Abstract

A method is described that permits the calculation of a cemented doublet with a given spherical aberration and coma at the edge of the lens. In particular the aberrations can be set to zero. Given one glass, the equations reported in this paper permit the determination of a second matching glass that minimizes the spherochromatism and coma of the lens. This result is obtained by the introduction, into the third-order thin-lens formulas, the third-order values of the aberration coefficients, as derived from the equation developed by Mossotti which yields zero finite aberrations for the same lens with added thickness. After a brief historical introduction, the third-order equations are developed and tables for the color-correcting glasses and S I and S II (the Seidel third-order coefficients) are given for objects at infinity and at a magnification of −1, both for flint- and crown-leading cases. The paper closes with a table of corrected doublets.

© 1996 Optical Society of America

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References

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  1. N. V. E. Nordenmark, J. Nordström, “The invention of the achromatic and aplanatic lens,” Lychnos 3, 1–52 (1938);“The invention of the achromatic and aplanatic lens,” Lychnos 4, 313–384 (1939);“The invention of the achromatic and aplanatic lens,” Meddelande, Stockholm Observatorium Reprint Series No. 46 (Almqvist Wiksells Boktryckeri-A.-B., Uppsala, Sweden, 1939), (both articles appeared in this volume together).
  2. A. C. Clairaut, “Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 1, 380–437 (1763) (this article was written in 1756; it was available for reading in 1761 and appeared in print in approximately 1763);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 2, 524–550 (1764) (this article, of the same title as that which appeared in 1763, was written in 1757; it was available for reading in 1761 and appeared in print in approximately 1764);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 3, 578–631 (1769) (this article, also of the same title as the two previous articles, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1768).
  3. J. d'Alembert, “Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 1, 75–145 (1767) (this article was written in 1764; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 2, 63–105 (1768) (this article, of the same title as that which appeared in 1767, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 3, 43–108 (1769) (this article, also bearing the same title as the two previous articles, was written in 1766; it was available for reading in 1767 and appeared in print in 1769).
  4. C. Moser, “Über Fernrohrobjective,” (Part 1), Z. Instrumentenkde. 7, 225–238 (1887);(Part 2), Z. Instrumentenkd. 7, 308–323 (1887).
  5. H. Boegehold, “Die Leistung von Clairaut und d'Alembert fürdie Theorie des Fernrohrobjective,” Z. Instrumentenkd. 55, 97–111 (1935); see especially p. 98.
  6. M. von Rohr, “Fraunhofer's work and its present-day signifi-cance,” Trans. Opt. Soc. 27, 277–294 (1925–1926).
    [CrossRef]
  7. O. F. Mossoti, “Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 4, 38–1651853;“Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 5, 5–951858;Nuova Theoria Instrumenti Ottici (Casa Editrice Nistri, Pisa, Italy, 1859), p. 171–191.
  8. E. Turrière, Optique Industrielle (Librairie Delagrave, Paris, 1920), pp. 28–36, para. 18.
  9. The practice of cementing doublets was begun in 1785 in Paris by the opticians Grateloupe and Putois. The first cement used, mastic en larmes fondu par l'action du feu, did not last very long, probably for only a few months.
