Review and experimental verification of x-ray dark-field signal interpretations with respect to quantitative isotropic and anisotropic dark-field computed tomography

Abstract

Talbot(-Lau) interferometric x-ray and neutron dark-field imaging has, over the past decade, gained substantial interest for its ability to provide insights into a sample’s microstructure below the imaging resolution by means of ultra small angle scattering effects. Quantitative interpretations of such images depend on models of the signal origination process that relate the observable image contrast to underlying physical processes. A review of such models is given here and their relation to the wave optical derivations by Yashiro et al and Lynch et al as well as to small angle scattering is discussed. Fresnel scaling is introduced to explain the characteristic distance dependence observed in cone beam geometries. Moreover, a model describing the anisotropic signals of fibrous objects is derived. The Yashiro-Lynch model is experimentally verified both in radiographic and tomographic imaging in a monochromatic synchrotron setting, considering both the effects of material and positional dependence of the resulting dark-field contrast. The effect of varying sample–detector distance on the dark-field signal is shown to be non-negligible for tomographic imaging, yet can be largely compensated for by symmetric acquisition trajectories. The derived orientation dependence of the dark-field contrast of fibrous materials both with respect to variations in autocorrelation width and scattering cross section is experimentally validated using carbon fiber reinforced rods.

Simulation study towards quantitative X-ray and neutron tensor tomography regarding the validity of linear approximations of dark-field anisotropy

“…proposed by Yashiro et al 12 and Lynch et al 13 in the context of their wave optical derivations of dark-field origination, and is also common in other theories of scattering. Based on these concepts, a minimal physically motivated model of dark-field orientation dependence for the case of arbitrary sample rotations (as opposed to rotations only about the optical axis) has been derived in Graetz et al 11 . The central results shall be briefly recapitulated here.…”

“…Fig. 1 ) and evaluating both its resulting mean variance over a fixed area (typically, the pixel size) and its auto-correlation function along the axis of interferometer sensitivity , the following minimal model of dark-field orientation dependence has been, based on concepts introduced in different ways by Yashiro et al 12 and Lynch et al 13 , derived in Graetz et al 11 : with denoting the sample-induced visibility loss measurable with grating interferometers. Given the purpose of Eq.…”

“…( 3 ) to capture the essential interrelations of scattering cross section and auto-correlation width of a rotating anisotropic scatterer, a number of leading order approximations are involved in the derivation of Eq. ( 3 ), for the details of which the reader shall be referred to Graetz et al 11 . In particular, any rotation invariant factors affecting only the global scale of have been dropped.…”

“…the overview given by Defrise and Gullberg 10 ) establish the theoretic feasibility of non-scalar tomography, the linear projection models assumed and required within the mathematical conception of tensor tomography are not actually well reproduced by the available physical contrast modality (dark-field). In a recent review, the origination and actual orientation dependence of dark-field contrast for anisotropic mass distributions has been investigated in detail (Graetz et al 11 ), yielding a minimal yet non-linear model capturing the central features of general dark-field anisotropy including in particular also the effect of varying scattering cross section in addition to the characteristic dependence of dark-field contrast on a structure’s correlation lengths. I.e., general dark-field anisotropy is concluded to be a function of two orientations (the optical axis and a perpendicular axis of interferometer sensitivity), which has not been taken into account so far and in particular challenges the general assumption in present literature that dark-field signals may be described as a function over the unit sphere.…”

Quantitative analysis of speckle-based X-ray dark-field imaging using numerical wave-optics simulations

“…Several studies have examined the dark-field signal strength for grating interferometry 21 , 22 . However, most studies in speckle-based X-ray imaging are focused on the speckle tracking accuracy and sensitivity for phase-contrast signal extraction 19 , 23 – 25 .…”