OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 7 — Jul. 1, 2006
  • pp: 1626–1630

Class of basis functions for use in optical systems analysis

Lee Estes, Adam Jilling, Gabriel Lombardi, and Jerry Butman  »View Author Affiliations

JOSA A, Vol. 23, Issue 7, pp. 1626-1630 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (159 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A method is described for modeling the effects of spatial apertures on optical sensor systems. The method consists of defining a set of basis functions that is obtained by partitioning the aperture image plane into a series of rectangular regions and replacing the field in each rectangular subregion with an orthogonal function series approximation. Each orthogonal function has a finite extent that is matched to the aperture image. The individual functions are propagated by application of the Fresnel approximation of the Rayleigh–Sommerfeld diffraction formula to other ranges, and the resultant functions are shown to be valid basis functions for defining a field at any other range. The technique is applied to a scattering problem using complex Fourier series.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(030.1640) Coherence and statistical optics : Coherence
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(070.2580) Fourier optics and signal processing : Paraxial wave optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: July 22, 2005
Revised Manuscript: January 11, 2006
Manuscript Accepted: January 17, 2006

Lee Estes, Adam Jilling, Gabriel Lombardi, and Jerry Butman, "Class of basis functions for use in optical systems analysis," J. Opt. Soc. Am. A 23, 1626-1630 (2006)

Sort:  Author  |  Journal  |  Reset  


  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 66-67, 104-106. [PubMed]

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited