Multifocal microscopy affords fast acquisition of microscopic 3D images. This is made possible using a multifocal grating optic; however, this induces chromatic dispersion effects in the point spread function, impacting image quality and single-molecule localization precision. To minimize this effect, researchers use narrow-band emission filters. However, the choice of optimal emission filter bandwidth in such systems is, thus far, unclear. This work presents a theoretical framework to investigate how the localization precision of a point emitter is affected by the emission filter bandwidth. We calculate the Cramér–Rao lower bound for the 3D position of a single emitter imaged using a chromatic multifocal microscope. Simulation results for a range of emission bandwidth systems show that in the absence of background photons and detector noise localization improves for broader emission filter bandwidth due to increased photon throughput despite a larger chromatic dispersion. When realistic background and measurement noise sources are considered in the imaging process being simulated, there is an optimal bandwidth (not the broadest emission filter bandwidth) which provides the highest localization precision. This study provides a framework for optimally designing chromatic multifocal optics and serves as a theoretical foundation for interpretting results.

中文翻译：

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彩色多焦成像中的定位精度

多焦点显微镜可快速获取显微 3D 图像。使用多焦点光栅光学器件可以实现这一点；然而，这会在点扩散函数中引起色散效应，影响图像质量和单分子定位精度。为了尽量减少这种影响，研究人员使用窄带发射滤波器。然而，迄今为止，此类系统中最佳发射滤波器带宽的选择尚不清楚。这项工作提出了一个理论框架来研究点发射器的定位精度如何受发射滤波器带宽的影响。我们计算了使用彩色多焦点显微镜成像的单个发射器的 3D 位置的 Cramér-Rao 下限。一系列发射带宽系统的仿真结果表明，在没有背景光子和探测器噪声定位的情况下，尽管色散较大，但由于光子吞吐量增加，因此可以改善更宽的发射滤波器带宽。当在模拟成像过程中考虑现实背景和测量噪声源时，有一个最佳带宽（不是最宽的发射滤波器带宽）可提供最高的定位精度。本研究为优化设计彩色多焦光学器件提供了一个框架，并作为解释结果的理论基础。当在模拟成像过程中考虑现实背景和测量噪声源时，有一个最佳带宽（不是最宽的发射滤波器带宽）可提供最高的定位精度。本研究为优化设计彩色多焦光学器件提供了一个框架，并作为解释结果的理论基础。当在模拟成像过程中考虑现实背景和测量噪声源时，有一个最佳带宽（不是最宽的发射滤波器带宽）可提供最高的定位精度。本研究为优化设计彩色多焦光学器件提供了一个框架，并作为解释结果的理论基础。