Binning method for artifact-free time-tag based correlation function calculations

Correlation functions are nowadays routinely computed using time-tagged photon information instead of a hardware autocorrelator. The algorithm developed by Laurence et al. [Opt. Lett.31, 829 (2006)10.1364/OL.31.000829] is a powerful example. Despite its ease of implementation and fast computation process, it presents a prevalent noisy feature at the short time-lag range when computed on commonly used logarithmically spaced bins. We identified that arbitral logarithmic spacing produces the mismatch between the edges of generated bins and acquisition frequency, resulting in an aliasing artifact at the short time-lag range of the correlation function. We introduce a binning method that considers the acquisition frequency during the bin generation. It effectively eliminates the artifact and improves the accuracy of the autocorrelation. Applying the binning method herein can be particularly crucial when one extracts photophysical processes from fluorescence correlation spectroscopy or the diffusion coefficient of nanoparticles from dynamic light scattering at the time range below 10^-5s lag time.