Phase contrast and coherent scatter imaging have the potential to improve the detection of materials of interest in x ray screening. While attenuation is dependent on atomic number, phase is highly dependent on electron density, and thus offers an additional discriminant. A major limitation of phase imaging has been the required spatial coherence of the xray illumination, which typically requires a small (10-50 μm) source or multiple images captured with precision gratings, both of which present challenges for high throughput image acquisition. An alternative approach uses a single coarse mesh. This significantly relaxes the source spot size requirement, improving acquisition times and allows near-real-time phase extraction using Fourier processing of the acquired images. Diffraction signatures provide a third approach which yields another set of information to identify materials. Specific angles characteristic of target materials are selected through broad slot apertures for rapid throughput. Depth information can be extracted from stereoscopic imaging using multiple slots. A system capable of simultaneous phase, coherent scatter, and absorption imaging was constructed. Discrimination of materials on the basis of both phase and coherent scatter signatures is demonstrated.

Phase and coherent scatter imaging for improved discrimination of low-density materials

A recently developed technique for phase imaging using table top sources is to use multiple fine-pitch gratings.
However, the strict manufacturing tolerences and precise alignment required have limited the widespread adoption
of grating-based techniques. In this work, we employ a technique recently demonstrated by Bennett et al.1 that
ultilizes a single grid of much coarser pitch. Phase is extracted using Fourier processing on a single raw image taken
using a focused mammography grid. The effects on the final image of varying grid, object, and detector distances,
window widths, and of a variety of windowing functions, used to separate the harmonics, were investigated.

Fourier transform image processing techniques for grid-based phase contrast imaging

Mesh-based phase contrast Fourier transform imaging

This paper presents the application of the spectral parameter power series method [Pauli, Math Method Appl Sci 33:459–468 (2010)] for constructing the Green’s function for the elliptic operator $$-\nabla \cdot I\nabla $$
 in a rectangular domain $$\varOmega \subset \mathbb R ^{2}$$
 , where $$I$$
 admits separation of variables. This operator appears in the transport-of-intensity equation (TLE) for undulatory phenomena, which relates the phase of a coherent wave with the axial derivative of its intensity in the Fresnel regime. We present a method for solving the TIE with Dirichlet boundary conditions. In particular, we discuss the case of an inhomogeneous boundary condition, a problem that has not been addressed specifically in other works, under the restricted assumption that the intensity $$I$$
 admits separation of variables. Several simulations show the validity of the method.

The phase retrieval problem: a spectral parameter power series approach

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed in this paper. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be ill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, we can see that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.

Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval

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Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval