Exciton-polaritons have many characteristic features, such as the Rabi splitting observed in linear spectroscopy when the cavity frequency is in resonance with a well-separated electronic transition (e.g. historically found in single-atom spectroscopy). Of course, there are many spectroscopic footprints of polariton formation that are of interest to the community for finding and exploring the physics of such quasi-particles; however, the spectroscopic results available experimentally may not be the most informational for probing local phenomena such as chemical reactions, charge transfer, or exciton diffusion. In these examples, the main features are stored in the excitonic part of the polariton, which is usually not directly visible in most experimental configurations due to the fast photon loss mechanisms and mirror absorption. However, examining the photonic contribution to the spectroscopy will give indirect information regarding the changes to the excitonic part of the polaritonic wavefunctions. In this section, we will outline the necessary steps to compute observables of polaritonic states using the direct diagonalization approach already discussed.