Direct determination of the wave field of an x-ray nanobeam

We present a remarkably accurate method for determining the wave field of an x-ray nanobeam. The intensity profile of a beam was directly measured over a range of three orders of magnitude while its phase distribution was successfully recovered using an iterative algorithm. The evolution of the wave field along the beam propagation direction was precisely simulated, and there was good agreement with the experimental results.

Figure 1

(Color online) Schematic diagram of x-ray intensity distribution sensing system using a microphase object (microbridge structure). (a) Hard x rays are focused by reflective optics. (b) Enlarged diagram of wave front in the vicinity of the beamwaist. (c) Wave front above and inside the microphase object.

Figure 2

(Color online) Microbridge structure used for measuring the intensity distributions of a hard x-ray line-focused beam. These images were obtained using a nanosearch microscope (Shimadzu Co.) that incorporates both a scanning confocal laser microscope and an atomic force microscope.

Figure 3

Results of measuring intensity profiles in the focal plane and phase retrieval calculations. (a) Intensity profiles in the focal plane. The gray line is the profile measured by scanning the microbridge, while the black line was obtained using phase retrieval calculations for determining the mirror surface profile. The plot interval is $1\mathrm{nm}$. (b) Single logarithmic plot of graph in (a). (c) Ideal profile of x-ray mirror. (d) Comparison of measured and reconstructed figure error profiles.

Figure 4

(Color online) Simulation results of intensity distributions of a line-focused hard x-ray beam near the focus. (a) Ideal intensity distribution near the focus. (b) Intensity distribution near the focus, calculated using the recovered figure error profile of Fig. 3d. (c) Intensity profile measured and simulated $50\mathrm{\mu }\mathrm{m}$ upstream from the focal plane.