S. W. Wilkins

Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object

We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin‐image problem of in‐line holography and is capable of analysing data obtained using X‐ray microscopy, electron microscopy, neutron microscopy or visible‐light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non‐iterative and computationally efficient method is applied to data obtained using an X‐ray phase contrast ultramicroscope.

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.

Phase-and-amplitude computer tomography

A tomographic technique is proposed for reconstruction under specified conditions of the three-dimensional distribution of complex refractive index in a sample from a single projection image per view angle, where the images display both absorption contrast and propagation-induced phase contrast. The algorithm achieves high numerical stability as a consequence of the complementary nature of the absorption and phase contrast transfer functions. The method is pertinent to biomedical imaging and nondestructive testing of samples exhibiting weak absorption contrast.

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.

X‐ray focusing using square channel‐capillary arrays

A class of imaging, condensing, and collimating devices for x rays is investigated which is based on the use of an array of small channels of square cross section. The focusing and collimating effect arises from external reflection of near‐grazing‐incidence rays at the interior channel surfaces. Rays are redirected by being singly reflected from two orthogonal channel surfaces and are imaged from a source point to a square region with a side length MT+1 times that of the channel side length, where MT is the transverse magnification. The image and source locations are related by a thin‐lens formula. The point spread function and the efficiency of these focusing devices are calculated. Two energy regimes with different channel reflectivity characteristics are examined in detail: the hard x‐ray regime (E>8 keV) and the soft x‐ray regime (E<200 eV). For these cases the efficiency of focusing x rays depends only on the channel aspect ratio and reflectivity parameters. A discussion is made of channel plates of ...

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.

Quantitative diffraction-enhanced x-ray imaging of weak objects

Theoretical aspects of quantitative diffraction-enhanced imaging of weak objects are considered using the Fourier optics approach. The amplitude and phase transfer functions are introduced by analogy with the well-known case of in-line (holographic) imaging. The inverse problem of the reconstruction of the phase and amplitude of the incident wave from recorded images is solved in the case of non-absorbing objects and objects consisting of a single material and in the general case of objects with uncorrelated refraction and absorption characteristics. A comparison is given between the solutions to the inverse problem obtained using the new formalism and the geometric-optics approximation.

Phase-contrast X-ray imaging with synchrotron radiation for materials science applications

Since R€ os discovery of X-rays just over a century ago the vast majority of radiographs have been collected and interpreted on the basis of absorption contrast and geometrical (ray) optics. Recently the possibility of obtaining new and complementary information in X-ray images by utilizing phase-contrast effects has received considerable attention, both in the laboratory context and at synchrotron sources (where much of this activity is a consequence of the highly coherent X-ray beams which can be produced). Phase-contrast X-ray imaging is capable of providing improved information from weakly absorbing features in a sample, together with improved edge definition. Four different experimental arrangements for achieving phase contrast in the hard X-ray regime, for the purpose of non-destructive characterization of materials, will be described. Two of these, demonstrated at ESRF in France and AR in Japan, are based on parallel-beam geometry; the other two, demonstrated at PLS in Korea and APS in USA, are based on spherical-beam geometry. In each case quite different X-ray optical arrangements were used. Some image simulations will be employed to demonstrate salient features of hard X-ray phase-contrast imaging and examples of results from each of the experiments will be shown. 2002 Elsevier Science B.V. All rights reserved.