X–ray absorption, phase and dark–field tomography through a beam tracking approach

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.

Multimodal Phase-Based X-Ray Microtomography with Nonmicrofocal Laboratory Sources

“…The method can reconstruct the three-dimensional maps of attenuation, phase, and USAXS of a given sample. Starting from our previous work on beam-tracking CT with monochromatic radiation [23] and on planar imaging with polychromatic radiation [15], we build a theoretical framework which describes the signal reconstructed in beamtracking CT with polychromatic radiation. The theoretical model is tested on samples of known composition and is shown to provide quantitatively correct values for the retrieved linear attenuation coefficient μ and for the difference from unity of the real part of the refractive index δ for low-attenuating materials.…”

“…The subscripts o and i refer to the quantities retrieved from the profiles acquired with and without the sample, respectively. In the case of monochromatic radiation [23], the attenuation, refraction, and USAXS retrieved from a particular aperture of the mask can be written as the following line integrals:…”

“…where λ is the x-ray wavelength, l is the sample thickness, x a is the position of the mask aperture along the x direction, μ ¼ ð4π=λÞβ is the linear attenuation coefficient, β is the imaginary part of the complex refractive index, δ is the difference from unity of the real part of the complex refractive index, and σ 2 ϕ is the variance of the local USAXS distribution function ϕ [23].…”

Scalable, large area compound array refractive lens for hard X-rays

“…To realize single-exposure acquisition without moving optical components, Hartmann sensors can be used. Here, the X-ray beam is propagated through individual sub-apertures in a fully absorbing plane leading to a 2D array of beamlets 1, 8,9 . This method, however, exhibits low overall efficiency due to the unfavorable area fraction of the sub-apertures, preventing its use for applications at low flux.…”

“…We used 2D-Gaussian fit 7,9,32 for the estimation of the height, position and width of the spots (for more details see supplementary material, section I A) for the CARL characterization. It is also possible to retrieve absorption, differential phase and scattering contrasts from Fourier analysis, assuming that the spots reside on a quadratic array with equal spacing 1,2,28,33 .…”