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

Santra, Kalyan; Smith, Emily A.; Petrich, Jacob W.; Song, Xueyu

doi:10.1021/acs.jpca.6b10728

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

Abstract

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 subdiffraction-limited 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 probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total number of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 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 bin-by-bin 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 »« less

Authors:

Santra, Kalyan ^[1]; Smith, Emily A. ^[1];

^[1];

^[1]

Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Chemistry

Publication Date:: Mon Dec 12 00:00:00 EST 2016

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1347904

Report Number(s):: IS-J-9225
Journal ID: ISSN 1089-5639

Grant/Contract Number:: AC02-07CH11358; W-7405-430 ENG-82

Resource 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 1089-5639

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    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., 2016. 
Web.  doi:10.1021/acs.jpca.6b10728.

Copy to clipboard


                    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.  https://doi.org/10.1021/acs.jpca.6b10728

Copy to clipboard


                    Santra, Kalyan, Smith, Emily A., Petrich, Jacob W., and Song, Xueyu. Mon .  
"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.  https://doi.org/10.1021/acs.jpca.6b10728.  https://www.osti.gov/servlets/purl/1347904.

Copy to clipboard


                    
@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 subdiffraction-limited 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 probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total number of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 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 bin-by-bin 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 probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited 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         = {Mon Dec 12 00:00:00 EST 2016},

  month        = {Mon Dec 12 00:00:00 EST 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1021/acs.jpca.6b10728

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

What Is the Best Method to Fit Time-Resolved Data? A Comparison of the Residual Minimization and the Maximum Likelihood Techniques As Applied to Experimental Time-Correlated, Single-Photon Counting Data
journal, February 2016

Santra, Kalyan; Zhan, Jinchun; Song, Xueyu
The Journal of Physical Chemistry B, Vol. 120, Issue 9
DOI: 10.1021/acs.jpcb.6b00154

The Number of Accumulated Photons and the Quality of Stimulated Emission Depletion Lifetime Images
journal, March 2014

Syed, Aleem; Lesoine, Michael D.; Bhattacharjee, Ujjal
Photochemistry and Photobiology
DOI: 10.1111/php.12248

Subdiffraction, Luminescence-Depletion Imaging of Isolated, Giant, CdSe/CdS Nanocrystal Quantum Dots
journal, February 2013

Lesoine, Michael D.; Bhattacharjee, Ujjal; Guo, Yijun
The Journal of Physical Chemistry C, Vol. 117, Issue 7
DOI: 10.1021/jp312231k

Supercontinuum Stimulated Emission Depletion Fluorescence Lifetime Imaging
journal, June 2012

Lesoine, Michael D.; Bose, Sayantan; Petrich, Jacob W.
The Journal of Physical Chemistry B, Vol. 116, Issue 27
DOI: 10.1021/jp303912p

Towards multi-exponential analysis in optically stimulated luminescence
journal, April 2010

Ankjærgaard, C.; Jain, M.; Hansen, P. C.
Journal of Physics D: Applied Physics, Vol. 43, Issue 19
DOI: 10.1088/0022-3727/43/19/195501

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves
journal, December 1991

Bajzer, ?eljko; Therneau, Terry M.; Sharp, Joseph C.
European Biophysics Journal, Vol. 20, Issue 5
DOI: 10.1007/BF00450560

Clarification of the use of CHI-square and likelihood functions in fits to histograms
journal, April 1984

Baker, Steve; Cousins, Robert D.
Nuclear Instruments and Methods in Physics Research, Vol. 221, Issue 2
DOI: 10.1016/0167-5087(84)90016-4

Data analysis in the shot noise limit. 1. Single parameter estimation with Poisson and normal probability density functions
journal, November 1989

Bialkowski, Stephen E.
Analytical Chemistry, Vol. 61, Issue 22
DOI: 10.1021/ac00197a006

Data analysis in the shot noise limit. 2. Methods for data regression
journal, November 1989

Bialkowski, Stephen E.
Analytical Chemistry, Vol. 61, Issue 22
DOI: 10.1021/ac00197a007

Comparison between time‐correlated single photon counting and fluorescence correlation spectroscopy in single molecule identification
journal, March 1998

Enderlein, Jörg; Köllner, Malte
Bioimaging, Vol. 6, Issue 1
DOI: 10.1002/1361-6374(199803)6:1<3::AID-BIO2>3.3.CO;2-D

