Cumulant-based formulation of higher-order fluorescence correlation spectroscopy

TL;DR

This paper develops a cumulant-based mathematical framework for higher-order fluorescence correlation spectroscopy, providing detailed derivations and variance calculations to enhance analysis of diffusing and reacting molecules.

Contribution

It introduces a novel cumulant-based formulation for higher-order FCS, including derivations of correlation functions and variance up to the fourth order.

Findings

Derived factorized correlation functions for diffusing molecules

Calculated variance of correlation functions up to fourth order

Reviewed multivariate cumulants and photon counting distributions

Abstract

Extended derivations regarding the cumulant-based formulation of higher-order fluorescence correlation spectroscopy (FCS) are presented. First, we review multivariate cumulants and their relation to photon counting distributions in single and multi-detector experiments. Then we derive the factorized correlation functions which describe system of diffusing and reacting molecules using two independent approaches. Finally, we calculate the variance of these correlation functions up to the fourth order.