We show how we can obtain improved resolution when imaging an object by filtering “high‐resolution” quantum states from impinging classical radiation. The method allows one to beat the Rayleigh diffraction bound that is intrinsic in any imaging apparatus. It is based on using focused classical illumination sources and N‐photon coincidence detection.
We show how we can obtain improved resolution when imaging an object by filtering “high‐resolution” quantum states from impinging classical radiation. The method allows one to beat the Rayleigh diffraction bound that is intrinsic in any imaging apparatus. It is based on using focused classical illumination sources and N‐photon coincidence detection.
I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber or coincidence detection. Using the same nonclassical states of light as those for quantum lithography, the proposed method requires only optical intensity measurements, followed by image postprocessing, to produce the same complex quantum interference patterns as those in quantum lithography. The method is expected to be experimentally realizable using current technology.
The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1∕N enhancement (standard quantum limit) or a 1∕N enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.
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.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
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 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.
In this paper we study the resolution of images illuminated by sources composed of N+1 photons in which one non-degenerate photon is entangled with N degenerate photons. The N degenerate photons illuminate an object and are collected by an N photon detector. The signal from the N photon detector is measured in coincidence with the non-degenerate photon giving rise to a ghost image. We discuss the case of three photons in various configurations and generalize to N+1. Using the Rayleigh criterion, we find that the system may give an improvement in resolution by a factor of N compared to using a classical source. For the case that the N-photon number detector is a point detector, a coherent image is obtained. If the N-photon detector is a bucket detector, the image is incoherent. The visibility of the image in both cases is 1. In the opposite case in which the non-degenerate photon is scattered by the object, then, using an N-photon point detector may reduce the Airy disk by a factor of N.