Quantitative grating-based x-ray dark-field computed tomography

Grating-based x-ray dark-field computed tomography is a functional method that utilizes the scattering contrast mechanism to explore the inaccessible spatially resolved internal structure of the sample. In this letter, we show that the second moment of the scattering angle distribution can be expressed as the minus logarithm of the visibility degradation of the oscillation curve in grating-based imaging. According to the conclusion of Khelashvili et al. [Phys. Med. Biol. 51, 221 (2006)], the minus logarithm of the visibility ratio fulfills the line integral condition; consequently the scattering information can be reconstructed quantitatively by conventional computed tomography algorithms. Results from a computer simulation and from an actual experiment both validate our deduction.