Iterative reconstruction in x-ray computed laminography from differential phase measurements

Phase-contrast X-ray computed laminography is demonstrated for the volume reconstruction of extended flat objects, not suitable to the usual tomographic scan. Using a Talbot interferometer, differential phase measurements are obtained and used to reconstruct the real part of the complex refractive index. The specific geometry of laminography leads to unsampled frequencies in a double cone in the reciprocal space, which degrades the spatial resolution in the direction normal to the object plane. First, the filtered backprojection formula from differential measurements is derived. Then, reconstruction is improved by the use of prior information of compact support and limited range, included in an iterative filtered backprojection algorithm. An implementation on GPU hardware was required to handle the reconstruction of volumes within a reasonable time. A synchrotron radiation experiment on polymer meshes is reported and results of the iterative reconstruction are compared with the simpler filtered backprojection.

Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm

X-ray Talbot interferometry is attractive as a method for X-ray phase imaging and phase tomography for objects that weakly absorb X-rays. Because X-ray Talbot interferometry has the advantage that X-rays of a broad energy bandwidth can be used, high-speed X-ray phase imaging is possible with white synchrotron radiation. In this paper, we demonstrate time-resolved three-dimensional observation with X-ray Talbot interferometry (namely, four-dimensional X-ray phase tomography). Differential phase images, from which a phase tomogram was reconstructed, were obtained through the Fourier-transform method, unlike the phase-stepping method that requires several (at least three) moiré images to be measured sequentially in order to generate one differential phase image. We demonstrate dynamic observation of a living worm in three dimensions with a time resolution of 0.5 s, visualizing a drastic change in the respiratory tract.