Statistical Analysis of Silicon Photomultiplier Output Signals.

Area of Science:

• Photonics and Detector Technology
• Statistical Signal Processing
• Optical Sensing

Background:

• Silicon photomultipliers (SiPMs) are advanced single-photon detectors known for compact size and low voltage.
• Their high sensitivity is crucial for detecting low-light optical signals in applications such as ranging and LIDAR.
• The output signal from SiPMs is a complex, non-stationary stochastic process.

Purpose of the Study:

• To develop an analytical solution for the statistical properties of SiPM output signals.
• To investigate the signal waveform characteristics, particularly the rising edge duration.
• To provide insights for optimizing laser pulse design and time-of-arrival estimation algorithms.

Main Methods:

• Utilizing a double-exponential approximation for individual avalanche pulses.
• Deriving analytical solutions for the mean and variance of the stochastic output signal.
• Analyzing the impact of optical pulse shape on the detected signal's rising edge.

Main Results:

• A simplified analytical solution for the mean and variance of the SiPM output signal was obtained.
• It was demonstrated that the detected signal's rising edge is longer than individual avalanche pulses, even for ideal square optical inputs.
• The study provides a method for characterizing the detected waveform.

Conclusions:

• The analytical model accurately describes the statistical behavior of SiPM output signals.
• Understanding the detected waveform is key to improving laser pulse design and signal processing for accurate time-of-arrival estimation.
• The proposed methods were validated experimentally, demonstrating their practical applicability.