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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 3 — Feb. 1, 2010
  • pp: 2076–2089

Bayesian estimation of weak material dispersion: theory and experiment

J. M. Nichols, M. Currie, F. Bucholtz, and W. A. Link  »View Author Affiliations


Optics Express, Vol. 18, Issue 3, pp. 2076-2089 (2010)
http://dx.doi.org/10.1364/OE.18.002076


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Abstract

This work considers the estimation of dispersion in materials via an interferometric technique. At its core, the problem involves extracting the quadratic variation in phase over a range of wavelengths based on measured optical intensity. The estimation problem becomes extremely difficult for weakly dispersive materials where the quadratic nonlinearity is very small relative to the uncertainty inherent in experiment. This work provides a means of estimating dispersion in the face of such uncertainty. Specifically, we use a Markov Chain Monte Carlo implementation of Bayesian analysis to provide both the dispersion estimate and the associated confidence interval. The interplay between various system parameters and the size of the resulting confidence interval is discussed. The approach is then applied to several different experimental samples.

© 2010 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(160.4760) Materials : Optical properties

ToC Category:
Materials

History
Original Manuscript: September 18, 2009
Revised Manuscript: November 12, 2009
Manuscript Accepted: November 21, 2009
Published: January 19, 2010

Citation
J. M. Nichols, M. Currie, F. Bucholtz, and W. A. Link, "Bayesian estimation of weak material dispersion: theory and experiment," Opt. Express 18, 2076-2089 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2076


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References

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