On the analysis of fluorescence decay kinetics by the method of least-squares
journal, June 1974

Grinvald, Amiram; Steinberg, Izchak Z.
Analytical Biochemistry, Vol. 59, Issue 2
DOI: 10.1016/0003-2697(74)90312-1

Better estimates of exponential decay parameters
journal, October 1981

Hall, Peter; Selinger, Ben
The Journal of Physical Chemistry, Vol. 85, Issue 20
DOI: 10.1021/j150620a019

Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments
journal, January 2001

Hauschild, T.; Jentschel, M.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 457, Issue 1-2
DOI: 10.1016/S0168-9002(00)00756-7

On the reliability of fluorescence decay data
journal, January 1977

Hinde, Al; Selinger, Bk; Nott, Pr
Australian Journal of Chemistry, Vol. 30, Issue 11
DOI: 10.1071/CH9772383

Single-Molecule Analysis And Lifetime Estimates Of Heterogeneous Low-Count-Rate Time-Correlated Fluorescence Data
journal, September 2011

Kim, Gi-Ho; Legresley, Sarah E.; Snyder, Nathaniel
Applied Spectroscopy, Vol. 65, Issue 9
DOI: 10.1366/10-06147

Efficient maximum likelihood estimator fitting of histograms
journal, May 2010

Laurence, Ted A.; Chromy, Brett A.
Nature Methods, Vol. 7, Issue 5
DOI: 10.1038/nmeth0510-338

An Experimental Comparison of the Maximum Likelihood Estimation and Nonlinear Least-Squares Fluorescence Lifetime Analysis of Single Molecules
journal, May 2001

Maus, Michael; Cotlet, Mircea; Hofkens, Johan
Analytical Chemistry, Vol. 73, Issue 9
DOI: 10.1021/ac000877g

Comparison of Methods for Rapid Evaluation of Lifetimes of Exponential Decays
journal, May 2004

Moore, Christopher; Chan, Sing Po; Demas, J. N.
Applied Spectroscopy, Vol. 58, Issue 5
DOI: 10.1366/000370204774103444

Artefacts in the analysis of temporal response functions measured by photon counting
journal, March 2005

Nishimura, Goro; Tamura, Mamoru
Physics in Medicine and Biology, Vol. 50, Issue 6
DOI: 10.1088/0031-9155/50/6/019

Analysis of Fluorescence Decay by the Nonlinear Least Squares Method
journal, November 1988

Periasamy, N.
Biophysical Journal, Vol. 54, Issue 5
DOI: 10.1016/S0006-3495(88)83032-7

Error Analysis of the Rapid Lifetime Determination Method for Double-Exponential Decays and New Windowing Schemes
journal, March 1999

Sharman, Kristin K.; Periasamy, Ammasi; Ashworth, Harry
Analytical Chemistry, Vol. 71, Issue 5
DOI: 10.1021/ac981050d

Analysis of fluorescence lifetime data for single Rhodamine molecules in flowing sample streams
journal, January 1994

Tellinghuisen, Joel.; Goodwin, Peter M.; Ambrose, W. Patrick.
Analytical Chemistry, Vol. 66, Issue 1
DOI: 10.1021/ac00073a013

Accurate Analysis of Fluorescence Decays from Single Molecules in Photon Counting Experiments
journal, August 2003

Turton, David A.; Reid, Gavin D.; Beddard, Godfrey S.
Analytical Chemistry, Vol. 75, Issue 16
DOI: 10.1021/ac034325k

Fluorescence Instrument Response Standards in Two-Photon Time-Resolved Spectroscopy
journal, August 2010

Luchowski, Rafal; Szabelski, Mariusz; Sarkar, Pabak
Applied Spectroscopy, Vol. 64, Issue 8
DOI: 10.1366/000370210792081000

Testing Fluorescence Lifetime Standards using Two-Photon Excitation and Time-Domain Instrumentation: Rhodamine B, Coumarin 6 and Lucifer Yellow
journal, May 2014

Kristoffersen, Arne S.; Erga, Svein R.; Hamre, Børge
Journal of Fluorescence, Vol. 24, Issue 4
DOI: 10.1007/s10895-014-1368-1

