The reduction in visibility in x-ray grating interferometry based on the Talbot effect is formulated by the autocorrelation function of spatial fluctuations of a wavefront due to unresolved micron-size structures in samples. The experimental results for microspheres and melamine sponge were successfully explained by this formula with three parameters characterizing the wavefront fluctuations: variance, correlation length, and the Hurst exponent. The ultra-small-angle x-ray scattering of these samples was measured, and the scattering profiles were consistent with the formulation. Furthermore, we discuss the relation between the three parameters and the features of the micron-sized structures. The visibility-reduction contrast observed by x-ray grating interferometry can thus be understood in relation to the structural parameters of the microstructures.

Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.

Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.

With the aim of clinical applications of X-ray phase imaging based on Talbot–Lau-type grating interferometry to joint diseases and breast cancer, machines employing a conventional X-ray generator have been developed and installed in hospitals. The machine operation especially for diagnosing rheumatoid arthritis is described, which relies on the fact that cartilage in finger joints can be depicted with a dose of several milligray. The palm of a volunteer observed with 19 s exposure (total scan time: 32 s) is reported with a depicted cartilage feature in joints. This machine is now dedicated for clinical research with patients.

We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moiré fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.