Autocorrelation Bias in Diffuse Correlation Spectroscopy Observable via SPAD Arrays

Diffuse correlation spectroscopy (DCS) is an emerging optical technique for non-invasive cerebral blood flow monitoring. Extraction of the DCS blood flow index typically involves calculating the temporal autocorrelation of the measured light intensity and then fitting its decay to a solution of the correlation diffusion equation. It is well-known that the experimental autocorrelation is a biased estimator of the true autocorrelation. This work explores this phenomenon as it relates to DCS, in particular implementations with single photon avalanche diode arrays (SPAD arrays). After deriving a first-order expression for the bias in DCS, we then quantify its impact as a function of sampling time in both simulation and experiment using SPAD array detection. We then present and explore two bias correction strategies to correct for its impact at fast sampling times (20-200 Hz) and in low-photon regimes.