A simple general treatment of x-ray image formation by Fresnel diffrac
tion is presented; The image can alternatively be considered as an in-
line hologram. Particular consideration is given to phase-contrast mic
roscopy and imaging using hard x rays. The theory makes use of the opt
ical 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 chromati
c coherence of lesser importance. Thus broadband microfocus sources ca
n give useful phase-contrast images. Both plane- and spherical-wave co
nditions are explicitly considered as limiting cases appropriate to ma
croscopic imaging and microscopy, respectively, while intermediate cas
es may also be of practical interest. Some results are presented for x
-ray images showing phase contrast. (C) 1997 American Institute of Phy
sics.