Extinction effects in x-ray holographic imaging with internal reference

Korecki, P.; Новиков, Д. В.; Tolkiehn, Martin; Materlik, G.

doi:10.1103/physrevb.69.184103

Cited by 33 publications

(37 citation statements)

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“…Second, for polychromatic hard x rays the scattering takes place in the forward-scattering geometry for which extinction does not influence the secondary yield significantly. 16 Experimentally the absence of the extinction effects for polychromatic radiation was demonstrated in Ref. 17.…”

Section: Introductionmentioning

confidence: 96%

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

2009

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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.

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Section: Introductionmentioning

confidence: 96%

“…An in-depth analysis of this effect was presented in Ref. 16. It was shown that the extinction-induced artifacts can interfere with the correct images at the atomic positions in the holographic reconstructions.…”

Section: Introductionmentioning

confidence: 99%

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

2009

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“…Such an information is not accessible in the recently proposed methods of direct structure retrieval from XH patterns, which probe only the real parts of the structure factors, i.e., the symmetrical part of the structure [16]. Besides, in XH and in Kikuchi electron diffraction, the asymmetry of the signal can also be due to dynamical extinction effects and does not ultimately arise from structural differences [17,18]. Here, a direct comparison of the data, recorded in the same condition for both crystal orientations, shows that the asymmetry comes solely from structural effects.…”

Section: Prl 96 035502 (2006) P H Y S I C a L R E V I E W L E T T E mentioning

confidence: 96%

X-Ray Tomographic Imaging of Crystal Structure at the Atomic Level

Korecki

Tolkiehn²,

Новиков³

et al. 2006

Phys. Rev. Lett.

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A direct nondiffractive tomographic algorithm is proposed for the determination of the crystal structure from real-space projections obtained by illuminating the sample with white x rays. This approach was applied to the pattern of the directional fine structure in absorption of white x rays recorded for a GaP crystal and allowed for a determination of the electron density distribution within the unit cell. DOI: 10.1103/PhysRevLett.96.035502 PACS numbers: 61.10.ÿi, 42.30.Rx, 81.70.Tx The majority of x-ray methods for crystal structure investigations are based on diffraction phenomena and sample the information in the reciprocal space by measuring the intensities at discrete Bragg peak positions [1]. Usually, a Fourier transformation is used to recover the electron density distribution of the object. However, a direct back transform is hindered by the lack of phase information in the recorded intensity data and the inversion algorithms are ambiguous. The phase information can become directly accessible, e.g., by using anomalous [2] or multibeam x-ray diffraction [3]. Another approach involves measuring the x-ray wave field intensity at atomic sites inside a crystal as it is performed in the x-ray standing wave technique [4] or in x-ray holography (XH) [5,6]. The absorption cross section in these methods is modulated by x-ray diffraction, which results in an angular dependent absorption fine structure measured through the secondary yield coming from specific sorts of atoms. This directional fine structure can be inverted to real space by using Fourier [7] or holographic reconstruction [8]. All these methods utilize monochromatic x-ray radiation.In this Letter we propose and demonstrate experimentally that crystal structure can be recovered from real-space projections obtained with polychromatic x rays (hereafter called white x rays), by using a nondiffractive tomographic algorithm. This approach is based on recent work [9], which showed that the directional absorption fine structure is related to the spherical projection of crystal structure. For a white x-ray beam, the wave field, formed by interference of the incident beam with the waves scattered on single atoms, cancels out by energy integration for all directions, except for the forward scattering component, coinciding with the incident beam. In a practical case, the white x-ray radiation is not uniform over the whole energy range, which leads to remnant high order diffraction effects. However, in the presence of long-range order, the distortion of the real-space projection is small for directions coinciding with the lattice planes and, as it will be shown, does not significantly influence tomographic reconstruction.Scattering of spherical waves from atoms of the sample onto an absorbing atom results in directional absorption fine structure [10]. For a white x-ray beam this fine structure can be written as [9] k ÿ2r 0 Rewherek is the beam direction, r 0 is the Thomson scattering length, Nk is the effective x-ray spectrum, r is the electron density, r is...

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“…Both of these two kinds of non-holographic terms manifest their effects as abrupt intensity changes in a very narrow angular region in the center of the Kossel lines, and therefore contribute mostly to the higher order harmonics. It has been demonstrated in previous studies [19] that the scattering from large crystals will also contribute to lower order harmonics. The non-holographic terms in these scattering contributions are negligible as they are mostly from the wide angular regions away from Kossel lines.…”

Section: The Integral Function In (11)mentioning

confidence: 99%

“…Therefore, the higher order spherical harmonics generated by sharp Kossel lines due to large crystal size can be excluded from the structure solving matrix without losing the structural information. This acts effectively as a low-pass filter for suppressing the non-holographic components, namely the object-object terms [18] and the secondary yield caused by extinction effect [19] in XFH data.…”

Section: The Integral Function In (11)mentioning

confidence: 99%