Observations of the extreme ultraviolet emission of helium ions at 30.4 nm can be used to study the global shape of the plasmasphere and its dynamical response to geomagnetic forcing. In order to retrieve number densities of plasmaspheric He+ from such observations, we have developed a new inversion technique based on discrete inverse theory, which uses the optical data to optimize a parameterized model of the He+ distribution. We apply this inversion technique to several orbits of data obtained from the Naval Research Laboratory extreme ultraviolet photometric experiment launched on the STP 72-1 satellite in October 1972. The inversion is limited to nighttime conditions where contamination from the topside ionosphere is minimal and where a simple parameterization of the He+ number density is applicable. We obtain excellent fits to the data; however, some of the retrieved model parameters have large uncertainties due to inadequate sampling of the plasmasphere. Our study shows that improved sampling using observations from different locations and view directions would significantly enhance the accuracy of the retrieved model parameters. Using a newly developed three-dimensional imaging tool to visualize the plasmaspheric regions being sampled remotely, we demonstrate that emission features observed from two of the STP 72-1 orbits originate beyond the plasmasphere. Estimated number densities of this feature are roughly consistent with observations of cold plasma seen at geosynchronous orbit by in situ experiments. ¿ 1998 American Geophysical Union