Imaging through a scattering medium: the Fisher information and the generalized Abbe limit

Enhanced-resolution imaging in complex scattering media is revisited from a parameter estimation perspective. A suitably defined Fisher information is shown to offer useful insights into the limiting precision of parameter estimation in a scattering environment and, hence, into the limiting spatial resolution that can be achieved in imaging-through-scattering settings. The Fisher information that defines this resolution limit via the Cramér-Rao lower bound is shown to scale with the number of adaptively controlled space-time modes of the probe field, suggesting a physically intuitive generalization of the Abbe limit to the spatial resolution attainable for complex scattering systems. In a conventional, direct-imaging microscopy setting, this bound is shown to converge to the canonical Abbe limit.