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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 16 — Jun. 1, 2010
  • pp: D69–D95

Theory of sixth-order wave aberrations

José Sasián  »View Author Affiliations


Applied Optics, Vol. 49, Issue 16, pp. D69-D95 (2010)
http://dx.doi.org/10.1364/AO.49.000D69


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Abstract

A sixth-order theory of wave aberrations for axially symmetric systems is developed. Specific formulas for the sixth-order extrinsic and intrinsic wave aberration coefficients are given, as well as relations between pupil and image aberrations. Equations are developed for the wavefront propagation to the sixth order of approximation. The concept of the irradiance function is developed, and the second-order irradiance coefficients are found via conservation of flux at the pupils of the optical system and in terms of pupil aberrations. From purely geometrical considerations a generalized irradiance transport equation that describes irradiance changes in an optical system is derived. Confirming the aberration coefficients with real ray-tracing data was found to be indispensable.

© 2010 Optical Society of America

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(080.2740) Geometric optics : Geometric optical design
(110.2990) Imaging systems : Image formation theory
(350.5500) Other areas of optics : Propagation
(080.1005) Geometric optics : Aberration expansions

ToC Category:
Optical Aberrations

History
Original Manuscript: November 6, 2009
Manuscript Accepted: December 11, 2009
Published: March 17, 2010

Citation
José Sasián, "Theory of sixth-order wave aberrations," Appl. Opt. 49, D69-D95 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-16-D69


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References

  1. R. Shack, course OPTI 518, “Introduction to Aberrations,” class notes, College of Optical Sciences, University of Arizona, 1995. The value of writing the aberration function in terms of the field and aperture vector is that further development in aberration theory is possible. See, for example, and the contributions in this paper as examples.
  2. K. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. 22, 1389-1401 (2005).
  3. K. Schwarzschild, “Untersuchungen zur geometrischen Optik I. Einleitung in die Fehlertheorie optischer Instrumente auf Grund des Eikonalbegriffs,” Abh. Königlichen Ges. Wiss. Göttingen Math. Phys. Kl. 4, 1-31 (1905).
  4. H. H. Hopkins, The Wave Theory of Aberrations (Oxford Univ. Press, 1950). [CrossRef]
  5. C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. London Sect. B 65, 429-437 (1952).
  6. J. Hoffman, “Induced aberrations in optical systems,” Ph. D. dissertation (University of Arizona, 1993). [CrossRef]
  7. J. Sasian, “Interpretation of pupil aberrations in imaging systems,” Proc. SPIE 634, 634208 (2006).
  8. J. Sasian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051-1056 (1988). [CrossRef]
  9. D. Shafer's triplet lens data can be found in .
  10. M. P. Rimmer, “Optical aberration coefficients,” M.S. thesis (University of Rochester, 1963).
  11. H. A. Buchdahl, Optical Aberration Coefficients (Dover, 1968).
  12. M. R. Teague, “Image formation in terms of the transport equation,” J. Opt. Soc. Am. A 2, 2019-2026(1985). [CrossRef]

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