Abstract
X-ray grating interferometry (XGI) can provide access to unresolved sub-pixel information by utilizing the so-called dark-field or visibility reduction contrast. A recently developed variant of conventional XGI named dual-phase grating interferometer, based only on phase-shifting structures, has allowed for straightforward micro-structural investigations over multiple length scales with conventional X-ray sources. Nonetheless, the theoretical framework of the image formation for the dark-field signal has not been fully developed yet, thus hindering the quantification of unresolved micro-structures. In this work, we expand the current theoretical formulation of dual-phase grating interferometers taking into account polychromatic sources and beam hardening effects. We propose a model that considers the contribution of beam hardening to the visibility reduction and accounts for it. Finally, the method is applied to previously acquired and new experimental data showing that discrimination between actual micro-structures and beam hardening effects can be achieved.
Highlights
X-ray grating interferometry (XGI) [1,2] is an imaging technique that simultaneously provides three complementary contrasts; absorption, differential phase, and visibility reduction known as dark-field contrast
We started with imaging a water phantom, where visibility reduction would solely be due to beam hardening effects which our model can predict
Through theoretical modeling and experimental investigations, we have demonstrated that this effect strongly depends on the distance between the two phase gratings, affecting measurements across different autocorrelation lengths which are performed by changing the inter-grating distance
Summary
X-ray grating interferometry (XGI) [1,2] is an imaging technique that simultaneously provides three complementary contrasts; absorption, differential phase, and visibility reduction known as dark-field contrast. Assuming weak dependence of phase signal on wavelength and given that phase variations are much smaller compared to pixel size of detector , it is shown that the autocorrelation length for a dual-phase grating interferometer is given by (see Appendix for complete derivation). To perform the microstructural analysis only the scattering term is of interest, an appropriate correction method is required to account for the spectral term To estimate this term, we need the following parameters: the geometric parameters of the system, the grating parameters such as period, material, and depth, the spectrum of the X-ray source, and estimation of the absorption coefficient of the sample or knowledge of the material composition. The most complex is the energy dependent absorption coefficient of an unknown sample which can be estimated by the method presented in the Appendix (subsection (5.3))
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