the spacing between either of the com—
ponents A, C of the stationary set and either of the com
ponents B, D of the movable set, such as the distances
sAB between members A and B and .999 between mem
35 bers C and D. The image distance Dip of attachment
Of the six unknown parameters f2, f3, f4, dm, dm and
A-D, measured between rear component D and image
d3’4 of the generalized four-component system described
plane IP, varies in substantially complementary fashion
above, the separations 82,3 and 83,4 between the proximal
to the relative spacing dAB, thereby maintaining virtually
notal points of the second, third and fourth components
invariable the back-focal length dip of the overall sys
may be chosen by the designer, permitting £123 and 40 tem as measured between back member E and image
d“ to be eliminated‘, since
plane IP.
The virtual secondary focus FA of negative front com
ponent A has been shown spaced from that component
and
by the latter’s focal length fA. This focal length, being
(5a)’
Only four parameters of the system remain to be de
termined, namely the three focal lengths f2, f3, f4 and
the interfocal spacing r1112 between the ?rst and second
components. These are given by the following four
equations:
a1=—Z2-Z3—-Z4
(6a)
a2==Z2Za+Z2Z4+Z3Z4
(6b)
a3=—z2Z3Z4
(6c)
Rf=(b3+b2+bl)/b3
(7)
The foregoing theory of four-component varifocal sys
tems will be further developed and explained wtih refer
ence to the accompanying drawing in which:
FIGS. 1A and 1B diagrammatically show, in different
positions of the movable components, an optical system
according to the invention utilizing a negative ?xed front
lens;
-
FIGS. 2A and 2B are analogous views of a system ac
cording to the invention employing a positive front lens;
FIG. 3 shows an afocal system adapted for use as a
camera front attachment, formed by combining the sys
directed toward the object side of the system, is added to
the spacing sAc between the components A, C of the sta
tionary set to give the parameter DAG, or the spacing be
tween the focal point FA and the ?xed rear component C,
which co-deterrnines the position of image plane IP.
The ?xed spacing between components B and D is indi
cated at sBD.
In FIGS. 2A and 2B there is shown a system similar
to that of FIGS. 1A and 1B, except for the ?xed front
component A’ which represents a collective lens element
substituted for the dispersive element A of the preceding
embodiment. The secondary focal point of element A’
has been shown at FA’ and is spaced from component C
by a distance DAG’ equal to the similarly designated dis
tance in FIG. 1A; since the focal length L,’ of the front
component is now directed toward the rear of the system,
it is subtracted from the inter-component spacing sAc'
to give the parameter DAG’. Inasmuch as elements B,
C, D, E are assumed to be identical with the thus desig
nated components in FIGS. 1A and 1B and the relative
, spacing thereof is the same, the position of the image
system;
plane IP is likewise unchanged.
In FIG. 3 the assembly A, B, C, D‘ of FIG. 1A pre
FIG. 4 shows an afocal system similar to that of FIG.
3 but with a supplemental collective lens, adapted to be
fE’ whose focal point FE’ coincides with the image plane
tem of FIGS. 1A and 1B with a supplemental dispersive
used as a varifocal telescope;
FIG. 5 shows another varifocal telescope according to
the invention formed by combining the system of FIGS.
2A and 213 with a supplemental lens of the type shown
in FIG. 3;
cedes a dispersive rear lens component E’ of focal length
IP of the varifocal group. This results in an afocal sys
tem adapted to be used, for example, as a camera front
attachment aifording a wide range of variations in image
size.
FIG. 4 shows a similar afocal system wherein, how
FIGS. 6A and 6B are views corresponding to FIGS. 75 ever, the dispersive member E’ has been replaced by a
3,051,052
6
component B will be found to be + 131.0, the focal length
collective member E" of focal length 155" positioned be
hind the image plane IP which coincides with its primary
focal point FE". ‘FIG. 5 illustrates another afocal sys
]‘c of component C to have a value of —7l.7, and the
focal length in of component D to have a value of
+1244. The parameter DAG, previously de?ned as the
algebraic difference of distance sAc and focal length fA,
tem in which the varifocal lens group A’, B, C, D of FIG.
