Detection Statistics in Geiger-Mode Avalanche Photodiode Quad-Cell Arrays With Crosstalk and Dead Time

The detection statistics of Geiger-mode photodetector subarrays with a combination of reset-time blocking loss and optical crosstalk are investigated. Closed-form expressions are obtained for the means and covariances of the numbers of counts in 2 × 2 subarrays (quad cells) used in Shack-Hartmann wavefront sensors. The predicted wavefront sensing precision is compared with that obtained with a charge-coupled device-based wavefront sensor with readout noise. The results of the theory are also used to predict photon transfer curves for the Geiger-mode device and these are compared with experiment.