Ya. I. Nesterets

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.

Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging

A novel theoretical treatment of linear shift-invariant imaging systems is developed, which allows explicit solution of forward and inverse problems in the case of large values of the generalized Fresnel number. The method will be useful in a variety of domains including optical instrumentation, biomedical imaging and materials science. Our approach is used to integrate two particularly topical x-ray imaging methods, namely propagation-based and analyser-crystal-based x-ray phase-contrast imaging.

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.

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.

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.

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.

Evaluation of the focusing performance of bent Laue crystals using wave‐optical theory

Quantitative analysis of the focusing performance of bent Laue crystals is carried out using the rigorous wave-optical formalism. Via numerical solution of the Takagi equations and the Fresnel integral, the influence of diffraction on the formation of the image of an X-ray source is analysed. The results are compared with those obtained using a formalism based on the geometrical optics approximation and significant differences are found. A formula for the geometrical aberration of a cylindrically bent crystal is derived. The effect of the aberration on image formation is analysed.

General reconstruction formulas for analyzer-based computed tomography

General formulas are derived for computed tomography reconstruction in analyzer-based imaging. Two image acquisition geometries are investigated. In the first geometry, which is widely used, the rotation axis of the object is perpendicular to that of the analyzer crystal. In the second geometry, in which the rotation axes are parallel, the reconstruction formulas are shown to be significantly simpler and more stable with respect to noise in experimental data.