# Патент USA US3051063

код для вставкиSEARCH 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 J4 ‘ ><A05 C W J) 1 r L N. _ fmw/ I1 A r. INVENTOR: L.BERGSTEIN_ {7% 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 MlyaArdu/“47.4% ..d 2 . FIG] E LE 7A El O5 5 OO 385S A. % 7. 2 a 3 PA m m a{I‘I(If A M C BD E M. W M h. LI“... |__> b, BEDF 5 R5 A56 36 w s 6 B l % N W2 m Ga2W ‘7| %v w Q06.04 6 5. as. 7. 7e6N 0L o o. 0.2 oo.5. o. RR‘ m. R. 0.“. mm mm. RR... R =2 F R = = __ = = __ = IwB“I 7w“5uinm.0aw5 4 W .m. 4% 1m A... dAw. d m 3 2 64D B |85 7 + A _ + _ o|l M205s.590as.250. w m d N 4 2 3 5 6 O 7 l _r .r m = __ __ __ __ K“.r6l2r, 2H. N7 n m w M m 2 S.3 . a B 4575 Q S w 0 O7 4I O NRI.BmI O 5O 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" 800" 700' 600-. 500 ~ Maximum Disrlmotmznt 10o. zMAX =1oc unut: -- -3oo " — ‘foo ---5oo --- éoa —— - 700 "-800 H010 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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