The theoretical framework for calculation of two-photon absorption cross sections for intermediate Hund’s cases (a) and (b) diatomic species is described in detail and applied toward the hydroxyl (OH) radical. Analytical expressions are derived for the 20 rotational branches that are present in the two-photon A ${}^2{\mathrm{\Sigma }}^{+}\leftarrow X{}^2\mathrm{\Pi }$ electronic transition. Calculation of the corresponding line strengths is necessary to permit accurate relative-concentration measurements obtained from the fluorescence induced by a broadband femtosecond excitation pulse. We demonstrate, in particular, that consideration of the temperature-dependent initial-state populations of OH is necessary to obtain accurate relative concentrations from observed two-photon-excitation based laser-induced-fluorescence measurements.