Phase retrieval in 3D X-ray magnified phase nano CT: Imaging bone tissue at the nanoscale

X-ray phase computed tomography (CT) offers higher sensitivity than conventional X-ray CT. A new phase-CT instrument producing a nano-focused beam has been developed at the ESRF (European Synchrotron Radiation Facility) for nano-imaging. In order to obtain final images, a suited phase retrieval algorithm is necessary, which is attracting broader interest recently. In this paper, we explicit the 3D phase CT image reconstruction problem, including the stage of phase retrieval prior to 3D CT reconstruction. The phase retrieval problem is solved by extending the single distance Paganin method to multi-distance acquisitions, followed by an iterative non-linear conjugate gradient descent optimization method. The method is evaluated on bone tissue samples imaged at voxel sizes of 120 nm. The results obtained from acquisition at 1 and 4 distances, with and without the iterative refinement are compared. The results show that this method yields improved images compared to other methods.