OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 49, Iss. 11 — Nov. 1, 1959
  • pp: 1113–1114

Optical Aberration Coefficients. V. On the Quality of Predicted Displacements

H. A. BUCHDAHL  »View Author Affiliations

JOSA, Vol. 49, Issue 11, pp. 1113-1114 (1959)

View Full Text Article

Acrobat PDF (782 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The author’s previous work on the computation of algebraic higher order aberration coefficients and their derivatives has been illustrated numerically by providing explicit calculations, relating to a certain simple triplet operating over a relatively small field and at low aperture. Doubts have been expressed as to the usefulness of using such aberration coefficients to describe the (geometrical) behavior of systems operating at higher apertures and over wider fields. In this paper, therefore, all the primary, secondary, and tertiary aberration coefficients, and the coefficient of quaternary spherical aberration are given for two further systems, viz. (i) a wide angle objective operating at an aperture of ƒ/4.5 and over a field of 70°; and (ii) an objective operating at an aperture of ƒ/2.3 over a field of 40°. A number of diagrams compare the predicted displacements, relative to the ideal image point, of the intersection points with the ideal image plane of certain selected (a) tangential pencils, (b) sagittal pencils, and (c) general skew pencils of rays, with the actual displacements as obtained from trigonometrical traces. The agreement is very satisfactory. Even in cases, however, in which the agreement—for the largest apertures or fields considered—leaves something to be desired a knowledge of the coefficients and their derivatives provides a powerful tool for the control over the performance of the system. A detailed elementary example illustrating this assertion is included.

H. A. BUCHDAHL, "Optical Aberration Coefficients. V. On the Quality of Predicted Displacements," J. Opt. Soc. Am. 49, 1113-1114 (1959)

Sort:  Author  |  Journal  |  Reset


  1. H. A. Buchdahi, Optical Aberration Coefficients (Oxford University Press, London, 1954). All references to this work will hereafter be distinguished by the letter M.
  2. C. G. Wynne, Proc. Phys. Soc. (London) B70, 1013 (1957).
  3. A. Reuschel, Intern. Math. News (April, 1956).
  4. The relevant theory and computing schemes are developed in the following papers: H. A. Buchdahl, J. Opt. Soc. Am. 48, 563, 747, 757 (1958). These are hereafter referred to as II, III, IV, respectively.
  5. W. Merté, Das Potographische Objektiv (Verlag Julius Springer, Berlin, 1932), p. 315.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited