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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)

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Simple polynomial formulas to calculate the FWHM and full width at 1/e2 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 f-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 f-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

Original Manuscript: August 8, 2003
Revised Manuscript: September 30, 2003
Published: January 20, 2004

Hakan Urey, "Spot size, depth-of-focus, and diffraction ring intensity formulas for truncated Gaussian beams," Appl. Opt. 43, 620-625 (2004)

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