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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 36 — Dec. 20, 2008
  • pp: 6842–6851

Gaussian profile estimation in two dimensions

Nathan Hagen and Eustace L. Dereniak  »View Author Affiliations


Applied Optics, Vol. 47, Issue 36, pp. 6842-6851 (2008)
http://dx.doi.org/10.1364/AO.47.006842


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Abstract

We extend recent results for estimating the parameters of a one-dimensional Gaussian profile to two-dimensional profiles, deriving the exact covariance matrix of the estimated parameters. While the exact form is easy to compute, we provide a set of close approximations that allow the covariance to take on a simple analytic form. This not only provides new insight into the behavior of the estimation parameters, but also lays a foundation for clarifying previously published work. We also show how to calculate the parameter variances for the case of truncated sampling, where the profile lies near the edge of the array detector. Finally, we calculate expressions for the bias in the classical formulation of the problem and provide an approach for its removal. This allows us to show how the bias affects the problem of choosing an optimal pixel size for minimizing parameter variances.

© 2008 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(100.2960) Image processing : Image analysis
(300.3700) Spectroscopy : Linewidth

ToC Category:
Image Processing

History
Original Manuscript: January 31, 2008
Revised Manuscript: June 7, 2008
Manuscript Accepted: October 20, 2008
Published: December 15, 2008

Citation
Nathan Hagen and Eustace L. Dereniak, "Gaussian profile estimation in two dimensions," Appl. Opt. 47, 6842-6851 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-36-6842

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