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.

We demonstrate for the first time (to our knowledge) that an image with high quality can still be obtained in scattering media by applying the second-order correlation of illuminating light field. The effect of multiple scattering on the imaging quality is analyzed both theoretically and experimentally. Potential applications and methods to further improve the imaging quality in scattering media are also discussed.

Correlated imaging through atmospheric turbulence is studied, and the analytical expressions describing turbulence effects on image resolution are derived. Compared with direct imaging, correlated imaging can reduce the influence of turbulence to a certain extent and reconstruct high-resolution images. The result is backed up by numerical simulations, in which turbulence-induced phase perturbations are simulated by random-phase screens inserted into propagation paths.

The Fourier-transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a lensless scheme. The experimental results are in good agreement with the standard Fourier transform of the corresponding objects. This scheme provides a route toward aberration-free diffraction-limited three-dimensional images with classically incoherent thermal light (or neutrons), which have no resolution and depth-of-field limitations of lens-based tomographic systems.

The image information acquisition ability of a conventional camera is usually much lower than the Shannon Limit since it does not make use of the correlation between pixels of image data. Applying a random phase modulator to code the spectral images and combining with compressive sensing (CS) theory, a spectral camera based on true thermal light ghost imaging via sparsity constraints (GISC spectral camera) is proposed and demonstrated experimentally. GISC spectral camera can acquire the information at a rate significantly below the Nyquist rate and the resolution of the cells in the three-dimensional (3D) spectral images data-cube can be achieved with a two-dimensional (2D) detector in a single exposure. For the first time, GISC spectral camera opens the way of approaching the Shannon Limit determined by Information Theory in optical imaging instruments.

Three-dimensional ghost imaging LiDAR via sparsity constraint (3D GISC LiDAR), as a staring imaging method, can obtain both the range information and spatial distribution of a remote target with a single-pixel time-resolved detector. However, previous demonstrations mainly focused on the relatively static scene in visible light. Here we propose an airborne near infrared 3D GISC LiDAR system and airborne high-resolution imaging is implemented. Experimental results show that an image with 0.48 m horizontal resolution as well as 0.5 m range resolution at approximately 1.04 km height can be achieved. Some considerations on the improvement of this LiDAR system are also discussed.