Imaging of Extended Objects Through a Turbulent Atmosphere

The extended Huygens-Fresnel principle is used to derive an explicit expression for the image plane illuminance distribution of an extended object with an arbitrary luminance emittance distribution. The combined simultaneous effects of attenuation, background luminance, and atmospheric turbulence are given. A quantitative comparison of these effects is made, and their contribution to the over-all loss in resolution is given. In particular, we derive a quantitative expression for the point spread function of the combined atmospheric-optical system. Explicit expressions are derived for both the atmospheric-optical system modulation transfer function (MTF) and image plane modulation. Numerical results for the image plane modulation are presented for imaging both up and down along an atmospheric path under various viewing conditions.