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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 4 — Feb. 1, 2009
  • pp: B1–B7

Laser system range calculations and the Lambert W function

Ove Steinvall  »View Author Affiliations


Applied Optics, Vol. 48, Issue 4, pp. B1-B7 (2009)
http://dx.doi.org/10.1364/AO.48.0000B1


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Abstract

The knowledge of range performance versus atmospheric transmission, often given by the visibility, is critical for the design, use, and prediction of laser and passive electro-optic systems. I present a solution of the ladar–lidar equation based on Lambert’s W function. This solution will reveal the dependence of the maximum range on the system and target parameters for different atmospheric attenuations and will also allow us to take the signal statistics into account by studying the influence on the threshold signal-to-noise ratio. The method is also applicable to many range calculations for passive systems where the atmospheric loss can be approximated by an exponential term.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.3640) Atmospheric and oceanic optics : Lidar
(280.3400) Remote sensing and sensors : Laser range finder
(280.3420) Remote sensing and sensors : Laser sensors
(280.3640) Remote sensing and sensors : Lidar
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

History
Original Manuscript: May 20, 2008
Manuscript Accepted: July 25, 2008
Published: August 28, 2008

Citation
Ove Steinvall, "Laser system range calculations and the Lambert W function," Appl. Opt. 48, B1-B7 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-4-B1


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References

  1. V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004). [CrossRef]
  2. Robert M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math., 5, 329-359 (1996).
  3. D. L. Hutt, J.-M. Thériault, V. G. Larochelle, P. Mathieu, and D. Bonnier, “Estimating atmospheric extinction for eyesafe laser rangefinders,” Opt. Eng. 33, 3762-3277 (1994). [CrossRef]
  4. H. M. Tulldahl and K. O. Steinvall, “Analytical waveform generation from small objects in lidar bathymetry,” Appl Opt. 38, 1021-1039 (1999). [CrossRef]
  5. G. R. Osche, Optical Detection Theory (Wiley, 2002).

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