GeoEye-1 and TMA Notes

The other day I read a Technology Review article on GeoEye-1, a commercial Earth-imaging satellite that will be launched into a 684 km sun-synchronous polar orbit August 22 from Vandenberg AFB, California. This satellite will provide the highest ground resolution color imagery to date of any commercial satellite - able to distinguish objects as small as 0.17 square meters (about 0.41 m x 0.41 m, beach ball size) and to locate this imagery within 3 meters of "ground truth." This is made possible by GPS and by the use of star trackers, auxiliary optical systems which allow the spacecraft to determine its position and alignment from guide stars. This technology has been used extensively in NASA and military systems, but not in commercial Earth-imagery satellites. There's another good Geo-Eye article here.

As an optical engineering sort of guy, I wondered who made the optical systems and what the specs were. Turns out it was ITT Space Systems in Rochester, NY, which for many years was part of Kodak (in the 1970's, Kodak made a backup primary mirror for Hubble that was not used, which was too bad because unlike the mirror made and tested at Perkin-Elmer, its prescription was the correct one!). I found a data sheet (PDF) which says that the telescope is a TMA design (three mirror anastigmat) with a 1.1 meter primary mirror with a focal length of 13.3 meters. It also includes two fold mirrors, presumably for more compact packaging.

When I read this, I first assumed that it was an off-axis TMA, a design form that has no central obscuration but which can be difficult (expensive) to fabricate and align. But looking at a graphic of the spacecraft (above), I saw that there is a fairly large central obscuration - a three-leg "spider" for the center-mounted secondary mirror. So I looked up axial TMA designs and found this paper (PDF). I set up the second of two lens data prescriptions in my optical design software, and although the design shown here is not necessarily the one ITT used for GeoEye-1, it has two folds and a pretty compact form. So it's probably something like this. JWST is also a TMA design.

I also noted that it doesn't use a "staring" sensor (2D array like a digital camera, where X and Y directions are read all at once), but rather a "line scan imaging system with time delay integration." This means that there is a single row of detectors to cover (say) the X coordinate (with 4 color bands, blue, green, red, and near IR) and some means to scan this in the perpendicular (Y) direction to capture the full frame line by line. This scanning can be done with something like a rotating polygon mirror, or it could possibly use the satellite's own north-south motion (not too sure about this!).

While searching I also found a great PowerPoint presentation on telescope history and optics by Jim Burge at the University of Arizona (5 MB PDF, 62 slides).

P.S. Just to add a bit more optics, how might you estimate the ground resolution of such an orbiting telescope? You could do it roughly with a simple formula (explained here) for angular resolution in radians, which is 1.22*(wavelength)/(Lens Diameter). This shows that resolution gets better (smaller) for smaller wavelengths and bigger mirrors. GeoSat-1's primary mirror is 1.1 meters in diameter, and you can use a wavelength of 500 nanometers (10^-9 meters) for the approximate center of of the visible spectrum. The angular resolution works out to about 0.55 microradians (0.55E-06). If you multiply this tiny angle by the satellite's typical altitude of 684 kilometers to turn this into a linear number (the short side of a very long, skinny triangle), you get 0.38 meters, pretty close to the stated 0.41 meters (square root of 0.17 square meters). This ignores things like the central obscuration, atmospheric effects, and satellite motion, but it's a pretty darn good estimate.