In this talk, a theoretical study is provided for the x-ray
dark-field tomography(XDT) assuming the spectral x-ran detection technology.
For XDT, a generalized Fockker-Planck equation(GFPE) is employed to
describe the light propagation for highly forward-peaked medium with small
but sufficient amount of large-angle scattering. Properties of GFPE are studied,
such as existence of a unique solution and positivity of the solution.
GFPE and its discrete analogues can be solved naturally with an iteration procedure,
and convergence of the iteration procedure is shown. XDT, as an inverse parameter problem
with GFPE as the forward model, is then studied. Numerical discretization schemes of
GFPE and the associated XDT are introduced. Simulation results are reported on several
numerical examples for GFPE and for XDT.