The Ionospheric Connection Explorer (ICON) Far Ultraviolet (FUV) imager, ICON FUV, will measure altitude profiles of OI 135.6 nm emissions to infer nighttime ionospheric parameters. Accurate estimation of the ionospheric state requires the development of a comprehensive radiative transfer model from first principles to quantify the effects of physical processes on the production and transport of the 135.6 nm photons in the ionosphere including the mutual neutralization contribution as well as the effect of resonant scattering by atomic oxygen and pure absorption by oxygen molecules. This forward model is then used in conjunction with a constrained optimization algorithm to invert the anticipated ICON FUV line-of-sight integrated measurements. In this paper, we describe the connection between ICON FUV measurements and the nighttime ionosphere, along with the approach to inverting the measured emission profiles to derive the associated O+ profiles from 150-450 km in the nighttime ionosphere that directly reflect the electron density in the F-region of the ionosphere.