Statistics of electron-multiplying charge-coupled devices

Electron-multiplying charge-coupled devices are efficient imaging devices for low-surface-brightness ultraviolet astronomy from space. The large amplification allows photon counting (PC), the detection of events versus nonevents. This paper provides the statistics of the observation process, the photon-counting process, the amplification process, and the compression. The expression for the signal-to-noise of PC is written in terms of the polygamma function. The optimal exposure time is a function of the clock-induced charge. The exact distribution of amplification process is a simple-to-compute powered matrix. The optimal cutoff for comparing to the read noise is close to a strong function of the read noise and a weak function of the electron-multiplying gain and photon rate. A formula gives the expected compression rate.