  10. H. A. Steinheil, E. Voit, eds., Handbuch der Angewandten Optik (Teubner, Leipzig, 1891), Vol. 1.
  11. H. Harting, “Zur Theorie der Zweitheiligen Verkitteten Ferm-rohrobjective,” Z. Instrumentenkd. 18, 357–380 (1898).
  12. E. von Hoegh, “Zur Theorie der Zweitheiligen Verkitteten Fernrohrobjective,” Z. Instrumentenkd. 19, 37–39 (1899).
  13. T. Smith, “The principles and methods of calculating telescope objectives,” in Collected Papers of T. Smith, compiled by E. G. Martin (University Microfilms, Ann Arbor, Mich., 1970), Vol. 2, pp. 99–120.
  14. E. Brown, T. Smith, “Systematic construction tables for thin cemented aplanatic lenses,” Philos. Trans. R. Soc. London, Ser. A 240, 59–116 (1948).
  15. G. G. Sliusarev, Methods of Calculation of Optical Systems (Gostekhizdat, Leningrad, USSR, 1937).
  16. G. G. Sliusarev, Tables for Designing Cemented Doublets (Vavilov State Optical Institute, Leningrad, USSR, 1949).
  17. S. V. Trubko, Calculation of Two Lens Cemented Objectives (Mashinostroenie, Leningrad USSR, 1984).
  18. M. H. Sussman, “Cemented aplanatic doublets,” J. Opt. Soc. Am. 52, 1185–1186 (1962).
    [CrossRef]
  19. M. Laikin, Lens Design (Dekker, New York, 1991), pp. 35–40.
  20. R. E. Hopkins, “Automatic design of telescope objectives,” J. Am. Opt. Soc. 45, 167–178 (1955).
  21. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 123–133.
  22. H. H. Hopkins, V. Rao, “The systematic design of two component objectives,” Opt. Acta 7, 497–514 (1970).
    [CrossRef]
  23. I. M. Khan, J. MacDonald, “Cemented doublets. A method for rapid design,” Opt. Acta 29, 807–822 (1982).
    [CrossRef]
  24. W. H. Steel, “On the choice of glasses for cemented achromatic aplanatic doublets,” Austral. J. Phys. 7, 244–253 (1954), see p. 245 in particular;“A general equation for the choice of glass for cemented doublets,” Austral. J. Phys. 8, 68–73 (1955).
    [CrossRef]
  25. A. Maréchal, “Étude des effects combines de la diffraction et des aberrations géométriques sur l'image d'un point lumi-neux,” Rev. Opt. 26, 257–277 (1947). Note that the use of the 1.1 zone is approximately correct for F/D = 4 doublets.
  26. The third-order SI and SII are the same as those used by German workers such as Berek, Köhler, Slevogt, and others. The tangential transverse aberration for an object at infinity is given byΔyk′=½F](x12+y12)y1S1−(x12+3y12)tanθSII+⋯+].
  27. D. Argentieri, Ottica Industriale, 2nd ed. (Hoepli, Milan, Italy, 1954).
  28. A. Kerber, “Über die Chromatische Korrektur von Doppelob-jektiven,” Zen-Ztg. Opt. Mech. 7, 157–158 (1886).
  29. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 1, p. 136;Applied Optics and Optical Design Vol. 2, pp. 627, 641, and especially 651.
  30. A. Maréchal, M. Françon, Diffraction (Revue d'Optique, Theorique et Instrumentale, Paris, 1950), pages 105–119; see chap. 8.
  31. See, however, the following: P. Mouroulis, T. Gyu Kim, G. Zhao, “Transverse color tolerances for visual optical systems,” Appl. Opt. 32, 7089–7094 (1993). The tolerances given in the present paper are several times those used in this article.
    [CrossRef] [PubMed]
  32. H. Koehler, K. Metzmacher, “The white light modulation transfer function of optical systems as a function of the state of color correction,” in Modulation Transfer Function, R. R. Shannon, R. J. Wollensak, eds. Proc. SPIE13, 195–204 (1968);“Beitrag zu der Optischen Abbildung in Weissen Licht,” Optik 24, 237–243 (1966–1967).
  33. Y. Väisäla, “Neue Methoden zur Untersuchung der Objek-tive,” Ann. Univ. Fennicae Aboensis Ser. A 1, 103–115 (1922).
  34. J. Picht, Optische Abbildung (Vieweg, Braunschweig, Germany, 1931), pp. 184–191.
  35. Schott optical glass (Schott Glasweke, Mainz, Germany).

