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arXiv · 1803.01776

Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics

Mikael P. Backlund·Yoav Shechtman·Ronald L. Walsworth
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Abstract

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here we consider the theoretical limits of such approaches by deriving the quantum Cram\'{e}r-Rao bound (QCRB). We show that existing methods for depth localization with single-objective detection exceed the QCRB by a factor $>\sqrt{2}$, and propose an interferometer arrangement that approaches the bound. We also show that for detection with two opposed objectives, established interferometric measurement techniques globally reach the QCRB.

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Mikael P. Backlund, Yoav Shechtman, Ronald L. Walsworth. 2018-03-05. Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics. https://doi.org/10.1103/physrevlett.121.023904

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