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

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Abstract

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.

© 2021 Optical Society of America

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Data underlying the results presented in this paper may be obtained from the author upon reasonable request.

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