X-ray imaging: a generalized approach using phase-space tomography.

We discuss the role of coherence in x-ray imaging and consider how phase-space tomography can be used to extract information about partial coherence. We describe the application of phase-space tomography to x-ray imaging and recover the spatial coherence properties of a one-dimensional soft (1.5 keV) x-ray beam from a synchrotron undulator source. We present phase-space information from a Young's experiment and observe negative regions in the quasi-probability distribution. We show that, given knowledge of the coherence of the beam, we can use partially coherent diffraction data to recover fully coherent information, and we present some simple experimental demonstrations of this capability.