Quantum theory of superresolution for two incoherent optical point sources

By Mankei Tsang, Ranjith Nair, Xiao-Ming Lu. 2015

473 citations recorded by the source corpus.

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern farfield superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh's criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.

Subfields: Acoustics and Ultrasonics, Atomic and Molecular Physics, and Optics, Biophysics

View Paper: https://www.semanticscholar.org/paper/5941a1bfa38cdc97754ad2be0cd39ea6888fee02

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Citations in the corpus

Imaging with quantum states of light (2019, background): “[140] M.”
Modes and states in quantum optics (2019, background): “the image (Wang et al., 2012). It was more recently studied for incoherent illumination, more precisely to derive the ultimate resolution limit on the separation between two TEM00 incoherent sources (Tsang et al., 2016). It was shown that the Fisher information contained in the intensity distributio”
A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging (2019, background): “the kind we are considering, the matrix is diagonal, and, remarkably, its element Q22 is a constant [137]; in particular, for Gaussian PSFs with width σ, the smallest achievable variance on λ2 is V22(λ) = 4σ (2)/M .”
Geometry of quantum phase transitions (2019, background): “Quantum parameter estimation finds applications in a wide variety of fields, from fundamental physics [292, 293, 294, 295, 296], to gravitational wave interferometry [297, 298], thermometry [299, 300], spectroscopy [301, 302], imaging [303, 304, 305], to name a few.”
Subdiffraction incoherent optical imaging via spatial-mode demultiplexing (2016, background): “[1] Mankei Tsang, Ranjith Nair, and Xiao-Ming Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Physical Review X 6, 031033 (2016).”
Quantum-enhanced measurements without entanglement (2017, background): “Thus, quantum detection strategies enables one to beat the so-called “Rayleigh’s curse” which affects classical imaging (Tsang et al., 2016).”
Advances in quantum cryptography (2019, unknown): “[605] M.”
Advances in quantum imaging (2024, unknown): “For example, saturation of the QCRB is particularly relevant in the context of parameters encoded in the modal structure of a light beam 24,25 .”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “With this result, it has been shown that direct imaging performs poorly for estimating small separations and other elaborate methods like spatial-mode demultiplexing and image inversion interferometry can be used to achieve the quantum limit [192,193].”
Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution (2017, methodology): “When only the intensity at the image is measured (the basis of all the conventional techniques), the Fisher information falls to zero as the separation between the sources decreases and the CRLB diverges accordingly; this is known as the Rayleigh curse [14].”