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Moment-based superresolution: Formalism and applications
- Source :
- Physical Review A, Physical Review A, American Physical Society 2021, 104 (3), ⟨10.1103/PhysRevA.104.033515⟩, Phys. Rev. A
- Publication Year :
- 2021
- Publisher :
- American Physical Society (APS), 2021.
-
Abstract
- Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.<br />Comment: 18 pages, 12 figures, 1 table. Comments are very welcome!
- Subjects :
- Physics
Quantum Physics
[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]
Photon
[PHYS.PHYS]Physics [physics]/Physics [physics]
FOS: Physical sciences
Observable
Image plane
01 natural sciences
Noise (electronics)
Photon counting
Computational physics
010309 optics
Moment (mathematics)
0103 physical sciences
Limit (mathematics)
Sensitivity (control systems)
Quantum Physics (quant-ph)
010306 general physics
Subjects
Details
- ISSN :
- 24699934 and 24699926
- Volume :
- 104
- Database :
- OpenAIRE
- Journal :
- Physical Review A
- Accession number :
- edsair.doi.dedup.....ab69b655cdcae60a627068c93dc92d05