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Abstract
We present a development of the beam–tracking approach that allows its implementation in computed tomography. One absorbing mask placed before the sample and a high resolution detector are used to track variations in the beam intensity distribution caused by the sample. Absorption, refraction, and dark–field are retrieved through a multi–Gaussian interpolation of the beam. Standard filtered back projection is used to reconstruct three dimensional maps of the real and imaginary part of the refractive index, and of the dark–field signal. While the method is here demonstrated using synchrotron radiation, its low coherence requirements suggest a possible implementation with laboratory sources.
Highlights
X–ray phase contrast imaging (XPCi) is an established technique for the non–destructive analysis and visualization of specimens in a wide range of fields[1], such as biomedical imaging, materials science, and others
We have recently shown how the edge illumination principle[6,15] can be used in a beam tracking approach[16,17] to reconstruct absorption, refraction and scattering
The main advantages of beam tracking over alternative XPCi approaches are that it does not require spatial or temporal coherence, can be adapted to work with laboratory sources, requires only one optical element placed before the sample, and can be used in a single–shot manner, reducing acquisition time and delivered dose, but at the cost of a reduced final resolution
Summary
X–ray phase contrast imaging (XPCi) is an established technique for the non–destructive analysis and visualization of specimens in a wide range of fields[1], such as biomedical imaging, materials science, and others. In XPCi, in addition to absorption, the phase shift experienced by x–ray wave fronts when travelling through matter is exploited, which leads to an increase in the final image contrast. Where μ is the attenuation coefficient, α the mean refraction angle, β the imaginary part of the sample complex refractive index, δ the difference from unity of the real part of the sample complex refractive index, f the scattering distribution, and θ the scattering angle These three parameters are calculated from the variations, with respect to reference values obtained from an image without the sample, of the zero-th, first and second momentum of the beam intensity profile, which correspond to the total area, mean value, and variance of a Gaussian function, respectively. Equations 1, 2 and 4 express the retrieved signals as line integrals along the photon path of three physical properties of the sample. β (x, y, z) and σφ[2] (x, y, z) can be reconstructed using standard filtered back projection. δ (x, y, z), instead, can be reconstructed from α with a modified version of the filtered back projection, which adopts the Hilbert filter, instead of the ramp filter, to invert the derivative along x in the Fourier space
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