Study of the Response of Silicon Photomultipliers in Presence of Strong Cross-talk Noise

Silicon Photomultipliers (SiPM) are interesting detectors for beam diagnostics applications due to their reduced dimensions and costs, and higher photon detection efficiency. Possible applications include longitudinal beam profile measurements by synchrotron light imaging, detection of optical transition radiation for energy spectrum measurements and medical imaging. However, quantitative measurement with SiPMs are jeopardized by the systematic reading error due to Optical Cross-talk (OC), i.e. optical coupling between neighbouring diodes in the array. OC results in overestimation of the impinging light level, and reflects the probability of a triggered avalanche creating a photon of suitable energy and direction to fire a second avalanche in another diode. In this paper, we derive a generalized response distribution for SiPM in presence of OC noise, which overcomes the limitations of assumptions currently made in literature and provides a correction of the SiPM response distribution valid for arbitrary large levels of OC.