Projections Of Local Atomic Structure Revealed By Wavelet Analysis Of X-Ray Absorption Anisotropy

We propose and verify in an experiment a wavelet transform approach for analysis of x-ray absorption anisotropy (XAA) 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.