OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 42, Iss. 5 — May. 1, 1952
  • pp: 306–307

Image Error Theory for Finite Aperture and Field

M. HERZBERGER and E. MARCHAND  »View Author Affiliations

JOSA, Vol. 42, Issue 5, pp. 306-307 (1952)

View Full Text Article

Acrobat PDF (1086 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An image error theory is developed for finite aperture and field. In the limit the formulas reduce to those of the well-known Seidel theory. The constants of the Seidel theory are replaced in the general theory by functions. It is shown that for a given object plane these functions can be reduced to two independent functions, the vanishing of one leading to a symmetrical image, the vanishing of both to a sharp image, and it also is proved that these two functions permit one to compute the caustic surfaces. The image error functions for a given plane can be identified as the second-order derivatives of a characteristic function. To ascertain the image quality for a different plane, transformation formulas are developed which permit one to compute the first- and second-order derivatives of this characteristic function for any shift of the object plane. The authors have found that the second-order derivatives of another characteristic function are invariant with respect to a shift of the object and that a complete system of invariants of the image errors can be obtained. The basic formulas demonstrate that the shifted image-errors are linear functions of the image errors of the original plane and their second- and thirdorder determinants. Applications to classical problems are given.

M. HERZBERGER and E. MARCHAND, "Image Error Theory for Finite Aperture and Field," J. Opt. Soc. Am. 42, 306-307 (1952)

Sort:  Author  |  Journal  |  Reset


  1. T. Smith, Trans. Opt. Soc. (London) 23, 311 (1921–1922).
  2. M. Herzberger, J. Opt. Soc. Am. 38, 736 (1948).

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