Quantum Limited Superresolution of an Incoherent Source Pair in Three Dimensions

Yu, Zhixian; Prasad, Sudhakar

doi:10.1103/physrevlett.121.180504

Cited by 65 publications

(65 citation statements)

References 33 publications

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“…This covariance matrix is a function of the spatial distribution of the collectors only. We can compute it explicitly, for example, for a continuous distribution of collectors that define a circular aperture, we reproduce the results of Yu and Prasad [31].…”

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confidence: 55%

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

2020

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We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent point-like emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a linear interferometer feeds into an array of photo-detectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of super-resolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry. arXiv:1909.09581v3 [quant-ph]

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confidence: 55%

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

2020

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“…This scaling law, which was first derived in Refs. [1,2] by applying quantum estimation theory to the problem of estimating the pair separation in one and two dimensions, seems to be entirely independent of the spatial dimensionality of the problem, as we showed in two papers [4,5] via an analysis considerably more general than that of Ref. [6] for full three-dimensional (3D) source pair separation and localization using apertures of arbitrary shape and size.…”

Section: Introductionmentioning

confidence: 87%

“…[4] for the problem of a pair of equally bright point sources. The independence of QFI on the relative brightness of the two sources and their separation supports our previous conjecture [4] that the determination of the separation of two point sources when their geometric center is known and fixed a priori (here at the coordinate origin) reduces fundamentally to a photon localization problem, independent of the nature, brightness, or locations of the point sources. This amounts, in effect, to the irrelevance of which source emits the photon.…”

Section: B Pair-separation Qfimentioning

confidence: 99%

“…Expression (24) for QFI may, as we saw in Ref. [4], may be expressed in terms of derivatives of the phase function, Ψ, and phase constant, φ. In view of the wave function (2), we may write…”

Section: B Pair-separation Qfimentioning

confidence: 99%

“…For a clear circular aperture, we may evaluate these averages further and thus obtain [4] the following diagonal form of the QFI matrix:…”

Section: B Pair-separation Qfimentioning

confidence: 99%

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Quantum limited super-resolution of an unequal-brightness source pair in three dimensions

Prasad

2020

Phys. Scr.

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This paper extends our previous quantum Fisher information (QFI) based analysis of the problem of separating a pair of equal-brightness incoherent point sources in three dimensions to the case of a pair of sources that are unequally bright. When the pair's geometric center is perfectly known in advance, QFI with respect to the estimation of the three separation coordinates remains independent of the degree of brightness asymmetry. For the experimentally more relevant case of perfect prior knowledge of the pair's brightness centroid, however, such QFI becomes dependent on the pair separation vector in a way that is controlled by the degree of its brightness asymmetry. This study yields potentially useful insights into the analysis of a more general superresolution imaging problem involving extended incoherent sources with nontrivial brightness distributions.

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Experimental 3D super-localization with Laguerre–Gaussian modes

Hu,

Xu,

Wang

et al. 2023

Quantum Front

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Improving three-dimensional (3D) localization precision is of paramount importance for super-resolution imaging. By properly engineering the point spread function (PSF), such as utilizing Laguerre–Gaussian (LG) modes and their superposition, the ultimate limits of 3D localization precision can be enhanced. However, achieving these limits is challenging, as it often involves complicated detection strategies and practical limitations. In this work, we rigorously derive the ultimate 3D localization limits of LG modes and their superposition, specifically rotation modes, in the multi-parameter estimation framework. Our findings reveal that a significant portion of the information required for achieving 3D super-localization of LG modes can be obtained through feasible intensity detection. Moreover, the 3D ultimate precision can be achieved when the azimuthal index l is zero. To provide a proof-of-principle demonstration, we develop an iterative maximum likelihood estimation (MLE) algorithm that converges to the 3D position of a point source, considering the pixelation and detector noise. The experimental implementation exhibits an improvement of up to two-fold in lateral localization precision and up to twenty-fold in axial localization precision when using LG modes compared to Gaussian mode. We also showcase the superior axial localization capability of the rotation mode within the near-focus region, effectively overcoming the limitations encountered by single LG modes. Notably, in the presence of realistic aberration, the algorithm robustly achieves the Cramér-Rao lower bound. Our findings provide valuable insights for evaluating and optimizing the achievable 3D localization precision, which will facilitate the advancements in super-resolution microscopy.

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Quantum Limited Superresolution of an Incoherent Source Pair in Three Dimensions

Cited by 65 publications

References 33 publications

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

Quantum limited super-resolution of an unequal-brightness source pair in three dimensions

Experimental 3D super-localization with Laguerre–Gaussian modes

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