Evaluation of phase retrieval approaches in magnified X-ray phase nano computerized tomography applied to bone tissue

X-ray phase contrast imaging offers higher sensitivity compared to conventional X-ray attenuation imaging and can be simply implemented by propagation when using a partially coherent synchrotron beam. We address the phase retrieval in in-line phase nano-CT using multiple propagation distances. We derive a method which extends Paganin's single distance method and compare it to the contrast transfer function (CTF) approach in the case of a homogeneous object. The methods are applied to phase nano-CT data acquired at the voxel size of 30 nm (ID16A, ESRF, Grenoble, France). Our results show a gain in image quality in terms of the signal-to-noise ratio and spatial resolution when using four distances instead of one. The extended Paganin's method followed by an iterative refinement step provides the best reconstructions while the homogeneous CTF method delivers quasi comparable results for our data, even without refinement step.