  A new method is developed for three-dimensional (3D) reconstruction of
multi-material objects using propagation-based X-ray phase-contrast tomography
(PB-CT) with phase retrieval via the contrast transfer function (CTF)
formalism. The approach differs from conventional PB-CT algorithms that apply
phase retrieval on individual two-dimensional (2D) projections. Instead, this
method involves performing phase retrieval to the CT-reconstructed volume in
3D. The CTF formalism is further extended to the cases of partially-coherent
illumination and strongly absorbing samples. Simulated results demonstrate that
the proposed post-reconstruction CTF method provides fast and stable phase
retrieval, producing results equivalent to conventional pre-reconstruction 2D
CTF phase retrieval. Moreover, it is shown that application can be highly
localised to isolated objects of interest, without a significant loss of
quality, thus leading to increased computational efficiency. Combined with the
extended validity of the CTF to greater propagation distances, this method
provides additional advantages over approaches based on the
transport-of-intensity equation.
