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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 46, Iss. 22 — Aug. 1, 2007
  • pp: 5374–5383

Gaussian profile estimation in one dimension

Nathan Hagen, Matthew Kupinski, and Eustace L. Dereniak  »View Author Affiliations


Applied Optics, Vol. 46, Issue 22, pp. 5374-5383 (2007)
http://dx.doi.org/10.1364/AO.46.005374


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Abstract

We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.

© 2007 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5240) Instrumentation, measurement, and metrology : Photometry
(300.3700) Spectroscopy : Linewidth

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: February 23, 2007
Revised Manuscript: May 10, 2007
Manuscript Accepted: May 11, 2007
Published: July 23, 2007

Citation
Nathan Hagen, Matthew Kupinski, and Eustace L. Dereniak, "Gaussian profile estimation in one dimension," Appl. Opt. 46, 5374-5383 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-22-5374

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