We demonstrate that interferometric imaging may be replaced by noninterferometric propagation-based techniques in many experiments. We explore propagation through the Poynting vector and find two classes of phase, one of which is topological in origin. Only this latter class may require interferometry to be determined, and even then only in specific well-defined circumstances. Our alternative definitions of phase are readily generalized to partially coherent radiation. Our analysis leads to an approach that is able to determine the absolute phase and the amplitude of a wave.

The quantitative imaging of a phase object using 16 keV x rays is reported. The theoretical basis of the techniques is presented along with its implementation using a synchrotron x-ray source. We find that our phase image is in quantitative agreement with independent measurements of the object.

X-ray sources are developing rapidly and their coherent output is growing correspondingly. The increased coherent flux from modern X-ray sources is being matched with an associated development in experimental methods. This article reviews the literature describing the ideas that utilize the increased brilliance from modern X-ray sources. It explores how ideas in coherent X-ray science are leading to developments in other areas, and vice versa. The article describes measurements of coherence properties and uses this discussion as a base from which to describe partially coherent diffraction and X-ray phase-contrast imaging, with applications in materials science, engineering and medicine. Coherent diffraction imaging methods are reviewed along with associated experiments in materials science. Proposals for experiments to be performed with the new X-ray free-electron lasers are briefly discussed. The literature on X-ray photon-correlation spectroscopy is described and the features it has in common with other coherent X-ray methods are identified. Many of the ideas used in the coherent X-ray literature have their origins in the optical and electron communities and these connections are explored. A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented.

We present a new method for the extraction of quantitative phase data from microscopic phase samples by use of partially coherent illumination and an ordinary transmission microscope. The technique produces quantitative images of the phase profile of the sample without phase unwrapping. The technique is able to recover phase even in the presence of amplitude modulation, making it significantly more powerful than existing methods of phase microscopy. We demonstrate the technique by providing quantitatively correct phase images of well-characterized test samples and show that the results obtained for more-complex samples correlate with structures observed with Nomarski differential interference contrast techniques.