Contrast and resolution in imaging with a microfocus x-ray source

A simple general treatment of x-ray image formation by Fresnel diffraction is presented; the image can alternatively be considered as an in-line hologram. Particular consideration is given to phase-contrast microscopy and imaging using hard x rays. The theory makes use of the optical transfer function in a similar way to that used in the theory of electron microscope imaging. Resolution and contrast are the criteria used to specify the visibility of an image. Resolution in turn depends primarily on the spatial coherence of the illumination, with chromatic coherence of lesser importance. Thus broadband microfocus sources can give useful phase-contrast images. Both plane- and spherical-wave conditions are explicitly considered as limiting cases appropriate to macroscopic imaging and microscopy, respectively, while intermediate cases may also be of practical interest. Some results are presented for x-ray images showing phase contrast.