Quote:

Mission - To image 1-meter-sized features including life, on planets up to 550 lightyears away. This volume of space contains an estimated 89,000 G-type stars like ours, and 1.8 million stars of all types. It would take many decades of operation to survey all of them. Angular Resolution - To see 1-meter sized features at 550 lightyears requires a pair of telescopes positioned 415-AU apart (415-times the Earth-Sun distance). They can be launched in opposite directions to positions 208-AU from Earth. Light Bucket - An earthlike planet may receive a similar amount of sunlight as Earth, about 1360 Watts per square meter. If we are viewing from a 90-deg angle, that radiation will be averaged over the 45-deg latitude zone of one hemisphere, giving an average 50 percent attenuation of reflected light. The above radiation muliplied by the surface area of one hemisphere, and reduced by the inverse square law over 550-lightyears distance, results in an exoplanet with a brightness of only 5.17E-22 Watts per square meter. If our videocamera is set up to detect 12 micron infrared light (1.66E-20 Joules per photon), with a 32x32 pixel single-photon avalanche diode (SPAD) detector running at 30 frames per second (that would be 30 photons per pixel per second) we would need a main reflecting mirror of 984,000 square meters area to collect a sufficient amount of light. This is equivalent to a circular mirror 1119-meters in diameter. Using shorter wavelength light, such as visible light versus infrared, increases the energy per photon and reduces the number of photons available per unit area, resulting in a larger main mirror to collect sufficient light, or alot of pixels not detecting any photons. Increasing the number of pixels in the camera and/or the frame rate has a similar negative effect. So we design for infrared light to minimize the mirror size required. With these parameters, we need a main parabolic reflector 1119-meters in diameter (smaller than my previous estimate). Mirror Segments - A parabolic bowl with a 1000-meter focal length is very shallow having a surface area only 2 percent larger than a flat circular disk of the same diameter. If we construct the parabola out of equilateral triangular segments with 1.0392-meter edge length, which are then assembled into hexagonal mirrors 1.8-meters across the flats, then it would require 2,145,432 triangular segments. With a thickness of 7.5-centimeters the total mass of fused silica glass would be 167,805-tonnes. A 300-nanometer thick reflective aluminum coating would have a mass of 813-kg. Manufacturing - Each factory would consist of a 19-meter diameter solar concentrator mirror focussing light on the interior of a metallized graphite crucible sheathed in zirconium orthosilicate. Inside the crucible the raw crushed silicate ore from an asteroid would be heated to 2273 deg Kelvin and melted to achieve a uniform composition, then stepped down to the softening temperature of 1956 deg Kelvin and extruded through a rectangular die. Four machines extruding a glass ribbon 0.9-meters wide x 0.075-meters thick at a rate of 11-centimeters per minute could manufacture all the required triangular glass blanks in under 60 months. After the glass ribbon is extruded it is stepped down to the annealing temperature of 1413 deg. Kelvin, where it is cut at angles of +60 and -60 degrees to produce triangular blanks. They are held at this temperature and annealed for 100 hrs to prevent shattering before cooling to room temperature. At a production rate of 12 blanks per hour per line, an annealing oven large enough to heat soak 4900 glass blanks would be needed. Once annealed the blanks are then polished to the diffraction limit (for 12 micron infrared radiation) and a 300-nm thick aluminum coating is applied to one surface. The mirrors are now externally reflective, the glass used merely as a geometric substrate for the reflective coating (glass is opaque to infrared). Assembly - About 3000 of the small mirror segments can be fitted into a larger triangular sheet with an edge length of about 57 meters. These large sheets can be stacked 54 meters high for transport. The 715 layers that comprise this stack can be unstacked again when the spacecraft reaches the 208-AU destination point, and re-assembled into an expansive array of mirrors, connected edge-to-edge, forming a parabolic reflector 1119-meters in diameter.