Spectral x-ray imaging: Conditions under which propagation-based phase-contrast is beneficial

Precise phase retrieval for propagation-based images using discrete mathematics

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these algorithms is typically formulated using continuous mathematics, which can result in a loss of spatial resolution in the reconstructed images. Herein we investigate how phase retrieval algorithms for propagation-based phase-contrast X-ray imaging can be rederived using discrete mathematics and result in more precise retrieval for single- and multi-material objects and for spectral image decomposition. We validate this theory through experimental measurements of spatial resolution using computed tomography (CT) reconstructions of plastic phantoms and biological tissues, using detectors with a range of imaging system point spread functions (PSFs). We demonstrate that if the PSF substantially suppresses high spatial frequencies, the potential improvement from utilising the discrete derivation is limited. However, with detectors characterised by a single pixel PSF (e.g. direct, photon-counting X-ray detectors), a significant improvement in spatial resolution can be obtained, demonstrated here at up to 17%.

Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization

Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard x-rays. Here, we propose a phase retrieval approach for inline x-ray holography based on Tikhonov regularization applied to the full nonlinear forward model of image formation. The approach can be seen as a nonlinear generalization of the well-established contrast transfer function (CTF) reconstruction method. While similar methods have been proposed before, the current work achieves nonlinear, constrained phase retrieval at competitive computation times. We thus enable high-throughput imaging of optically strong objects beyond the scope of CTF. Using different examples of inline holograms obtained from illumination by a x-ray waveguide-source, we demonstrate superior image quality even for samples which do not obey the assumption of a weakly varying phase. Since the presented approach does not rely on linearization, we expect it to be well suited also for other probes such as visible light or electrons, which often exhibit strong phase interaction.

Dual-energy phase retrieval algorithm for inline phase sensitive x-ray imaging system

Phase retrieval is vital for quantitative x-ray phase contrast imaging. This work presents an iterative method to simultaneously retrieve the x-ray absorption and phase images from a single x-ray exposure. The proposed approach uses the photon-counting detectors' energy-resolving capability in providing multiple spectrally resolved phase contrast images from a single x-ray exposure. The retrieval method is derived, presented, and experimentally tested with a multi-material phantom in an inline phase contrast imaging setup. By separating the contributions of photoelectric absorption and Compton scattering to the attenuation, the authors divide the phase contrast image into two portions, the attenuation map arises from photoelectric absorption and a pseudo phase contrast image generated by electron density. This way one can apply the Phase Attenuation Dualiby (PAD) algorithm and Fresnel propagation for the iteration. The retrieval results from the experimental images show that this iterative method is fast, accurate, robust against noise, and thus yields noticeable enhancement in contrast to noise ratios.

Material Decomposition Using Spectral Propagation-Based Phase-Contrast X-Ray Imaging

Material decomposition in X-ray imaging uses the energy-dependence of attenuation to digitally decompose an object into specific constituent materials, generally at the cost of enhanced image noise. Propagation-based X-ray phase-contrast imaging is a developing technique that can be used to reduce image noise, in particular from weakly attenuating objects. In this paper, we combine spectral phase-contrast imaging with material decomposition to both better visualize weakly attenuating features and separate them from overlying objects in radiography. We derive an algorithm that performs both tasks simultaneously and verify it against numerical simulations and experimental measurements of ideal two-component samples composed of pure aluminum and poly(methyl methacrylate). Additionally, we showcase first imaging results of a rabbit kitten's lung. The attenuation signal of a thorax, in particular, is dominated by the strongly attenuating bones of the ribcage. Combined with the weak soft tissue signal, this makes it difficult to visualize the fine anatomical structures across the whole lung. In all cases, clean material decomposition was achieved, without residual phase-contrast effects, from which we generate an un-obstructed image of the lung, free of bones. Spectral propagation-based phase-contrast imaging has the potential to be a valuable tool, not only in future lung research, but also in other systems for which phase-contrast imaging in combination with material decomposition proves to be advantageous.