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We present a novel approach to perform Rayleigh-to-Comptom (RC) measurements using a bent analyzer crystal in Laue geometry. The ratio of the elastically to the inelastically scattered photons gives directly access to the effective atomic number of the same by eliminating several side effects falsifying the scattered spectrum, eg. absorption in the sample. The use of the analyzer crystal, instead of an energy dispersive detector, enables us to measure in forward scattering geometry, where the method is optimized in respect to the contrast-to-noise ratio for low Z materials. The first generation computed tomography approach enables us to reconstruct the RC-value independently from the scattering geometry on a square image grid. We give this method the acronym RC-CT. The identity of values in the RC method and the RC-CT method will be derived. he conical bent crystal is focused on the source line where the incident monochromatic beam traverses the sample. The analyzer crystal reflects the elastic line of the scatter spectrum into a scintillation detector. The inelastic part of the spectrum passes the crystal and is recorded in a second scintillation detector. By rocking the analyzer, the whole energy distribution of the scatter spectrum can be obtained with an energy resolution dominated by the rocking curve width of the bent crystal. We will discuss the requirements and the constraints on the geometrical parameter of the experiment. From this, it is concluded that the method requires high flux sources like synchrotron. Employing the contrast-to-noise ratio introduced by Harding et al, the wavelength dispersive approach to the RC method is evaluated for a wide range of elements. Finally, we show a first reconstruction of a bone sample and discus s possible applications in medical and material science.
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