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. 20, Iss. 12 — Dec. 1, 2003
  • pp: 2393–2396

Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: reply to comment

J. E. A. Landgrave and L. R. Berriel-Valdos  »View Author Affiliations


JOSA A, Vol. 20, Issue 12, pp. 2393-2396 (2003)
http://dx.doi.org/10.1364/JOSAA.20.002393


View Full Text Article

Enhanced HTML    Acrobat PDF (116 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The Comment by Kowalczyk [J. Opt. Soc. Am. A 20, 2390 (2003)] on our paper on sampling expansions for three-dimensional light amplitude distributions in the vicinity of an axial image point [J. Opt. Soc. Am. A 14, 2962 (1997)] presents a “new” derivation of the axial sampling expansion (ASE), pointing out some “faults” in our derivation and that of ArsenaultBoivin [J. Appl. Phys. 38, 3988 (1967)], a derivation of which we were not aware. Finally, it also summarizes work done in generalizing the ASE to the case of nonrotationally symmetric pupil functions. The purpose of this reply is to clarify some relevant issues concerning the derivation of this kind of expansion, since, judging from some ideas expressed in their Comment, we believe these issues were left insufficiently clear in our paper. In doing this, we derive some additional sampling expansions.

© 2003 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(110.1220) Imaging systems : Apertures
(220.1230) Optical design and fabrication : Apodization

History
Original Manuscript: May 20, 2003
Manuscript Accepted: August 6, 2003
Published: December 1, 2003

Citation
J. E. A. Landgrave and L. R. Berriel-Valdos, "Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: reply to comment," J. Opt. Soc. Am. A 20, 2393-2396 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-12-2393


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. E. A. Landgrave, L. R. Berriel-Valdos, “Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point,” J. Opt. Soc. Am. A 14, 2962–2976 (1997). To avoid multiple references to this article, in the present work we shall often refer to it as “our paper.” [CrossRef]
  2. A. W. Lohmann, “Optical information processing” (Lecture Notes), 2nd ed. (Erlangen, Germany, 1978), p. 21. Available from the author at Telecommunications Institute, Signal Processing and Multimedia Communications, Universitaet Erlangen-Nuremberg, Cauerstrasse 7/VI, 91058 Erlangen, Germany. Phone, 49-9131-852-7664; e-mail, Lohmann@LNT.de.
  3. A. W. Lohmann, D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. 6, 1567–1570 (1967). [CrossRef] [PubMed]
  4. M. Kowalczyk, T. Cichocki, M. Martı́nez-Corral, L. Muñoz-Escrivá, “Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment,” J. Opt. Soc. Am. A 20, 2390–2392 (2003). [CrossRef]
  5. H. Arsenault, A. Boivin, “An axial form of the sampling theorem and its application to optical diffraction,” J. Appl. Phys. 38, 3988–3990 (1967). [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 23.
  7. V. Mangulis, Handbook of Series for Scientists and Engineers (Academic, New York, 1966), p. 29, Eqs. (16), (17), and (18).
  8. Staff of the Bateman Manuscript Project, Higher Transcendental Functions (Krieger, Malabar, Fla., 1970), Vol. II, pp. 68–72.
  9. F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), Chap. I.
  10. A. Boivin, Théorie et Calcul des Figures de Diffraction de Révolution (Les Presses de L’Université Laval, Québec, Canada, 1964), p. 198, Eq. II.C-37.
  11. B. Dossier, “Recherches sur l’apodisation des images optiques,” (doctoral thesis) (Éditions de la revue d’Optique, Paris, 1954).
  12. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 7.
  13. M. Martı́nez-Corral, L. Muñoz-Escrivá, M. Kowalczyk, T. Cichocki, “One-dimensional iterative algorithm for three-dimensional point-spread function engineering,” Opt. Lett. 26, 1861–1863 (2001). [CrossRef]

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.


« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited