Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B
It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffractionlimited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probabilitybased techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimizationbased techniques for retrieving the fluorescence decay parameters for various twofluorophore mixtures, as a function of the total number of photon counts, in timecorrelated, singlephoton counting experiments. The probabilitybased techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 23 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a binbybin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters butmore »
 Authors:

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 Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Chemistry
 Publication Date:
 Report Number(s):
 ISJ9225
Journal ID: ISSN 10895639
 Grant/Contract Number:
 AC0207CH11358; W7405430 ENG82
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory
 Additional Journal Information:
 Journal Volume: 121; Journal Issue: 1; Journal ID: ISSN 10895639
 Publisher:
 American Chemical Society
 Research Org:
 Ames Laboratory (AMES), Ames, IA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
 OSTI Identifier:
 1347904
Santra, Kalyan, Smith, Emily A., Petrich, Jacob W., and Song, Xueyu. Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B. United States: N. p.,
Web. doi:10.1021/acs.jpca.6b10728.
Santra, Kalyan, Smith, Emily A., Petrich, Jacob W., & Song, Xueyu. Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B. United States. doi:10.1021/acs.jpca.6b10728.
Santra, Kalyan, Smith, Emily A., Petrich, Jacob W., and Song, Xueyu. 2016.
"Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B". United States.
doi:10.1021/acs.jpca.6b10728. https://www.osti.gov/servlets/purl/1347904.
@article{osti_1347904,
title = {Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B},
author = {Santra, Kalyan and Smith, Emily A. and Petrich, Jacob W. and Song, Xueyu},
abstractNote = {It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffractionlimited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probabilitybased techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimizationbased techniques for retrieving the fluorescence decay parameters for various twofluorophore mixtures, as a function of the total number of photon counts, in timecorrelated, singlephoton counting experiments. The probabilitybased techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 23 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a binbybin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. Lastly, these probabilitybased methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffractionlimited microscopies.},
doi = {10.1021/acs.jpca.6b10728},
journal = {Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory},
number = 1,
volume = 121,
place = {United States},
year = {2016},
month = {12}
}