[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

Nal with the difference that the cross section of

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nal with the difference that the cross-section of scattering is replaced by the fluorescence one and the absorption coefficient at the scattered energy (close to the incident energy E 0 ) is replaced by the one at the fluorescence emission line E . Note that while µ ( E 0 ) can be reconstructed from the transmission tomography, µ ( E ) is a difficult quantity to evaluate. As a practical solution, the absorption at the fluorescent line energies is sometimes scaled as E 3 , independent of the composition, under the assumption that the main con- tribution to the absorption is the photoelectric effect. This approximation is justified only if the scaling interval is not in the vicinity of the absorption edges of the sample elements or is much larger than them. Another approach is to try to solve a more complex numerical problem, where the dependency of µ on all the element concentrations is taken into account . A method that provides a numerical solution to the reconstruction problem by combining the information that comes from transmission, Compton/Rayleigh and flu- orescence tomography has been developed [78]. This method uses so-called “optimal-estimate functions” to extrapolate the absorption coefficient µ ( E ) at all fluorescence lines energies from µ ( E 0 ) and p scat ( E 0 , Θ ). For the flu- orescence reconstruction it is necessary to estimate µ ( E ) at the energies of elements not accessible in fluorescence ( Z 15). When the mass-density dis- tribution of some elements is known, one can separate the contribution of the known elements to µ ( E 0 ) and p scat ( E 0 , Θ ) from the contribution of the unknown treated as a whole. The reconstruction algorithm starts from an initial guess of the distribu- tions of all the elements with Z 15 which can be obtained by a reconstruc- tion with no self-absorption corrections. Further details of the reconstruction algorithm, combining the three tomographic signals can be found in the paper by Golosio et al. [78]. This method was applied to the study of a grain ex- tracted from the martian meteorite NWA817 and stored in a silica container. Special care was given to the determination of the Fe and Mn contents since they are key values to discuss the martian origin. The grain was placed inside a pure silica capillary having a 170 µ m-internal diameter and 45- µ m-thick walls. A monochromatic beam of 25 keV was used, with a transverse beamsize of 3 × 5 µ m 2 (Vert. × Hor.). The beamspot was obtained using compound refractive lenses for focusing coupled to a 5- µ m pinhole to reduce the horizontal size. The measured flux on the sample was about 10 10 ph s 1 in the focused beam. The capillary was placed on a system
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496 A. Simionovici and P. Chevallier (a) (b) (c) Fig. 7.33. NWA 817 grain reconstructed in (a) transmission, (b) Compton and (c) Rayleigh for vertical translation and rotation around a horizontal axis (vertical scanning geometry). A Si-drift detector placed at 90 in the vertical plane was used for measuring the intensity of the fluorescent/scattered signals. The sample
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  • Spring '14
  • MichaelDudley

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