Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Gaussian profile estimation in one dimension

Not Accessible

Your library or personal account may give you access

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

Full Article  |  PDF Article

Corrections

Nathan Hagen, Matthew Kupinski, and Eustace L. Dereniak, "Gaussian profile estimation in one dimension: erratum," Appl. Opt. 61, 4710-4710 (2022)
https://opg.optica.org/ao/abstract.cfm?uri=ao-61-16-4710

More Like This
Gaussian profile estimation in two dimensions

Nathan Hagen and Eustace L. Dereniak
Appl. Opt. 47(36) 6842-6851 (2008)

Gaussian profile estimation in one dimension: erratum

Nathan Hagen, Matthew Kupinski, and Eustace L. Dereniak
Appl. Opt. 61(16) 4710-4710 (2022)

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions

Harrison H. Barrett, Christopher Dainty, and David Lara
J. Opt. Soc. Am. A 24(2) 391-414 (2007)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (89)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved