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Figure 6
Wavelet transform of the experimental XAA pattern. (a) Three-dimensional view of the wavelet transform coefficients [\widetilde{\chi}_{{+}}] showing two spherical shells at distances of 3.75 Å and 40 Å and a single radial slice. (b) A radial slice of wavelet transform [\widetilde{\chi}_{{+}}]. The dashed circles and lines correspond to the angular range where the data were recorded, small circles mark the positions of Nb atoms, and squares mark artefacts. A false-color scale was used in order to show both strong and weak features. For a better visualization the radial coordinate is equal to the square root of the real-space distance. The dash-dotted hemicircle has a radius of 12 Å. (c) Profiles of [\widetilde{\chi}] along the [[2\overline{2}1]] and [[\overline{4}41]] directions. The thick solid (black) lines show the experimental wavelet coefficients. The dashed (blue) lines present the theoretical wavelet transforms calculated for nearest Nb atoms located along corresponding directions. The thin solid (red) lines correspond to the theoretical wavelet transforms calculated for single periodic atomic rows. The dash-dotted lines mark the position of Nb atoms in these rows.

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