Baur Manuel, Uhlmann Norman, Pöschel Thorsten, Schröter Matthias
Institute for Multiscale Simulation, Friedrich-Alexander-Universität, Nägelsbachstrasse 49b, 91052 Erlangen, Germany.
Fraunhofer Institute for Integrated Circuits, Flugplatzstrasse 75, 90768 Fürth, Germany.
Rev Sci Instrum. 2019 Feb;90(2):025108. doi: 10.1063/1.5080540.
The intensity of a monochromatic X-ray beam decreases exponentially with the distance it has traveled inside a material; this behavior is commonly referred to as Beer-Lambert's law. Knowledge of the material-specific attenuation coefficient μ allows us to determine the thickness of a sample from the intensity decrease the beam has experienced. However, classical X-ray tubes emit a polychromatic bremsstrahlung-spectrum. And the attenuation coefficients of all materials depend on the photon energy: photons with high energy are attenuated less than photons with low energy. In consequence, the X-ray spectrum changes while traveling through the medium; due to the relative increase in high energy photons, this effect is called beam hardening. For this varying spectrum, the Beer-Lambert law only remains valid if μ is replaced by an effective attenuation coefficient μ which depends not only on the material but also on its thickness x and the details of the X-ray setup used. We present here a way to deduce μ(x) from a small number of auxiliary measurements using a phenomenological model. This model can then be used to determine an unknown material thickness or in the case of a granular media its volume fraction.
单色X射线束的强度会随着其在材料内部传播的距离呈指数下降；这种行为通常被称为比尔-朗伯定律。了解特定材料的衰减系数μ，能让我们根据光束强度的下降来确定样品的厚度。然而，传统的X射线管发射的是多色轫致辐射光谱。而且所有材料的衰减系数都取决于光子能量：高能光子的衰减比低能光子小。因此，X射线光谱在穿过介质时会发生变化；由于高能光子的相对增加，这种效应被称为束硬化。对于这种变化的光谱，只有当μ被一个有效衰减系数μ替代时，比尔-朗伯定律才仍然有效，这个有效衰减系数μ不仅取决于材料，还取决于其厚度x以及所使用的X射线装置的细节。我们在此提出一种方法，使用一个唯象模型从少量辅助测量中推导出μ(x)。然后这个模型可用于确定未知材料的厚度，或者在颗粒介质的情况下确定其体积分数。
