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Conventional imaging techniques acquire information of an object based on the point-to-point correspondence between the object-space and the image-space. It usually results in data redundancy, and the information acquisition efficiency is much lower than the Shannon Limit determined by Information Theory. However, in ghost imaging, the information of an object is coded by the fluctuations of light field. Combining with compressive sensing theory, ghost imaging via sparsity constraints (GISC) provides the way of approaching the Shannon Limit, and it has many potential applications, such as three-dimensional lidar and spectral camera in real space, x-ray Fourier-transform diffraction imaging in reciprocal space, etc.
The experimental demonstration of x-ray Fourier-transform ghost imaging via sparsity constraints has been fulfilled recently, which may extend x-ray crystallography to non-crystalline samples. However, there are still some obstacles in the road to x-ray GISC nanoscope. Here we present a tabletop microscopy system based on the x-ray Fourier-transform GISC method. Since efficient information coding and sampling is essential in GISC, we optimize the fluctuations of x-ray field to achieve a high quality pseudothermal source and propose a data-multiplexing algorithm. Researches show that x-ray speckle patterns with better contrast in a large area can be obtained by positioning an appropriate pinhole array in front of a designed diffuser, and the sampling efficiency can be greatly improved by the multiplexing of the intensities at different detecting positions.
Further work in progress concentrates on the enhancement of imaging sensitivity, the improvement of phase recovery algorithms, and taking full advantage of the prior knowledge to obtain more high-frequency information of nanoscale samples.