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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 48, Iss. 10 — Oct. 1, 1958
  • pp: 747–756

Optical Aberration Coefficients. III. The Computation of the Tertiary Coefficients

H. A. BUCHDAHL  »View Author Affiliations

JOSA, Vol. 48, Issue 10, pp. 747-756 (1958)

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In the course of the design of an optical system a knowledge of higher order aberration coefficients and of the contributions thereto by the individual surfaces is of great value. The present paper provides a computing scheme for the full set of tertiary (and of course primary and secondary) monochromatic aberration coefficients of symmetrical optical systems composed of spherical surfaces. This particular scheme is intended for use with ordinary desk calculating machines, and comprises only 192 entries of the usual kind per surface. The method of construction of the scheme is discussed, and a complete numerical example provided. The checks used to ensure the correctness of the scheme at the same time test the correctness of certain long sets of equations contained in the author’s monograph on optical aberration coefficients; and one misprint in them was thus discovered. This is corrected here. A new nomenclature for higher order aberrations is proposed.

H. A. BUCHDAHL, "Optical Aberration Coefficients. III. The Computation of the Tertiary Coefficients," J. Opt. Soc. Am. 48, 747-756 (1958)

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  1. F. D. Cruickshank, Australian J. Phys. 11, 41 (1958).
  2. Mr. G. A. Hills of this Laboratory hopes to publish an account of the design of a 48-in. telephoto lens by these means in the near future.
  3. H. A. Buchdahl, Optical Aberration Coefficients (Oxford University Press, New York, 1954). This work will hereafter be referred to as M.
  4. H. A. Buchdahl, J. Opt. Soc. Am. 48, 563 (1958). This paper will be referred to as II. The first paper of the series [J. Opt. Soc. Am. 46, 941 (1956)] will be referred to as I.
  5. It should be kept in mind that the differences between the values of the parameters specifying the initial and final designs, respectively, will generally be such that in view of the stability of the tertiary coefficients, all the information required can be obtained from the tertiary coefficients as calculated for the initial design. In other words, they need not be recalculated after every change of the design and their derivatives are thus not required. In practice the same is often found to be true even of the secondary coefficients although this fact is not of such great consequence when one considers how easily they can be calculated.
  6. As regards the numerical example, see Sec. 3.
  7. i.e., tertiary cubic coma (see Sec. 7).
  8. It should however be firmly kept in mind that even where such predictions are not very satisfactory a knowledge of the contributions can be of the utmost value in the course of optical design.
  9. G. C. Steward. The Symmetrical Optical System [Cambridge Tracts No. 25 (1928)], Chap. 3, Sec. 16, p. 47.
  10. It does however correspond reasonably closely to established usage; e.g., "circular coma" becomes "linear coma."

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