In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is imaged by fluorescence microscopy. As accuracy in parameter estimation is closely related to the Fisher information matrix, we first give a general expression of the Fisher information matrix for the estimated parameters for a single object moving in three-dimensional (3D) space. Explicit Cramér-Rao lower bound (CRLB) expressions are then obtained from the Fisher information matrix for a single object moving in the two-dimensional (2D) focus plane with the object trajectory being either linear or circular. We also investigate how extraneous noise sources, pixelation, parameters of the detection system and parameters of the trajectory affect the limit of the accuracy. The results obtained in this paper provide insights that enable the experimentalists to optimize their experimental setups for tracking single molecules in order to achieve the best possible accuracy. They are also applicable to the general problem of tracking an object using quantum limited detectors.

中文翻译：

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荧光显微镜成像的移动单分子参数估计精度的限制

在本文中，我们考虑了估计运动单分子的位置和其他属性的准确性问题，该分子的轨迹通过荧光显微镜成像。由于参数估计的准确性与Fisher信息矩阵密切相关，我们首先给出了在三维（3D）空间中移动的单个物体的估计参数的Fisher信息矩阵的一般表达式。然后从 Fisher 信息矩阵中获得在二维 (2D) 焦平面中移动的单个对象的显式 Cramér-Rao 下限 (CRLB) 表达式，对象轨迹为线性或圆形。我们还研究了外来噪声源、像素化、检测系统参数和轨迹参数如何影响精度极限。本文中获得的结果提供了见解，使实验人员能够优化他们的实验设置以跟踪单个分子，以实现最佳可能的准确性。它们也适用于使用量子受限探测器跟踪物体的一般问题。