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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 36 — Dec. 20, 2009
  • pp: 6913–6922

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background

Serge Minin and Farzad Kamalabadi  »View Author Affiliations

Applied Optics, Vol. 48, Issue 36, pp. 6913-6922 (2009)

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We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, χ 2 , in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer–Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry–Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

© 2009 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(300.2140) Spectroscopy : Emission
(300.3700) Spectroscopy : Linewidth
(300.6320) Spectroscopy : Spectroscopy, high-resolution
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:

Original Manuscript: August 5, 2009
Revised Manuscript: November 12, 2009
Manuscript Accepted: November 15, 2009
Published: December 10, 2009

Serge Minin and Farzad Kamalabadi, "Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background," Appl. Opt. 48, 6913-6922 (2009)

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