US3694057A - Modified triplets with reduced secondary spectrum - Google Patents

Modified triplets with reduced secondary spectrum Download PDF

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Publication number
US3694057A
US3694057A US185496A US3694057DA US3694057A US 3694057 A US3694057 A US 3694057A US 185496 A US185496 A US 185496A US 3694057D A US3694057D A US 3694057DA US 3694057 A US3694057 A US 3694057A
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doublet
lens
numbered
abbe number
partial dispersion
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US185496A
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William H Price
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Eastman Kodak Co
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Eastman Kodak Co
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B9/00—Optical objectives characterised both by the number of the components and their arrangements according to their sign, i.e. + or -
    • G02B9/12—Optical objectives characterised both by the number of the components and their arrangements according to their sign, i.e. + or - having three components only

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  • ABSTRACT A lens particularly usable in a printer, consists of a middle negative component surrounded by two positive doublets. Secondary spectrum is reduced by choosing refractive materials and element focal lengths to minimize the expression (P... PJV, V where P, and V, are the partial dispersion and Abbe number for the negative component and P, and V,, are the mean equivalent partial dispersion and mean equivalent Abbe number for the doublets.
  • Secondary spectrum is the inability of a lens, even when corrected for longitudinal chromatic aberration, to focus all wavelengths of light at the same point.
  • secondary spectrum becomes the limiting aberration of the lens.
  • monochromatic prints secondary spectrum tends to reduce the contrast of the final print, particularly in fine detail areas.
  • color prints secondary spectrum is manifested as a spreading of color from dark areas into adjacent light areas, a phenomenon known as color fringing or halo.
  • SUMMARY OF THE INVENTION provide such a printer lens with improved secondary spectrum correction which also is well corrected for other aberrations such as axial and oblique spherical aberration, coma, field curvature and astigmatism.
  • P, and V are the mean equivalent partial dispersion and mean equivalent Abbe number for the doublets.
  • FIG. 1 is a diagrammatic axled cross-section of a lens according to the invention
  • FIG. 2 is a graph of partial dispersion P against Abbe number V, illustrating the selection of the refractive materials and focal lengths for the elements in the lens of this invention.
  • FIG. 3 is the spherical aberration curve for the lens of Example 1, illustrating the improved secondary spectrum correction achieved by this invention.
  • lens shall be used to describe the complete lens and not elements or components thereof.
  • the long conjugate side of the lens is considered in front and is shown on the left in FIG. 1.
  • partial dispersion for a refractive material shall refer to the partial dispersion for the g line of mercury and may be calculated from the following formula:
  • secondary spectrum shall be defined as the difference between the focus for the e line of mercury and the common focus for the C line of hydrogen and the g line of mercury.
  • Primary color correction in a positive doublet is obtained by using a refractive material of low dispersion for the positive element of the doublet and a refractive material of high dispersion for the negative element.
  • a positive doublet which is well corrected for primary color is characterized by a large difference in Abbe number between its two elements.
  • Secondary spectrum for a doublet is known to be proportional to the slope of the line on a plot of partial dispersion versus Abbe number which is defined by the parameters of the elements of the doublet. This slope is given by the following relationship:
  • FIG. 2 is a graph of partial dispersion, P versus Abbe number, V.
  • Most available glasses lie along or near the line K of FIG. 2, which has a slope of 0.00170. Included are the glasses represented by the points 10, 12, 16 and 18 which are the glasses selected for use in the triplet of this invention as will be more fully described hereinafter. Because of this restriction of the parameters of available glasses it may be seen that the two conditions required for a doublet to be well corrected cannot be presently met. Selection of a pair of glasses with widely differing Abbe numbers insures a wide difference in partial dispersion. Selection of glasses with equal partial dispersion insures near equality of Abbe numbers.
  • component I is a positive doublet consisting of a front positive biconvex element 1 and a rear negative biconcave element 2.
  • Component II consists of a negative biconcave element 3.
  • Component III is a positive doublet consisting of a front meniscus negative element 4, concave to the rear, and a rear positive biconvex element 5.
  • a doublet, consisting of two elements aand b, may be considered as equivalent to a single element of equivalent focal length I. made from a hypothetical glass having equivalent V and P values defined by the following equations:
  • component I consists of a front element 1 with parameters represented on FIG. 2 by'pointltl and a rear element 2 with parameters represented on FIG. 2 by point 12.
  • Points 10 and 12 define a line L along which lies point 14, representing the equivalent parameters of the hypothetical glass of component I.
  • Component III consists of a front element 4 with parameters represented in FIG. 2 by point 16 and a rear element 5 with parameters represented on FIG. 2 by point 18.
  • Points 16 and 18 define a line M along which lies point 20, representing the equivalent parameters of the hypothetical glass of component III.
  • the exact values of P and V, are determined by the selected element focal lengths for given glasses and may be positioned to the right, to the left or in between the points representing the element glasses.
  • Dotted line N on FIG. 2 is defined by points 14 and 20, representing the equivalent partial dispersion and equivalent Abbe number of the hypothetical glasses found in components I and III.
  • the mean value of these hypothetical parameters, represented by point 22 on line N of FIG. 2 may be seen to lie substantially away from line K, which represents the ordinarily available glasses.
  • Secondary spectrum for the triplet is then proportional to the slope of the line 0, defined by the mean equivalent parameters represented by point 22 and the parameters for negative component 11.
  • the slope of the PV line for the triplet may be substantially reduced below that available in a simple triplet, thereby insuring substantially improved correction of secondary spectrum.
  • the lens components are numbered from front to rear with Roman numerals; the lens elements are numbered from front to rear with Arabic numerals.
