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.

A quantitative study of monochromatic X-ray transmission through zinc wires.

X-ray transmission through zinc wires of various diameters has been investigated systematically at different beam energies and sample-to-detector distances at the Shanghai Synchrotron Radiation Facility. This analysis shows that the experimentally measured transmission differs significantly from the theoretical estimation unless an appropriate point-spread function/line-spread function (PSF/LSF) is incorporated in the analysis. A number of other possible factors which may contribute to the observed inconsistencies were also assessed and these factors included higher harmonics and fluorescence; however, it was determined that these were not the dominant contributors underlying the inconsistencies. The investigation has demonstrated that the PSF/LSF is a major factor for consideration in quantitative X-ray micro-computed tomography.

A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data.

The application of powder diffraction methods to problems in structural biology is generally regarded as intractable because of the large number of unresolved, overlapping X-ray reflections. Here, we use information about unit cell lattice parameters, space group transformations, and chemical composition as a priori information in a bootstrap process that resolves the ambiguities associated with overlapping reflections. The measured ratios of reflections that can be resolved experimentally are used to refine the position, the shape, and the orientation of low-resolution molecular structures within the unit cell, in leading to the resolution of the overlapping reflections. The molecular model is then made progressively more sophisticated as additional diffraction information is included in the analysis. We apply our method to the recovery of the structure of the bacteriorhodopsin molecule (bR) to a resolution of 7 Å using experimental data obtained from two-dimensional purple membrane crystals. The approach can be used to determine the structure factors directly or to provide reliable low-resolution phase information that can be refined further by the conventional methods of protein crystallography.

Phase-contrast imaging using a scanning-double-grating configuration.

A new double-grating-based phase-contrast imaging technique is described. This technique differs from the conventional double-grating imaging method by the image acquisition strategy. The novelty of the proposed method is in lateral scanning of both gratings simultaneously while an image is collected. The collected image is not contaminated by a Moiré pattern and can be recorded even by using a high-spatial-resolution integrating detector (e.g. X-ray film), thus facilitating improved resolution and/or contrast in the image. A detailed theoretical analysis of image formation in the scanning-double-grating method is carried out within the rigorous wave-optical formalism. The transfer function for the scanning-double-grating imaging system is derived. An approximate geometrical-optics solution for the image intensity distribution is derived from the exact wave-optical formula using the stationary-phase approach. Based on the present formalism, the effects of finite source size on the preferred operating conditions and of polychromaticity on the image contrast and resolution are investigated.

On qualitative and quantitative analysis in analyser-based imaging.

Using rigorous wave-optical formalism, a general expression is obtained for the image intensity distribution in combined analyser-based/propagation-based phase-contrast imaging. This expression takes into account partial coherence of the wave incident on the object as well as the finite resolution of the detector system. Using this general expression, two approaches based on the geometrical optics and weak-object approximations are applied to derive simple solutions to the inverse problem of reconstruction of the phase and amplitude of the object wave. With the help of numerical experiments, the two approaches are compared in terms of their validity conditions and are shown to impose certain restrictions on the properties of the object wave. In particular, it is shown that violation of the validity conditions of the geometrical optics or weak-object approximations results in the appearance of strong reconstruction artefacts in the transmitted intensity near the edges of the objects. The effect of the incident wavefront non-uniformity due to imperfections of the imaging set-up on image formation and phase/amplitude reconstruction is also discussed. A solution to this problem is proposed in the form of a multi-image phase/amplitude reconstruction algorithm based on the geometrical optics approximation. This algorithm and an algorithm based on the weak-object approximation are applied to simulated and experimental images of fibres.

Generalized eikonal of partially coherent beams and its use in quantitative imaging.

The generalized eikonal of a partially coherent paraxial wave is introduced via a differential equation describing the evolution of the time-averaged intensity. The theoretical formalism provides an analytical tool for the study of partially coherent imaging systems. It also makes possible quantitative phase retrieval and compositional mapping of weakly absorbing samples using phase-contrast imaging with broadband polychromatic radiation of known spectral distribution. An experimental demonstration is presented of the quantitative reconstruction of the projected thickness of a sample, given a phase-contrast image obtained using a polychromatic microfocus x-ray source.

