  Individual vibrational band spectroscopy presents an opportunity to examine
exoplanet atmospheres in detail by distinguishing where the vibrational state
populations of molecules differ from the current assumption of a Boltzmann
distribution. Here, retrieving vibrational bands of OH in exoplanet atmospheres
is explored using the hot Jupiter WASP-33b as an example. We simulate
low-resolution spectroscopic data for observations with the JWST's NIRSpec
instrument and use high resolution observational data obtained from the Subaru
InfraRed Doppler instrument (IRD). Vibrational band-specific OH cross section
sets are constructed and used in retrievals on the (simulated) low and (real)
high resolution data. Low resolution observations are simulated for two
WASP-33b emission scenarios: under the assumption of local thermal equilibrium
(LTE) and a toy non-LTE model for vibrational excitation of selected bands. We
show that mixing ratios for individual bands can be retrieved with sufficient
precision to allow the vibrational population distributions of the forward
models to be reconstructed. A simple fit for the Boltzmann distribution in the
LTE case shows that the vibrational temperature is recoverable in this manner.
For high resolution, cross-correlation applications, we apply the individual
vibrational band analysis to an IRD spectrum of WASP-33b, applying an
'un-peeling' technique. Individual detection significances for the two
strongest bands are shown to be in line with Boltzmann distributed vibrational
state populations consistent with the effective temperature of the WASP-33b
atmosphere reported previously. We show the viability of this approach for
analysing the individual vibrational state populations behind observed and
simulated spectra including reconstructing state population distributions.
