Skip to main content

Research Repository

Advanced Search

Towards superresolution surface metrology: quantum estimation of angular and axial separations

Napoli, Carmine; Piano, Samanta; Leach, Richard; Adesso, Gerardo; Tufarelli, Tommaso


Carmine Napoli


We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the subwavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh’s criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for the Gaussian instance. This analysis may have relevant applications in three-dimensional surface measurements.


Napoli, C., Piano, S., Leach, R., Adesso, G., & Tufarelli, T. (2019). Towards superresolution surface metrology: quantum estimation of angular and axial separations. Physical Review Letters, 122(14), Article 140505.

Journal Article Type Article
Acceptance Date Mar 22, 2019
Online Publication Date Apr 12, 2019
Publication Date Apr 12, 2019
Deposit Date Apr 29, 2019
Publicly Available Date Apr 29, 2019
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 122
Issue 14
Article Number 140505
Keywords Quantum Physics; Mesoscale and Nanoscale Physics; Instrumentation and Detectors; Optics
Public URL
Publisher URL


You might also like

Downloadable Citations