1993 (1)

1982 (1)

I. M. Khan, J. MacDonald, “Cemented doublets. A method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

1970 (1)

H. H. Hopkins, V. Rao, “The systematic design of two component objectives,” Opt. Acta 7, 497–514 (1970).
[CrossRef]

1962 (1)

1955 (1)

R. E. Hopkins, “Automatic design of telescope objectives,” J. Am. Opt. Soc. 45, 167–178 (1955).

1954 (1)

W. H. Steel, “On the choice of glasses for cemented achromatic aplanatic doublets,” Austral. J. Phys. 7, 244–253 (1954), see p. 245 in particular;“A general equation for the choice of glass for cemented doublets,” Austral. J. Phys. 8, 68–73 (1955).
[CrossRef]

1948 (1)

E. Brown, T. Smith, “Systematic construction tables for thin cemented aplanatic lenses,” Philos. Trans. R. Soc. London, Ser. A 240, 59–116 (1948).

1947 (1)

A. Maréchal, “Étude des effects combines de la diffraction et des aberrations géométriques sur l'image d'un point lumi-neux,” Rev. Opt. 26, 257–277 (1947). Note that the use of the 1.1 zone is approximately correct for F/D = 4 doublets.

1938 (1)

N. V. E. Nordenmark, J. Nordström, “The invention of the achromatic and aplanatic lens,” Lychnos 3, 1–52 (1938);“The invention of the achromatic and aplanatic lens,” Lychnos 4, 313–384 (1939);“The invention of the achromatic and aplanatic lens,” Meddelande, Stockholm Observatorium Reprint Series No. 46 (Almqvist Wiksells Boktryckeri-A.-B., Uppsala, Sweden, 1939), (both articles appeared in this volume together).

1935 (1)

H. Boegehold, “Die Leistung von Clairaut und d'Alembert fürdie Theorie des Fernrohrobjective,” Z. Instrumentenkd. 55, 97–111 (1935); see especially p. 98.

1922 (1)

Y. Väisäla, “Neue Methoden zur Untersuchung der Objek-tive,” Ann. Univ. Fennicae Aboensis Ser. A 1, 103–115 (1922).

1899 (1)

E. von Hoegh, “Zur Theorie der Zweitheiligen Verkitteten Fernrohrobjective,” Z. Instrumentenkd. 19, 37–39 (1899).

1898 (1)

H. Harting, “Zur Theorie der Zweitheiligen Verkitteten Ferm-rohrobjective,” Z. Instrumentenkd. 18, 357–380 (1898).

1887 (1)

C. Moser, “Über Fernrohrobjective,” (Part 1), Z. Instrumentenkde. 7, 225–238 (1887);(Part 2), Z. Instrumentenkd. 7, 308–323 (1887).

1886 (1)

A. Kerber, “Über die Chromatische Korrektur von Doppelob-jektiven,” Zen-Ztg. Opt. Mech. 7, 157–158 (1886).

1853 (1)

O. F. Mossoti, “Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 4, 38–1651853;“Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 5, 5–951858;Nuova Theoria Instrumenti Ottici (Casa Editrice Nistri, Pisa, Italy, 1859), p. 171–191.

1767 (1)

J. d'Alembert, “Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 1, 75–145 (1767) (this article was written in 1764; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 2, 63–105 (1768) (this article, of the same title as that which appeared in 1767, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 3, 43–108 (1769) (this article, also bearing the same title as the two previous articles, was written in 1766; it was available for reading in 1767 and appeared in print in 1769).

1763 (1)

A. C. Clairaut, “Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 1, 380–437 (1763) (this article was written in 1756; it was available for reading in 1761 and appeared in print in approximately 1763);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 2, 524–550 (1764) (this article, of the same title as that which appeared in 1763, was written in 1757; it was available for reading in 1761 and appeared in print in approximately 1764);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 3, 578–631 (1769) (this article, also of the same title as the two previous articles, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1768).

Argentieri, D.

D. Argentieri, Ottica Industriale, 2nd ed. (Hoepli, Milan, Italy, 1954).

Boegehold, H.

H. Boegehold, “Die Leistung von Clairaut und d'Alembert fürdie Theorie des Fernrohrobjective,” Z. Instrumentenkd. 55, 97–111 (1935); see especially p. 98.

Brown, E.

E. Brown, T. Smith, “Systematic construction tables for thin cemented aplanatic lenses,” Philos. Trans. R. Soc. London, Ser. A 240, 59–116 (1948).

Clairaut, A. C.

A. C. Clairaut, “Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 1, 380–437 (1763) (this article was written in 1756; it was available for reading in 1761 and appeared in print in approximately 1763);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 2, 524–550 (1764) (this article, of the same title as that which appeared in 1763, was written in 1757; it was available for reading in 1761 and appeared in print in approximately 1764);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 3, 578–631 (1769) (this article, also of the same title as the two previous articles, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1768).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 1, p. 136;Applied Optics and Optical Design Vol. 2, pp. 627, 641, and especially 651.

d'Alembert, J.

J. d'Alembert, “Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 1, 75–145 (1767) (this article was written in 1764; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 2, 63–105 (1768) (this article, of the same title as that which appeared in 1767, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 3, 43–108 (1769) (this article, also bearing the same title as the two previous articles, was written in 1766; it was available for reading in 1767 and appeared in print in 1769).

Françon, M.

A. Maréchal, M. Françon, Diffraction (Revue d'Optique, Theorique et Instrumentale, Paris, 1950), pages 105–119; see chap. 8.

