A veil of atmospheric haze reduces the visibility of all distant objects by decreasing their apparent contrast. In this paper equations are derived which describe the manner in which the apparent contrast of any object depends upon the distance of the observer. The treatment is not limited to horizontal paths of sight, but applies also to the apparent contrast of objects on the ground as seen from the air, and to the apparent contrast of objects aloft as viewed from the ground. The equations are not limited to the case of a homogeneous standard atmosphere; they may be applied to many kinds of non-standard atmospheric conditions. For every path of sight there exists a luminance level which will be transmitted unchanged. The apparent luminance of any receding object approaches this equilibrium level. For many paths of sight the equilibrium luminance is matched by the luminance of some portion of the horizon sky.
SEIBERT Q. DUNTLEY, "The Reduction of Apparent Contrast by the Atmosphere," J. Opt. Soc. Am. 38, 179-187 (1948)