  For point sets and tilings that can be constructed with the projection
method, one has a good understanding of the correlation structure, and also of
the corresponding spectra, both in the dynamical and in the diffraction sense.
For systems defined by substitution or inflation rules, the situation is less
favourable, in particular beyond the much-studied class of Pisot substitutions.
In this contribution, the geometric inflation rule is employed to access the
pair correlation measures of self-similar and self-affine inflation tilings and
their Fourier transforms by means of exact renormalisation relations. In
particular, we look into sufficient criteria for the absence of absolutely
continuous spectral contributions, and illustrate this with examples from the
class of block substitutions. We also discuss the Frank-Robinson tiling, as a
planar example with infinite local complexity and singular continuous spectrum.
