Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Tsang, Mankei

doi:10.1088/1367-2630/aa60ee

Cited by 94 publications

(138 citation statements)

References 82 publications

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“…In other words, the rank-deficient nature of the QFIM shows that a form of the Rayleigh limit resurfaces for any N>2. This had been suggested by previous works based on order-of-magnitude bounds for the diagonal elements on the CFIM [36] or uppers bounds on the diagonal elements of the QFIM [37]. Our analytical expression for the full QFIM-its diagonal and off-diagonal elements for any N-shows that this rank two behaviour is truly quantum mechanical in origin.…”

Section: Analytical Expression Of Qfimsupporting

confidence: 72%

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Quantum limits of localisation microscopy

2019

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Localisation microscopy of multiple weak, incoherent point sources with possibly different intensities in one spatial dimension is equivalent to estimating the amplitudes of a classical mixture of coherent states of a simple harmonic oscillator. This enables us to bound the multi-parameter covariance matrix for an unbiased estimator for the locations in terms of the quantum Fisher information matrix, which we obtained analytically. In the regime of arbitrarily small separations we find it to be no more than rank two-implying that no more than two independent parameters can be estimated irrespective of the number of point sources. We use the eigenvalues of the classical and quantum Fisher information matrices to compare the performance of spatial-mode demultiplexing and direct imaging in localisation microscopy with respect to the quantum limits.

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Section: Analytical Expression Of Qfimsupporting

confidence: 72%

“…where μ is the order the eigenvalue when arranged in descending order and⌊·⌋is the floor function. These scalings are now extracted from the elements of the full QFIM of the localisation parameters a-rather than from bounds on estimating the various moments independently as in previous works [36,37].…”

Section: Discussionmentioning

confidence: 99%

Quantum limits of localisation microscopy

2019

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“…Meanwhile, the adapted SPLICE estimate shows an rms error that decreases with the separation. This was first discussed in [22], where it was shown that projective phase measurements for the statistical moments of a source distribution, in the style of SPADE [2] or SPLICE, provide unbiased estimates and have substantially lower CRB than IPC in the sub-Rayleigh region. Figure 5 shows the resulting rms errors when estimating δ, and q, by either IPC, SPLICE, or adapted SPLICE for the same cases of q as above.…”

Section: Adapting Splice For Unequal-intensity Emittersmentioning

confidence: 99%

“…where f j is the corresponding position of the single-mode fiber, and the set {g j } represent the positions of the right-most edges of n j π phase-shifters, so that for every x<g j there is a phase shift of π. Figure 7 By casting the SPLICE modes into the HG basis, we can use the same treatment as in [22] to show how the jth statistical moment of F(X) is extracted in the sub-Rayleigh regime. Here we will consider when the SPLICE measurements are centered about μ 1 , the mean of F(X), which is to say that the specified positions of the fiber Figure 7.…”

Section: Estimating Higher Momentsmentioning

confidence: 99%

“…Generalized SPLICE functions f j (x, 0) (solid black, equation (5)) are used to estimate the jth moment. The relevant HG functions (gray, equation (7)) are plotted for comparison: HG k,0 (x, 0) for the k 2 th moment; and [22]). For odd j only the plus superpositions are shown for brevity; the minus superpositions are reflections about the origin.…”

Section: Estimating Higher Momentsmentioning

confidence: 99%

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Realistic sub-Rayleigh imaging with phase-sensitive measurements

et al. 2019

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As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh's 'curse' can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call 'adapted SPLICE', requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.

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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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Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Cited by 94 publications

References 82 publications

Quantum limits of localisation microscopy

Quantum limits of localisation microscopy

Realistic sub-Rayleigh imaging with phase-sensitive measurements

Experimental 3D super-localization with Laguerre–Gaussian modes

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