Projections of local atomic structure revealed by wavelet analysis of x-ray absorption anisotropy

Abstract

We propose and verify in an experiment a wavelet transform approach for analysis of x-ray absorption anisotropy ͑XAA͒ patterns recorded using a broadband polychromatic x-ray beam. XAA results from the interference between an incident plane wave with spherical waves scattered from atoms inside the sample. This interference modifies the total x-ray field amplitude at the sites of absorbing atoms and effectively changes the atomic absorption cross section. XAA is monitored by measuring the secondary yield while the sample is rotated relative to the incident-beam direction. For broadband polychromatic hard x-ray illumination, owing to the short coherence length, significant anisotropy in absorption is only found close to directions of the incident radiation coinciding with interatomic directions. In this work, we show that the signals from individual atoms have the same universal shape and differ only in the scale and angular position. Combined with the directional localization this allows us to construct a spherical wavelet family matched to the shape of the observed signal. Application of the wavelet transform to experimental x-ray absorption anisotropy has provided high-resolution projections of the local atomic structure in an InAs crystal up to the sixth coordination shell. While in a recent work XAA delivered a three-dimensional image of the unit cell obtained through a tomographic algorithm, the wavelet approach provides projections of the local structure of absorber atoms with depth resolution and does not depend on the translational long-range order. This opens a way for a quantitative analysis of polychromatic beam x-ray absorption anisotropy for local structure imaging.

Element sensitive holographic imaging of atomic structures using white x rays

“…In order to retrieve the structural information from the measured holograms, two approaches were used: wavelet analysis 16,25 and a linear regression approach. 18 The first method is model free and allows one to obtain projections of the local atomic structure.…”

“…As the wavelet analysis of white-beam x-ray holograms has been described previously, 25 here we will give only a brief description of it. The wavelet analysis takes advantage of unique properties of the holographic signal recorded for a white beam, which can be written as…”

X-ray holography

“…17). Figure 18 shows the holographic pattern of X-ray absorption anisotropy for an InAs crystalline sample [186]. Figure 18 shows the holographic pattern of X-ray absorption anisotropy for an InAs crystalline sample [186].…”

“…The sum and difference of symmetrically recorded holograms always correspond to holograms with amplitudes of purely imaginary or purely real scattering. Holographic X-ray absorption anisotropy pattern for an InAs crystal with (001) surface orientation [186]. Figure 18.…”

X-ray holography

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