  In quantum communication systems, the precise estimation of the detector's
response to the incoming light is necessary to avoid security breaches. The
typical working regime uses a free-running single-photon avalanche diode in
combination with attenuated laser pulses at telecom wavelength for encoding
information. We demonstrate the validity of an analytical model for this regime
which considers the effects of dark counts and dead time on the measured count
rate. For the purpose of gaining a better understanding of these effects, the
photon detections were separated from the dark counts via a software-induced
gating mechanism. The model was verified by experimental data for mean photon
numbers covering three orders of magnitude as well as for laser repetition
frequencies below and above the inverse dead time. Consequently, our model
would be of interest for predicting the detector response not only in the field
of quantum communications, but also in any other quantum physics experiment
where high detection rates are needed.
