Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics

Mikael P. Backlund, Yoav Shechtman, Ronald L. Walsworth

Research output: Contribution to journalArticlepeer-review


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 prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.

Original languageEnglish (US)
Article number023904
JournalPhysical review letters
Issue number2
StatePublished - Jul 11 2018
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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