Not sure I've got a good source for you, but if you use the Rayleigh criterion you get that you can just about make out earth-sized objects using visible light at 4 ly. You could use much higher energy photons (better resolution from lower wavelength), but this gives you other problems. Anything beyond visible light won't make it through the atmosphere (1 km is a BIG thing to put into space), and x and gamma rays are really hard to build optics for.