The attenuation of x-rays in a material forms the basis of x-ray radiography and tomography. By measuring the transmission of the x-rays over a large amount of raypaths, the three-dimensional (3D) distribution of the x-ray linear attenuation coefficient can be reconstructed in a 3D volume. In x-ray microtomography ($\mu \mathrm{CT}$), however, the x-ray refraction yields a significant signal in the transmission image and the 3D distribution of the refractive index can be reconstructed in a 3D volume. To do so, several methods exist, on both a hardware and software level. In this paper, we compare two similar software methods, the modified Bronnikov algorithm and the simultaneous phase-and-amplitude retrieval. The first method assumes a pure phase object, whereas the latter assumes a homogeneous object. Although these assumptions seem very restrictive, both methods have proven to yield good results on experimental data.

© 2012 Optical Society of America

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