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In fluorescence fluctuation polarization sensitive experiments, the limitations associated with detecting the rotational timescale are usually eliminated by applying fluorescence correlation spectroscopy analysis. In this paper, the variance of the time-averaged fluorescence intensity extracted from the second moment of the measured fluorescence intensity is analyzed in the short time limit, before fluctuations resulting from rotational diffusion average out. Since rotational correlation times of fluorescence molecules are typically much lower than the temporal resolution of the system, independently of the time bins used, averaging over an ensemble of time-averaged trajectories was performed in order to construct the time-averaged intensity distribution, thus improving the signal-to-noise ratio. Rotational correlation times of fluorescein molecules in different viscosities of the medium within the range of the anti-bunching time (1-10 ns) were then extracted using this method.

In order to maximize the signal-to-noise ratio for a given temporal-resolution of typical photon counting single-molecule polarization-sensitive system, this talk suggests examining the rate of convergence and the variance of the time-averaged measured fluorescence intensity.

A general framework to include fluctuations in the single molecule fluorescence intensity (FI) signal due to random changes in molecule dipole orientation was introduced at Optics Express (21, 2007). By assuming continuous changes in dipole orientation described by Brownian rotational diffusion, this research derives the probability density function (PDF) equation of FI fluctuations. Solution of the proposed equation for several limiting cases and different correlation times yields the short time behavior of FI fluctuations. Monte Carlo simulations results, in accordance with those found in theory will be presented during our talk.

We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.