X-ray omni microscopy.

The science of wave-field phase retrieval and phase measurement is sufficiently mature to permit the routine reconstruction, over a given plane, of the complex wave-function associated with certain coherent forward-propagating scalar wave-fields. This reconstruction gives total knowledge of the information that has been encoded in the complex wave-field by passage through a sample of interest. Such total knowledge is powerful, because it permits the emulation in software of the subsequent action of an infinite variety of coherent imaging systems. Such 'virtual optics', in which software forms a natural extension of the 'hardware optics' in an imaging system, may be useful in contexts such as quantitative atom and X-ray imaging, in which optical elements such as beam-splitters and lenses can be realized in software rather than optical hardware. Here, we develop the requisite theory to describe such hybrid virtual-physical imaging systems, which we term 'omni optics' because of their infinite flexibility. We then give an experimental demonstration of these ideas by showing that a lensless X-ray point projection microscope can, when equipped with the appropriate software, emulate an infinite variety of optical imaging systems including those which yield interferograms, Zernike phase contrast, Schlieren imaging and diffraction-enhanced imaging.

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 micro m 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.

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.

Quantitative analysis of two-component samples using in-line hard X-ray images.

Methods for rapid quantitative phase-sensitive X-ray imaging of non-crystalline samples consisting of two distinct components are investigated. The transverse spatial distribution of the projected thickness of each component is reconstructed by computer processing of in-line images collected using synchrotron-generated hard X-rays and a position-sensitive detector with submicrometre spatial resolution. Different imaging techniques and associated image-processing algorithms are considered, with relative advantages and difficulties of each approach compared. A possible generalization of the method for the case of n-component samples is briefly discussed.

The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays.

OBJECTIVE: This study describes the application of a new radiographic imaging modality, phase-contrast radiography, to in vitro human temporal bone imaging and investigates its use in the development of new electrode arrays for cochlear implants. BACKGROUND: The development of perimodiolar electrode arrays for cochlear implants requires detailed information from postoperative radiologic assessment on the position of the array in relation to the cochlear structures. Current standard radiographic techniques provide only limited details. MATERIALS AND METHODS: Nucleus standard electrode arrays and perimodiolar Contour electrode arrays were implanted into the scala tympani of 11 human temporal bones. Both conventional and phase-contrast radiographs were taken of each temporal bone for comparative purposes. RESULTS: Phase-contrast imaging provides better visualization of anatomic details of the inner ear and of the structure of the intracochlear electrode array, and better definition of electrode location in relation to cochlear walls. CONCLUSION: Phase-contrast radiography offers significant improvement over conventional radiography in images of in vitro human temporal bones. It seems to be a valuable tool in the development of intracochlear electrode arrays and cochlear implant research. However, this new radiographic technique still requires certain computational and physics challenges to be addressed before its clinical use can be established.

Quantitative in-line phase-contrast imaging with multienergy X rays.

We present a new method for quantitative nondestructive characterization of objects by x-ray phase-contrast imaging. Spatial distributions of the projected values of the complex refractive index in the sample are reconstructed by processing near-field images collected at a fixed sample-to-detector distance using a polychromatic incident beam and an energy-sensitive area detector, such as a CCD used in the photon-counting spectroscopy mode. The method has the potential advantages of decreased radiation dose and increased accuracy compared to conventional techniques of x-ray imaging.

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.

Phase-contrast radiography.

For the past 100 years, the paradigm for radiography has been premised on absorption as the sole means of contrast formation and on ray optics as the basis for image interpretation. A new conceptual approach to radiography has been developed that includes phase (ie, refractive) contrast and requires wave optics for proper treatment. This new approach greatly increases the amount of information that can be obtained with radiographic techniques and is particularly well suited to the imaging of soft tissue and of very small features in biologic samples. A key feature of the present technique of phase-contrast radiography is the use of a microfocus x-ray source about an order of magnitude (< or = 20 microm) smaller than that used in conventional radiography. Phase-contrast radiography offers a number of improvements over conventional radiography in a clinical setting, especially in soft-tissue imaging. These improvements include increased contrast resulting in improved visualization of anatomic detail, reduced absorbed dose to the patient, inherent image magnification and high spatial resolution, use of harder x rays, and relative ease of implementation. More technologically advanced detectors are currently being developed and commercialized, which will help fully realize the considerable potential of phase-contrast imaging.

