Sparse phase-stepping in two-dimensional x-ray phase contrast imaging.

We have developed a sparse phase-stepping (SPS) method for x-ray Talbot-Lau interferometry, which first constructs a SPS intensity pattern of fewer images than the conventional phase-stepping (PS) method and then fills the data gap with neighboring pixels for phase retrieval. The SPS method is highly beneficial in practice since the fundamental difference in spatial resolution between the SPS and PS methods becomes negligible due to the blur caused by an interferometer. The concept of the SPS method has been proved by the experiment using a small effective source size. Furthermore, the experiment using a large effective source size has verified that in practical situations the SPS method can reduce the required number of images for phase retrieval and still offer the retrieved images with as high a spatial resolution as the PS method.

A phase demodulation method with high spatial resolution for two-dimensional single-shot X-ray Talbot interferometry.

A new phase demodulation approach is proposed that uses windowed Fourier transforms to achieve high spatial resolution in fringe pattern analysis with a high signal-to-noise ratio for single-shot X-ray grating-based interferometry. Conventionally, Fourier transforms have been used to demodulate single-fringe patterns, but this requires a fringe pattern with a long period to obtain an acceptable signal-to-noise ratio among the demodulated parameters. However, by controlling the signal-to-noise ratio, the spatial resolution of demodulated parameters is degraded below that obtained from the phase-stepping method, which requires several images to obtain these parameters. In this paper, we introduce the use of a windowed Fourier transform with a process for analyzing the objective spectrum in isolation from other spectra on the Fourier space to overcome the limitations of the Fourier transform method. It is proved that with suitable assumptions the objective spectrum is isolated theoretically, and the spatial resolution is improved by practically accepting the limitations from the assumptions. We demonstrate the validity of the proposed method by comparing the modulation transfer function of a synthetic phantom with the conventional FT method. The proposed method is also valid on practical data obtained by an experimental setup, by which it is demonstrated that a high spatial resolution with high signal-to-noise ratio can be achieved by our proposed method.

Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube.

A Talbot-Lau interferometer using two-dimensional gratings and a conventional x-ray tube has been used to investigate a phase-contrast imaging technique that is sensitive to phase gradients in two orthogonal directions. Fourier analysis of Moiré fringe patterns was introduced to obtain differential phase images and scattering images from a single exposure. Two-dimensional structures of plastic phantoms and characteristic features of soft tissue were clearly obtained at 17.5 keV. The phase-stepping technique was also examined to investigate the spatial resolution of different phase retrieval methods. In the presented setup we found that the choice of phase retrieval method made little difference in image blur, and a large effective source size was found to give a high intensity in the image plane.

Single-nanometer focusing of hard x-rays by Kirkpatrick-Baez mirrors.

We have constructed an extremely precise optical system for hard-x-ray nanofocusing in a synchrotron radiation beamline. Precision multilayer mirrors were fabricated, tested, and employed as Kirkpatrick-Baez mirrors with a novel phase error compensator. In the phase compensator, an at-wavelength wavefront error sensing method based on x-ray interferometry and an in situ phase compensator mirror, which adaptively deforms with nanometer precision, were developed to satisfy the Rayleigh criterion to achieve diffraction-limited focusing in a single-nanometer range. The performance of the optics was tested at BL29XUL of SPring-8 and was confirmed to realize a spot size of approximately 7 nm.

Wavefield characterization of nearly diffraction-limited focused hard x-ray beam with size less than 10 nm.

In situ wavefront compensation is a promising method to realize a focus size of only a few nanometers for x-ray beams. However, precise compensation requires evaluation of the wavefront with an accuracy much shorter than the wavelength. Here, we characterized a one-dimensionally focused beam with a width of 7 nm at 20 keV using a multilayer mirror. We demonstrate that the wavefront can be determined precisely from multiple intensity profiles measured around the beamwaist. We compare the phase profiles recovered from intensity profiles measured under the same mirror condition but with three different aperture sizes and find that the accuracy of phase retrieval is as small as λ∕12.