  Non-resonant Raman spectroscopy in the hard X-ray regime has been used to
explore the electronic structure of the first two members of the
Ruddlesden-Popper series Sr$_{n+1}$Ir$_n$O$_{3n+1}$ of iridates. By tuning the
photon energy transfer around 530 eV we have been able to explore the oxygen K
near edge structure with bulk sensitivity. The angular dependence of the
spectra has been exploited to assign features in the 528-535 eV energy range to
specific transitions involving the Ir 5d orbitals. This has allowed us to
extract reliable values for both the t2g-eg splitting arising from the cubic
component of the crystal field (10Dq), in addition to the splitting of the eg
orbitals due to tetragonal distortions. The values we obtain are (3.8, 1.6) eV
and (3.55, 1.9) eV for Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$, respectively.
