OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 43, Iss. 3 — Jan. 20, 2004
  • pp: 620–625

Spot Size, Depth-of-Focus, and Diffraction Ring Intensity Formulas for Truncated Gaussian Beams

Hakan Urey  »View Author Affiliations

Applied Optics, Vol. 43, Issue 3, pp. 620-625 (2004)

View Full Text Article

Acrobat PDF (206 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Simple polynomial formulas to calculate the FWHM and full width at 1/<i>e</i><sup>2</sup> intensity diffraction spot size and the depth of focus at a Strehl ratio of 0.8 and 0.5 as a function of a Gaussian beam truncation ratio and a system <i>f</i>-number are presented. Formulas are obtained by use of the numerical integration of a Huygens-Fresnel diffraction integral and can be used to calculate the number of resolvable spots, the modulation transfer function, and the defocus tolerance of optical systems that employ laser beams. I also derived analytical formulas for the diffraction ring intensity as a function of the Gaussian beam truncation ratio and the system <i>f</i>-number. Such formulas can be used to estimate the diffraction-limited contrast of display and imaging systems.

© 2004 Optical Society of America

OCIS Codes
(110.3000) Imaging systems : Image quality assessment
(120.2040) Instrumentation, measurement, and metrology : Displays
(120.5800) Instrumentation, measurement, and metrology : Scanners
(170.5810) Medical optics and biotechnology : Scanning microscopy
(260.1960) Physical optics : Diffraction theory
(350.5730) Other areas of optics : Resolution

Hakan Urey, "Spot Size, Depth-of-Focus, and Diffraction Ring Intensity Formulas for Truncated Gaussian Beams," Appl. Opt. 43, 620-625 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. H. Urey, D. Wine, and T. Osborn, “Optical performance requirements for MEMS scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi and R. Goering, eds., Proc. SPIE 4178, 176–185 (2000).
  2. G. Marshall, ed., Optical Scanning (Marcel-Dekker, New York, 1991).
  3. H. Urey and F. B. Mccormick, “Storage limits of two-photon based three-dimensional memories,” in Optical Computing, Vol. 8 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1997), pp. 134–136.
  4. M. M. Wang, S. C. Esener, F. B. McCormick, I. Cokgor, A. S. Dvornikov, and P. M. Rentzepis, “Experimental characterization of a two-photon memory,” Opt. Lett. 22, 558–560 (1997).
  5. V. N. Mahajan, “Axial irradiance and optimum focusing of laser beams,” Appl. Opt. 22, 3042–3053 (1983).
  6. V. N. Mahajan, “Uniform versus Gaussian beams: a comparison of the effects of the diffraction, obscuration, and aberrations,” J. Opt. Soc. Am. A 3, 470–485 (1986).
  7. Y. Li, “Degeneracy in the Fraunhofer diffraction of truncated Gaussian beam,” J. Opt. Soc. Am. A 4, 1237–1242 (1987).
  8. H. T. Yura, “Optimum truncation of a Gaussian beam for propagation through atmospheric turbulence,” Appl. Opt. 34, 2774–2779 (1995).
  9. H. T. Yura and T. S. Rose, “Gaussian beam transfer through hard-aperture optics,” Appl. Opt. 34, 6826–6828 (1995).
  10. P. Belland and J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982).
  11. K. Tanaka, N. Saga, and H. Mizokami, “Field spread of a diffracted Gaussian beam through a circular aperture,” Appl. Opt. 24, 1102–1106 (1985).
  12. G. Lenz, “Far-field diffraction of truncated higher-order Laguerre-Gaussian beams,” Opt. Commun. 123, 423–429 (1996).
  13. V. Nourrit, J.-L. de Bougrenet de la Tocnaye, and P. Chanclou, “Propagation and diffraction of truncated Gaussian beams,” J. Opt. Soc. Am. A 18, 546–556 (2001).
  14. E. M. Drege, N. G. Skinner, and D. M. Byrne, “Analytical far-field divergence angle of a truncated Gaussian beam,” Appl. Opt. 39, 4918–4925 (2000).
  15. V. N. Mahajan, Optical Imaging and Aberration Part II, Wave Diffraction Optics (SPIE Press, Bellingham, Wash., 2001).
  16. M. Abromovitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  17. H. Urey, “Diffraction limited resolution and maximum contrast for scanning displays,” Proc. Soc. Inf. Disp. 31, 866–869 (2000).
  18. G. de Wit, “Contrast budget of head mounted displays,” Opt. Eng. 41, 2419–2426 (2002).
  19. H. Urey, “Diffractive exit-pupil expander for display applications,” Appl. Opt. 40, 5840–5851 (2001).

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