An inversion technique for recovering the scattering coefficient as a function of height in the earth's atmosphere is investigated. The most sensitive method of aerosol detection requires that spacecraft measurements of the horizon radiance be made during periods of spacecraft twilight in order to utilize the forward scattering properties of aerosols. A solar occultation technique, which allows the twilight measurements to be made when the sun is still above (but close to) the horizon, greatly reduces the complexity of the inversion problem. If the extinction of the setting (rising) sun is also measured, the total scattering coefficient can be recovered with an uncertainty which is approximately twice that of the noise in the radiance signal. Although only single scattering is employed in the analysis, an iterative method of including multiple scattering is suggested.