Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.

Fourier-Transform Ghost Imaging with Hard X Rays

Quantum states of light are at the same time endowed with two superposition principles: the one of the classical Maxwell waves and the one of the quantum states occupying these waves. This article reviews the interplay between these two aspects of quantum optics. A summary of the description of multimode quantum states is presented along with an example of the characterization of correlations and entanglement with applications in metrology and quantum computation.

Modes and states in quantum optics

Time-delayed optoelectronic oscillators are at the center of a large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudorandom number generation, optoelectronic machine learning based on reservoir computing, ultrapure microwave generation, optical pulse-train synthesis, and sensing. The aim of this review is to provide a comprehensive survey of this field, to outline the latest achievements, and discuss the main challenges ahead.

Optoelectronic oscillators with time-delayed feedback

The resolution of conventional optical equipment is always restricted by the diffraction limit, and improving on this was previously considered improbable. Optical super-resolution imaging, which has recently experienced rapid growth and attracted increasing global interest, will result in applications in many domains, benefiting fields such as biology, medicine and material research. This review discusses the contributions of different researchers who identified the diffractive barrier and attempted to realize optical super-resolution. This is followed by a personal viewpoint of the development of optical nanoscopy in recent decades and the road towards the next generation of optical nanoscopy. Researchers in China have reviewed techniques for imaging at resolutions beyond the diffraction limit of light. Xiang Hao and co-workers from Zhejiang University in China describe how superlenses made from thin silver films and hyperlenses incorporating meta-materials can capture near-field evanescent waves that provide fine and rich spatial information about an object. Alternative approaches include placing transparent microspheres onto the object or scanning a microscale optical fiber across it. The role of popular fluorophore-based schemes such as STED, STORM and PALM, which achieve super-resolution imaging by employing the controlled switching of fluorescence in space and time, is also described. Finally, the authors comment on the emergence of approaches such as the HIRES lens, which uses light scattering to achieve enhanced resolution.

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From microscopy to nanoscopy via visible light

We present a compressive sensing protocol that tracks a moving object by removing static components from a scene. The implementation is carried out on a ghost imaging scheme to minimize both the number of photons and the number of measurements required to form a quantum image of the tracked object. This procedure tracks an object at low light levels with fewer than 3% of the measurements required for a raster scan, permitting us to more effectively use the information content in each photon.

Compressive object tracking using entangled photons

A fiber-distributed Ultra-wideband (UWB) noise radar was achieved, which consists of a chaotic UWB noise source based on optoelectronic oscillator (OEO), a fiber-distributed transmission link, a colorless base station (BS), and a cross-correlation processing module Due to a polarization modulation based microwave photonic filter and an electrical UWB pass-band filter embedded in the feedback loop of the OEO, the power spectrum of chaotic UWB signal could be shaped and notch-filtered to avoid the spectrum-overlay-induced interference to the narrow band signals Meanwhile, the wavelength-reusing could be implemented in the BS by means of the distributed polarization modulation-to-intensity modulation conversion The experimental comparison for range finding was carried out as the chaotic UWB signal was notch-filtered at 52 GHz and 78 GHz or not Measured results indicate that space resolution with cm-level could be realized after 3-km fiber transmission thanks to the excellent self-correlation property of the UWB noise signal provided by the OEO The performance deterioration of the radar raised by the energy loss of the notch-filtered noise signal was negligible

Fiber-distributed Ultra-wideband noise radar with steerable power spectrum and colorless base station.

Sparsity constraint is a priori knowledge of the signal, which means that in some properly chosen basis only a small percentage of the total number of the signal components is nonzero. Sparsity constraint has been used in signal and image processing for a long time. Recent publications have shown that the Sparsity constraint can be used to achieve super-resolution of optical sparse objects beyond the diffraction limit. In this paper we present the quantum theory which establishes the quantum limits of super-resolution for the sparse objects. The key idea of our paper is to use the discrete prolate spheroidal sequences (DPSS) as the sensing basis. We demonstrate both analytically and numerically that this sensing basis gives superior performance of super-resolution over the Fourier basis conventionally used for sensing of sparse signals. The explanation of this phenomenon is in the fact that the DPSS are the eigenfunctions of the optical imaging system while the Fourier basis are not. We investigate the role of the quantum fluctuations of the light illuminating the object, in the performance of reconstruction algorithm. This analysis allows us to formulate the criteria for stable reconstruction of sparse objects with super-resolution. Our results imply that sparsity of the object is not the only parameter which describes super-resolution achievable via sparsity constraint.

Quantum limits of super-resolution of optical sparse objects via sparsity constraint

A fiber-distributed Ultra-wideband (UWB) noise radar is proposed and demonstrated, in which a nonlinear electro-optic oscillator with inbuilt UWB band-pass filter is applied as signal source to provide the chaotic-UWB signals with ideal spectral shape. In order to improve the compatibility but reduce the cost and complexity, the colorless base station is implemented for the first time by utilizing the distributed intensity modulation. A proof-of-concept experiment is achieved for one-dimensional distance measurement with cm-level spatial resolution.

Fiber-optic remote Ultra-wideband noise radar with colorless base station

Compressed Sensing (CS) is a new method of signal and image processing which allows for exact recovery of an image from a number of samples much smaller than that required by the Nyquist/Shannon theorem. Compressed Sensing uses a priori information about the object called “sparsity”, which means that only a small number of image samples are nonzero. We have analyzed the superresolution behavior of CS taking into account the quantum fluctuations in the image. Our analysis allows to characterize the ultimate capabilities of CS imposed by the quantum nature of the light.

Hui Wang

Papers

Fiber-distributed Ultra-wideband noise radar with steerable power spectrum and colorless base station.

Quantum limits of super-resolution of optical sparse objects via sparsity constraint

Fiber-optic remote Ultra-wideband noise radar with colorless base station

Quantum fluctuations in Compressed Sensing