Least squares arrival time estimators for photons detected using a photomultiplier tube

The optimal arrival time estimators for single and multiple photons arriving at the surface of a photomultiplier tube (PMT) are developed. The optimal timing estimator considered is a weighted and nonlinear least squares estimate of the detection time for a high-gain PMT with Gaussian statistics. The least squares estimator is constructed using the mean and covariance function of the photomultiplier output for different arrival times. The root-mean-square error for the least squares arrival time estimator was calculated and compared with the performance of other common timing estimators, including the first photoelectron timing estimators, using a Burle/RCA 8850 PMT. The weighted least square arrival time estimator has been shown to outperform the leading edge and peak timing estimators.<>