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A theoretical analysis of the combined analyser-based/propagation-based x-ray phase-contrast imaging of weak objects is presented in the case of partially coherent illumination. It takes into account the finite size and divergence of a polychromatic x-ray source as well as the detector point-spread function. The proposed formalism describes the diffraction of x-rays in the monochromator and analyser crystals and free-space propagations between various elements of the imaging system. As in the case of a monochromatic plane wave incident on the object, the intensity in the image is expressed in terms of the amplitude and phase transfer functions. Analytical expressions for the new 'polychromatic' transfer functions are obtained and compared with the corresponding 'monochromatic' transfer functions by numerical simulations. The crucial role of the monochromator is elucidated in the formation of the analyser-based phase-contrast images with polychromatic illumination.

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.

Micro-CT scanners find applications in many areas ranging from biomedical research to material sciences. In order to provide spatial resolution on a micron scale, these scanners are usually equipped with micro-focus, low-power x-ray sources and hence require long scanning times to produce high resolution 3D images of the object with acceptable contrast-to-noise.Propagation-based phase-contrast tomography (PB-PCT) has the potential to significantly improve the contrast-to-noise ratio (CNR) or, alternatively, reduce the image acquisition time while preserving the CNR and the spatial resolution. We propose a general approach for the optimisation of the PB-PCT imaging system. When applied to an imaging system with fixed parameters of the source and detector this approach requires optimisation of only two independent geometrical parameters of the imaging system, i.e. the source-to-object distance R1 and geometrical magnification M, in order to produce the best spatial resolution and CNR. If, in addition to R1 and M, the system parameter space also includes the source size and the anode potential this approach allows one to find a unique configuration of the imaging system that produces the required spatial resolution and the best CNR.

We report the results of quantitative phase-contrast imaging experiments using synchrotron radiation, in-line imaging geometry and a non-interferometric phase retrieval technique. This quantitative imaging method is fast, simple, robust, does not require sophisticated x-ray optical elements and can potentially provide submicron spatial resolution over a field of view of the order of centimetres. In the present experiment a spatial resolution of approximately 0.8 m has been achieved in images of a polystyrene sphere using 19.6 keV x-rays. We demonstrate that appropriate processing of phase-contrast images obtained in the in-line geometry can reveal important new information about the internal structure of weakly absorbing organic samples. We believe that this technique will also be useful in phase-contrast tomography.

Three phase-retrieval algorithms, based on the transport-of-intensity equation and on the contrast transfer function for propagation-based imaging, and on the linearized geometrical optics approximation for analyser-based imaging, are investigated. The algorithms are compared in terms of their effect on propagation of noise from projection images to the corresponding phase-retrieved images and further to the computed tomography (CT) images/slices of a monomorphous object reconstructed using filtered backprojection algorithm. The comparison is carried out in terms of an integral noise characteristic, the variance, as well as in terms of a simple figure-of-merit, i.e. signal-to-noise ratio per unit dose. A gain factor is introduced that quantitatively characterizes the effect of phase retrieval on the variance of noise in the reconstructed projection images and in the axial slices of the object. Simple analytical expressions are derived for the gain factor and the signal-to-noise ratio, which indicate that the application of phase-retrieval algorithms can increase these parameters by up to two orders of magnitude compared to raw projection images and conventional CT, thus allowing significant improvement in the image quality and/or reduction of the x-ray dose delivered to the patient.

The three-dimensional distribution of the materials composing a sample is reconstructed using multiple-energy computed tomography techniques. The a priori knowledge about the specific materials that are present in the sample is used for decomposing the measured intensity projections into projected thicknesses of each component material. Those decomposed projections are then processed using iterative reconstruction algorithms to separately obtain the three-dimensional distribution of each material. A new iterative reconstruction algorithm has been implemented and its performance is compared to the standard filtered back projection and to another existing iterative algorithm based on histogram manipulation. The method is first tested with simulations on data for a realistic, three-materials' numerical sample and then applied to experimental micro-tomography data. The accuracy of the reconstruction from experimental data is tested by means of an energy dispersive x-ray spectroscopy scan of the sample.