The photophysics of rhodamine B
journal, January 1982

Snare, M. J.; Treloar, F. E.; Ghiggino, K. P.
Journal of Photochemistry, Vol. 18, Issue 4
DOI: 10.1016/0047-2670(82)87023-8

Photophysical properties of laser dyes: picosecond laser flash photolysis studies of Rhodamine 6G, Rhodamine B and Rhodamine 101
journal, January 1993

Beaumont, Paul C.; Johnson, David G.; Parsons, Barry J.
Journal of the Chemical Society, Faraday Transactions, Vol. 89, Issue 23
DOI: 10.1039/ft9938904185

Wavelength dependence of timing properties of the XP 2020 photomultiplier
journal, December 1978

Calligaris, F.; Ciuti, P.; Gabrielli, I.
Nuclear Instruments and Methods, Vol. 157, Issue 3
DOI: 10.1016/0029-554X(78)90025-3

Wavelength dependence of the time resolution of high-speed photomultipliers used in single-photon timing experiments
journal, January 1976

Sipp, B.; Miehe, J. A.; Lopez-Delgado, R.
Optics Communications, Vol. 16, Issue 1
DOI: 10.1016/0030-4018(76)90085-7

Systematic errors in χ2-fitting of Poisson distributions
journal, March 1996

Jading, Y.; Riisager, K.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 372, Issue 1-2
DOI: 10.1016/0168-9002(95)01397-0

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part I
journal, July 1928

Neyman, J.; Pearson, E. S.
Biometrika, Vol. 20A, Issue 1/2
DOI: 10.2307/2331945

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part II
journal, December 1928

Neyman, J.; Pearson, E. S.
Biometrika, Vol. 20A, Issue 3/4
DOI: 10.2307/2332112

Works referencing / citing this record:

A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments
journal, December 2018

Santra, Kalyan; Smith, Emily A.; Song, Xueyu
Photochemistry and Photobiology, Vol. 95, Issue 3
DOI: 10.1111/php.13057

Coumarin‐based Fluorescent Probes for Selectively Targeting and Imaging the Endoplasmic Reticulum in Mammalian Cells
journal, August 2018

Wijesooriya, Chamari S.; Nieszala, Megan; Stafford, Alex
Photochemistry and Photobiology, Vol. 95, Issue 2
DOI: 10.1111/php.12985

Similar Records in DOE PAGES and OSTI.GOV collections:

What is the best method to fit time-resolved data? A comparison of the residual minimization and the maximum likelihood techniques as applied to experimental time-correlated, single-photon counting data

Journal Article Santra, Kalyan ; Zhan, Jinchun ; Song, Xueyu ; ... - Journal of Physical Chemistry. B, Condensed Matter, Materials, Surfaces, Interfaces and Biophysical Chemistry

The need for measuring fluorescence lifetimes of species in subdiffraction-limited volumes in, for example, stimulated emission depletion (STED) microscopy, entails the dual challenge of probing a small number of fluorophores and fitting the concomitant sparse data set to the appropriate excited-state decay function. This need has stimulated a further investigation into the relative merits of two fitting techniques commonly referred to as “residual minimization” (RM) and “maximum likelihood” (ML). Fluorescence decays of the well-characterized standard, rose bengal in methanol at room temperature (530 ± 10 ps), were acquired in a set of five experiments in which the total number ofmore »« less
Cited by 19
https://doi.org/10.1021/acs.jpcb.6b00154

Full Text Available
Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

Journal Article Laurence, T ; Chromy, B - Nature Methods, vol. 7, no. 5, May 1, 2010, pp. 338-339

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms ofmore »« less
Full Text Available
The Number of Accumulated Photons and the Quality of Stimulated Emission Depletion Lifetime Images

Journal Article Syed, Aleem ; Lesoine, Michael D ; Bhattacharjee, Ujjal ; ... - Photochemistry and Photobiology

Time binning is used to increase the number of photon counts in the peak channel of stimulated emission depletion (STED) fluorescence lifetime decay curves to determine how it affects the resulting lifetime image. The fluorescence lifetime of the fluorophore, Alexa Fluor 594 phalloidin, bound to F-actin is probed in cultured S2 cells at a spatial resolution of ~40 nm. This corresponds to a tenfold smaller probe volume compared to confocal imaging, and a reduced number of photons contributing to the signal. Pixel-by-pixel fluorescence lifetime measurements and error analysis show that an average of 40 ± 30 photon counts in themore »« less
https://doi.org/10.1111/php.12248
Analysis of fluorescence lifetime data for single rhodamine molecules in flowing sample streams

