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. 17, Iss. 7 — Jul. 1, 2000
  • pp: 1185–1191

Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system

Carlos J. Zapata-Rodríguez, Pedro Andrés, Manuel Martínez-Corral, and Laura Muñoz-Escrivá  »View Author Affiliations


JOSA A, Vol. 17, Issue 7, pp. 1185-1191 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001185


View Full Text Article

Acrobat PDF (312 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approximation, it is possible to find a similar pattern but magnified and situated at another plane within the Kirchhoff theory. Moreover, we may evaluate this correspondence as the action of a virtual thin lens located at the focal plane and whose focus is situated at the axial point of the aperture plane. As a result, we give a geometrical interpretation of the focal-shift effect and present a brief comment on the problem of the best-focus location.

© 2000 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(110.1220) Imaging systems : Apertures
(180.6900) Microscopy : Three-dimensional microscopy

Citation
Carlos J. Zapata-Rodríguez, Pedro Andrés, Manuel Martínez-Corral, and Laura Muñoz-Escrivá, "Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system," J. Opt. Soc. Am. A 17, 1185-1191 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-7-1185

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. 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