Image contrast of diffraction-limited telescopes for circular incoherent sources of uniform radiance

A simple approximate formula is derived for the background intensity beyond the edge of the image of uniform incoherent circular light source relative to the irradiance near the center of the image. The analysis applies to diffraction-limited telescopes with or without central beam obscuration due to a secondary mirror. Scattering off optical surfaces is neglected. The analysis is expected to be most applicable to spaceborne IR telescopes, for which diffraction can be the major source of off-axis response.