Gyu Kim, T.

Harting, H.

H. Harting, “Zur Theorie der Zweitheiligen Verkitteten Ferm-rohrobjective,” Z. Instrumentenkd. 18, 357–380 (1898).

Hopkins, H. H.

H. H. Hopkins, V. Rao, “The systematic design of two component objectives,” Opt. Acta 7, 497–514 (1970).
[CrossRef]

Hopkins, R. E.

R. E. Hopkins, “Automatic design of telescope objectives,” J. Am. Opt. Soc. 45, 167–178 (1955).

Kerber, A.

A. Kerber, “Über die Chromatische Korrektur von Doppelob-jektiven,” Zen-Ztg. Opt. Mech. 7, 157–158 (1886).

Khan, I. M.

I. M. Khan, J. MacDonald, “Cemented doublets. A method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 123–133.

Koehler, H.

H. Koehler, K. Metzmacher, “The white light modulation transfer function of optical systems as a function of the state of color correction,” in Modulation Transfer Function, R. R. Shannon, R. J. Wollensak, eds. Proc. SPIE13, 195–204 (1968);“Beitrag zu der Optischen Abbildung in Weissen Licht,” Optik 24, 237–243 (1966–1967).

Laikin, M.

M. Laikin, Lens Design (Dekker, New York, 1991), pp. 35–40.

MacDonald, J.

I. M. Khan, J. MacDonald, “Cemented doublets. A method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Maréchal, A.

A. Maréchal, “Étude des effects combines de la diffraction et des aberrations géométriques sur l'image d'un point lumi-neux,” Rev. Opt. 26, 257–277 (1947). Note that the use of the 1.1 zone is approximately correct for F/D = 4 doublets.

A. Maréchal, M. Françon, Diffraction (Revue d'Optique, Theorique et Instrumentale, Paris, 1950), pages 105–119; see chap. 8.

Metzmacher, K.

H. Koehler, K. Metzmacher, “The white light modulation transfer function of optical systems as a function of the state of color correction,” in Modulation Transfer Function, R. R. Shannon, R. J. Wollensak, eds. Proc. SPIE13, 195–204 (1968);“Beitrag zu der Optischen Abbildung in Weissen Licht,” Optik 24, 237–243 (1966–1967).

Moser, C.

C. Moser, “Über Fernrohrobjective,” (Part 1), Z. Instrumentenkde. 7, 225–238 (1887);(Part 2), Z. Instrumentenkd. 7, 308–323 (1887).

Mossoti, O. F.

O. F. Mossoti, “Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 4, 38–1651853;“Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 5, 5–951858;Nuova Theoria Instrumenti Ottici (Casa Editrice Nistri, Pisa, Italy, 1859), p. 171–191.

Mouroulis, P.

Nordenmark, N. V. E.

N. V. E. Nordenmark, J. Nordström, “The invention of the achromatic and aplanatic lens,” Lychnos 3, 1–52 (1938);“The invention of the achromatic and aplanatic lens,” Lychnos 4, 313–384 (1939);“The invention of the achromatic and aplanatic lens,” Meddelande, Stockholm Observatorium Reprint Series No. 46 (Almqvist Wiksells Boktryckeri-A.-B., Uppsala, Sweden, 1939), (both articles appeared in this volume together).

Nordström, J.

N. V. E. Nordenmark, J. Nordström, “The invention of the achromatic and aplanatic lens,” Lychnos 3, 1–52 (1938);“The invention of the achromatic and aplanatic lens,” Lychnos 4, 313–384 (1939);“The invention of the achromatic and aplanatic lens,” Meddelande, Stockholm Observatorium Reprint Series No. 46 (Almqvist Wiksells Boktryckeri-A.-B., Uppsala, Sweden, 1939), (both articles appeared in this volume together).

Picht, J.

J. Picht, Optische Abbildung (Vieweg, Braunschweig, Germany, 1931), pp. 184–191.

Rao, V.

H. H. Hopkins, V. Rao, “The systematic design of two component objectives,” Opt. Acta 7, 497–514 (1970).
[CrossRef]

Sliusarev, G. G.

G. G. Sliusarev, Methods of Calculation of Optical Systems (Gostekhizdat, Leningrad, USSR, 1937).

G. G. Sliusarev, Tables for Designing Cemented Doublets (Vavilov State Optical Institute, Leningrad, USSR, 1949).

Smith, T.