2A has been combined with the dispersive lens member
has a numerical value of 407.5. The effective distance
'
sBD between the components B and D is 130.0
It should be noted that in the two last-mentioned sys
The overall focal length of the system variessubstan
tems, in which there are even numbers of negative com
tially between 2.34fA and 0.3911 as the spacing be
ponents, the image will be upright so that the system may
tween the movable and stationary sets is varied from
be used directly as a telescope with variable magni?ca
tion. These latter systems may also be used in conjunc 10 SBc=117.62 and SOD-‘1:12.37 (21:0) to SBc=17-62 and
tion with photographic cameras or the like if the righted
sCD=112.37 (z4=10O). The maximum image deviation
E’ of FIG. 3.
image is non-objectionable.
occurring between points of full compensation at which
As a numerical example, the parameters of the lens
systems of FIGS. 1-5 will be given for an assembly with a
desired ratio R, of maximum to minimum overall focal
curve y(z) of FIG. 8 intersects the z axis has an absolute
value of 0.35.
.
Since focal length fA, as previously pointed out, may
be selected quite arbitrarily, this focal length has only the
length equal to 6:1 (determined by the lens designer)
which is to produce a real image behind the system. The
example will be more clearly understood with reference
to the graphs of FIGS. 8, 9 and 10.
FIG. 8 shows a graph of the image-plane deviation y
restriction that, at a varifocal-coe?icient value of
K=O.71, it must be less than —-289.88 in order to permit
a variation of z from 0 to 100. It is advantageous, how
as a function of the displacement z of the movable com
photographic objectives or as attachments to photo
graphic objectives, to use a negative front component
ever, in case any of the above systems are to be used as
ponents, thus illustrating the signi?cance of the zero
with ]’A equal substantially to —279.00. With this value
points Z1, Z2, Z3, and Z4 (points of full compensation).
of 11,, not only is the spacing sAB variable from 10.88
It will be noted that the peaks of curve y(z) between
these zeros, and particularly the ?rst and the third one, 25 (11:0) to 110.88 (z4=100) and thus the minimum re
quired, but it will also be found that Petzval’s sum (pre
are of substantially equal magnitudes.
viously de?ned) is substantially zero, thereby making it
FIG. 9 is a graph showing the variation of Z2 and 23
possible to correct for the aforementioned aberrations.
with the varifocal coe?icient K (assuming zl to be zero
In that case, the overall focal length will be variable be
and z.,=100) in a system according to the invention, de—
signed for minimum image deviation. It will be seen 30 tween substantially 652.8 and 108.8.
Since the movable components (lenses B and D) of the
that the slopes of the substantially parallel curves for 22
aforedescribed example are positively retracting, the more
and Z3 are negative and generally symmetrical about the
forwardly positioned movable component will be seen to
z-axis and that the values of Z2 on one side of this axis
have the greater focal length. The lens system, there
complement those of Z3 on the other side thereof, for
equal absolute values of K. The maximum displace 35 fore, has two movable components whose focal lengths
have a ratio of 1.05 (fc/fD) for optimum results. From
ment z of the movable components is given a total of 100
the graph of FIG. 10, the maximum focal length of a
units.
four-component system (fmax) and the focal lengths of
FIG. 10 shows shaded areas A and D, bounded by
the movable components (fc, fD) may be determined
curves Fmax and F'max which in the regions illustrated are
generally parabolic, whence the maximum focal length 40 upon the selection of a varifocal coefficient as shown, for
a system whose movable components have a focal-length
fmax of the system may be selected with different positive
ratio of 1.05. From the preceding equations, similar
and negative values, respectively, of K. Areas B and C,
curves may be obtained for the focal lengths of the other
bounded by curves F1, F3 and F1’, F3’, respectively,
lens components and for movablev components Whose
which are generally hyperbolic and asymptotic to the line
focal-length ratio falls within the optimum range (1.03
K=0 indicate corresponding ranges of variations for the
1.20) in order to simplify the lens-designing task.
focal lengths 13;, fl; of the movable components, the two
A particularly useful embodiment of the above system
dotted-line curves so labeled within area B representing
is shown in FIGS. 6A and 6B.
values for which these focal lengths have the preferred
ratio of 1:105.
