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Yukio Takahashi1 2

1, Osaka University, Suita, Osaka, Japan
2, RIKEN SPring-8 Center, Sayo, Hyogo, Japan

X-ray ptychography is a method of coherent X-ray diffractive imaging that applies translational diversity, in which the object of interest is scanned in small steps by an overlapping probe, providing redundancy in collected data. So far, X-ray ptychography has been applied to structural imaging of various specimens in biology and materials science at the nanoscale. X-ray ptychography can also provide us with chemical information of a sample by using an X-ray absorption edge, which is often referred to as X-ray spectro-ptychography. Recently, the X-ray absorption fine structure (XAFS) of nanomaterials has been reconstructed by soft X-ray spectro-ptychography[1]. Extending this approach to the hard X-ray region will enable us to visualize the chemical state of nanostructures buried within bulk materials. However, a limitation of this method is the weak absorption of incident X-rays in the hard X-ray region. To improve the convergence of the phase retrieval for complex-valued images in X-ray spectro-ptychography, we proposed and demonstrated the addition of a constraint based on the Kramers–Kronig relation (KKR constraint) to the phase retrieval algorithm[2]. A numerical simulation showed that the speed of convergence was increased by using the improved algorithm with the KKR. We successfully demonstrated its usefulness in a proof-of-principle experiment using a test sample at SPring-8. We applied hard X-ray spectro-ptychography to visualize the oxidation state of oxygen storage and release particles, CZx (Ce2Zr2Ox, 7≦x≦8), which are used in automobile exhaust gas cleaning systems owing to their high oxygen storage and release property. Twenty-eight energies were selected between 5.717 keV and 5.817 keV around the Ce L3 absorption edge. Diffraction patterns were measured with 4 s exposure at each scan position. After reconstructing the object functions at each energy using the KKR constraint, an oxidation state mapping was derived with 13 nm pixel resolution by linear combination of the XAFS spectra of fully reduced CZ7 and oxidized CZ8. Nanodomain structures due to the heterogeneous oxidation state in CZ7.6 particles were clearly visualized[3].

References
[1] D. A. Shapiro et al., Nat. Photonics 8, 765-769 (2014).
[2] M. Hirose, K. Shimomura, N. Burdet, and Y. Takahashi, Opt. Express 25, 8593-8603 (2017).
[3] M. Hirose, N. Ishiguro, K. Shimomura, N. Burdet, H. Matsui, M. Tada, and Y. Takahashi, submitted

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