OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 8 — Aug. 1, 1999
  • pp: 1958–1969

Beyond the Fresnel approximation for focused waves

M. A. Alonso, A. A. Asatryan, and G. W. Forbes  »View Author Affiliations


JOSA A, Vol. 16, Issue 8, pp. 1958-1969 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001958


View Full Text Article

Enhanced HTML    Acrobat PDF (251 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

By extension of the transitional operator method developed by Wünsche, the Rayleigh–Sommerfeld and Kirchhoff solutions to the diffraction of a converging spherical (or cylindrical) wave are expressed in terms of a series of derivatives of the field estimate that follows from the Fresnel approximation. This result allows a systematic assessment of the error associated with the paraxial wave model for focused fields and offers simple corrections to this model. In particular, for simple diffracting masks, the Fresnel approximation leads to estimates of the field that have a relative error near focus that is of the order of one on the square of the f-number. The number of significant digits in the field estimate is shown to be doubled by retaining just the first of the series of corrections derived here.

© 1999 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(260.1960) Physical optics : Diffraction theory

History
Original Manuscript: March 22, 1999
Manuscript Accepted: April 7, 1999
Published: August 1, 1999

Citation
M. A. Alonso, A. A. Asatryan, and G. W. Forbes, "Beyond the Fresnel approximation for focused waves," J. Opt. Soc. Am. A 16, 1958-1969 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-8-1958

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited