Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2009.10042 · Physical Review A

Optimal correlation order in superresolution optical fluctuation microscopy

Svetlana V. Vlasenko, Alexander B. Mikhalychev, Ilya Karuseichyk, Dmitry A. Lyakhov, Dominik Ludewig Michels, Dmitri S. Mogilevtsev

Published Dec 4, 2020• 12 citations
arXivHTMLPDF

Abstract

Here, we show that superresolution optical fluctuation microscopy might not lead to ideally infinite superresolution enhancement with increasing of the order of measured cumulants. Using information analysis for estimating error bounds on the determination of point-source positions, we show that reachable precision per measurement might be saturated with increasing of the order of the measured cumulants in the superresolution regime. In fact, there is an optimal correlation order beyond which there is practically no improvement for objects of three and more point sources. However, for objects of just two sources, one still has an intuitively expected resolution increase with the cumulant order.

DOI
10.1103/physreva.102.063507

Related papers

Quantum limits to optical point-source localization

Mankei Tsang

Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that overcome a long-held belief about the resolution have revolutionized biological imaging. Termed "superresolution" microscopy, these techniques work by accurately locating optical point sources from far field. To investigate the fundamental localization limits, here I derive quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. These bounds are valid for any measurement technique, as long as it obeys quantum mechanics, and serve as general no-go theorems for the resolution of microscopes. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the root-mean-square position estimation error is on the order of $λ_0/\sqrt{N}$, where $λ_0$ is the free-space wavelength and $N$ is the average number of radiated photons. For two sources, owing to the statistical effect of nuisance parameters, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to enhance further the accuracy of locating one classical point source and the localization limits for partially coherent sources and single-photon sources are also discussed. The presented theory establishes a rigorous quantum statiscal inference framework for the study of superresolution microscopy and points to the possibility of using quantum techniques for true resolution enhancement.

arXiv:1411.2954•Optica•Jul 10, 2015•70 citations

Higher order correlation scaling for optical super-resolution imaging: implications of photon counting and quantum imaging for practical nanoscopy

Joshua Gray, Josef G. Worboys, Daniel W. Drumm +2 more

Techniques of optical superresolution imaging are vital for uncovering the complex dynamics of biochemistry in cellular environments. However the practical resolution for superresolution imaging is limited by the increased photon budget for superresolution, compared with conventional microscopy. For this reason it is important to determine the optimal methods for analysing all of the incoming information. Most approaches to microscopy use only the wave-like properties of light, but the particle-like nature of light provides extra information that is normally inaccessible and can be used to increase imaging resolution. Here we theoretically study the localisation of quantum emitters using higher-order quantum correlation functions to understand the resolution that is practically achievable for bio-imaging tasks. We show explicit imaging results for varying number of emitters as a function of correlation order to illustrate the necessary tradeoffs between imaging resolution and acquisition time.

Biophotonics Australasia•Dec 30, 2019•0 citations

Quantum fluctuations in superresolving microscopy with squeezed light

Vladislav N. Beskrovnyy, Mikhail I. Kolobov

We numerically investigate the role of quantum fluctuations in superresolution of optical objects. First, we confirm that when quantum fluctuations are not taken into account, one can easily improve the resolution by one order of magnitude beyond the diffraction limit. Then we investigate the standard quantum limit of superresolution which is achieved for illumination of an object by a light wave in a coherent state. We demonstrate that this limit can be beyond the diffraction limit. Finally, we show that further improvement of superresolution beyond the standard quantum limit is possible using the object illumination by a multimode squeezed light.

arXiv:quant-ph/0312049•Dec 5, 2003•0 citations

Superresolution via structured illumination quantum correlation microscopy

Anton Classen, Joachim von Zanthier, Marlan O. Scully +1 more

We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far beyond the Rayleigh limit. Combining intensity measurements and intensity auto correlations up to order $m$ creates an effective PSF with FWHM shrunk by the factor $\sqrt{m}$. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as $m + \sqrt{m}$ in dependence of the correlation order $m$. Hence, yielding this technique to be of interest in microscopy for imaging a variety of samples including biological ones. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.

arXiv:1702.04319•Optica•May 25, 2017•83 citations

A superresolution-enhanced spectrometer beyond the Cramer–Rao bound in phase sensitivity

Byoung Seung HAM

Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability density function of independently and identically distributed random variables. The Cramer-Rao lower bound (CRLB) indicates the minimum error of the Fisher information, generally known as the shot-noise limit. On the other hand, coherence has pushed the resolution limit further overcoming the diffraction limit using many-wave interference strictly confined to the first-order intensity correlation. However, practical implementation is limited by the lithographic constraints in, e.g., optical gratings. Recently, a coherence technique of superresolution has been introduced to overcome the diffraction limit in phase sensitivity using higher-order intensity correlations of a phase-controlled output field from an interferometer. Here, the superresolution is adopted for precision metrology in an optical spectrometer, whose enhanced frequency resolution is linearly proportional to the intensity-product order, overcoming CRLB. Unlike quantum sensing using entangled photons, this technique is purely classical and offers robust performance against environmental noises, benefiting from the interferometer's scanning mode for fringe counting.

arXiv:2409.00642•Scientific Reports•Feb 22, 2025•5 citations

Superresolution via structured illumination quantum correlation microscopy (Conference Presentation)

G. S. Agarwal

We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far into the sub-classical regime. Combining intensity measurements and intensity auto correlations up to order m creates an effective PSF with FWHM shrunk by the factor p m. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as m+sqrt m in dependence of the correlation order m. Hence, yielding this technique to be of the utmost interest for biological imaging. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.

