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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 38, Iss. 4 — Apr. 1, 1948
  • pp: 324–327

Performance of an Optical System as the Sum of the Contributions of Its Construction Elements

M. HERZBERGER  »View Author Affiliations

JOSA, Vol. 38, Issue 4, pp. 324-327 (1948)

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The investigations of Cruikshank have brought to the attention of American scientists different methods of analyzing the optical image, methods which were also suggested by A. Kerber and the author. However, all these methodS are, for the most part, restricted to the analysis of meridional rays.

In previous papers the author has shown the importance of the analysis of the diapoint configuration for the optical image. He here gives a simple formula to show how the diapoint deviations can be considered as the sum of errors originating at the single surfaces. In this way, and with the help of a series of diagrams, the lens designer can obtain an accurate picture of the effect of the single surface on all the rays traversing the optical system. Diagrams for two photographic lenses are included.

M. HERZBERGER, "Performance of an Optical System as the Sum of the Contributions of Its Construction Elements," J. Opt. Soc. Am. 38, 324-327 (1948)

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  1. F. Cruikshank, "A system of transfer coefficients for use in the design of lens systems," Proc. Phys. Soc. 57, 350, 362, 414, 426, 430 (1945).
  2. H. L. M'Auley, "A transfer method for deriving the effect on the image," Proc. Phys. Soc. 57, 435 (1945).
  3. L. Seidel, "Trigonometrie der Formel für den allgemeinen Fall," Müchener Sitzber. (2) 263 (1866).
  4. A. Kerber, Beiträge zur Dioptrik (Leipzig, 1895/99).
  5. K. Schwarzschild, Über differenzen Formeln zur Durchrechnung oplischer Systeme, (Göttingen, 1907).
  6. F. Nusl, "Über allgemeine differenzen Formeln," Bull. Int. Acad. Sci. de Boheme, 12, 84 (1907).
  7. T. Smith, "The general form of the Smith-Helmholtz equation," Trans. Opt. Soc. 31, 241 (1929).
  8. T. Smith, "Variational formulae in opties," Proc. Phys. Soc. 57, 558 (1945).
  9. M. Herzberger, "Über die Durchrechnung von Strahlen durch optische Systeme," Zeits. f. Physik 43, 750 (1927).
  10. M. Herzberger, "A new theory of optical image formation," J. Opt. Soc. Am. 26, 197 (1936).
  11. M. Herzberger, "The limitations of optical image formation," Ann. N. Y. Acad. Sci. 48, 1 (1946).
  12. F. Staeble, "Über den Zusammenhang von Koma and Sinusbedingung," Zeits. f. Instrumenten. 27, 241 (1907).
  13. E. Lihotzky, "Verallgemeinerung der Abbe'schen Sinusbedingung," Wiener Sitzber. 128, 85 (1919).
  14. M. Herzberger, "A direct image error theory," Quart. App. Math. 1, 69 (1943).
  15. M. Herzberger, "Light distribution in the optical image," J. Opt. Soc. Am. 37, 485 (1947).

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