Statistical Treatment of Photon/Electron Counting: Extending the Linear Dynamic Range from the Dark Count Rate to Saturation
Statistical Treatment of Photon/Electron Counting: Extending the Linear Dynamic Range from the Dark Count Rate to Saturation
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DOI：
10.1021/ac102219c
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发表时间：
2010-12-15
影响因子：
7.4
通讯作者：
Simpson, Garth J.
中科院分区：
文献类型：
--
作者：
Kissick, David J.;Muir, Ryan D.;Simpson, Garth J.
提出了一种简单的光子计数方法，在单个光电倍增管探测器上实现了7个数量级的线性动态范围。在传统的光子/电子计数方法中，线性范围由计数事件的二项式分布测量与光子/电子的潜在泊松分布之间的一致性决定。通过明确地考虑作为存在的光子数和光子的泊松分布的函数的电压瞬变中的对数正态概率分布，对于给定阈值的观测计数可以与远远超出常规限制的光子的平均数相关。解析表达式推导出相关的计数和光子，扩展的线性范围的平均值类似于11个光子同时到达一个单一的阈值。这些表达式可以数值计算的多个阈值扩展的线性范围的饱和点的PMT。峰值电压分布的实验结果表明，遵循泊松加权和的对数正态分布，可以都来自单个光电子电压峰高分布。将从该方法得到的LDR与传统的单光子计数（SPC）和通过模数转换（ADC）的信号平均进行比较。
An experimentally simple photon counting method is demonstrated providing 7 orders of magnitude in linear dynamic range (LDR) for a single photomultiplier tube (PMT) detector. In conventional photon/electron counting methods, the linear range is dictated by the agreement between the binomially distributed measurement of counted events and the underlying Poisson distribution of photons/electrons. By explicitly considering the log-normal probability distribution in voltage transients as a function of the number of photons present and the Poisson distribution of photons, observed counts for a given threshold can be related to the mean number of photons well beyond the conventional limit. Analytical expressions are derived relating counts and photons that extend the linear range to an average of similar to 11 photons arriving simultaneously with a single threshold. These expressions can be evaluated numerically for multiple thresholds extending the linear range to the saturation point of the PMT. The peak voltage distributions are experimentally shown to follow a Poisson weighted sum of log-normal distributions that can all be derived from the single photoelectron voltage peak-height distribution. The LDR that results from this method is compared to conventional single photon counting (SPC) and to signal averaging by analog to digital conversion (ADC).