Quantum Communications and Quantum Imaging•Sep 21, 2017•0 citations
Here, we show that superresolution optical fluctuation microscopy might not lead to ideally infinite superresolution enhancement with increasing of the order of measured cumulants. Using information analysis for estimating error bounds on the determination of point-source positions, we show that reachable precision per measurement might be saturated with increasing of the order of the measured cumulants in the superresolution regime. In fact, there is an optimal correlation order beyond which there is practically no improvement for objects of three and more point sources. However, for objects of just two sources, one still has an intuitively expected resolution increase with the cumulant order.
Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that overcome a long-held belief about the resolution have revolutionized biological imaging. Termed "superresolution" microscopy, these techniques work by accurately locating optical point sources from far field. To investigate the fundamental localization limits, here I derive quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. These bounds are valid for any measurement technique, as long as it obeys quantum mechanics, and serve as general no-go theorems for the resolution of microscopes. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the root-mean-square position estimation error is on the order of λ0/Nλ_0/\sqrt{N}λ0​/N​, where λ0λ_0λ0​ is the free-space wavelength and NNN is the average number of radiated photons. For two sources, owing to the statistical effect of nuisance parameters, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to enhance further the accuracy of locating one classical point source and the localization limits for partially coherent sources and single-photon sources are also discussed. The presented theory establishes a rigorous quantum statiscal inference framework for the study of superresolution microscopy and points to the possibility of using quantum techniques for true resolution enhancement.
Techniques of optical superresolution imaging are vital for uncovering the complex dynamics of biochemistry in cellular environments. However the practical resolution for superresolution imaging is limited by the increased photon budget for superresolution, compared with conventional microscopy. For this reason it is important to determine the optimal methods for analysing all of the incoming information. Most approaches to microscopy use only the wave-like properties of light, but the particle-like nature of light provides extra information that is normally inaccessible and can be used to increase imaging resolution. Here we theoretically study the localisation of quantum emitters using higher-order quantum correlation functions to understand the resolution that is practically achievable for bio-imaging tasks. We show explicit imaging results for varying number of emitters as a function of correlation order to illustrate the necessary tradeoffs between imaging resolution and acquisition time.
We numerically investigate the role of quantum fluctuations in superresolution of optical objects. First, we confirm that when quantum fluctuations are not taken into account, one can easily improve the resolution by one order of magnitude beyond the diffraction limit. Then we investigate the standard quantum limit of superresolution which is achieved for illumination of an object by a light wave in a coherent state. We demonstrate that this limit can be beyond the diffraction limit. Finally, we show that further improvement of superresolution beyond the standard quantum limit is possible using the object illumination by a multimode squeezed light.
We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far beyond the Rayleigh limit. Combining intensity measurements and intensity auto correlations up to order mmm creates an effective PSF with FWHM shrunk by the factor m\sqrt{m}m​. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as m+mm + \sqrt{m}m+m​ in dependence of the correlation order mmm. Hence, yielding this technique to be of interest in microscopy for imaging a variety of samples including biological ones. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability density function of independently and identically distributed random variables. The Cramer-Rao lower bound (CRLB) indicates the minimum error of the Fisher information, generally known as the shot-noise limit. On the other hand, coherence has pushed the resolution limit further overcoming the diffraction limit using many-wave interference strictly confined to the first-order intensity correlation. However, practical implementation is limited by the lithographic constraints in, e.g., optical gratings. Recently, a coherence technique of superresolution has been introduced to overcome the diffraction limit in phase sensitivity using higher-order intensity correlations of a phase-controlled output field from an interferometer. Here, the superresolution is adopted for precision metrology in an optical spectrometer, whose enhanced frequency resolution is linearly proportional to the intensity-product order, overcoming CRLB. Unlike quantum sensing using entangled photons, this technique is purely classical and offers robust performance against environmental noises, benefiting from the interferometer's scanning mode for fringe counting.
We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far into the sub-classical regime. Combining intensity measurements and intensity auto correlations up to order m creates an effective PSF with FWHM shrunk by the factor p m. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as m+sqrt m in dependence of the correlation order m. Hence, yielding this technique to be of the utmost interest for biological imaging. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.