TY - JOUR

T1 - Reconstruction algorithm for atomic-resolution holography using translational symmetry

AU - Matsushita, Tomohiro

AU - Guo, Fang Zhun

AU - Suzuki, Motohiro

AU - Matsui, Fumihiko

AU - Daimon, Hiroshi

AU - Hayashi, Kouichi

PY - 2008/10/29

Y1 - 2008/10/29

N2 - The most widely used methods for reconstructing three-dimensional atomic arrangements from a photoelectron hologram and an x-ray fluorescence hologram are based on an integral kernel, for example, the Fourier transformation. These methods require many holograms that are recorded using multiple energies since the Fourier transformation requires an infinite integral interval. Therefore, it is difficult to reconstruct an atomic arrangement from a single-energy hologram. In order to accomplish to reconstruct the three-dimensional atomic arrangement from a single-energy hologram, we have proposed a scattering pattern extraction algorithm using the maximum-entropy method (SPEA-MEM) for photoelectron holography. In this paper, we also describe the application of this algorithm to x-ray fluorescence holography. We have succeeded in reconstructing 58 Au atoms from a single-energy x-ray fluorescence hologram that we have measured. However, artifacts have been observed in the reconstructed image. This is due to the long coherent length and the mean-free path of the x rays. Hence, we have incorporated crystal translational symmetry into SPEA-MEM to solve this problem. We have applied this algorithm to an x-ray fluorescence hologram of Au and a photoelectron hologram of Cu that we have measured. We have succeeded in reconstructing a very clear atomic arrangement with an accuracy of 0.01 nm in three-dimensional real space for both holograms.

AB - The most widely used methods for reconstructing three-dimensional atomic arrangements from a photoelectron hologram and an x-ray fluorescence hologram are based on an integral kernel, for example, the Fourier transformation. These methods require many holograms that are recorded using multiple energies since the Fourier transformation requires an infinite integral interval. Therefore, it is difficult to reconstruct an atomic arrangement from a single-energy hologram. In order to accomplish to reconstruct the three-dimensional atomic arrangement from a single-energy hologram, we have proposed a scattering pattern extraction algorithm using the maximum-entropy method (SPEA-MEM) for photoelectron holography. In this paper, we also describe the application of this algorithm to x-ray fluorescence holography. We have succeeded in reconstructing 58 Au atoms from a single-energy x-ray fluorescence hologram that we have measured. However, artifacts have been observed in the reconstructed image. This is due to the long coherent length and the mean-free path of the x rays. Hence, we have incorporated crystal translational symmetry into SPEA-MEM to solve this problem. We have applied this algorithm to an x-ray fluorescence hologram of Au and a photoelectron hologram of Cu that we have measured. We have succeeded in reconstructing a very clear atomic arrangement with an accuracy of 0.01 nm in three-dimensional real space for both holograms.

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U2 - 10.1103/PhysRevB.78.144111

DO - 10.1103/PhysRevB.78.144111

M3 - Article

AN - SCOPUS:55349117491

VL - 78

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 0163-1829

IS - 14

M1 - 144111

ER -