First discovered by Ernest Abbe in 1873, the resolution limit of a far-field microscope is considered determined by the numerical aperture and wavelength of light, approximately $\lambda$/2NA. With the advent of modern fluorescence microscopy and nanoscopy methods over the last century, it is recognized that Abbe's resolution definition alone could not solely characterize the resolving power of the microscope system. To determine the practical resolution of a fluorescence microscope, photon noise remains one essential factor yet to be incorporated in a statistics-based theoretical framework. Techniques such as confocal allow trading photon noise in gaining its resolution limit, which may increase or worsen the resolvability towards fluorescently tagged targets. Proposed as a theoretical measure of fluorescence microscopes' resolving power with finite photons, we quantify the resolvability of periodic structures in fluorescence microscopy systems considering both the diffraction limit and photon statistics. Using the Cramer-Rao Lower Bound of a parametric target, the resulting precision lower bound establishes a practical measure of the theoretical resolving power for various modern fluorescence microscopy methods in the presence of noise.

翻译：1873年首次由恩斯特·阿贝发现的远场显微镜分辨率极限，通常被认为由数值孔径和光波长决定，约等于$\lambda$/2NA。随着上个世纪现代荧光显微镜和纳米成像方法的出现，人们认识到仅凭阿贝分辨率定义无法全面表征显微镜系统的分辨能力。为确定荧光显微镜的实际分辨率，光子噪声仍是亟待纳入基于统计理论框架的关键因素。共聚焦等技术通过权衡光子噪声来突破分辨率极限，这可能会增强或削弱对荧光标记目标的可分辨性。本文提出一种基于有限光子的荧光显微镜分辨能力理论度量方法，在同时考虑衍射极限与光子统计效应的条件下，量化荧光显微成像系统对周期性结构的可分辨性。通过参数化目标的克拉美-罗下限，所获得的精度下限建立了各类现代荧光显微方法在噪声环境中理论分辨能力的实用度量标准。