A Practical Calibration Method for Correcting Count-Rate Nonlinearity in Free-Running Silicon SPADs

Single-photon avalanche diodes (SPADs) operated in free-running mode exhibit three major nonideal effects: dead time, recovery time, and afterpulsing. Together, these effects cause the measured count rate to deviate from the true incident photon rate, degrade photon counting accuracy, and limit the linear dynamic range of the detector. Here, we establish a joint correction model for dead time, recovery time, and afterpulsing, based on a nonhomogeneous Poisson process, and propose a staged decoupling calibration strategy spanning from low to high count rates to systematically extract the afterpulse probability, dead time, and recovery-time constant. The proposed model is benchmarked on a commercial silicon SPAD module. Over a dynamic range of 550 kHz to 30 MHz, the mean absolute percentage error (MAPE) between model predictions and factory-provided correction factors is 2.74%, with a coefficient of determination (R2) of 0.985; relative deviations remain within 3% at low and moderate count rates. The proposed scheme requires only a continuous wave (CW) light source and a single channel TDC, eliminating the need for pulsed sources and external gated synchronization. It therefore provides a practical calibration route for commercial free-running silicon SPAD modules that require rapid on-site nonlinearity correction over a wide dynamic range. The demonstration and benchmark are performed on one commercial module, and extension to other low-afterpulse silicon SPADs is expected after local calibration and verification of the afterpulse-template separability conditions.