Shadow Imaging of Geosynchronous Satellites

Abstract

Geosynchronous (GEO) satellites are essential for modern communication networks. If communication to a GEO satellite is lost and a malfunction occurs upon orbit insertion such as a solar panel not deploying there is no direct way to observe it from Earth. Due to the GEO orbit distance of ~36,000 km from Earth's surface, the Rayleigh criteria dictates that a 14 m telescope is required to conventionally image a satellite with spatial resolution down to 1 m using visible light. Furthermore, a telescope larger than 30 m is required under ideal conditions to obtain spatial resolution down to 0.4 m. This dissertation evaluates a method for obtaining high spatial resolution images of GEO satellites from an Earth based system by measuring the irradiance distribution on the ground resulting from the occultation of the satellite passing in front of a star. The representative size of a GEO satellite combined with the orbital distance results in the ground shadow being consistent with a Fresnel diffraction pattern when observed at visible wavelengths. A measurement of the ground shadow irradiance is used as an amplitude constraint in a Gerchberg-Saxton phase retrieval algorithm that produces a reconstruction of the satellite's 2D transmission function which is analogous to a reverse contrast image of the satellite. The advantage of shadow imaging is that a terrestrial based redundant set of linearly distributed inexpensive small telescopes, each coupled to high speed detectors, is a more effective resolved imaging system for GEO satellites than a very large telescope under ideal conditions. Modeling and simulation efforts indicate sub-meter spatial resolution can be readily achieved using collection apertures of less than 1 meter in diameter. A mathematical basis is established for the treatment of the physical phenomena involved in the shadow imaging process. This includes the source star brightness and angular extent, and the diffraction of starlight from the satellite. Atmospheric effects including signal attenuation, refraction/dispersion, and turbulence are also applied to the model. The light collection and physical measurement process using highly sensitive geiger-mode avalanche photo-diode (GM-APD) detectors is described in detail. A simulation of the end-to-end shadow imaging process is constructed and then utilized to quantify the spatial resolution limits based on source star, environmental, observational, collection, measurement, and image reconstruction parameters.