E. Brown, T. Smith, “Systematic construction tables for thin cemented aplanatic lenses,” Philos. Trans. R. Soc. London, Ser. A 240, 59–116 (1948).

T. Smith, “The principles and methods of calculating telescope objectives,” in Collected Papers of T. Smith, compiled by E. G. Martin (University Microfilms, Ann Arbor, Mich., 1970), Vol. 2, pp. 99–120.

Steel, W. H.

W. H. Steel, “On the choice of glasses for cemented achromatic aplanatic doublets,” Austral. J. Phys. 7, 244–253 (1954), see p. 245 in particular;“A general equation for the choice of glass for cemented doublets,” Austral. J. Phys. 8, 68–73 (1955).
[CrossRef]

Sussman, M. H.

Trubko, S. V.

S. V. Trubko, Calculation of Two Lens Cemented Objectives (Mashinostroenie, Leningrad USSR, 1984).

Turrière, E.

E. Turrière, Optique Industrielle (Librairie Delagrave, Paris, 1920), pp. 28–36, para. 18.

Väisäla, Y.

Y. Väisäla, “Neue Methoden zur Untersuchung der Objek-tive,” Ann. Univ. Fennicae Aboensis Ser. A 1, 103–115 (1922).

von Hoegh, E.

E. von Hoegh, “Zur Theorie der Zweitheiligen Verkitteten Fernrohrobjective,” Z. Instrumentenkd. 19, 37–39 (1899).

von Rohr, M.

M. von Rohr, “Fraunhofer's work and its present-day signifi-cance,” Trans. Opt. Soc. 27, 277–294 (1925–1926).
[CrossRef]

Zhao, G.

(Part 1), Z. Instrumentenkde. (1)

C. Moser, “Über Fernrohrobjective,” (Part 1), Z. Instrumentenkde. 7, 225–238 (1887);(Part 2), Z. Instrumentenkd. 7, 308–323 (1887).

Anal. Univ. Toscana Pisa (1)

O. F. Mossoti, “Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 4, 38–1651853;“Nuova theoria degli instrumenti ottici,” Anal. Univ. Toscana Pisa 5, 5–951858;Nuova Theoria Instrumenti Ottici (Casa Editrice Nistri, Pisa, Italy, 1859), p. 171–191.

Ann. Univ. Fennicae Aboensis Ser. A (1)

Y. Väisäla, “Neue Methoden zur Untersuchung der Objek-tive,” Ann. Univ. Fennicae Aboensis Ser. A 1, 103–115 (1922).

Appl. Opt. (1)

Austral. J. Phys. (1)

W. H. Steel, “On the choice of glasses for cemented achromatic aplanatic doublets,” Austral. J. Phys. 7, 244–253 (1954), see p. 245 in particular;“A general equation for the choice of glass for cemented doublets,” Austral. J. Phys. 8, 68–73 (1955).
[CrossRef]

J. Am. Opt. Soc. (1)

R. E. Hopkins, “Automatic design of telescope objectives,” J. Am. Opt. Soc. 45, 167–178 (1955).

J. Opt. Soc. Am. (1)

Lychnos (1)

N. V. E. Nordenmark, J. Nordström, “The invention of the achromatic and aplanatic lens,” Lychnos 3, 1–52 (1938);“The invention of the achromatic and aplanatic lens,” Lychnos 4, 313–384 (1939);“The invention of the achromatic and aplanatic lens,” Meddelande, Stockholm Observatorium Reprint Series No. 46 (Almqvist Wiksells Boktryckeri-A.-B., Uppsala, Sweden, 1939), (both articles appeared in this volume together).

Mém. Acad. R. Sci. Paris (2)

A. C. Clairaut, “Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 1, 380–437 (1763) (this article was written in 1756; it was available for reading in 1761 and appeared in print in approximately 1763);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 2, 524–550 (1764) (this article, of the same title as that which appeared in 1763, was written in 1757; it was available for reading in 1761 and appeared in print in approximately 1764);“Mémoires sur les moyens de perfectionner les lunettes d'approche par l'usage d'objectifs composés de plusieurs matières différement réfringentes,” Mém. Acad. R. Sci. Paris 3, 578–631 (1769) (this article, also of the same title as the two previous articles, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1768).