Protein Crystal Diffraction Patterns Using a Capillary-Focused Synchrotron X-ray Beam.

A paraboloidally tapered glass monocapillary was used to focus an 8 keV monochromated synchrotron bending-magnet X-ray beam into a 40 (+/-5) mum focal spot located 45 (+/-5) mm from the exit of the capillary. This focal spot had a measured intensity gain of 120 (+/-10) times the intensity present in an equivalent cross section of the unfocused beam from the monochromator. This focused beam was used to obtain oscillation diffraction patterns on image plates from a hen egg-white lysozyme protein crystal in two distinct geometries: one with the specimen crystal at the capillary exit and the other with the crystal at the beam focus. In the first geometry, focused Bragg reflections were observed at the focal plane. In the second geometry, diverging Bragg reflections of high intensity from a small crystal volume were observed. Image-plate diffraction patterns for these two geometries were compared with exposures with equivalent integrated diffracted intensities obtained using a 100 x 100 mum unfocused X-ray beam with the same crystal. The use of the focused beam resulted in a reduction in the exposure time required to produce equivalent patterns by a factor of between 70 and 100.

Focusing of X-rays by Total External Reflection from a Paraboloidally Tapered Glass Capillary.

The first observation of a true geometrical focus of X-rays well beyond the exit of a paraboloidally tapered glass monocapillary is reported. An intensity gain of 250 +/- 20 into a 6 x 9 mum pinhole for 8 keV X-rays and transmission efficiencies of more than 90% below 20 keV were observed.

X-ray focusing using cylindrical-channel capillary arrays. I. Theory.

A detailed analysis of the focusing and collimation of x rays by circular-pore microchannel plates (MCP's), or arrays of cylindrical capillaries, is presented. The focusing effect derives from external reflection of grazing-incidence rays at the interior surfaces of the hollow channels of the MCP and is similar to optical focusingby a spherical mirror. We give the point spread function of an MCP, taking into account surface roughness and misaligned channels. The calculation is based on multiply reflected rays and skew rays and is valid for a spherically curved MCP of any thickness. For comparison with experimental results the effects of a finite source and a detector aperture are also evaluated. This theory is compared with experiment.

X-ray focusing using cylindrical-channel capillary arrays. II. Experiments.

A microchannel plate (MCP) detector blank has been used to focus x rays of 0.154-, 0.62-, and 0.84-nm wavelength generated by a microfocus x-ray tube and a laser-produced plasma. The focusing effect of MCP's arises from total external reflection of x rays at the interior channel surfaces. Measurements of the intensity profiles of the images formed by the MCP have been made and compared with the predictions of a detailed model developed in Part I. [Appl. Opt. 32, 6316 (1993)]. It was found that the model gives a reliable description of the data. A consistent set of parameters was found from fits to the data at all three wavelengths.

Focusing and collimation of x rays using microchannel plates: an experimental investigation.

Focusing and collimation of 8 keV x rays has been demonstrated using microchannel plate (MCP) blanks with cylindrical channels. The focusing effect arises from total external reflection of x rays at the interior surfaces of the channels of a MCP and has been described previously by the authors. Point to point focusing was observed with flat and curved MCPs, and collimation from a point source to a quasi-parallel beam was observed with a curved MCP. Intensity profiles at the image plane and at other planes behind a flat MCP were obtained for a 20 × 40 µm2 x-ray source, and agree well with theoretical predictions. The flux in a 40-µm-diameter collector in the image plane was compared with the flux in the same plane, but without a MCP. The relative gain in flux increases linearly with the source to MCP distance, as predicted. A maximum relative gain in flux of 18 ± 1 was observed for a source to detector distance of 50 cm.