Shadow imaging of geostationary satellites: experimental demonstration with accurate polychromatic modelling of diffraction and atmospheric disturbances
Résumé
Shadow imaging is an original and simple method to meet the challenge of characterizing and identifying distant satellites. It is based on observing the shadow cast on the ground during a stellar occultation. The shadow is sampled, then the signal is processed in order to derive the contour of the object. Our objective is to identify and quantify the limitations of the method and to optimize and demonstrate solutions. We show that atmospheric refraction and turbulence can be numerically corrected and that Fresnel diffraction can be efficiently modelled using the decomposition of the incident light in a truncated basis of Hermite-Gauss functions. This leads to sampling requirements for the shadow in terms of spectral width, position and number of telescopes for a given specification of resolution and maximum size of the satellite. For instance, submetrically resolving a 15 m object at 40 000 km from the ground necessitates a spectral bandwidth of 40 nm. Moreover, the shadow should be traced over about 60 m and a good sampling in this case demands a telescope to be placed almost every 30 cm. Our inversion algorithm, based on a maximum a posteriori estimator coupled with non-linear modern optimization, confirms from simulation and small-scale laboratory data that successful reconstructions can be performed with stars of magnitude 6. An innovative output of this work is that the wide and continuous spectrum of the stars can be used to relax requirements on the spatial sampling of the shadow.
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