Analysis of time-correlated single photon counting data: a comparative evaluation of deterministic and probabilistic approaches

Abstract

We review various methods for analysing time-resolved fluorescence data acquired using the time-correlated single photon counting method in an attempt to evaluate their benefits and limitations. We have applied these methods to both experimental and simulated data. The relative merits of using deterministic approaches, such as the commonly used iterative reconvolution method, and probabilistic approaches, such as the smoothed exponential series method, the maximum entropy method and recently proposed basis pursuit denoising (compressed sensing) method, are outlined. In particular, we show the value of using multiple methods to arrive at the most appropriate choice of model. We show that the use of probabilistic analysis methods can indicate whether a discrete component or distribution analysis provides the better representation of the data.

Site-Directed Fluorescence Approaches for Dynamic Structural Biology of Membrane Peptides and Proteins

“…Therefore, fitting the fluorescence intensity decay data to a probability distribution of lifetimes is judicious than conventional fitting of fluorescence decay curves to a sum of discrete exponentials. This model-independent, probability distribution analysis is known as Maximum Entropy Method (MEM), which maximizes the entropy while minimizing the χ 2 has been widely used for analysing fluorescence lifetime distribution (Brochon, 1994; Esposito et al, 2015; Smith et al, 2017; Krishnamoorthy, 2018a).…”

Spectral Dependencies of the Stretched Exponential Dispersion Factor and Photoluminescence Quantum Yield as a Common Feature of Nanocrystalline Si

“…However, deterministic approaches (when a function with a given shape is applied for fitting) are a priori biased, i.e., the recovered distribution depends on the applied model. Alternatively, one can try a probabilistic approach (no a priori knowledge on the distribution shape) to unbiasedly obtain the distribution of decay constants . To our best knowledge, in the past, there were only a few such attempts related to Si NCs that are probably due to the complexity of inverse Laplace transform with multiple solutions (Section ).…”

“…Alternatively, one can try a probabilistic approach (no a priori knowledge on the distribution shape) to unbiasedly obtain the distribution of decay constants. [39] To our best knowledge, in the past, there were only a few such attempts [20,40] related to Si NCs that are probably due to the complexity of inverse Laplace transform with multiple solutions (Section 5).…”

“…To select one representative image from this so-called "feasible set" of images, a regularization algorithm can be applied. An overview on the development of regularization approaches was recently published by Smith et al [39] One of the most powerful approaches is still MEM that minimizes the entropy of a given distribution. In this article, the data were analyzed with open-source code [41,66] MEMExp 5.0 that uses hybrid MEM/NLS (MEM with nonlinear least squares).…”

Data analysis in transient electronic spectroscopy – an experimentalist's view

“…As such, a (brief) comparison between the methods and a guide of when they are useful to use is presented here. A more detailed discussion has recently been presented by Smith et al [134] The Tikhonov regulariser, as discussed, assumes that the noise and fit parameters are normally distributed. If this assumption is known to hold it may be advantageous to use this method as due to the augmented matrix implementation it is both fast and easy -however it will have difficulty separating out closely spaced kinetic contributions and so if one does not anticipate a broad distribution of rates it may not be of use.…”