Journal Article Tellinghuisen, J ; Goodwin, P M ; Ambrose, W P ; ... - Analytical Chemistry (Washington); (United States)

Fluorescence events of individual molecules of Rhodamine 110 dye in a stream of methanol occur as bursts of 5-300 photoelectrons when the dye molecules transit the volume interrogated by the pulsed excitation laser. The arrival times for these events, extracted by use of time-correlated single-photon counting techniques, are distributed exponentially over a approximately 10-ns time window gated to discriminate against prompt scattered light. Still, residual scattered light and solvent-impurity fluorescence contribute significantly to the recorded time distributions, which therefore must be analyzed as sums of an exponential decay and a background. Results obtained from two-parameter nonlinear least-squares fits are comparedmore »« less
https://doi.org/10.1021/ac00073a013
Supercontinuum Stimulated Emission Depletion Fluorescence Lifetime Imaging

Journal Article Lesoine, Michael ; Bose, Sayantan ; Petrich, Jacob ; ... - Journal of Physical Chemistry B

Supercontinuum (SC) stimulated emission depletion (STED) fluorescence lifetime imaging is demonstrated by using time-correlated single-photon counting (TCSPC) detection. The spatial resolution of the developed STED instrument was measured by imaging monodispersed 40-nm fluorescent beads and then determining their fwhm, and was 36 ± 9 and 40 ± 10 nm in the X and Y coordinates, respectively. The same beads measured by confocal microscopy were 450 ± 50 and 430 ± 30 nm, which is larger than the diffraction limit of light due to underfilling the microscope objective. Underfilling the objective and time gating the signal were necessary to achieve themore »« less
https://doi.org/10.1021/jp303912p

Similar Records

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

Abstract

Citation Formats

What Is the Best Method to Fit Time-Resolved Data? A Comparison of the Residual Minimization and the Maximum Likelihood Techniques As Applied to Experimental Time-Correlated, Single-Photon Counting Data journal, February 2016

The Number of Accumulated Photons and the Quality of Stimulated Emission Depletion Lifetime Images journal, March 2014

Subdiffraction, Luminescence-Depletion Imaging of Isolated, Giant, CdSe/CdS Nanocrystal Quantum Dots journal, February 2013

Supercontinuum Stimulated Emission Depletion Fluorescence Lifetime Imaging journal, June 2012

Towards multi-exponential analysis in optically stimulated luminescence journal, April 2010

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves journal, December 1991

Clarification of the use of CHI-square and likelihood functions in fits to histograms journal, April 1984

Data analysis in the shot noise limit. 1. Single parameter estimation with Poisson and normal probability density functions journal, November 1989

Data analysis in the shot noise limit. 2. Methods for data regression journal, November 1989

Comparison between time‐correlated single photon counting and fluorescence correlation spectroscopy in single molecule identification journal, March 1998

On the analysis of fluorescence decay kinetics by the method of least-squares journal, June 1974

Better estimates of exponential decay parameters journal, October 1981

Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments journal, January 2001

On the reliability of fluorescence decay data journal, January 1977

Single-Molecule Analysis And Lifetime Estimates Of Heterogeneous Low-Count-Rate Time-Correlated Fluorescence Data journal, September 2011

Efficient maximum likelihood estimator fitting of histograms journal, May 2010

An Experimental Comparison of the Maximum Likelihood Estimation and Nonlinear Least-Squares Fluorescence Lifetime Analysis of Single Molecules journal, May 2001

Comparison of Methods for Rapid Evaluation of Lifetimes of Exponential Decays journal, May 2004

Artefacts in the analysis of temporal response functions measured by photon counting journal, March 2005

Analysis of Fluorescence Decay by the Nonlinear Least Squares Method journal, November 1988

Error Analysis of the Rapid Lifetime Determination Method for Double-Exponential Decays and New Windowing Schemes journal, March 1999

Analysis of fluorescence lifetime data for single Rhodamine molecules in flowing sample streams journal, January 1994

Accurate Analysis of Fluorescence Decays from Single Molecules in Photon Counting Experiments journal, August 2003

Fluorescence Instrument Response Standards in Two-Photon Time-Resolved Spectroscopy journal, August 2010

