Photon Counting Distribution for Arrays of Single-Photon Detectors

TL;DR

This paper derives an efficient photon counting distribution model for arrays of single-photon detectors, accounting for efficiency and dark counts, and analyzes how array size affects photon resolution accuracy.

Contribution

It introduces a computationally efficient expression for photon counting distribution in detector arrays, considering key detector parameters and error analysis.

Findings

High quantum efficiency is essential for resolving multiple photons accurately.

Array size must scale quadratically with the number of photons for reliable resolution.

Optimal array size minimizes error in photon detection.

Abstract

We derive a computationally efficient expression of the photon counting distribution for a uniformly illuminated array of single photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark-count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of a ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a hand-full of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters and we compute optimal size of the array that yields the smallest error.