4. A venture capital group is evaluating your proposal for an Infrared Google Earth telescope to take LWIR (A = 8-12 pym) photos of Planet Earth from an altitude R = 500 km with a GSD = 0.5 meters. The Director of Engineering in charge of evaluating your proposal has a couple of questions on topics that were not addressed in your presentation: A common pixel pitch for LWIR FPAs is 20 um, and you would like to measure temperature differences in the scene using adjacent pixels. Assuming a 100% fill factor for the FPA, what diameter D is needed for the optical aperture? (15 points)