Reading out Fisher information from the zeros of the point spread function

Paúr, Martin; Stoklasa, Bohumil; Koutný, Dominik; Řeháček, J.; Hradil, Z.; Grover, Jai; Krzic, A.; Sánchez-Soto, Luis L.

doi:10.1364/ol.44.003114

Cited by 26 publications

(19 citation statements)

References 23 publications

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“…However, our result differs in kind from that of Ref. [33], which reported a factor of γ (in our notation) improvement in the scaling of the direct imaging Fisher information using a hard aperture compared with that using a Gaussian attenuated aperture model. In the case of binary hypothesis testing, we find that the integrals of the individual terms of Q s up to third order in γ always converge [Eq.…”

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confidence: 99%

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Identifying Objects at the Quantum Limit for Super-Resolution Imaging

Grace¹,

Guha²

2021

Preprint

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We consider imaging tasks involving discrimination between known objects and investigate the best possible accuracy with which the correct object can be identified. Using the quantum Chernoff bound, we analytically find the ultimate achievable asymptotic error rate for symmetric hypothesis tests between any two incoherent 2D objects when the imaging system is dominated by optical diffraction. Furthermore, we show that linear-optical demultiplexing of the spatial modes of the collected light exactly saturates this ultimate performance limit, enabling a quadratic improvement over the asymptotic error rate achieved by direct imaging as the objects become more severely diffraction-limited. We extend our results to identify the quantum limit and optimal measurement for discrimination between an arbitrary number of candidate objects. Our work constitutes a complete theoretical treatment of the ultimate quantitative limits on passive, sub-diffraction, incoherent object discrimination and is readily applicable to a multitude of real-world applications.

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contrasting

confidence: 99%

“…A similar situation was encountered in Ref. [33], which pointed out that the sub-Rayleigh scaling of the Fisher information for estimating an object parameter cannot be evaluated by expanding the integrand as a Taylor series and integrating individual terms when there are zeros in the PSF. Likewise, our integration of the individual terms of Eq.…”

mentioning

confidence: 57%

Identifying Objects at the Quantum Limit for Super-Resolution Imaging

Grace¹,

Guha²

2021

Preprint

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“…Reality is necessarily uglier, but the results here remain relevant by serving as fundamental limits (via the data-processing inequality [51,68]) and offering insights into the essential physics. The theoretical and experimental progress on SPADE and related methods so far [69][70][71] has provided encouragement that the theory has realistic potential, and the general results here should motivate further research into the wider applications of quantuminspired imaging methods.…”

Section: Discussionmentioning

confidence: 75%

Semiparametric estimation for incoherent optical imaging

Tsang

2019

Phys. Rev. Research

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The theory of semiparametric estimation offers an elegant way of computing the Cramér-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent imaging under the effects of diffraction and photon shot noise. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cramér-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.

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“…This situation is the orientation analog of MINFLUX nanoscopy [48], where infinitely good orientation measurement precision per photon may be obtained by receiving zero signal [49]; in this case, zero photons detected in the y-polarized channel implies M yy = 0. It is remarkable that quantum estimation theory provides fundamental bounds on measurement performance that are both instrument independent and achievable by readily built imaging systems, such as the dual-objective system with vortex wave plates and interferometric detection proposed here.…”

Section: Discussionmentioning

confidence: 99%

“…That is, there exists some position(s) ( u , v ) in image space such that I ( u , v ; μ = [1, 0, 0] † ) = 0 and ∂ I ( u , v )/∂ M yy > 0; i.e., we expect certain region(s) of the image to be dark for x -oriented dipoles but bright for y -oriented dipoles. Therefore,

This situation is the orientation analog of MINFLUX nanoscopy [ 48 ], where infinitely good orientation measurement precision per photon may be obtained by receiving zero signal [ 49 ]; in this case, zero photons detected in the y -polarized channel implies M yy = 0.…”

Section: Discussionmentioning

confidence: 99%

Quantum limits for precisely estimating the orientation and wobble of dipole emitters

Zhang

Lew

2020

Phys. Rev. Research

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Precisely measuring molecular orientation is key to understanding how molecules organize and interact in soft matter, but the maximum theoretical limit of measurement precision has yet to be quantified. We use quantum estimation theory and Fisher information (QFI) to derive a fundamental bound on the precision of estimating the orientations of rotationally fixed molecules. While direct imaging of the microscope pupil achieves the quantum bound, it is not compatible with wide-field imaging, so we propose an interferometric imaging system that also achieves QFI-limited measurement precision. Extending our analysis to rotationally diffusing molecules, we derive conditions that enable a subset of second-order dipole orientation moments to be measured with quantum-limited precision. Interestingly, we find that no existing techniques can measure all second moments simultaneously with QFI-limited precision; there exists a fundamental trade-off between precisely measuring the mean orientation of a molecule versus its wobble. This theoretical analysis provides crucial insight for optimizing the design of orientation-sensitive imaging systems.

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Reading out Fisher information from the zeros of the point spread function

Cited by 26 publications

References 23 publications

Identifying Objects at the Quantum Limit for Super-Resolution Imaging

Identifying Objects at the Quantum Limit for Super-Resolution Imaging

Semiparametric estimation for incoherent optical imaging

Quantum limits for precisely estimating the orientation and wobble of dipole emitters

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