Wavelength dependence of timing properties of the XP 2020 photomultiplier

Calligaris, F.; Ciuti, P.; Gabrielli, I.; Giamcomich, R.; Mosetti, Renzo

doi:10.1016/0029-554x(78)90025-3

Cited by 8 publications

(5 citation statements)

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“…The probability that a photon is detected in the j th bin, p j , is proportional to the discrete convolution of the IRF and the model for the fluorescence decay given in eq . where j 0 is given by b = j 0 ϵ. The parameter b describes the linear shift between the instrument response function and the fluorescence decay. ,,, The probability that a photon is detected in the range t 1 ≤ t ≤ t max = t 1024 must be ∑ j p j = 1. We have, therefore …”

Section: Discussionmentioning

confidence: 99%

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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

et al. 2016

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It is often convenient to know the minimum amount of data needed 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 not only for the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. These probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited microscopies. Disciplines Chemistry | Physical Chemistry CommentsThis document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication as Santra, Kalyan, Emily A. Smith, Jacob W. Petrich, and Xueyu Song. ABSTRACTIt 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 twofluorophore mixtures, as a function of the total number of photon counts, in time-correlated, singlephoton 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 statistic...

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Section: Discussionmentioning

confidence: 99%

“…The parameter b describes the linear shift between the instrument response function and the fluorescence decay. 1,3,32,33 The probability that a photon is detected in the range t 1 ≤ t ≤ t max = t 1024 must be ∑ j p j = 1. We have, therefore…”

Section: ■ Materials and Methodsmentioning

confidence: 99%

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

et al. 2016

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“…This shift parameter is necessary because the lower energy ("redder") fluorescence photons travel at a different speed through dispersive optics than the higher energy ("bluer") excitation photons that are used to generate the IRF in a scattering experiment. 1,38,39 The probability that a photon is detected in the range t 1 ≤ t ≤ t max = t 1024 must be ∑ j p j = 1. We therefore have…”

Section: ■ Materials and Methodsmentioning

confidence: 99%

“…The probability that a photon is detected in the j th bin, p j , is proportional to the convolution of the IRF and the model for the fluorescence decay. where j 0 is given by b = j 0 ϵ. b is a linear shift between the instrument response function and the fluorescence decay. This shift parameter is necessary because the lower energy (“redder”) fluorescence photons travel at a different speed through dispersive optics than the higher energy (“bluer”) excitation photons that are used to generate the IRF in a scattering experiment. ,, …”

Section: Methodsmentioning

confidence: 99%

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

et al. 2016

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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 of "photon counts" was approximately 20, 200, 1000, 3000, and 6000 and there were about 2-200 counts at the maxima of the respective decays. Each set of experiments was repeated 50 times to generate the appropriate statistics. Each of the 250 data sets was analyzed by ML and two different RM methods (differing in the weighting of residuals) using in-house routines and compared with a frequently used commercial RM routine. Convolution with a real instrument response function was always included in the fitting. While RM using Pearson's weighting of residuals can recover the correct mean result with a total number of counts of 1000 or more, ML distinguishes itself by yielding, in all cases, the same mean lifetime within 2% of the accepted value. For 200 total counts and greater, ML always provides a standard deviation of <10% of the mean lifetime, and even at 20 total counts there is only 20% error in the mean lifetime. The robustness of ML advocates its use for sparse data sets such as those acquired in some subdiffraction-limited microscopies, such as STED, and, more importantly, provides greater motivation for exploiting the time-resolved capacities of this technique to acquire and analyze fluorescence lifetime data.

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“…This is because linear focused photomultipliers have a major advantage over side-on PMTs as there is a lower transit time dependence on the point of illumination of the photocathode. This has been measured as ∼ 13 ps mm −1 by Calligaris et al (1978) for an XP 2020 photomultiplier.…”

Section: Linear Focused Photomultipliersmentioning

confidence: 99%