A theory of optimum photon-counting detectors

Abstract

It has been shown that the matched filter and correlation type of receiver provides the maximum detection probability for strong optical signals in the presence of thermal and quantum noise. The transmitted wave form is allowed to take any of the L pre-specified values in each observation time corresponding to one of the r dimensions of each transmitted waveform P_t, i = 0, 1,..., M -1. An upper limit on the average error probability of all such multiphoton-count optical systems haa been derived. The problem of efficient signal selection has been considered in the light of the above limit. The special case of a two-photon-count system has been studied and clear superiority of the L-lovel signals has been established.