-
The ratio Rf=6zl yields a varifocal coef?cient K=0.71
50
The component A has been shown as a single dispersive
lens L1, having radii R1, R2 and thickness :11. Spaced
from this lens by a variable distance d2 is component BB
here shown to comprise a pair of air-spaced collective
(from
lenses L2 (radii R3, R4 and thickness ds) and L3 (radii
55
since the systems of FIGS. 1-5 have positively refragcting
movable components). lFrom FIG. 9, a varifocal co
e?icient K=0.71 will be seen to de?ne points of full com
pensation at z1=0, 22:22, z3=62, and 24:100. The
R5, R6 and thickness d5) whose spacing is indicated at d4. _
A variable air space d6 separates lens L3 from component
C, shown as a single dispersive lens L4 having radii R7, R8
and thickness d7. Spaced from this member by a variable
distance (is is component DD, consisting of a collective
designer must also choose values for the spacings .9130, 60 lens L5 (radii R9, R10 and thickness d9) cemented onto
a dispersive lens L6 (radii R10. R11 and thickness dm). The
variable diaphragm space dn separates component DD
from back member EE, here shown as a positive lens L7
to account for the ?nite thicknesses of the component
(radii R12, R13 and thickness dm) airspaced by a distance
son. Taking sBC=l17.62 and scD=12.37 (at z1=0, and
assuming the maximum displacement zmax=to 100 units)
lenses, and substituting these values in Equations 2, 6 and
7
(Rr=6, 21:0: 22:22, 13:62, Z4='100, 52,a=SBc=117-6Z,
s3,4=scD=12.37), we obtain four equations
r113 vfrom a negative lens L8 (radii R14, R15 and thickness
The spacing (115 ‘between lens L8 and the image
plane IP corresponds, substantially, to image distance dip
of the preceding ?gures.
65 (114).
FIGS. 6A and 6B also illustrate an adjustment of front
lens L1 relative to the other components of the system
from solid-line position to dotted-line position for the
purpose of focusing the objective lens system L1—L8 upon
an object located at a ?nite distance in front thereof; the
image plane may be assumed to represent the position of
From the algebraic solution of the above relationships
together with the Equations 3, 4, the focal length f3 of 75 a photosensitive ?lm, a ground-glass plate, a photocathode
3,051,052
'
7
varying as a fourth-order polynomial of z according to
or some other receiving surface upon which a sharp image
the equation.
of the desired object can thus be projected. The result
ing image plane for ?nite focusing will be subject to the
same compensation as the in?nite-distance image plane ob
tained in the solid-line position of the lens since the posi- 5 y— z3+b1z2+b2z+b3
tion of the image produced by the front lens will remain
_
_
unchanged.
the coefficients al to as and b1 to ha of said polynomial
The following speci?c numerical values for the parameters of the system of FIGS. 6A and 6B, including the
satlsfylng a set of three equations
_b
..
-
4
.
.
.
,
a1—
I'adll, thicknesses, spacings,
refractive indices Nd and Abbe 10
numbers 11 of the various lens elements, have been found
1—x0
_
2
a :17 __x b +1. 26
a2—b2—x0b1+f4
to give particularly good aberration correction through
3 3 0 2 ‘4 1
the operative range and have been reproduced in FIG. 7.
the Values 0f 51 to ha and 6'1 1361118 glven in terms of the
The values for the radii, thicknesses and air spaces are
principal focal lengths f1 to f3 of said ?rst through third
based upon a numerical value of 100 units for the dis- 15 components and 0f the interfocal spacings all; to (13,4 of
placement 2mm of the movable components between the
all of said components, measured from the secondary
?rst and fourth points of exact image shift compensation.
focal point of any higher-order component to the primary
Glass
Element
Lens
Radii
Na
Thicknesses and
Separations
11
R1 =-345.00
A ................ __ Li
1.617
50.0
d, =5.00.
R2 =+345.00
L2
1. 620
60.0
R; =+675.40
d2 =irorn 2.47 to 102.47.
ds =12.00
R. =-25s.75
BB ______________ .-
d4 =1.12.
