  X-ray diffraction microscopy (XDM) is a new form of x-ray imaging that is
being practiced at several third-generation synchrotron-radiation x-ray
facilities. Although only five years have elapsed since the technique was first
introduced, it has made rapid progress in demonstrating high-resolution
threedimensional imaging and promises few-nm resolution with much larger
samples than can be imaged in the transmission electron microscope. Both life-
and materials-science applications of XDM are intended, and it is expected that
the principal limitation to resolution will be radiation damage for life
science and the coherent power of available x-ray sources for material science.
In this paper we address the question of the role of radiation damage. We use a
statistical analysis based on the so-called "dose fractionation theorem" of
Hegerl and Hoppe to calculate the dose needed to make an image of a lifescience
sample by XDM with a given resolution. We conclude that the needed dose scales
with the inverse fourth power of the resolution and present experimental
evidence to support this finding. To determine the maximum tolerable dose we
have assembled a number of data taken from the literature plus some
measurements of our own which cover ranges of resolution that are not well
covered by reports in the literature. The tentative conclusion of this study is
that XDM should be able to image frozen-hydrated protein samples at a
resolution of about 10 nm with "Rose-criterion" image quality.
