Statistics of electron-multiplying charge-coupled devices

EMCCDs are efficient imaging devices for low surface brightness UV astronomy. The large amplification allows photon counting, the detection of events versus non-events. 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 photon counting 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.

电子倍增电荷耦合器件（EMCCDs）是低表面亮度紫外天文学领域的高效成像器件。其高增益特性可实现光子计数，从而区分有效事件与无效事件。本文提供了观测过程、光子计数过程、放大过程及压缩过程的统计特性。光子计数的信噪比表达式以多伽马函数（polygamma function）表示。最优曝光时间是时钟感应电荷（clock-induced charge）的函数。放大过程的精确分布为易于计算的幂矩阵。与读出噪声（read noise）比较的最优阈值强烈依赖于读出噪声，而对电子倍增增益和光子率的依赖较弱。此外，本文还给出了计算预期压缩率的公式。