Hanae Labriji, DTIS, ONERA, Université Paris Saclay; Olivier Herscovici-Schiller, DTIS, ONERA, Université Paris Saclay; Frederic Cassaing, DTIS, ONERA, Université Paris Saclay
Keywords: Shadow imaging, resolved imaging, geostationary satellite imaging, geostationary satellite characterization, synthetic-aperture silhouette imaging, non-conventional imaging.
Abstract:
Resolving a GEO satellite with a sub-metric resolution requires a few milli-arcseconds resolution, the diffraction limit of an optical aperture of several tens of meters. Shadow imaging is an alternative approach that consists in observing the shadow cast by the satellite when passing in front of a star, allowing the sub-metric contour details of the space object to be reconstructed. This method is innovative as it offers significant photometric gains through the recording of the direct occulted starlight. The two-dimensional generated pattern, which is turbulence-insensitive due to short occultation times, is acquired using a row of sub-apertures, used as light buckets. The first dimension of the shadow image is the spatial sampling by the telescopes. The second dimension is time-related and results from the displacement of the shadow, caused by the satellite relative velocity with respect to the star. In order to obtain the contour of the satellite, one has to reproduce the reverse path of light propagation, strongly distorted by diffraction in the far Fresnel region and atmospheric disturbances.
The idea of observing a satellite shadow on Earth was first proposed by R. Burns (SPIE 2005). The main advances are first the detailed study by J. Luu (AMOS 2008) of the resolution-limiting factors such as the angular extent of the occulted star, its polychromatic light, and its brightness. J. Luu consequently proposed a spectrally resolved shadow imaging. Then, Douglas (SPIE 2017) quantified some of those factors and more importantly studied the thorny question of the shadow prediction (AMOS 2016). Last, Paxman (AMOS 2020) demonstrated for the first time a reduced-scale shadow imaging in the Lab, reproducing the same Fresnel number. Paxman did away with the classically used Gerchberg-Saxton phase retrieval algorithm, and was the first to use a modern non-linear optimization tool to recover the object’s silhouette, using experimental data.
In our study, the goal was first to quantify numerically the resolution loss induced by the atmospheric disturbances and to study the diffraction in the Fresnel region. The star’s light undergoes two main disturbances. First, the atmospheric refraction induces a chromatic shift that is a potential source of distortions. We computed analytically and numerically the chromatic shift (published in Labriji et al., A&A 2022 (accepted)); we have found that this effect is manageable. Secondly, the atmospheric scintillation leads to a random variation of the intensity received by the collecting sub-apertures. We quantified these losses through analytic formulas and our results indicate that indeed, in many cases, shadow imaging is robust against atmospheric scintillation.
When modelling Fresnel diffraction, looking for accuracy and knowing the constraints of our problem, we have chosen to compute the diffracted shadow using the decomposition of the incident light in a truncated basis of Hermite-Gauss functions. These functions are analytical solutions of the paraxial wave equation and thus provide a continuous solution that is more versatile than the usual FFT-based methods. Computing diffraction in this way is the key piece that eased the construction of an efficient inversion algorithm, based on the maximum a posteriori estimator.
In addition, we made an experimental setup to reproduce shadow imaging using a single mode fibre, a millimetre-sized object, and a CCD camera. Our aim is to recover a silhouette from shadows acquired at several narrow spectral bins. Stars with various magnitudes are simulated to evaluate the SNR impact. We have successfully reconstructed silhouettes from experimental data using our algorithm based on the maximum a posteriori estimator and non-linear optimization methods.
Finally, since there is no published proof of a recorded satellite occultation as of March 1st, 2022, our efforts during spring and summer will be focused on the observation of a GEO shadow from the ONERA site in Palaiseau, France, using a 35cm telescope. Finally, our efforts during the next months will include the acquisition of an actual shadow signal from a GEO satellite with our 35cm telescope that should be installed soon in our premises. This would to the first published feasibility demonstration of shadow imaging. We will present our results at the conference.
Date of Conference: September 27-20, 2022
Track: Non-Resolved Object Characterization