  We define spherical diffraction measures for a wide class of weighted point
sets in commutative spaces, i.e. proper homogeneous spaces associated with
Gelfand pairs. In the case of the hyperbolic plane we can interpret the
spherical diffraction measure as the Mellin transform of the auto-correlation
distribution. We show that uniform regular model sets in commutative spaces
have a pure point spherical diffraction measure. The atoms of this measure are
located at the spherical automorphic spectrum of the underlying lattice, and
the diffraction coefficients can be characterized abstractly in terms of the
so-called shadow transform of the characteristic functions of the window. In
the case of the Heisenberg group we can give explicit formulas for these
diffraction coefficients in terms of Bessel and Laguerre functions.
