Generalization of DT equations for time dependent sources

Abstract

New equations for paralyzable, non paralyzable and hybrid DT models, valid for any time dependent sources are presented. We show how such new equations include the equations already used for constant rate sources, and how it's is possible to correct DT losses in the case of time dependent sources. Montecarlo simulations were performed to compare the equations behavior with the three DT models. Excellent accordance between equations predictions and Montecarlo simulation was found. We also obtain good results in the experimental validation of the new hybrid DT equation. Passive quenched SPAD device was chosen as a device affected by hybrid DT losses and active quenched SPAD with 50 ns DT was used as DT losses free device.

Keywords: Dead Time correction; Single Photon Avalanche Diode; time dependent sources.

Figure 1.

(A) Structure of the two DT produced in a hybrid DT model. (B) Time intervals rate that produces losses into the following i-th instant and type of DT losses actuated.

Figure 2.

Histograms of rate vs. time; blue circle, simulated photon source rate; dark green square, P-DT model simulation; red triangle, NP-DT model simulation; cyan asterisk, hybrid DT model simulation.

Figure 3.

(A) black, true count rate, measured with active quenched SPAD; blue, measured count rate that suffer Hybrid DT losses (passive quenched SPAD). (B) Comparison between calculated rate and measured one; blue, calculated with Equation (12); black, calculated with Equation (11).