A Bayesian Model to Count the Number of Two-State Emitters in a Diffraction Limited Spot

We address the problem of inferring the number of independently blinking fluorescent light emitters, when only their combined intensity contributions can be observed. This problem occurs regularly in light microscopy of objects smaller than the diffraction limit, where one wishes to count the number of fluorescently labeled subunits. Our proposed solution directly models the photophysics of the system, as well as the blinking kinetics of the fluorescent emitters as a fully differentiable hidden Markov model, estimating a posterior distribution of the total number of emitters. We show that our model is more accurate and increases the range of countable subunits by a factor of 2 compared to current state-of-the-art methods. Furthermore, we demonstrate that our model can be used to investigate the effect of blinking kinetics on counting ability and therefore can inform optimal experimental conditions.