Phase retrieval applied to stellar occultation for asteroid silhouette characterization

Here we expand on the current methods of characterizing small astronomical bodies, particularly asteroids, by viewing stellar occultation events. Stellar occultation has proven to be a viable method for determining the size of moons and asteroids; however, it comes with some limitations. In general the method does not consider or use all of the known diffraction effects that occur and thus provides a nominal radius--not a shape--of the occluder. We show that most stellar occultation events involving small near-Earth asteroids occur with low Fresnel numbers. This in effect renders the traditional methods useless to characterize the shape, because no sharp shadow exists. We show that using similar data collection to that of the traditional occultation method and inverting a Fresnel diffraction equation by a phase retrieval process can yield a complete reconstruction of the silhouette of the occluder. The effect of noise in the measurements is also discussed. A practical example applied to the asteroid 25143 Itokawa is shown.