Abstract
The mathematical formalism of generating functionals was adopted for the unified statistical description of a typical experiment in fluorescence fluctuation spectroscopy. The generating functionals formalism leads to a set of functional equations, linking the statistical characteristics of the excitation and detected photons via the characteristics of a molecular system. The statistical characteristics of the detected photons can then be obtained in a straightforward and consistent way. We particularly show how characteristics such as the photocount correlation function and the probability distribution of the number of photocounts per detection interval can be derived based on the developed theory. We further demonstrate that the probability density distribution of the first and single photocount time occurrences in the detection interval also can be used for probing molecular behavior. The presented approach is applicable to a broad range of experimental configurations (continuous and pulsed excitation, one-photon and two-photon laser excitation, scanning laser excitation) and molecular movements (diffusion in two and three dimensions, fluid flows).
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