  Inelastic $^{16}$O +$^{12}$C rainbow scattering to the $2^+$ (4.44 MeV) state
of $^{12}$C was measured at the incident energies, $E_L$ = 170, 181, 200, 260
and 281 MeV. A systematic analysis of the experimental angular distributions
was performed using the coupled channels method with an extended double folding
potential derived from realistic wave functions for $^{12}$C and $^{16}$O
calculated with a microscopic $\alpha$ cluster model and a finite-range
density-dependent nucleon-nucleon force.The coupled channels analysis of the
measured inelastic scattering data shows consistently some Airy-like structure
in the inelastic scattering cross sections for the first $2^+$ state of
$^{12}$C, which is somewhat obscured and still not clearly visible in the
measured data. The Airy minimum was identified from the analysis and the
systematic energy evolution of the Airy structure was studied. The Airy minimum
in inelastic scattering is found to be shifted backward compared with that in
elastic scattering.
