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Optical and Quantum Sensing and Precision Metrology II

Theory for super-resolution quantum coincidence imaging

Lihong V. Wang

Published Mar 5, 2026• 0 citations
Publisher

Abstract

We present a theoretical framework for super-resolution imaging based on quantum coincidence detection. By comparing the classical Airy point spread function with the two-photon wavefunction of entangled photon pairs, we derive that coincidence detection yields an effective narrowing of the point spread function by a factor of two or the square root of two, depending on the maintenance of correlation. This model highlights the role of transverse phase accumulation in the image plane and predicts a quantum resolution limit that is half of the classical diffraction limit when correlation is maintained. The results offer clear insight into recent experimental demonstrations of quantum imaging beyond the classical diffraction limit.

DOI
10.1117/12.3085873

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We present a theoretical framework for super-resolution imaging based on quantum coincidence detection. By comparing the classical Airy point spread function with the two-photon wavefunction of entangled photon pairs, we derive that coincidence detection yields an effective narrowing of the point spread function by a factor of two or the square root of two, depending on the maintenance of correlation. This model highlights the role of transverse phase accumulation in the image plane and predicts a quantum resolution limit that is half of the classical diffraction limit when correlation is maintained. The results offer clear insight into recent experimental demonstrations of quantum imaging beyond the classical diffraction limit.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.
Abstract Quantum imaging can beat classical resolution limits, imposed by the diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable resolution by illuminating an object by entangled light and measuring coincidences of photons. If an n-photon entangled state is used and the nth-order correlation function is measured, the point-spread function (PSF) effectively becomes n\sqrt{n}n​ n times narrower relatively to classical coherent imaging. Quite surprisingly, measuring n-photon correlations is not the best choice if an n-photon entangled state is available. We show that for measuring (n − 1)-photon coincidences (thus, ignoring one of the available photons), PSF can be made even narrower. This observation paves a way for a strong conditional resolution enhancement by registering one of the photons outside the imaging area. We analyze the conditions necessary for the resolution increase and propose a practical scheme, suitable for observation and exploitation of the effect.
High Resolution Image Download MS PowerPoint Slide The resolution of a classical imaging system is limited by diffraction. This limit can be overcome, for example, by implementing various forms of localization microscopy in which the center of a fluorescence distribution is estimated to an accuracy scaling with the square root of the number of detected photons, N . In quantum imaging the object can be illuminated using correlated photon-pairs, leading early work to suggest that a 2 improvement could be obtained as a result of averaging the position of N = 2 events. However, similar to quantum lithography, which relies upon quantum illumination using entangled photon-pairs and two-photon absorption, the minimum resolvable feature size is reduced by a factor of 2, not just 2 . Quantum imaging schemes can also lead to a factor of 2 improvement. By using a similar source of correlated photon-pairs to illuminate an object, a single-photon sensitive camera to detect the photon-pairs, and an image processing algorithm to record and sum the bisector positions of the transmitted photon-pairs, we realize a similar factor of ×2 improvement in image resolution, surpassing that of most earlier quantum imaging work.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated NNN-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N1/N1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated N-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.