Recording and identifying faint objects through atmospheric scattering media by an optical system are fundamentally interesting and technologically important. We introduce a comprehensive model that incorporates contributions from target characteristics, atmospheric effects, imaging systems, digital processing, and visual perception to assess the ultimate perceptible limit of geometrical imaging, specifically the angular resolution at the boundary of visible distance. The model allows us to reevaluate the effectiveness of conventional imaging recording, processing, and perception and to analyze the limiting factors that constrain image recognition capabilities in atmospheric media. The simulations were compared with the experimental results measured in a fog chamber and outdoor settings. The results reveal good general agreement between analysis and experiment, pointing out the way to harnessing the physical limit for optical imaging in scattering media. An immediate application of the study is the extension of the image range by an amount of 1.2 times with noise reduction via multiframe averaging, hence greatly enhancing the capability of optical imaging in the atmosphere.