OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 22, Iss. 19 — Oct. 1, 1983
  • pp: 3042–3053

Axial irradiance and optimum focusing of laser beams

Virendra N. Mahajan  »View Author Affiliations


Applied Optics, Vol. 22, Issue 19, pp. 3042-3053 (1983)
http://dx.doi.org/10.1364/AO.22.003042


View Full Text Article

Enhanced HTML    Acrobat PDF (1643 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Using the Rayleigh-Sommerfeld theory of diffraction we obtain an exact expression for the axial irradiance of a focused annular laser beam valid for all axial points. Conditions for the validity of the Fresnel theory are obtained. We discuss why and how the depth of focus and asymmetry of focused fields about the focal plane depend on the Fresnel number of the beam aperture as observed from the geometric focus. When a beam is focused on a distant target so that the Fresnel number is small (≲5), the principal maximum of axial irradiance occurs at a point which is significantly away from the geometric focus in the direction of the aperture. We discuss how to optimally focus a beam to illuminate a moving distant target in terms of the encircled energy on it. We show that, to obtain the maximum possible concentration of energy on a target, the beam must be focused on it, thus requiring active focusing for a moving target. However, if energy concentration is adequate for a beam focused on a target at a certain distance, it is more than adequate for a considerable range of the distance of a moving target without active focusing. In a shared-aperture optical system the aperture used for focusing a beam on the target is also used for imaging the target. Hence, in such a system the optical transfer function is also more than adequate over a wide range of the target distance without active focusing.

© 1983 Optical Society of America

History
Original Manuscript: December 27, 1982
Published: October 1, 1983

Citation
Virendra N. Mahajan, "Axial irradiance and optimum focusing of laser beams," Appl. Opt. 22, 3042-3053 (1983)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-22-19-3042


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981). [CrossRef]
  2. M. P. Givens, Opt. Commun. 41, 145 (1982). [CrossRef]
  3. Y. Li, E. Wolf, Opt. Commun. 42, 151 (1982). [CrossRef]
  4. W. H. Carter, Appl. Opt. 21, 1989 (1982). [CrossRef] [PubMed]
  5. Y. Li, J. Opt. Soc. Am. 72, 770 (1982). [CrossRef]
  6. H. Osterberg, L. W. Smith, J. Opt. Soc. Am. 51, 1050 (1961). [CrossRef]
  7. D. A. Holmes, J. E. Korka, P. V. Avizonis, Appl. Opt. 11, 565 (1972). [CrossRef] [PubMed]
  8. A. Arimoto, Opt. Acta 23, 245 (1976). [CrossRef]
  9. M. A. Gusinow, M. E. Riley, M. A. Palmer, Opt. Quantum Electron. 9, 465 (1977). [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980). Sec. 8.8.
  11. E. Collett, E. Wolf, Opt. Lett. 5, 264 (1980).See E. Wolf, Y. Li, Opt. Commun. 39, 205 (1981). [CrossRef] [PubMed]
  12. A. Sommerfeld, Optics, Vol. 4 (Academic, New York, 1972), pp. 199–201;substitute Eq. (8) on p. 201 into Eq. (6) on p. 199.
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 43–44;substitute Eq. (3–23) on p. 44 into Eq. (3–15) on p. 43.
  14. Ref. 13, p. 59.
  15. The sag of a surface is defined as its deviation along its axis from a plane normal to the axis and passing through its vertex.
  16. V. N. Mahajan, J. Opt. Soc. Am. 72, 1258 (1982). [CrossRef]
  17. J. E. Harvey, R. V. Shack, Appl. Opt. 17, 3003 (1978);also J. E. Harvey, Am. J. Phys. 47, 974 (1979). [CrossRef] [PubMed]
  18. V. N. Mahajan, Appl. Opt. same issue 22, 0000 (1983).
  19. P. A. Stokseth, J. Opt. Soc. Am. 59, 1313 (1969). [CrossRef]
  20. R. Barakat, J. Opt. Soc. Am. 54, 920 (1963).J. Opt. Soc. Am. 55, 538 (1965);Appl. Opt. 5, 1850 (1966). [CrossRef] [PubMed]
  21. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge, U.P., New York, 1966), p. 576.

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  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited