Richard Paxman, Maxar; Kurt Gleichman, Maxar; Alexander S. Iacchetta, Maxar; Bradley M. Jost, Maxar
Keywords: SASI, silhouette, ground-based imaging of satellites, shadow imaging
Abstract:
The problem of ground-based fine-resolution imaging of Geosynchronous Earth Orbit (GEO) satellites continues to be an important unsolved space-surveillance problem. If one wants to achieve 10cm resolution at a range of 36,000km (range to geosynchronous satellite) at a wavelength of 0.5um via conventional means, then a 180m diameter telescope with adaptive optics is needed. Such a system is prohibitively expensive and is currently not within technical reach. This has led researchers to investigate interferometric-imaging approaches that have sufficiently large baselines (e.g. 180m) to collect the spatial-frequency information needed to achieve the desired resolution on target. We are investigating a passive-illumination approach which is radically different from amplitude, intensity, or heterodyne-interferometry approaches. This approach, called SASI, produces a fine-resolution image of the satellite silhouette.
When plane-wave radiation emanating from a bright star is occluded by a geosynchronous satellite, the light is diffracted and a moving diffraction pattern (shadow) is cast on the surface of the earth. With prior knowledge of the satellite orbit and star location, the track of the moving shadow can be predicted. A linear array of inexpensive hobby telescopes can be deployed roughly perpendicular to the west-east shadow track to collect a time history of the star intensity as the shadow passes by. This synthetic aperture allows us to capture the entire 2D diffraction pattern cast by the occluding satellite. Given the Fresnel diffraction pattern and use of the constraint that the object is binary (a silhouette), we can use phase retrieval to obtain a fine-resolution image of the silhouette.
A compelling reason to pursue the SASI concept is that it is extremely cost effective relative to other ground-based approaches. The hardware required is embarrassingly inexpensive. SASI only requires an array of tracking hobby-class telescopes, each with a low-cost APD detector. The telescopes can be deployed in a linear array that spans the desired effective diameter. The linear array provides a 2D data set via temporal synthesis. The telescope/sensor modules can be identical, enabling economies of scale. Each telescope tracks the designated star and collects its time history with the aid of a field stop and a single APD detector. Signals must be detected at ~10kHz bandwidths and must be synchronized to sub-millisecond accuracy, which is straightforward to achieve.
Another advantage of the SASI concept is that the signal depends on the star magnitude, not the magnitude of the satellite. The target satellite can be arbitrarily faint. In fact, SASI works well for unilluminated satellites (in the earths shadow) or satellites with low optical signature. Countermeasures against imaging based on occlusion are very difficult to engineer. Finally, SASI is insensitive to atmospheric-turbulence effects, unlike many ground-based observational methods. SASI indirectly measures Fresnel amplitude, which is insensitive to turbulence-induced aberrations, so long as the turbulence is near the pupil. This obviates the need for phase-tracking and wavefront-sensing instrumentation.
The use of SASI for the imaging of satellites, also referred to as shadow imaging, was first proposed by Burns [1] and has been studied by others [2-4]. We formulated the SASI concept without knowledge of others work, which gave us an independent perspective.
To test the SASI concept with real data, we designed a scaled laboratory experiment that directly traces to the ground-based GEO-satellite-imaging geometry. The experimental setup fits conveniently on an optical table top, with a footprint smaller than a meter squared. Collimated narrow-band light, emulating filtered starlight, is directed toward a target which consists of a chrome deposition of a helicopter silhouette on a microscope slide. The extent of the occluding helicopter silhouette is 1mm which corresponds to a 10m target in a geosynchronous orbit. The light propagates beyond the occluding target and the associated diffraction pattern falls on a detector array at a range of 36cm from the target. This range corresponds to the range from the earth to a GEO satellite. A careful examination of the Fresnel integral equation reveals that the range and cross-range dimensions scale differently, so long as the optical wavelength is held constant. The detector array collects the intensity of the diffraction pattern. To model SASI intensity data, we aggregated pixels on our camera to emulate an array of 30cm diameter hobby telescopes. The collected data closely match simulated data derived by computing the Fresnel diffraction pattern from our target model. The only difference is that the laboratory data have a low level of mottled texture which we attribute to the optical quality of the slide surfaces. We estimated the object by iteratively optimizing an objective function that penalizes deviations from a binary object and discrepancies from the laboratory data. This process is effectively performing phase retrieval with an opacity (binary) constraint. The resulting estimate is a high-fidelity representation of the truth and has significant intelligence value. We believe that the quality of the estimate is limited by the mottle texture in the data, which would not be present with field data. The resolution achieved on the slide was calculated to be 35um which traces to 35cm resolution on a geosynchronous satellite. This corresponds to collecting data with a 60m linear array of 100 hobby telescopes (30cm diameter), each separated by 60cm (50% duty cycle). Alternatively, this resolution could have been achieved with a 60m diameter conventional telescope and aggressive adaptive optics! This is a much larger diameter than any current telescope and the corresponding SASI system would be far easier to design and construct.
References
[1] R.H. Burns, et al., Shadow imaging of GEO satellites, Proc. SPIE 5896 (2005).
[2] J. Luu, et al., Shadow imaging efforts at MIT Lincoln Laboratory, in Advanced Maui Optical and Space Surveillance Technologies Conference (2008).
[3] D.M. Douglas, et al., Shadow imaging of geosynchronous satellites, in Advanced Maui Optical and Space Surveillance Technologies Conference (2016).
[4] R.G. Paxman, Synthetic-aperture silhouette imaging, in Advanced Maui Optical and Space Surveillance Technologies Conference (2016).
Date of Conference: September 14-17, 2021
Track: Optical Systems & Instrumentation