Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography.

A well-known problem in x-ray microcomputed tomography is low sensitivity. Phase contrast imaging offers an increase of sensitivity of up to a factor of 10(3) in the hard x-ray region, which makes it possible to image soft tissue and small density variations. If a sufficiently coherent x-ray beam, such as that obtained from a third generation synchrotron, is used, phase contrast can be obtained by simply moving the detector downstream of the imaged object. This setup is known as in-line or propagation based phase contrast imaging. A quantitative relationship exists between the phase shift induced by the object and the recorded intensity and inversion of this relationship is called phase retrieval. Since the phase shift is proportional to projections through the three-dimensional refractive index distribution in the object, once the phase is retrieved, the refractive index can be reconstructed by using the phase as input to a tomographic reconstruction algorithm. A comparison between four phase retrieval algorithms is presented. The algorithms are based on the transport of intensity equation (TIE), transport of intensity equation for weak absorption, the contrast transfer function (CTF), and a mixed approach between the CTF and TIE, respectively. The compared methods all rely on linearization of the relationship between phase shift and recorded intensity to yield fast phase retrieval algorithms. The phase retrieval algorithms are compared using both simulated and experimental data, acquired at the European Synchrotron Radiation Facility third generation synchrotron light source. The algorithms are evaluated in terms of two different reconstruction error metrics. While being slightly less computationally effective, the mixed approach shows the best performance in terms of the chosen criteria.