Generalization of DT equations for time dependent sources.

Area of Science:

• Physics
• Electrical Engineering
• Photonics

Background:

• Dead time (DT) is a critical parameter in single-photon avalanche diode (SPAD) detectors, affecting count accuracy.
• Existing DT models are often limited to constant rate sources, failing to address time-dependent scenarios.
• Accurate modeling of DT losses is essential for precise photon detection and timing measurements.

Purpose of the Study:

• To introduce novel equations for modeling dead time (DT) losses in paralyzable, non-paralyzable, and hybrid SPAD models.
• To demonstrate that these new equations encompass existing models for constant rate sources.
• To provide a method for correcting DT losses in time-dependent source scenarios.

Main Methods:

• Development of new mathematical equations for three distinct DT models (paralyzable, non-paralyzable, hybrid).
• Validation through Monte Carlo simulations comparing equation predictions against DT model behaviors.
• Experimental validation using a passive quenched SPAD (hybrid DT losses) and an active quenched SPAD (DT loss-free).

Main Results:

• Excellent agreement was observed between the predictions of the new equations and Monte Carlo simulation results for all three DT models.
• The new equations were shown to include previously established equations for constant rate sources.
• Successful experimental validation of the new hybrid DT equation was achieved.

Conclusions:

• The presented equations provide a unified and accurate framework for modeling DT losses in SPADs under time-dependent conditions.
• These equations enable effective correction of DT losses, improving measurement accuracy.
• The findings have significant implications for applications requiring precise photon counting with SPADs.