  Super-resolution microscopy is rapidly gaining importance as an analytical
tool in the life sciences. A compelling feature is the ability to label
biological units of interest with fluorescent markers in living cells and to
observe them with considerably higher resolution than conventional microscopy
permits. The images obtained this way, however, lack an absolute intensity
scale in terms of numbers of fluorophores observed. We provide an elaborate
model to estimate this information from the raw data. To this end we model the
entire process of photon generation in the fluorophore, their passage trough
the microscope, detection and photo electron amplification in the camera, and
extraction of time series from the microscopic images. At the heart of these
modeling steps is a careful description of the fluorophore dynamics by a novel
hidden Markov model that operates on two time scales (HTMM). Besides the
fluorophore number, information about the kinetic transition rates of the
fluorophore's internal states is also inferred during estimation. We comment on
computational issues that arise when applying our model to simulated or
measured fluorescence traces and illustrate our methodology on simulated data.
