Distant contrast measurements through fog and thick haze

Koschmieder's contrast reduction law has been verified in medium visibility conditions by means of distant contrast measurements of two or more black targets placed at different distances from a telephotometer, as well as by comparing the contrast with transparency measurements. On the contrary, in foggy conditions the measurement results do not obey the law and markedly disagree with transmissometer readings. By reexamining Koschmieder's equations in the light of Foitzik's suggestion about the dependence of a target apparent luminance in fog on its geometrical dimensions, the following results are obtained: (i) contrast reduction law does not hold in fog because the target apparent luminance depends on the droplet size distribution, and (ii) this fact is entirely due to the truncated integration over the scattering angle of the air luminance gradient in the view direction because of the target's finite dimensions. These statements are confirmed by field experiments' results.