We demonstrate quantitative noninterferometric x-ray phase-amplitude measurement. We present results from two experimental geometries. The first geometry uses x rays diverging from a point source to produce high-resolution holograms of submicrometer-sized objects. The measured phase of the projected image agrees with the geometrically determined phase to within +/-7%. The second geometry uses a direct imaging microscope setup that allows the formation of a magnified image with a zone-plate lens. Here a direct measure of the object phase is made and agrees with that of the magnified object to better than +/-10%. In both cases the accuracy of the phase is limited by the pixel resolution.

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The phase of a coherent wave is an intuitively well understood concept and efforts to measure the phase of a wave are a staple of visible, x-ray, electron and atom optics. However, in a subtle way, phase is often measured where it is not even defined. An example of this is adaptive optics where the atmospheric phase distortion of light from astronomical objects is measured using polychromatic light. The assumption buried under this work is that it is possible to sensibly talk about phase even though the context of the discussion does not permit phase to be defined according to elementary concepts.We have been undertaking an ongoing program investigating the nature of wavefields and exploring their characterisation using more robust approaches than standard techniques such as interferometry In a very recent paper we have developed a new viewpoint on phase defined via the Poynting vector of the radiation and where the phase acts as a set of potentials leading to the Poynting vector field.