It is shown that the in-water, shape factor formulation of the radiative transfer equation (RTE) (1) yields exact in-air expressions for the remote sensing reflectance R _rs and the equivalent remotely sensed reflectance RSR _a and (2) can be configured for inherent optical property (IOP) retrievals using standard linear matrix inversion methods. Inversion of the shape factor RTE is exact in the sense that no approximations are made to the RTE. Thus errors in retrieved IOPs are produced only by uncertainties in (1) the models for the shape factors and related quantities and (2) the IOP models required for inversion. Hydrolight radiative transfer calculations are used to derive analytical models for the necessary backscattering shape factor, radiance shape factor, fractional forward scattering coefficient, ratio of air-to-water mean cosines, and diffuse attenuation coefficient for in-water upwelling radiance. These models predict the various shape factors with accuracies ranging typically from 2 to 20%. Using the modeled shape factors the in-air remotely sensed reflectance RSR _a can be predicted to within 20% of the correct (Hydrolight-computed) values 96% of the time (or ±0.0005 sr⁻¹ 86% of the time) for the synthetic data used to determine the shape factor models. Inversion of this shape factor RTE using field data is a comprehensive study to be published in a later paper.