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Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations

Metz, Thomas LU ; Walewski, Joachim LU and Kaminski, Clemens LU (2003) In Applied Optics 42(9). p.1551-1563
Abstract
Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result.. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment.... (More)
Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result.. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment. Statistical data evaluation contains the following steps. First,one has to provide a measurement model that considers statistical variation of all enclosed variables. Second, an evaluation scheme applicable to this particular model has to be derived or provided. Third, the scheme has to be characterized in terms of accuracy and precision. A criterion for accepting an evaluation scheme is that it have accuracy and precision as close as possible to the theoretical limit. The,fitting scheme derived for experiments with pulsed lasers is compared to well-established schemes in terms of fitting power and rational functions. The precision is found to be as much as three times better than for simple least-squares fitting. Our scheme also suppresses the bias on the estimated model parameters that. other methods may exhibit if they are applied in an uncritical fashion. We focus on experiments in nonlinear spectroscopy, but the fitting scheme derived is applicable in many scientific disciplines. (C) 2003 Optical Society of America. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
in
Applied Optics
volume
42
issue
9
pages
1551 - 1563
publisher
OSA
external identifiers
  • pmid:12665086
  • wos:000181708400001
  • scopus:0041381144
ISSN
2155-3165
language
English
LU publication?
yes
id
a3f73a80-18cd-4d76-8400-427aa7ddaf05 (old id 315583)
alternative location
http://www.opticsinfobase.org/abstract.cfm?URI=ao-42-9-1551
date added to LUP
2007-09-18 12:25:20
date last changed
2018-10-03 10:36:24
@article{a3f73a80-18cd-4d76-8400-427aa7ddaf05,
  abstract     = {Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result.. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment. Statistical data evaluation contains the following steps. First,one has to provide a measurement model that considers statistical variation of all enclosed variables. Second, an evaluation scheme applicable to this particular model has to be derived or provided. Third, the scheme has to be characterized in terms of accuracy and precision. A criterion for accepting an evaluation scheme is that it have accuracy and precision as close as possible to the theoretical limit. The,fitting scheme derived for experiments with pulsed lasers is compared to well-established schemes in terms of fitting power and rational functions. The precision is found to be as much as three times better than for simple least-squares fitting. Our scheme also suppresses the bias on the estimated model parameters that. other methods may exhibit if they are applied in an uncritical fashion. We focus on experiments in nonlinear spectroscopy, but the fitting scheme derived is applicable in many scientific disciplines. (C) 2003 Optical Society of America.},
  author       = {Metz, Thomas and Walewski, Joachim and Kaminski, Clemens},
  issn         = {2155-3165},
  language     = {eng},
  number       = {9},
  pages        = {1551--1563},
  publisher    = {OSA},
  series       = {Applied Optics},
  title        = {Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations},
  volume       = {42},
  year         = {2003},
}