J. d'Alembert, “Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 1, 75–145 (1767) (this article was written in 1764; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 2, 63–105 (1768) (this article, of the same title as that which appeared in 1767, was written in 1765; it was available for reading in 1766 and appeared in print in approximately 1767);“Nouvelles recherches sur les verres optiques,” Mém. Acad. R. Sci. Paris 3, 43–108 (1769) (this article, also bearing the same title as the two previous articles, was written in 1766; it was available for reading in 1767 and appeared in print in 1769).

Opt. Acta (2)

H. H. Hopkins, V. Rao, “The systematic design of two component objectives,” Opt. Acta 7, 497–514 (1970).
[CrossRef]

I. M. Khan, J. MacDonald, “Cemented doublets. A method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. A (1)

E. Brown, T. Smith, “Systematic construction tables for thin cemented aplanatic lenses,” Philos. Trans. R. Soc. London, Ser. A 240, 59–116 (1948).

Rev. Opt. (1)

A. Maréchal, “Étude des effects combines de la diffraction et des aberrations géométriques sur l'image d'un point lumi-neux,” Rev. Opt. 26, 257–277 (1947). Note that the use of the 1.1 zone is approximately correct for F/D = 4 doublets.

Trans. Opt. Soc. (1)

M. von Rohr, “Fraunhofer's work and its present-day signifi-cance,” Trans. Opt. Soc. 27, 277–294 (1925–1926).
[CrossRef]

Z. Instrumentenkd. (3)

H. Harting, “Zur Theorie der Zweitheiligen Verkitteten Ferm-rohrobjective,” Z. Instrumentenkd. 18, 357–380 (1898).

E. von Hoegh, “Zur Theorie der Zweitheiligen Verkitteten Fernrohrobjective,” Z. Instrumentenkd. 19, 37–39 (1899).

H. Boegehold, “Die Leistung von Clairaut und d'Alembert fürdie Theorie des Fernrohrobjective,” Z. Instrumentenkd. 55, 97–111 (1935); see especially p. 98.

Zen-Ztg. Opt. Mech. (1)

A. Kerber, “Über die Chromatische Korrektur von Doppelob-jektiven,” Zen-Ztg. Opt. Mech. 7, 157–158 (1886).

Other (16)

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 1, p. 136;Applied Optics and Optical Design Vol. 2, pp. 627, 641, and especially 651.

A. Maréchal, M. Françon, Diffraction (Revue d'Optique, Theorique et Instrumentale, Paris, 1950), pages 105–119; see chap. 8.

H. Koehler, K. Metzmacher, “The white light modulation transfer function of optical systems as a function of the state of color correction,” in Modulation Transfer Function, R. R. Shannon, R. J. Wollensak, eds. Proc. SPIE13, 195–204 (1968);“Beitrag zu der Optischen Abbildung in Weissen Licht,” Optik 24, 237–243 (1966–1967).

J. Picht, Optische Abbildung (Vieweg, Braunschweig, Germany, 1931), pp. 184–191.

Schott optical glass (Schott Glasweke, Mainz, Germany).

The third-order SI and SII are the same as those used by German workers such as Berek, Köhler, Slevogt, and others. The tangential transverse aberration for an object at infinity is given byΔyk′=½F](x12+y12)y1S1−(x12+3y12)tanθSII+⋯+].

D. Argentieri, Ottica Industriale, 2nd ed. (Hoepli, Milan, Italy, 1954).

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 123–133.

E. Turrière, Optique Industrielle (Librairie Delagrave, Paris, 1920), pp. 28–36, para. 18.

The practice of cementing doublets was begun in 1785 in Paris by the opticians Grateloupe and Putois. The first cement used, mastic en larmes fondu par l'action du feu, did not last very long, probably for only a few months.

H. A. Steinheil, E. Voit, eds., Handbuch der Angewandten Optik (Teubner, Leipzig, 1891), Vol. 1.

T. Smith, “The principles and methods of calculating telescope objectives,” in Collected Papers of T. Smith, compiled by E. G. Martin (University Microfilms, Ann Arbor, Mich., 1970), Vol. 2, pp. 99–120.

M. Laikin, Lens Design (Dekker, New York, 1991), pp. 35–40.

G. G. Sliusarev, Methods of Calculation of Optical Systems (Gostekhizdat, Leningrad, USSR, 1937).

G. G. Sliusarev, Tables for Designing Cemented Doublets (Vavilov State Optical Institute, Leningrad, USSR, 1949).

S. V. Trubko, Calculation of Two Lens Cemented Objectives (Mashinostroenie, Leningrad USSR, 1984).

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Figures (9)

Fig. 1
Fig. 1

Longitudinal zonal aberration (z = 0.71) for F/D = 3, 4, 5 for crown leading with m = 0. Note the change in crown thickness.

Fig. 2
Fig. 2

Longitudinal zonal aberration (z = 0.71) for F/D = 3, 4, 5 for flint leading with m = 0. Note the change in crown thickness.

Fig. 3
Fig. 3

Same as Fig. 2 but for m = −1.

Fig. 4
Fig. 4

Spherochromatic aberration in wavelength versus the crown-leading refractive index for different flint-leading refractive-index values (see labels on individual curves) for F/D = 3, 4, 5 for crown leading with m = 0.

Fig. 5
Fig. 5

Same as Fig. 4 but for flint leading.

Fig. 6
Fig. 6

Same as Fig. 5 but for m = −1.

Fig. 7
Fig. 7

Emergent wave rms (in wavelength) versus the crown-leading refractive index for different flint-leading refractive indices (see labels on individual curves) for F/D = 3, 4, 5 for crown leading with m = 0.

Fig. 8
Fig. 8

Same as Fig. 7 but for flint leading.

Fig. 9
Fig. 9

Same as Fig. 8 but for m 5= −1.

Tables (9)

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Table 1 Rayleigh Tolerances for Various Aberrations with Different Focal Numbers a

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Table 2 Computations of Aberrations for Three Values of F/D for a Thin Doublet with PCR = 0 and F = 100 mm a

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Table 3 Computations of Aberrations for Three Values of F/D for a Thick Doublet with Zero Spherical Aberration and Zero Coma at the 1.1 Aperture and with F = 100 mm

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Table 4 Values of R and T Used in the Calculations for the Thick Doublet from Table 3

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Table 5 Computations for Achromatization Values of (ν + Δν2) for Flint Leading at m = 0, −1 and for Crown Leading at m = 0 and Satisfying Zero-Longitudinal Secondary Chromatic Aberration for the 0.71 Zone a

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Table 6 Flint-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1 a

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Table 7 Crown-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1 a

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Table 8 Flint-Leading Values, at m = −1, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1; F = 100 mm a

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Table 9 Aplanatic Doublets a Computed for Various Glasses for F/D = 4

Equations (19)

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ϕ 1 = ϕ / ( 1 + κ ) , ϕ 2 = ϕ κ / ( 1 + κ ) .
μ 2 = μ 1 ( B 1 ϕ 1 + B 2 ϕ 2 ) ,
ω 1 = ϕ 1 + 2 σ , ω 2 = ω 1 + ϕ .
s , n 1 , n 2 , S I , S II , ϕ ,
2 S II = μ 1 ( C 1 ϕ 1 + C 2 ϕ 2 ) C 2 ϕ 2 ( B 1 ϕ 1 + B 2 ϕ 2 ) ( 2 σ ϕ + ϕ 2 ) ,
4 S I = i = 1 2 ϕ i ( A i μ i 2 2 μ i ω i + B i 2 ϕ i 2 ) .
c 1 = ½ μ 1 + ½ B 1 ϕ 1 + σ , c 2 = c 1 ϕ 1 / ( n 1 1 ) , c 3 = c 2 ϕ 2 / ( n 2 1 ) ,
ϕ 1 / ν 1 + ϕ 2 / ν 2 = 0 ,
( ϕ 1 / ν 1 + ϕ 2 / ν 2 ) = ( s λ s F ) / s 2 .
Δ s k = 0.0916 ( h / 10 ) 4 + 0.0092 ( h / 10 ) 6 + 0.0009 ( h / 10 ) 8 + + .
rms ( λ d ) = [ 0 1 h ( r / R ) 2 d ( r / R ) 2 w 2 ] 1 / 2 ,
h ( r / R ) 2 = w 2 ,
I = 1 ( 2 π / λ ) 2 ( rms ) 2 + 0.45 ( 2 π / λ ) 4 ( rms ) 4 .
1.8 λ ( F / D ) / y k
Δ S m
Δ S z
Δ S m
Δ S z
Δ y k = ½ F ] ( x 1 2 + y 1 2 ) y 1 S 1 ( x 1 2 + 3 y 1 2 ) tan θ S II + + ] .

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