  This publication focuses on the study of silicon photomultipliers (SiPMs) in
view of a reconstruction of the incident photon flux in the regime of highly
non-linear response. SiPMs are semiconductor based light detectors compiled of
avalanche photodiodes operated in Geiger mode. They are both mechanically and
optically very robust and have a high gain and photon detection efficiency.
These features make them ideal photonsensors in a wide range of applications
and they are nowadays replacing conventional photomultiplier tubes in many
experiments. The cellular structure of SiPMs where each cell can only detect
one photon at a time results in a non-linear dynamic range limiting the
possible applications.
  We studied a commonly used SiPM model based on an equivalent electronic
circuit that allows the simulation of the SiPM response in many situations.
Dedicated measurements with two consecutive light pulses prove its
applicability. By adapting the model to the measurements, intrinsic parameters
of the SiPM such as quenching resistance or diode capacitance can be
determined. With the obtained intrinsic parameters, the model correctly
describes the recharge behavior of the SiPM cells.
  Based on the model, an algorithm was developed to correct the non-linearity
of the dynamic range of SiPMs. As the model contains full information on the
recharge of the SiPM cells, the effects leading to the non-linearity can be
corrected for. The algorithm exploits the time information in the measured
voltage signal and reconstructs the number of incident photons. It has shown an
excellent performance and allows to increase the dynamic range with only 10%
deviation from linearity by at least two orders of magnitude.
