The statistics for the detection of light by nonideal photomultipliers

The detection of low-level optical frequency radiation, such as that encountered in laser communication systems, is often accomplished with a photomultiplier tube. The photomultiplication process, however, is itself a random process. In this paper a formula for the statistics of the number of electrons after
k
stages is derived in the form of a recurrence relation. A Polya distribution is assumed as a model for each stage, and the probability of error for a laser communication system is examined in terms of the Polya
b
-parameter and the gain per stage. A simple closed-form expression for the decibel loss as a function of the photomultiplier parameters is also derived.