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.
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.
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.
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.
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 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.
The scheme of optical imaging using scattering lens can provide a resolution beyond the classical optical diffraction limit with a coherent-state input. Nevertheless, due to the shot noise of the coherent state, the corresponding signal-to-noise ratio and resolution are both still shot-noise-limited. In order to circumvent this problem, we theoretically propose an alternative scheme where the squeezed state (with a sub-shot noise) is considered as input and the quantum noise is then suppressed below the shot-noise level. Consequently, when comparing with the previous imaging scheme (using combination of coherent state and scattering lens), our proposal is able to achieve an enhanced signal-to-noise ratio for a given scattering lens. Meanwhile, it is demonstrated that the resolution is also improved. We believe that this method may afford a new way of using squeezed states and enable a higher performance than that of using coherent state and scattering lens.
Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.