Shadow Imaging of Geostationary Satellites: silhouette reconstruction from accurate polychro-matic modelling of diffraction and atmospheric disturbances
Creators: name:  H. LABRIJI 
name:   O. HERSCOVICI-SCHILLER 
name:   F. CASSAING 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: SPACE DEBRIS
OBSERVATION
ORBIT DETERMINATION
ACTIVE DEBRIS REMOVAL

description: Geostationary satellites are beyond the scope of the biggest ground-based telescopes due to their size and distance from Earth. In fact, imaging a GEO satellite to a sub-metric resolution requires an angular resolu-tion of just a few milli-arcseconds, the performance of a diffraction-limited optical aperture of several tens of meters. Shadow imaging is an innovative and cost effective technique that provides the sub-metric con-tour of a space object from the shadow it casts when passing in front of a star [1]. Unlike classical meth-ods, such as interferometry, that rely on the optical combination of coherent light beams collected over hectometric apertures, shadow imaging relies on the much simpler electronic processing of light resulting from the combination of the satellite diffracted wave and the star plane wave. Thanks to this homodyne detection, the critical phase information can be partially recorded at the telescope level and the generated pattern is turbulence-insensitive and highly measurable. Moreover, this 2D pattern can be acquired along the north-south dimension by a single row of sub-apertures, and along the East-West dimension by a tem-poral sampling benefiting from the displacement of the shadow induced by the satellite velocity. Shadow imaging is nevertheless a challenging method. First, the bare observation of the shadow critically depends on the accurate estimation of its position on the ground. Second, the satellite contour is numerically ex-tracted from its shadow, requiring a very fine knowledge of the complete propagation chain. This commu-nication will focus on the study of the direct light path and its numerical inversion. The main physical phenomenon involved here is the diffraction of light at the end of the near field. Con-sidering the constraints of our problem, we have chosen to compute numerically the Fresnels diffracto-grams using the decomposition of incident light in a truncated basis of Hermite-Gauss functions. These functions are analytical solutions of the wave equation [2] and hence provide a modal approach that is more flexible than the usual FFT-based methods. One of the issues arising in shadow imaging is the chro-maticity of diffraction, so in order to fully exploit the broadband stellar flux, we scatter the light over sev-eral spectral channels. Along its path through Earths atmosphere, the diffracted light undergoes two main disturbances. First, the atmospheric refraction induces a chromatic shift [3], which blurs the shadow image. Second, the atmos-pheric scintillation leads to a random variation of the intensity received by the collecting sub-apertures. Those two effects have to be taken into account in the simulation of the direct light path. In this communication, we will start by describing how shadow imaging works. Then, we will briefly out-line the atmospheric disturbances and expose how we tackled them. Next, we will detail the direct Fresnel propagation and the estimation of the geometric silhouette, using a maximum a posteriori framework and combining several narrow band observations. Supported by simulations, we will show the strong potential of the method and its robustness against the different disturbances and the chromaticity of the observation. We believe shadow imaging is an efficient ground-based approach that can meet in the near future the challenge of resolving GEO satellites.