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.
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