  We prove that the set of visible points of any lattice of dimension at least
2 has pure point diffraction spectrum, and we determine the diffraction
spectrum explicitly. This settles previous speculation on the exact nature of
the diffraction in this situation, see math-ph/9903046 and references therein.
Using similar methods we show the same result for the 1-dimensional set of k-th
power free integers with k at least 2. Of special interest is the fact that
neither of these sets is a Delone set --- each has holes of unbounded inradius.
We provide a careful formulation of the mathematical ideas underlying the study
of diffraction from infinite point sets.
