Quantitative phase tomography by holographic reconstruction

The coherence of third generation synchrotron beams makes a trivial form of phase-contrast radiography possible. It is based on simple propagation and corresponds to the defocusing technique of electron microscopy. Most of the work until now uses this technique to detect phase discontinuities associated with edges in the specimen. The tomographic reconstruction was initially performed using the algorithm for X-ray absorption tomography, a temporary and obviously unsatisfactory approach. This results in a decent solution for some cases, but gives rise to artifacts and does not reveal quantitatively the inner structure of the object. However the Fresnel diffraction fringes contain in an entangled form the phase modulation by the sample. We have successfully implemented a method for quantitative phase tomography based on the propagation technique. The reconstruction of the 3D refractive index distribution involves two steps. First the phase modulation is numerically retrieved from the combination of several images recorded at different distances. This holographic reconstruction process is repeated for a large number of angular positions of the specimen. Then the conventional filtered backprojection algorithm is used to determine the three dimensional distribution from the retrieved phase maps. The reconstructed 3D image of a complicated polystyrene foam sample has a straightforward interpretation with a spatial resolution limited by the detector to 1-2 microns.