Three-dimensional contrast transfer functions in propagation-based tomography

A single-step method is developed for three-dimensional reconstruction of the spatial distribution of complex refractive index in weakly scattering objects from multiple planar transmission images. The images are collected using coherent or partially-coherent illumination at a range of incident directions in the Fresnel region after free-space propagation from the object to the detector. The method is based on the contrast transfer function formalism extended to the cases of partially-coherent illumination and strongly absorbing samples. The proposed tomographic methods can be used for 3D reconstruction of internal structure of objects with X-rays, electrons and other forms of radiation and matter waves. Compared to related previously published methods for propagation-based phase-contrast tomography, the results reported in the present paper can be applied to a wider range of imaging conditions and can be also advantageous in terms of computational efficiency and robustness with respect to noise.