Testing Fluorescence Lifetime Standards using Two-Photon Excitation and Time-Domain Instrumentation: Rhodamine B, Coumarin 6 and Lucifer Yellow journal, May 2014

The photophysics of rhodamine B journal, January 1982

Photophysical properties of laser dyes: picosecond laser flash photolysis studies of Rhodamine 6G, Rhodamine B and Rhodamine 101 journal, January 1993

Wavelength dependence of timing properties of the XP 2020 photomultiplier journal, December 1978

Wavelength dependence of the time resolution of high-speed photomultipliers used in single-photon timing experiments journal, January 1976

Systematic errors in χ2-fitting of Poisson distributions journal, March 1996

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part I journal, July 1928

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part II journal, December 1928

A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments journal, December 2018

Coumarin‐based Fluorescent Probes for Selectively Targeting and Imaging the Endoplasmic Reticulum in Mammalian Cells journal, August 2018

What Is the Best Method to Fit Time-Resolved Data? A Comparison of the Residual Minimization and the Maximum Likelihood Techniques As Applied to Experimental Time-Correlated, Single-Photon Counting Data
journal, February 2016

The Number of Accumulated Photons and the Quality of Stimulated Emission Depletion Lifetime Images
journal, March 2014

Subdiffraction, Luminescence-Depletion Imaging of Isolated, Giant, CdSe/CdS Nanocrystal Quantum Dots
journal, February 2013

Supercontinuum Stimulated Emission Depletion Fluorescence Lifetime Imaging
journal, June 2012

Towards multi-exponential analysis in optically stimulated luminescence
journal, April 2010

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves
journal, December 1991

Clarification of the use of CHI-square and likelihood functions in fits to histograms
journal, April 1984

Data analysis in the shot noise limit. 1. Single parameter estimation with Poisson and normal probability density functions
journal, November 1989

Data analysis in the shot noise limit. 2. Methods for data regression
journal, November 1989

Comparison between time‐correlated single photon counting and fluorescence correlation spectroscopy in single molecule identification
journal, March 1998

On the analysis of fluorescence decay kinetics by the method of least-squares
journal, June 1974

Better estimates of exponential decay parameters
journal, October 1981

Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments
journal, January 2001

On the reliability of fluorescence decay data
journal, January 1977

Single-Molecule Analysis And Lifetime Estimates Of Heterogeneous Low-Count-Rate Time-Correlated Fluorescence Data
journal, September 2011

Efficient maximum likelihood estimator fitting of histograms
journal, May 2010

An Experimental Comparison of the Maximum Likelihood Estimation and Nonlinear Least-Squares Fluorescence Lifetime Analysis of Single Molecules
journal, May 2001

Comparison of Methods for Rapid Evaluation of Lifetimes of Exponential Decays
journal, May 2004

Artefacts in the analysis of temporal response functions measured by photon counting
journal, March 2005

Analysis of Fluorescence Decay by the Nonlinear Least Squares Method
journal, November 1988

Error Analysis of the Rapid Lifetime Determination Method for Double-Exponential Decays and New Windowing Schemes
journal, March 1999

Analysis of fluorescence lifetime data for single Rhodamine molecules in flowing sample streams
journal, January 1994

Accurate Analysis of Fluorescence Decays from Single Molecules in Photon Counting Experiments
journal, August 2003

Fluorescence Instrument Response Standards in Two-Photon Time-Resolved Spectroscopy
journal, August 2010

Testing Fluorescence Lifetime Standards using Two-Photon Excitation and Time-Domain Instrumentation: Rhodamine B, Coumarin 6 and Lucifer Yellow
journal, May 2014

The photophysics of rhodamine B
journal, January 1982

Photophysical properties of laser dyes: picosecond laser flash photolysis studies of Rhodamine 6G, Rhodamine B and Rhodamine 101
journal, January 1993

Wavelength dependence of timing properties of the XP 2020 photomultiplier
journal, December 1978

Wavelength dependence of the time resolution of high-speed photomultipliers used in single-photon timing experiments
journal, January 1976

Systematic errors in χ2-fitting of Poisson distributions
journal, March 1996

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part I
journal, July 1928

On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part II
journal, December 1928

A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments
journal, December 2018

Coumarin‐based Fluorescent Probes for Selectively Targeting and Imaging the Endoplasmic Reticulum in Mammalian Cells
journal, August 2018