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.