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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2442–2458

Derivation of the propagation equations for higher order aberrations of local wavefronts

Gregor Esser, Wolfgang Becken, Werner Müller, Peter Baumbach, Josep Arasa, and Dietmar Uttenweiler  »View Author Affiliations


JOSA A, Vol. 28, Issue 12, pp. 2442-2458 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002442


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Abstract

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analytical propagation equations for HOA do not exist. Since HOA play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the propagation equations of power and astigmatism to the case of HOA (e.g., coma and spheri cal aberration). This is achieved by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the aberrations of a propagated wavefront directly from the aberrations of the original wavefront containing both low-order and high-order aberrations.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2720) Geometric optics : Mathematical methods (general)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(080.1005) Geometric optics : Aberration expansions
(080.1753) Geometric optics : Computation methods
(080.7343) Geometric optics : Wave dressing of rays

History
Original Manuscript: June 17, 2011
Revised Manuscript: September 23, 2011
Manuscript Accepted: September 23, 2011
Published: November 10, 2011

Citation
Gregor Esser, Wolfgang Becken, Werner Müller, Peter Baumbach, Josep Arasa, and Dietmar Uttenweiler, "Derivation of the propagation equations for higher order aberrations of local wavefronts," J. Opt. Soc. Am. A 28, 2442-2458 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-12-2442

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