L3
1. 620
60.0
R5 =+141.65
d; =12.00.
R6 =0:
d0 =from 107.35 to 7.35.
R1 =-127.55
C ................ .._ L4
1.720
50.0
L5
1.620
60.0
Ls
1. 620
36. 2
DD .............. -_
d7 =4.50.
Ra =+8S.05
Rn =+77.20
d5 =from 11.35 to 111.35.
d9 =13.50.
R1o=—50.50
dm=4.50.
Ru=°°
Diaphragm ...... ._
dn=fron1 122.85 to 22.85.
L1
1.517
EE .............. -_
La
1.720
R12=+59.50
64.5
R1a=-403.50
R|¢=—59.50
50.0
Rrs=—403.50
d1z=6.14.
dn=20.27.
dn=5.00.
d15==87.64.
The above system has a focal length 1‘ variable between 45 focal point of the nearest lower-order component, by
the expressions
substantially 109 and 654 in the absence of back member
EE or between about 62.5 and 375 with member BE in
cluded, thus a ratio Ri=6zl within its operative range.
The focal length L; of front element A equals —279.(), so
that substantially 0.39fA_S_f§2.34fA in the absence of 50
member EE and 0.224fAéfgl344fA with member EE
and further satisfying the relationship
present. The maximum image deviation iymx, occur
ring between points of full compensation (Z1, Z2, Z3, and
Rr=(bs+b2+b1)/bs
Z4), at which the curve y(z) of FIG. 8 intersects the
where
R,
is
the
varifocal
range; said focal lengths f1
z-axis, has an absolute value of 0.35 without member EE
and is being different from each other with the larger
and of 0.018 with member EE.
focal length equaling substantially 1.03 to 1.20 times the
I claim:
smaller focal length.
.
1. A varifocal optical lens system comprising four
2. An optical lens system according to claim 1 wherein
air-spaced components including a movable ?rst com
ponent at the image side of the system, a stationary sec 60 said coe?‘icients al to a3 and b1 to 123 have such magnitudes
that, with the ?rst root zl and the fourth root Z4 having
ond component ahead of said ?rst component, a mov
numerical values of 0 and 100, respectively, the roots
able third component ahead of said second component,
Z3 and 23 have values lying on two substantially parallel
and a stationary fourth component ahead of said third
curves which, when plotted on a graph having as its
component, the refractive powers of said components be
ordinates the values of z and as its abscissae a parameter
ing of alternate sign; and means for axially displacing
said ?rst and third components at the same rate with re
spect to said second and fourth components; said system
having an image distance x, measured between an image
plane and the secondary focal point of said ?rst com
fmax‘i'fmin
where fmax and fmm are the values of the overall focal
ponent, equal to xo+z for four predetermined values 70 lengths of the system in two positions of adjustment in
Z1, Z2, Z3, Z4, of a variable 2 representing the extent of
which z=cither of the two roots Z1 and Z4, are continuous
displacement of said movable components from a refer
ence position toward the image side of the system, x0
being a constant; said image distance being increased by
:y for other values of y where y is an image deviation
between K=i1 and have slopes of invariable sign which
are substantially symmetrical about the ordinate axis,
said curves passing respectively through points having
ordinates of approximately 30 and 70 units for K=0
3,051,052
and through points having ordinates of approximately
22 and 62 units for K=O.7.
