OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 54, Iss. 1 — Jan. 1, 1964
  • pp: 45–46

Aberrations Arising from Decentrations and Tilts

PAUL L. RUBEN  »View Author Affiliations

JOSA, Vol. 54, Issue 1, pp. 45-46 (1964)

View Full Text Article

Acrobat PDF (690 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Equations for the third-order aberrations in the meridional plane of a symmetrical optical system in the presence of finite tilts and decentrations are derived, based on the stop-shift equations of H. H. Hopkins. To demonstrate the application of these formulas and to show the degree of agreement between these equations and an exact ray trace, a numerical example is included.

PAUL L. RUBEN, "Aberrations Arising from Decentrations and Tilts," J. Opt. Soc. Am. 54, 45-46 (1964)

Sort:  Author  |  Journal  |  Reset


  1. Many early references as to the first-order properties of tilted or decentered lenses may be found in the book by S. Czapski and O. Eppenstein, Grundzüge der Theorie der Optischen Instrumente (Johann Ambrosius Barth, Leipzig, Germany, 1924), especially on p. 65.
  2. A. Maréchal, Rev. Opt., 1–24 (1950). Many references are also found in the bibliography on p. 24.
  3. A. L. Ingalls and K. Pestrecov, J. Opt. Soc. Am. 38, 343–349 (1948).
  4. P. C. Foote and R. A. Woodson, J. Opt. Soc. Am. 39, 590–599 (1949).
  5. L. I. Epstein, J. Opt. Soc. Am. 39, 847–853 (1949).
  6. G. Wooters, J. Opt. Soc. Am. 40, 521–523 (1950).
  7. H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950), pp. 76–118.
  8. C. G. Wynne, Proc. Phys. Soc. (London) B65, 429–437 (1952).
  9. Reference 7, p. 87.
  10. Reference 8, p. 430.
  11. Reference 7, p. 104.
  12. Reference 8, p. 431.

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