A High-Accuracy Single-Photon Time-Interval Measurement in Mega-Hz Detection Rates With Collaborative Variance Reduction: Theoretical Analysis and Realization Methodology

An almost all-digital time-to-digital converter possessing sub-picosecond resolution, scalable dynamic range, calibratable linearity, high noise-immunity, and fast conversion-rates can be achieved by a stochastic random sampling-and-averaging approach with the proposed collaborative variance reduction (VR) technique for a wide range of time-correlated single-photon counting applications. This paper presents detailed theoretical analysis and behavior-model verifications of both self-antithetic and control-variate VR techniques to enhance the conversion-rate of an asynchronous RSA-based TDC up to 1.5 MHz with 12-ENOB accuracy, 0.36-pJ/step energy efficiency, and 23% power overhead. Also, the conversions of the mathematical closed-form expressions into digital signal-processing implementations are derived and demonstrated for the forthcoming silicon-photonics integrated-circuit realization.