  We study Raman response of Heisenberg antiferromagnets on the
$\mathbf{C}_\mathrm{5v}$ Penrose and $\mathbf{C}_\mathrm{8v}$ Ammann-Beenker
lattices within and beyond the Loudon-Fleury second-order perturbation scheme
intending to explore optical features peculiar to quasiperiodic magnets. Within
the Loudon-Fleury mechanism, we find one and only Raman-active mode of
$\mathrm{E}_2$ symmetry without any dependence on linear incident and scattered
polarizations. Beyond the Loudon-Fleury mechanism, two more symmetry species
$\mathrm{A}_1$ and $\mathrm{A}_2$ are activated via dynamic ring exchange and
chiral spin fluctuations, respectively, which can be extracted by the use of
circular as well as linear polarizations. We employ Green's functions on one
hand and configuration-interaction wavefunctions on the other hand to calculate
the multimagnon contributions to inelastic light scatterings. Demonstrating the
great advantage of the configuration-interaction scheme, we reveal that a major
portion of the Shastry-Shraiman fourth-order Raman intensity is mediated by
multimagnon fluctuations.
