The high quantum efficiency of the charge-coupled device (CCD) has rendered it the imaging technology of choice in diverse applications. However, under extremely low light conditions where few photons are detected from the imaged object, the CCD becomes unsuitable as its readout noise can easily overwhelm the weak signal. An intended solution to this problem is the electron-multiplying charge-coupled device (EMCCD), which stochastically amplifies the acquired signal to drown out the readout noise. Here, we develop the theory for calculating the Fisher information content of the amplified signal, which is modeled as the output of a branching process. Specifically, Fisher information expressions are obtained for a general and a geometric model of amplification, as well as for two approximations of the amplified signal. All expressions pertain to the important scenario of a Poisson-distributed initial signal, which is characteristic of physical processes such as photon detection. To facilitate the investigation of different data models, a “noise coefficient” is introduced which allows the analysis and comparison of Fisher information via a scalar quantity. We apply our results to the problem of estimating the location of a point source from its image, as observed through an optical microscope and detected by an EMCCD.

中文翻译：

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用于电子倍增电荷耦合器件的分支过程的 Fisher 信息矩阵

电荷耦合器件 (CCD) 的高量子效率使其成为各种应用中首选的成像技术。然而，在极低光照条件下，从成像对象检测到的光子很少，CCD 变得不合适，因为它的读出噪声很容易压倒微弱的信号。这个问题的一个预期解决方案是电子倍增电荷耦合器件 (EMCCD)，它随机放大获取的信号以消除读出噪声。在这里，我们开发了用于计算放大信号的 Fisher 信息内容的理论，该理论被建模为分支过程的输出。具体来说，Fisher 信息表达式是针对放大的一般模型和几何模型以及放大信号的两个近似获得的。所有表达式都与泊松分布初始信号的重要场景有关，这是物理过程（如光子检测）的特征。为了便于研究不同的数据模型，引入了“噪声系数”，它允许通过标量分析和比较 Fisher 信息。我们将我们的结果应用于从图像估计点源位置的问题，如通过光学显微镜观察并由 EMCCD 检测。