We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.
Summary form only given. To achieve super-resolution one must take into account a priori information about localization of the object. Such an a priori information exists in the case of an object of finite size. Its Fourier transform located in the focal plane of the lens is an entire analytic function, and analytic continuation of the object spectrum outside the spatial-frequency band allows for unlimited resolution. However such a super-resolution is extremely sensitive to the noise in the detected image. The ultimate limit of super-resolution is determined by the quantum fluctuations of light in the detection plane. We present the quantum theory of super-resolution for a one-dimensional coherent optical imaging scheme and discuss possibilities of improving the resolution limit by using multimode squeezed light. For quantum-mechanical description of this scheme we take into account the vacuum fluctuations of the electromagnetic field in the input plane outside the object. Interference of these vacuum fluctuations with the field amplitude of the object in the detection plane is the origin of the standard quantum limit or shot noise of photodetection in the image. To go beyond this limit we suggest to illuminate the object with multimode squeezed light having the spot size much larger than the object area. Then the vacuum fluctuations outside the object can be effectively suppressed resulting in sub-shot-noise detection of the image.
We discuss the ultimate limit imposed by quantum fluctuations of light for resolution of fine details in optical images. For this purpose, we extend in the quantum domain the classical analysis of the object reconstruction, or superresolution, in terms of prolate spheroidal function basis. We derive the expression for ultimate resolution limit in the reconstructed object using an illumination of the full object plane by a multimode squeezed vacuum. We show that the gain in resolution using multimode squeezed light is maximum when the Shannon number of the imaging system is close to unity.
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.
Inspired by the results from quantum information processing, spatial-mode demultiplexing offers resolution of objects at the quantum limit, below the well-known Rayleigh-Abbe diffraction limit. An intriguing aspect of these results is that, while the analysis leading to the ultimate sub-diffraction limit is quantum, semi-classical devices can be used to build “super-resolving” sensors that achieve this limit. Therefore, these developments have potential to significantly improve the quality of imaging systems in the near term. However, these quantum-inspired systems are sensitive to fluctuation in nuisance parameters, whether they are natural or adversarial. In this paper we analyze the impact of such fluctuations and provide methods to mitigate it. We focus on a problem of resolving two point sources, which has immediate practical applications in, e.g., space situation awareness.
Quantum imaging can be defined as an area of quantum optics that investigates the ultimate performance limits of optical imaging allowed by the quantum nature of light. Quantum Imaging techniques possess a high potential for improving the performance in recording, storage, and readout of optical images beyond the limits set by the standard quantum level of fluctuations known as the shot noise. This talk aims at giving an overview of the fundamentals of Quantum Imaging as well as its most important directions. We shall discuss generation of the spatially multimode squeezed states of light be means of a travelling-wave optical parametric amplifier. We shall demonstrate that this kind of light allows us to reduce the spatial fluctuations of the photocurrent in a properly chosen homodyne detection scheme with a highly efficient CCD camera. It will be shown that using the amplified quadrature of the light wave in a travelling-wave optical parametric amplifier, one can perform noiseless amplification of optical images. We shall provide recent experimental results demonstrating a single-shot noiseless image amplification by a pulsed optical parametric amplifier. One of important experimental achievements of Quantum Imaging, coined in the literature as quantum laser pointer, is a precise measurement of position and transverse displacement of a laser beam with resolution beyond the limit imposed by the shot noise. We shall describe briefly the idea of the experiment in which the transverse displacement of a laser beam was measured with resolution of the order of Angstrom. The problem of precise measurement of transverse displacement of a light beam brings us to a more general question about the quantum limits of optical resolution. The classical resolution criterion, derived in the nineteen century by Abbe and Rayleigh, states that the resolution of an optical instrument is limited by diffraction and is related to the wavelength of the light used in the imaging scheme. However, it was for a long time recognised in the literature that in some cases when one has some a priori information about the object, one can improve the resolution beyond the Rayleigh limit using the so-called super-resolution techniques. As a final topic in this talk, we shall discuss the quantum limits of optical super-resolution. In particular, we shall formulate the standard quantum limit of super-resolution and demonstrate how one can go beyond this limit using specially designed multimode squeezed light.
The diffraction, or Rayleigh, limit was long thought to determine the ultimate resolving power of optical imaging devices. Using techniques from quantum statistical inference, Tsang et al. [1] demonstrated that this limit can be circumvented, and derived an alternative measurement strategy capable of resolving two incoherent point sources no matter how arbitrarily small their separation is. However, these measurements require perfect knowledge of the sources centroid position, and are extremely sensitive to any source of misalignment about this position [2] , [3] . In this work, we study the problem of super-resolution from a more global point of view.