A statistical resolution measure of fluorescence microscopy with finite photons

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 $$ . With the advent of modern fluorescence microscopy and nanoscopy methods over the last century, this definition is insufficient to fully describe a microscope's resolving power. To determine the practical resolution limit of a fluorescence microscope, photon noise remains one essential factor yet to be incorporated in a statistics-based theoretical framework. We proposed an information density measure quantifying the theoretical resolving power of a fluorescence microscope in the condition of finite photons. The developed approach not only allows us to quantify the practical resolution limit of various fluorescence and super-resolution microscopy modalities but also offers the potential to predict the achievable resolution of a microscopy design under different photon levels.