Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics
arXiv:1803.01776 · doi:10.1103/PhysRevLett.121.023904
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 Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective detection exceed the QCRB by a factor , 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.
arXiv commentUpdated to include Supplemental Material as ancillary file
References in corpus (22)
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Quantum Enhanced Multiple Phase Estimation
- Compatibility in Multiparameter Quantum Metrology
- State estimation for large ensembles
- A new approach to the Cramer-Rao type bound of the pure state model
- Fisher information in quantum statistics
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Beating Rayleigh's Curse by Imaging Using Phase Information
- Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
- Ultimate precision bound of quantum and sub-wavelength imaging
- Fourier Magnetic Imaging with Nanoscale Resolution and Compressed Sensing Speed-up using Electronic Spins in Diamond
- Quantum limit for two-dimensional resolution of two incoherent optical point sources
- Interferometric superlocalization of two incoherent optical point sources
- Measurement-based estimation of global pupil functions in 3D localization microscopy
- Quantum limits to optical point-source localization
- Superresolution optical magnetic imaging and spectroscopy using individual electronic spins in diamond
- Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatment
- Maximum Fisher information in mixed state quantum systems
- Maximal quantum Fisher information matrix
- Semiclassical Theory of Superresolution for Two Incoherent Optical Point Sources
- Fundamental limit of resolving two point sources limited by an arbitrary point spread function
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