3. A varifocal optical lens system comprising four
ing a minimum overall focal length fmm, a maximum
overall focal length fmx, and a varifocal coef?cient K
equal to
air-spaced components including a movable ?rst com
ponent at the image side of the system, a stationary second
. component ahead of said ?rst component, a movable
third component ahead of said second component, and
a stationary fourth component ahead of said third com
fmax “fruit:
said ?rst component having a focal length in, said third
compent having a focal length f3, said focal length fD
equaling 0.97 to 0.85 times said focal length f,;; the maxi
ponent, the refractive powers of said components being
of alternate sign; and means for axially displacing said 10 mum axial displacement of said ?rst and third com
ponents being 100 units; said system having a maximum
?rst and third components at the same rate with respect
overall focal length of a magnitude substantially falling
to said second and fourth components; said system having
a minimum overall focal length fmm, and a maximum
overall focal length fmx, and a varifocal coef?cient K
equal to
'
within an area whose lower limit is delineated by a gen
erally parabolic curve in the third quadrant of a graph
15 having as its abscissa values of K between the limits of
K=+1 and K=-l and as its ordinate units of distance
in terms of focal length, said parabolic curve passing sub
stantially through the point (-0.70, —-795), said focal
lengths ]‘D and f3 having values falling within the area
of said graph delineated by a pair of generally hyper
said ?rst component having a focal length 13;, said third
component having a focal length 13;, said focal length 1‘); 20
bolic curves in the third quadrant substantially asymptotic
equaling 1.03 to 1.20 times said focal length f3; the maxi
to the line K=0 and passing substantially through the
mum axial displacement of said ?rst and third com
points (—~0.6, -—-120) and (0.6, -—2l5), respectively.
ponents being 100 units; said system having a maximum
5. A varifocal optical system comprising four air
overall focal length of a magnitude substantially falling
within an area whose lower limit is delineated by a gen
25 spaced components including a stationary ?rst com
erally parabolic curve in the ?rst quadrant of a graph
ponent comprising a single ?rst lens L1 at the object
having as its abscissa values of K between the limits of
K=+1 and K=--1 and as its ordinate units of distance
in terms of focal length, said parabolic curve passing sub
side of the system, a movable second component behind
said ?rst component comprising a second lens L2 and a
)‘D and )‘B having values falling Within the area of said
graph delineated by a pair of generally hyperbolic curves
in the ?rst quadrant substantially asymptotic to the line
ing a single fourth lens L4, and a movable fourth com
ponent behind said third component comprising a ?fth
lens L5 and a sixth lens L6 cemented together; and means
air-spaced components including a movable ?rst com
ponent at the image side of the system, a stationary sec
ond component ahead of said ?rst component, a movable
radii, thicknesses, relative separations, refractive indices
third lens L3 air-spaced from each other, a stationary
stantially through the point (071,654), said focal lengths 30 third component behind said second component compris
for axially displacing said second and fourth components
K=O and passing substantially through the points
35 relative to said ?rst and third components; said ?rst lens
(06,120) and (06,215), respectively.
L1, said second lens L2, said third lens L3, said fourth
4. A varifocal optical lens system comprising four
lens L4, said ?fth lens L5 and said sixth lens L6 having
Nd and Abbé numbers 11 substantially as given in the
third component ahead of said second component, and 40 following table:
Element
Glass
Lens
Radll
Na
9
1. 017
50.0
Thicknesses and
Separations
R1 =-345.00
A ........ .... .... .. L1
In
1. 620
60.0
’
BB .............. ..
La
1.620
60.0
R, =+345.00
B; =+675A0
at =5.90.
d1 =£rom 2.47 to 102.47.
d: =12.00
R4 =--258.75
R; =+141.65
Ru IQ
d‘ =1.12.
(16 =12.00.
de =fr0m 107.35 to 7.35.
R1 =-127.55
0 ................ .- L4
1.720
50.0
La
1. 620
60.0
Lo
1.620
36.2
DD .............. .-
R1 =+ss.05
R9 =+77.20
d1=4.50.
de =from 11.35 to 111.35.
d: =13.50.
R1o=-50.50
R
dr0=4.50.
?=cn
Diaphragm ...... -.
dn=fr0m 122.85 to 22.85.
,
Bu=+59.50
I’n
1.517
- 64.5
be
1.720
50.0
EE .............. ..
a stationary fourth component ahead of said th1rd component, the refractive powers of said components being
of alternate sign; and means for axially displacing sa1d
?rst and third components at the same rate with respect
to said second and fourth components; said system hav-
RIF-403.50
R14=—59.50
Rim-403.50
d1z=6.14.
du=20.27.
111F500.
d1s=37.64.
References Cited in the ?le of this patent
UNITED STATES PATENTS
2,566,485
2,778,272
Cuvillier ____________ __ Sept. 4, 1951
Reymond ____________ __ Jan. 22, 1957
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