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：Ernest Abbe于1873年首次发现,远地显微镜的分辨率极限由光的数值孔径和波长(约合$=lambda$/2NA)来决定。随着上个世纪现代荧光显微镜和纳米显微镜方法的出现,人们认识到,Abbe的分辨率定义不能仅仅描述显微镜系统的分辨率力量。为了确定荧光显微镜的实际分辨率,光子噪音仍然是尚未纳入基于统计的理论框架的重要因素之一。诸如confocal允许光噪音交易以达到其分辨率极限的技术,这可能会增加或加剧对荧光标记目标的可溶性。作为荧光显微镜用有限的光解力的理论衡量尺度,我们将荧光显微镜系统定期结构的可溶性量化,同时考虑到了底线限制和光子统计数据。使用光谱目标的Cramer-Rao低波,由此而得出的精确度较低约束度为各种现代微声镜的理论解力提供了一种实用的尺度。