  Fluorescence microscopy is of vital importance for understanding biological
function. However most fluorescence experiments are only qualitative inasmuch
as the absolute number of fluorescent particles can often not be determined.
Additionally, conventional approaches to measuring fluorescence intensity
cannot distinguish between two or more fluorophores that are excited and emit
in the same spectral window, as only the total intensity in a spectral window
can be obtained. Here we show that, by using photon number resolving
experiments, we are able to determine the number of emitters and their
probability of emission for a number of different species, all with the same
measured spectral signature. We illustrate our ideas by showing the
determination of the number of emitters per species and the probability of
photon collection from that species, for one, two, and three otherwise
unresolvable fluorophores. The convolution Binomial model is presented to model
the counted photons emitted by multiple species. And then the
Expectation-Maximization (EM) algorithm is used to match the measured photon
counts to the expected convolution Binomial distribution function. In applying
the EM algorithm, to leverage the problem of being trapped in a sub-optimal
solution, the moment method is introduced in finding the initial guess of the
EM algorithm. Additionally, the associated Cram\'er-Rao lower bound is derived
and compared with the simulation results.
