Inherent stochasticity, noise and limits of detection in continuous and time-gated fluorescence systems

We present a model for the noise and inherent stochasticity of fluorescence signals in both continuous wave (CW) and time-gated (TG) conditions. When the fluorophores are subjected to an arbitrary excitation photon flux, we apply the model and compute the evolution of the probability mass function (pmf) for each quantum state comprising a fluorophore's electronic structure, and hence the dynamics of the resulting emission photon flux. Both the ensemble and stochastic models presented in this work have been verified using Monte Carlo molecular dynamic simulations that utilize the Gillespie algorithm. The implications of the model on the design of biomolecular fluorescence detection systems are explored in three relevant numerical examples. For a given system, the quantum-limited signal-to-noise ratio (QSNR) and limits of detection are computed to demonstrate how key design tradeoffs are quantified. We find that as systems scale down to micro- and nano- dimensions, the interplay between the fluorophore's photophysical qualities and use of CW or TG has ramifications on optimal design strategies when considering optical component selection, measurement speed, and system energy requirements. While CW systems remain a gold standard, TG systems can be leveraged to overcome cost and system complexity hurdles when paired with the appropriate fluorophore.