Analytic image reconstruction in local phase-contrast tomography

Phase-contrast tomography is a non-interferometric imaging technique for reconstructing the refractive index distribution of a weakly absorbing object from a set of tomographic projection measurements. In many practical situations, the spatial resolution of the reconstructed image can be increased by minimizing the field of view (FOV) of the imaging system. When the object of interest is larger than the FOV, the measured projections are truncated and one is faced with a local tomography reconstruction problem. In this work, we analytically and numerically investigate the problem of reconstructing tomographic images from truncated phase-contrast projection data. A simple backprojection algorithm for reconstructing object discontinuities from truncated phase-contrast projection data is proposed and investigated that involves no explicit filtering of the projection data. We also investigate the use of the filtered backprojection algorithm and a local tomography reconstruction algorithm developed for absorption CT. These reconstruction algorithms are implemented and numerically investigated to corroborate our theoretical assertions.