Accuracy and precision of reconstruction of complex refractive index in near-field single-distance propagation-based phase-contrast tomography

Abstract

We investigate the quantitative accuracy and noise sensitivity of reconstruction of the 3D distribution of complex refractive index, n(r)=1−δ(r)+iβ(r), in samples containing materials with different refractive indices using propagation-based phase-contrast computed tomography (PB-CT). Our present study is limited to the case of parallel-beam geometry with monochromatic synchrotron radiation, but can be readily extended to cone-beam CT and partially coherent polychromatic X-rays at least in the case of weakly absorbing samples. We demonstrate that, except for regions near the interfaces between distinct materials, the distribution of imaginary part of the refractive index, β(r), can be accurately reconstructed from a single projection image per view angle using phase retrieval based on the so-called homogeneous version of the Transport of Intensity equation (TIE-Hom) in combination with conventional CT reconstruction. In contrast, the accuracy of reconstruction of δ(r) depends strongly on the choice of the “regularization” parameter in TIE-Hom. We demonstrate by means of an instructive example that for some multi-material samples, a direct application of the TIE-Hom method in PB-CT produces qualitatively incorrect results for δ(r), which can be rectified either by collecting additional projection images at each view angle, or by utilising suitable a priori information about the sample. As a separate observation, we also show that, in agreement with previous reports, it is possible to significantly improve signal-to-noise ratio by increasing the sample-to-detector distance in combination with TIE-Hom phase retrieval in PB-CT compared to conventional (“contact”) CT, with the maximum achievable gain of the order of 0.3δ/β. This can lead to improved image quality and/or reduction of the X-ray dose delivered to patients in medical imaging.