Analytical and Simulation-Based Evaluation of Signal-to-Background-Noise Ratio in Photon Detection Systems with Front-End Circuit

This paper presents an analytical and MATLAB-based simulation model for evaluating background current variance and Signal-to-Background Noise Ratio (SBNR) in photon detection systems. The model integrates stochastic photon arrival statistics with a pulse shape derived from a realistic mixed-signal front-end, enabling direct investigation of how pulse fall time τ and photon flux influence noise performance. A closed-form expression for background variance is derived under the assumption of independent arrivals and triangular pulses, and is validated through extensive simulations spanning a range of fall times and background photon rates. The SBNR is then formulated by considering coherent signal photon accumulation—enabled by a laser FWHM much shorter than τ—and is shown to closely match simulation results across diverse pulse fall time conditions.