A Complementary Approach for Characterizing Dark Count Rate in First-Photon-Gated Single-Photon Detectors

In single-photon detection, dark count represents a critical limitation, particularly for high-sensitivity applications. Conventional estimators based on the binary per-gate observable become ill-conditioned when the dark count per-gate probability approaches unity, a situation common in first-photon-gated detectors with extended gate width. This work proposes a complementary characterization method based on the statistical expectation of dark count arrival time. This approach captures the cumulative temporal behavior of dark count across multiple gating cycles, providing a more accurate estimation of the dark count rate. Both numerical simulations and experimental results demonstrate that our method yields significantly more stable and precise measurements compared to the conventional approach. Specifically, while the conventional method introduces errors up to ±4% at larger gate widths, the proposed timing-based method converges to a significantly lower residual error of approximately −0.17%. These findings offer a promising route to enhance the characterization and performance of first-photon-gated single-photon detectors in practical applications.