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High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications

Imaging with visible light today uses numerous contrast mechanisms, including bright- and dark-field contrast, phase-contrast schemes and confocal and fluorescence-based methods. X-ray imaging, on the other hand, has only recently seen the development of an analogous variety of contrast modalities. Although X-ray phase-contrast imaging could successfully be implemented at a relatively early stage with several techniques, dark-field imaging, or more generally scattering-based imaging, with hard X-rays and good signal-to-noise ratio, in practice still remains a challenging task even at highly brilliant synchrotron sources. In this letter, we report a new approach on the basis of a grating interferometer that can efficiently yield dark-field scatter images of high quality, even with conventional X-ray tube sources. Because the image contrast is formed through the mechanism of small-angle scattering, it provides complementary and otherwise inaccessible structural information about the specimen at the micrometre and submicrometre length scale. Our approach is fully compatible with conventional transmission radiography and a recently developed hard-X-ray phase-contrast imaging scheme. Applications to X-ray medical imaging, industrial non-destructive testing and security screening are discussed.

Hard-X-ray dark-field imaging using a grating interferometer

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal $ \boldsymbol {x}\in \mathbb {C}^{n}$ about which we have phaseless samples of the form $y_{r} = \left |{\langle \boldsymbol {a}_{r}, \boldsymbol {x} \rangle }\right |^{2}$ , $r = 1,\ldots , m$ (knowledge of the phase of these samples would yield a linear system). This paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm. In a nutshell, this algorithm starts with a careful initialization obtained by means of a spectral method, and then refines this initial estimate by iteratively applying novel update rules, which have low computational complexity, much like in a gradient descent scheme. The main contribution is that this algorithm is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements. Indeed, the sequence of successive iterates provably converges to the solution at a geometric rate so that the proposed scheme is efficient both in terms of computational and data resources. In theory, a variation on this scheme leads to a near-linear time algorithm for a physically realizable model based on coded diffraction patterns. We illustrate the effectiveness of our methods with various experiments on image data. Underlying our analysis are insights for the analysis of nonconvex optimization schemes that may have implications for computational problems beyond phase retrieval.

Phase Retrieval via Wirtinger Flow: Theory and Algorithms

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

http://iopscience.iop.org/article/10.1088/0031-9155/58/1/R1/pdf

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

The understanding and management of strain is of fundamental importance in the design and implementation of materials. The strain properties of nanocrystalline materials are different from those of the bulk because of the strong influence of their surfaces and interfaces, which can be used to augment their function and introduce desirable characteristics. Here we explain how new X-ray diffraction techniques, which take advantage of the latest synchrotron radiation sources, can be used to obtain quantitative three-dimensional images of strain. These methods will lead, in the near future, to new knowledge of how nanomaterials behave within active devices and on unprecedented timescales.

Coherent X-ray diffraction imaging of strain at the nanoscale.

We report on a method for tomographic phase contrast imaging of centimeter sized objects. As opposed to existing techniques, our approach can be used with low-brilliance, lab based x-ray sources and thus is of interest for a wide range of applications in medicine, biology, and nondestructive testing. The work is based on the recent development of a hard x-ray grating interferometer, which has been demonstrated to yield differential phase contrast projection images. Here we particularly focus on how this method can be used for tomographic reconstructions using filtered back projection algorithms to yield quantitative volumetric information of both the real and imaginary part of the samples's refractive index.

/pdf/hard-x-ray-phase-tomography-with-low-brilliance-sources-167lq2tp88.pdf

Hard X-Ray Phase Tomography with Low-Brilliance Sources

Fabrication of diffraction gratings for hard X-ray phase contrast imaging

We report on significant advances and new results concerning a recently developed method for grating-based hard x-ray phase tomography. We demonstrate how the soft tissue sensitivity of the technique is increased and show in vitro tomographic images of a tumor bearing rat brain sample, without use of contrast agents. In particular, we observe that the brain tumor and the white and gray brain matter structure in a rat's cerebellum are clearly resolved. The results are potentially interesting from a clinical point of view, since a similar approach using three transmission gratings can be implemented with more readily available x-ray sources, such as standard x-ray tubes. Moreover, the results open the way to in vivo experiments in the near future.

https://iopscience.iop.org/article/10.1088/0031-9155/52/23/010/pdf

High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography

A technique has been developed that allows determination of the concentration profiles of colloidal solutions or any kind of fluid under confinement. Currently, submicrometre-wide channels are sampled with a resolution in the 10 nm range. The method comprises regular arrays of microfluidic channels and one-dimensional X-ray phase-retrieval techniques for the analysis of small-angle X-ray diffraction from the array structures. Recording the X-ray diffraction data requires a low dose on each individual channel since the sum of the signals from all channels is detected. The determined concentration profiles represent the ensemble average rather than individual entities and are obtained in a model-independent way. As an example, amplitude and phase of the exit field and concentration profiles for a colloidal fluid within confining channels of different widths are shown.

/pdf/diffractive-imaging-for-periodic-samples-retrieving-one-1x4f96uy2l.pdf

Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels.

We report on a method for tomographic phase contrast imaging of centimeter sized objects. As opposed to existing techniques, our approach can be used with low-brilliance, lab based X-ray sources and thus is of interest to a wide range of applications in medicine, biology, and non-destructive testing. The work is based on the recent development of a hard X-ray grating interferometer, which has been demonstrated to yield differential phase contrast projection images. Here we particularly focus on how this method can be used for tomographic reconstructions using filtered backprojection algorithms to yield quantitative volumetric information of the real part of the samples's refractive index.

C. David

Papers

Hard X-Ray Phase Tomography with Low-Brilliance Sources

Fabrication of diffraction gratings for hard X-ray phase contrast imaging

High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography

Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels.

Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images