  • the element focal lengths F, the indexes of refraction N for the D line of the spectrum the Abbe numbers V, the radii of curvature R, the thicknesses T and the separations S, and the partial dispersions P are numbered by subscript from front to rear. Radii of curvature having centers of curvatures to the rear of the surface are considered positive; those with centers of curvature to the front of the surface are considered negative. All parameters are based upon a lens focal length of mm.
  • front component I consists of a front element 1 which is characterized by a Abbe number of 63.5 and a partial dispersion of 0.542 with an element focal length of 28.8.
  • Rear element 2 of front component I is characterized by a Abbe number of 64.5 and a partial dispersion of 0.534 with an element focal length of 62.6.
  • the equivalent Abbe number and equivalent partial dispersion of front component I may be calculated and are found to be 62.7 and 0.549 respectively.
  • Points 10 and 12 define a straight line L on which the parameters of the resulting equivalent hypothetical glass are represented by point 14. Analogous computations may be performed on the parameters of rear component III with a resulting equivalent Abbe number and partial dispersion of 58.2 and 0.549 respectively.
  • Rear component III is represented on FIG. 2 by line M with the parameters of front element 4 of rear component III represented by point 16 and the parameters of rear element 5 of rear component llI represented by point 18.
  • the equivalent Abbe number and equivalent partial dispersion of the resulting hypothetical glass of rear component III are represented by point 20 on line M.
  • the mean equivalent Abbe number and mean equivalent partial dispersion of front and rear components l and III lies along line N, defined by points 14 and 20, and are calculated to be 60.45 and 0.549 respectively.
  • a glass for negative component ll may now be selected using the mean equivalent Abbe number and mean equivalent partial dispersion of components I and III in such a manner as to assure proper primary color correction by utilizing a large difference in Abbe number while simultaneously assuring good secondary color correction by minimizing the slope of the P rV line for the triplet as described above.
  • the glass selected for element 3 in Example I which is the same glass as used for element 4, results in a slope of the P V line of 0.00092, a substantial improvement over the slope for the normal glasses which it is to be remembered is 0.00170.
  • FIG. 3 illustrates the improved secondary spectrum correction achieved by the design of this invention. Not only is the secondary spectrum reduced to 0.10 percent of the effective focal length of the lens, but it may be seen that spherical aberration has also been substantially reduced from available lenses. Thus both primary and secondary color aberrations have been corrected by the selection of glasses as described above.
  • Example 2 is similar to Example 1, as may be seen by a comparison of the corresponding parameters.
  • Example 2 illustrates that variation in these parameters does not prevent good secondary spectrum correction, so long as the conditions established above for selection of element glasses and focal lengths are satisfied.
  • Example 3 is a modification of Example 2 in which a different glass is utilized in element 5 of component III.
  • Example 3 illustrates that selection of difierent glasses does not prevent good secondary spectrum correction, so long as the conditions established above for selection of element glasses and focal lengths are satisfied.
  • Examples 4-8, 9 and 10 are further examples of printer lenses characterized by reduced secondary spectrum which were designed by W. H. Vangraff' eiland in accordance with the principals of this invention and which are disclosed and claimed in copending U. S. application Ser. No. 185,602.
  • Examples 11-13 are still further examples of printer lenses characterized by reduced secondary spectrum which were designed by C. J. Melech in accordance with the principals of this invention and which are disclosed and claimed in copending U. S. application Ser. No. l85,630.
  • a lens comprising a front positive doublet, a middle negative component and a rear positive doublet, wherein the following inequality is satisfied:
  • P, and V are respectively the partial dispersion and Abbe number of said middle negative component and P and V,, are respectively the mean equivalent partial dispersion and mean equivalent Abbe number for said front and said rear doublets.
  • a lens comprising a front positive doublet, a middle negative component, and a rear positive doublet, said front and rear doublets consisting of one or more refractive materials such that each element in said rear doublet has a lower Abbe number and a higher partial dispersion than either of the elements in said front doublet; the focal lengths of each element in said front doublet being selected so that said front doublet has a lower equivalent Abbe number and a higher equivalent partial dispersion than either of the elements in said front doublet; the focal lengths of each element in said rear doublet being selected so that said rear doublet has a higher equivalent Abbe number and a lower equivalent partial dispersion than either of the elements in said rear doublet; and said negative component consisting of a refractive material having an Abbe number V and a partial dispersion P, which satisfy the following inequality;
  • a lens comprising a front positive doublet, a middle negative component, and a rear positive doublet, in which the lens elements, numbered from the front side of the lens, are made of refractive materials having substantially the following parameters, wherein V is the Abbe number and P is the partial dispersion:-
  • the lens elements are numbered from 1-5, the corresponding indexes of refraction and Abbe numbers are for the D line of the spectrum, the radii are numbered from R, to R,the thicknesses are numbered from T, to T, and the air spaces are numbered from S, to S,.
  • a lens having a middle negative singlet surrounded by two positive doublets said lens being constructed wherein, from front to rear, the lens elements are numbered from l-5, the corresponding indexes of refraction and Abbe numbers are for the D line of the spectrum, the radii are numbered from R, to R,, the thicknesses are numbered from T, to T, and the air spaces are numbered from S, to 5,.
  • a lens having a middle negative singlet surrounded by two positive doublets said lens being constructed according to the following table:
  • the lens elements are numtrum, the radii are numbered from R, to R the bered from 1-5, the corresponding indexes of refracthicknesses are numbered from T to T, and the air tion and Abbe numbers are for the D line of the specspaces are numbered from S to 5,.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
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US185496A 1971-10-01 1971-10-01 Modified triplets with reduced secondary spectrum Expired - Lifetime US3694057A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140146404A1 (en) * 2011-08-25 2014-05-29 Fujifilm Corporation Imaging lens, and imaging apparatus including the imaging lens
US10288845B2 (en) 2017-06-14 2019-05-14 Largan Precision Co., Ltd. Image capturing lens system, image capturing unit and electronic device
CN112136068A (zh) * 2018-05-28 2020-12-25 株式会社尼康 光学系统、光学设备以及光学系统的制造方法

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2279384A (en) * 1941-01-09 1942-04-14 Eastman Kodak Co Photographic objective
US2419804A (en) * 1942-08-26 1947-04-29 Warmisham Arthur Optical objective
US2645154A (en) * 1949-10-17 1953-07-14 Voigtlander & Sohn Ag Five-lens photographic objective

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2279384A (en) * 1941-01-09 1942-04-14 Eastman Kodak Co Photographic objective
US2419804A (en) * 1942-08-26 1947-04-29 Warmisham Arthur Optical objective
US2645154A (en) * 1949-10-17 1953-07-14 Voigtlander & Sohn Ag Five-lens photographic objective

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140146404A1 (en) * 2011-08-25 2014-05-29 Fujifilm Corporation Imaging lens, and imaging apparatus including the imaging lens
US9239448B2 (en) * 2011-08-25 2016-01-19 Fujifilm Corporation Imaging lens, and imaging apparatus including the imaging lens
US10288845B2 (en) 2017-06-14 2019-05-14 Largan Precision Co., Ltd. Image capturing lens system, image capturing unit and electronic device
CN112136068A (zh) * 2018-05-28 2020-12-25 株式会社尼康 光学系统、光学设备以及光学系统的制造方法

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JPS4843930A (enrdf_load_stackoverflow) 1973-06-25
DE2247860A1 (de) 1973-04-05

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