Andrew Pogany

Contrast and resolution in imaging with a microfocus x-ray source

A simple general treatment of x-ray image formation by Fresnel diffraction is presented; the image can alternatively be considered as an in-line hologram. Particular consideration is given to phase-contrast microscopy and imaging using hard x rays. The theory makes use of the optical transfer function in a similar way to that used in the theory of electron microscope imaging. Resolution and contrast are the criteria used to specify the visibility of an image. Resolution in turn depends primarily on the spatial coherence of the illumination, with chromatic coherence of lesser importance. Thus broadband microfocus sources can give useful phase-contrast images. Both plane- and spherical-wave conditions are explicitly considered as limiting cases appropriate to macroscopic imaging and microscopy, respectively, while intermediate cases may also be of practical interest. Some results are presented for x-ray images showing phase contrast.

X-ray phase-contrast microscopy and microtomography

In-line phase contrast enables weakly absorbing specimens to be imaged successfully with x-rays, and greatly enhances the visibility of fine scale structure in more strongly absorbing specimens. This type of phase contrast requires a spatially coherent beam, a condition that can be met by a microfocus x-ray source. We have developed an x-ray microscope, based on such a source, which is capable of high resolution phase-contrast imaging and tomography. Phase retrieval enables quantitative information to be recovered from phase-contrast microscope images of homogeneous samples of known composition and density, and improves the quality of tomographic reconstructions.

Quantitative X‐ray projection microscopy: phase‐contrast and multi‐spectral imaging

We outline a new approach to X‐ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high‐brightness field‐emission gun (FEG)‐based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 µm and have demonstrated novel features such as: (i) phase‐contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy‐resolved imaging to simultaneously produce multiple quasi‐monochromatic images using broad‐band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude‐retrieval algorithms to enable new real‐time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object–plane information from intermediate‐field images, unlocking the potentially greater contrast and resolution of the intermediate‐field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.

Refracting Röntgen’s rays: Propagation-based x-ray phase contrast for biomedical imaging

Absorption-contrast x-ray imaging serves to visualize the variation in x-ray attenuation within the volume of a given sample, whereas phase contrast allows one to visualize variations in x-ray refractive index. The former imaging mechanism has been well known and widely utilized since the time of Rontgen’s Nobel prize winning work, whereas the latter mechanism—sought for, but not found, by Rontgen himself—has laid the foundation for a revolution in x-ray imaging which is the central topic of this review. We consider the physical imaging mechanisms underlying both absorption contrast and phase contrast, together with the associated inverse problem of how one may obtain quantitative two- or three-dimensional information regarding a sample, given one or more phase-contrast images of the same. Practical questions are considered, regarding optimized phase-contrast imaging geometries as a function of detector resolution, source size, x-ray spectrum, and dose. Experimental examples pertaining to biomedical appli...

On the optimization of experimental parameters for x-ray in-line phase-contrast imaging

General principles and results for the optimization of the performance of x-ray in-line phase-contrast imaging systems for spatially incoherent sources are investigated. In particular, formulas expressing the dependence of image contrast, spatial resolution, and signal-to-noise ratio on instrumental parameters including source size, detector resolution, geometrical factors, x-ray energy as well as sample properties are derived for different models of sample features. The results for some special cases of interest are presented. Optimization procedures are proposed that are expected to be useful in the design of imaging systems seeking to exploit x-ray in-line phase contrast.

Optical phase retrieval by use of first Born-and rytov-type approximations

The first Born and Rytov approximations of scattering theory are introduced in their less familiar near-field versions. Two algorithms for phase retrieval based on these approximations are then described. It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields. The algorithms are applied to derive explicit solutions to four phase-retrieval problems of practical relevance to quantitative phase-contrast imaging and tomography. An example of successful phase reconstruction by use of the Born-type algorithm with an experimental x-ray image is presented.

Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging

Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated. The analytical expressions are compared with the results of numerical simulations using Kirchhoff diffraction theory, as well as with experimental X-ray measurements.

On the evolution and relative merits of hard X-ray phase-contrast imaging methods

This review provides a brief overview, albeit from a somewhat personal perspective, of the evolution and key features of various hard X-ray phase-contrast imaging (PCI) methods of current interest in connection with translation to a wide range of imaging applications. Although such methods have already found wide-ranging applications using synchrotron sources, application to dynamic studies in a laboratory/clinical context, for example for in vivo imaging, has been slow due to the current limitations in the brilliance of compact laboratory sources and the availability of suitable high-performance X-ray detectors. On the theoretical side, promising new PCI methods are evolving which can record both components of the phase gradient in a single exposure and which can accept a relatively large spectral bandpass. In order to help to identify the most promising paths forward, we make some suggestions as to how the various PCI methods might be compared for performance with a particular view to identifying those which are the most efficient, given the fact that source performance is currently a key limiting factor on the improved performance and applicability of PCI systems, especially in the context of dynamic sample studies. The rapid ongoing development of both suitable improved sources and detectors gives strong encouragement to the view that hard X-ray PCI methods are poised for improved performance and an even wider range of applications in the near future.

Carbide and hydride formation during mechanical alloying of titanium and aluminium with hexane

Abstract Mixtures of elemental titanium and aluminium powders of overall composition TixAl1+x (x = 0.02, 0.3, 0.4, 0.5, 0.6, 0.7, 0.75, 0.8) were mechanically alloyed in a planetary-type ball mill. Hexane was added as a process control agent to reduce powder agglomeration during milling. The as-milled powders were characterized using X-ray diffraction, differential scanning calorimetry, scanning electron microscopy and transmission electron microscopy. During milling, the hexane is partially dissociated, with the free carbon and hydrogen incorporated within the TixAl1 − x alloy powders in increasing amounts with increasing milling time. The amount of incorporated carbon increases with the initial Ti content of the powder mixture, reaching a maximum of 12 wt.% incorporated into an initial Ti0.8Al0.2 powder mixture after 100 h of milling. The hydrogen is found to combine with elemental Ti to form TiH2−x, with an initial Ti0.5Al0.5 powder mixture milled for 40 h incorporating 0.95 wt.% H. The milled (TixAl1 − x + C) powder mixtures form a large fraction of amorphous phase near x = 0.5. Annealing of the as-milled powders incorporating dissolved carbon and hydrogen produced a mixture of Al2Ti4C2, TiC and TiAl.

Quantitative methods in phase-contrast x-ray imaging.

A new method for extracting quantitative information from phase-contrast x-ray images obtained with microfocus x-ray sources is presented. The proposed technique allows rapid noninvasive characterization of the internal structure of thick optically opaque organic samples. The method does not generally involve any sample preparation and does not need any x-ray optical elements (such as monochromators, zone plates, or interferometers). As a consequence, samples can be imaged in vivo or in vitro, and the images are free from optical aberrations. While alternative techniques of x-ray phase-contrast imaging usually require expensive synchrotron radiation sources, our method can be implemented with conventional, albeit microfocus, x-ray tubes, which greatly enhances its practicality. In the present work, we develop the theoretical framework, perform numerical simulations, and present the first experimental results, demonstrating the viability of the proposed approach. We believe that this method should find wide-ranging applications in clinical radiology and medical research.