Angles and Range: Initial Orbital Determination with the Air Force Space Surveillance Telescope (AFSST)
Abstract : The institution of a robust, comprehensive program of Space Situational Awareness (SSA) necessarily includes observations by ground-based optical and infrared (OIR) telescopes. The Air Force Space Surveillance Telescope (AFSST) has been proposed as a system of telescopes designed to address the ground-based component of comprehensive SSA. A hallmark of our definition of AFSST is that it be composed of inexpensive, replicable telescopes programmed to accomplish multiple surveillance programs, but designed to achieve the difficult design-driving task of accomplishing an uncued search for small objects in Low Earth Orbit (LEO). We discuss the configuration of AFSST and describe one technique by which AFSST simultaneously acquires angle and range data for accurate real-time determination of LEO orbital elements, even upon first detection of the object.
Demonstration of Uncued Surveillance of LEO
J.T. McGraw and Associates, LLC, in collaboration with the University of New Mexico (UNM), has built and is operating two proof-of-concept wide-field imaging systems to test novel techniques for uncued surveillance of LEO. The imaging systems are built from off-the-shelf optics and detectors resulting in a 350mm aperture and a 6 square degree field of view. For satellite streak detection, field of view is of critical importance because the maximum exposure time on the object is limited by its crossing time and measurements of apparent angular motion are better constrained with longer streaks. The current match of the detector to the optical system is optimized for detection of objects at altitudes above 450km, which for a circular orbit corresponds to apparent motions of approximately 1 deg./sec. Using our GPU-accelerated detection scheme, the proof-of-concept systems have detected objects fainter than V=12.3, which approximately corresponds to a 24 cm object at 1000 km altitude – at better than 6 sigma significance, from sites near and within Albuquerque, NM. This work demonstrates scalable optical systems designed for near real time detection of fast moving objects, which can be then handed off to other instruments capable of tracking and characterizing them. The two proof-of-concept systems, separated by ~30km, work together by taking simultaneous images of the same orbital volume to constrain the orbits of detected objects using parallax measurements. These detections are followed-up by photometric observations taken at UNM to independently assess the objects and the quality of the derived orbits. We assert this demonstrates the potential of small telescope arrays for detecting and cataloguing heretofore unknown LEO objects. 1. FINDING AND TRACKING LEO OBJECTS WITH OPTICAL TELESCOPES There has been increased interest in the potential for optical telescopes to make significant SSA contributions to the LEO volume. Optical techniques are not likely to supplant radar in the LEO regime, but can take advantage of some of the strengths of optical techniques. The principal advantage of optical SSA of LEO is that it is passive, using the Sun as the illuminator rather than having to project power. For radar this leads to the usual 1/R signal reduction because the projected power diverges both from transmitter to object and from object to detector. Optical telescopes are also relatively inexpensive, becoming more so every year, making them easily and cost effectively deployable around the world. Compared to radar the most significant shortcoming of optical techniques for uncued LEO SSA are that the Sun illuminates LEO for only a few hours per day and are not effective under moderate cloud cover. Depending on the observatory site and the altitude within LEO (lower altitudes are illuminated in terminator for less time than higher ones), this can easily lead to a coverage factor in the range of 5-10%. The work presented here is adding to the case that that small telescopes (by which we mean meter-class or smaller) can rapidly and robustly detect small objects (10cm or smaller) and thus should be seriously considered for the SSA portfolio. In the next section, we will summarize the scope of observing objects in LEO orbits with ground-based optical sensors. Section 3 details the hardware we have deployed to serve as a proof of concept and test bed for our techniques. Section 4 presents a small sample of the type of data and detections that have been made with these systems. Section 5 reports on some preliminary measurements of parallax range using our two optical systems together. Section 6 offers some suggestions about the possibilities and potential of larger telescopes systems. 2. SIGNAL-TO-NOISE OF FAST MOVING OBJECTS – AN OVERVIEW We have previously detailed the challenges and scope of the problem of detecting small objects in the LEO volume using wide field optical telescopes (Ackermann et al. 2003 [1]) and the particular approach we use for detecting the streaks they leave in images (Zimmer, Ackermann and McGraw 2013 [2]). The relevant highlights of this are:  Objects in LEO are bright by astronomical standards o A 10cm object at 1000km ~12 magnitude (A=1) to 14 magnitude (A=0.12) o A golf ball (4.2cm) at 1000km range with a 90% albedo is ~14 magnitude o Even under bright skies, 16 magnitude is bright enough to detect in 1s with a 300mm telescope  Objects in LEO have a high apparent angular velocity o ~0.2 deg/s at 2000km, 0.4 deg/s at 1000km, and up to ~1.5 deg/s at 300km, observed near zenith o Light from LEO objects is therefore trailed over many pixels, each contributing noise – so-called trailing losses o The resulting loss in per-pixel signal-to-noise ratio scales as the number of pixels in the streak, which can be hundreds to thousands of pixels long  Signal-to-noise in the whole LEO streak is more significant by approximately the square root of the streak length o If you can find it in the first place. o The low per-pixel S/N is most often ignored as part of the background by traditional source detection techniques because the per kernel S/N does not cross a statistical significance threshold  Rapid cadence (~1s) imaging with zero deadtime of wide instantaneous fields of view (FOV >> 1 square degree) can catch LEO objects as they streak through the field o Exposure time tailored so that a 1 deg/s object will cover half of the short dimension of the FOV o Zero deadtime for maximum efficiency and no lost objects between exposures o Optimize for existing hardware, minimum read noise and feasibility of real time detection  No need to track – for the short exposures we use, we can allows stars to trail without reducing effective system coverage of the LEO volume These factors have guided the overall development of our hardware and software techniques and represent one set of solutions to detect faint objects in LEO orbits given real world constraints and conditions. Detector technology and computer hardware capabilities continue to grow exponentially and these trends only serve to make optical SSA of LEO more effective and affordable. 3. DEPLOYMENT AND TESTING OF PROOF-OF-CONCEPT SYSTEMS The initial phase of this work investigated available COTS telescopes systems to try to find the most cost-effective telescope system to provide a real demonstration and test bed for our techniques. Available detectors are consistently the limiting factor. Our budgetary constraints effectively eliminated backside illuminated CCDs, which are desirable for their high quantum efficiency, though they do require a mechanical shutter and the readout time overheads are often of the order 100% for one second cadence images, reducing much of the photoelectric efficiency gain. Our need for rapid observing cadence with minimal dead time drove us to use 35mm format interline CCDs that are commercially available in cameras from several vendors, because they can be read out while the next exposure is accumulating, eliminating readout overhead. Non-interline, front illuminated sensors were eliminated because the readout time overhead reduced the allowable exposure times, despite the availability of physically larger sensors. Having settled on a family of detectors, we examined camera/telescope combinations to find the best etendue, collecting area (A) multiplied by the field of view (Omega), per dollar. The standout system in this analysis was a 14” Celestron Schmidt-Cassegrain optical tube with a HyperStar f/1.9 prime-focus corrector. Combined with an ON Semiconductor (formerly TrueSense (formerly Kodak)) KAF-16070 4864 x 3232 sensor with 7.4 micron pixels, this gives a 3° x 2° field of view with 2.23 arcsecond pixels, albeit with significant vignetting from the corrector in the corners of the field. These sensors are integrated into Finger Lakes Instruments Microline cameras, which were chosen because they allowed a rapid dual amplifier read rate of 10MHz resulting in a 1Hz frame rate (principally limited by the USB2.0 bus) in a compact housing with integrated thermoelectric cooling. Because these cameras are operating at prime focus, the form factor is critical to preclude adding to the system obscuration, and the Microline camera adds only a small fraction compared to the corrector housing. The net result is an instrumental etendue of almost 0.5 mdeg for a 6 square degree FOV that can read out at 1 Hz with 11eof read noise, essentially zero dead time between exposures, with parts available off-the-shelf for around $20,000. We have deployed two of these systems in the Albuquerque metropolitan area, as shown in Figure 1. Siting telescopes this close to a major population center is not ideal and incurs a cost in detectivity, especially for the system within Albuquerque city limits, but it provides easily accessible systems for development and testing. The added noise from night sky is easily quantified and we can readily extrapolate the performance that would be expected from a dark sky site. Given the relatively small apertures involved and the rapid image cadence, a truly dark astronomical site (West Texas, Hawaii, Chile, etc.) is not crucial. Each telescope and camera system is installed on a Paramount MX German Equatorial mount allowing precision pointing. These are attached to Parallax Instruments portable piers and installed in 7 foot diameter Astrohaven domes. The deployed systems in their domes are shown in Figures 2 and 3. Altogether optical systems, mounts, domes and computers the total cost per system is approximately $50,000, and the entire system can be deployed by a small team in about two hours, crate-to-sky. Figure 1 – Google Earth views of the present deployment of JTMA’s Proof-of-Concept LEO SSA Optical Systems. The systems are separated by 27 km enabling them to simultaneously observe the same volume of LEO and obtain range estimates based on parallax for objects detected with both systems. Figure 2 (left) and Figure 
Improved optical design for the Large Synoptic Survey Telescope (LSST)
This paper presents an improved optical design for the LSST, an f/1.25 three-mirror telescope covering 3.0 degrees full field angle, with 6.9 m effective aperture diameter. The telescope operates at five wavelength bands spanning 386.5 nm to 1040 nm (B, V, R, I and Z). For all bands, 80% of the polychromatic diffracted energy is collected within 0.20 arc-seconds diameter. The reflective telescope uses an 8.4 m f/1.06 concave primary, a 3.4 m convex secondary and a 5.2 m concave tertiary in a Paul geometry. The system length is 9.2 m. A refractive corrector near the detector uses three fused silica lenses, rather than the two lenses of previous designs. Earlier designs required that one element be a vacuum barrier, but now the detector sits in an inert gas at ambient pressure, with the last lens serving as the gas barrier. Small adjustments lead to optimal correction at each band. Each filter has a different axial thickness, and the primary and tertiary mirrors are repositioned for each wavelength band. Features that simplify manufacturing include a flat detector, a far less aspheric convex secondary (10 μm from best fit sphere) and reduced aspheric departures on the lenses and tertiary mirror. Five aspheric surfaces, on all three mirrors and on two lenses, are used. The primary is nearly parabolic. The telescope is fully baffled so that no specularly reflected light from any field angle, inside or outside of the full field angle of 3.0 degrees, can reach the detector.