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We present a x-ray microscopy technique based on structured illumination in a microscope that characterizes the size of the subresolution-limit features. The technique is effective for characterizing fine structures substantially beyond the Rayleigh resolution of the microscope. We carried out optical experiments to demonstrate the basic principle of this new technique. Experimental results show good agreement with theoretical predictions. This technique should find a wide range of important imaging applications with a feature size down to nanometer scale, such as oil and gas reservoir rocks, advanced composites, and functional nanodevices and materials.

In this Letter, we present a single-shot approach to quantitatively retrieve x-ray absorption and phase shift in grating interferometry. The proposed approach makes use of the energy-resolving capability of x-ray photon-counting detectors. The retrieval method is derived and presented and is tested based on numerical simulations, including photon shot noise. The good agreement between retrieval results and theoretical values confirms the feasibility of the presented approach.

A fast discrete curvelet transform based focus-stacking algorithm for extending the depth of focus of a transmission x-ray microscope (TXM) is presented. By analyzing an image stack of a sample taken in a Z-scan, a fully in-focus image can be generated by the proposed scheme. With the extended depth of focus, it is possible to obtain 3D structural information over a large volume at nanometer resolution. The focus-stacking method has been demonstrated using a dataset taken with a laboratory x-ray source based TXM system. The possibility and limitations of generalizing this method to a synchrotron based TXM are also discussed. We expect the proposed method to be of important impact in 3D x-ray microscopy.