Reconstructing photon-number distributions for ultra-low-flux optical fields

As a byproduct of cellular metabolism, the emission of endogenous photons is a promising biomarker for physiological processes. However, direct biological applications are, so far, challenging because of the very low intensity and the intrinsically non-stationary characteristics of this photon emission. Here, we outline and demonstrate the efficacy of a statistical procedure for reconstructing the real photon-number distributions from the photocounts provided by a single-photon detector. We develop a staged model-based regularized maximum-likelihood method capable of addressing this inverse problem in the few-photon regime. When applied to an ultra-low laser flux, the method recovers the expected Poisson statistics, whereas in the case of weak biophoton emission, the reconstruction of windowed counted photons reveals deviations from Poisson behavior in the unfolded photon-number distributions over time, underlying the typical non-stationary dynamics of biological emission.