  We develop the full t-matrix theory of quasiparticle interference (QPI) for
non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling. We
give a closed solution for the QPI spectrum for arbitrary combination and
strength of nonmagnetic (Vc) and magnetic (Vm) impurity scattering potentials
in terms of integrated normal and anomalous Green's functions. The theory is
applied to a realistic 2D model of the Ce-based 131- type heavy fermion
superconductors. We discuss the QPI dependence on frequency, composition and
strength of scattering and compare with Born approximation results. We show
that the QPI pattern is remarkably stable against changes in the scattering
model and can therefore give reliable information on the properties of
Rashba-split Fermi surface sheets and in particular on the accidental nodal
position of the mixed singlet-triplet gap function in NCS superconductors.
