Quantum limit for two-dimensional resolution of two incoherent optical point sources

Ang, Shan Zheng; Nair, Ranjith; Tsang, Mankei

doi:10.1103/physreva.95.063847

Cited by 72 publications

(67 citation statements)

References 29 publications

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“…Although Eq. (4.14) assumes one-dimensional imaging, previous studies of two-dimensional imaging in quantum estimation theory [3,4,10,21] show no new surprises, and it is reasonable to conjecture that the quantum limit on the Fisher information becomes N O(∆ −2 |µ|/2 )-the same as the SPADE performance-where |µ| = j µ j is the total moment order [3,4].…”

Section: Discussionmentioning

confidence: 95%

Quantum limit to subdiffraction incoherent optical imaging

Tsang

2019

Phys. Rev. A

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The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond the case of two sources, here I evaluate a quantum bound on the Fisher information that can be extracted by any far-field optical measurement about the moments of a subdiffraction object. The bound matches the performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in terms of its scaling with the object size, indicating that SPADE is close to quantum-optimal. Coincidentally, the result is also applicable to the estimation of diffusion parameters with a quantum probe subject to random displacements.

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Section: Discussionmentioning

confidence: 95%

Quantum limit to subdiffraction incoherent optical imaging

Tsang

2019

Phys. Rev. A

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“…For two point sources, there are now two parameters for their vectoral separation. The quantum limits for the two parameters are the same as that for the onedimensional case, and SPADE with respect to the transverseelectromagnetic (TEM) modes or a pair of SLIVER devices can still estimate the vectoral separation near the quantum limit [53]. For extended sources in two dimensions, a generalization of the PAD and iPAD modes have been studied in Refs.…”

Section: E Two-dimensional Imagingmentioning

confidence: 99%

Resolving starlight: a quantum perspective

Tsang

2019

Contemporary Physics

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The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a quantum object, consider any quantum measurement, and pick the one that gives the best statistics. While Helstrom pioneered the theory half a century ago and first applied it to incoherent imaging, it was not until recently that the approach offered a genuine surprise on the age-old topic by predicting a new class of superior imaging methods. For the resolution of two sub-Rayleigh sources, the new methods have been shown theoretically and experimentally to outperform direct imaging and approach the true quantum limits. Recent efforts to generalize the theory for an arbitrary number of sources suggest that, despite the existence of harsh quantum limits, the quantum-inspired methods can still offer significant improvements over direct imaging for subdiffraction objects, potentially benefiting many applications in astronomy as well as fluorescence microscopy.

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“…Third, while it is true that spatial coherence develops in the field during diffraction even for spatially incoherent sources by virtue of the Van Cittert-Zernike theorem [5], the effect has already been properly incorporated in the model used in Refs. [2][3][4]9], and one should not confuse this effect with partial coherence at the sources.…”

Section: Arxiv:181012166v1 [Quant-ph] 29 Oct 2018mentioning

confidence: 99%