## Contrast Transmittance in Real Space

Any landscape feature can be thought of as consisting of many small pieces, or elements, with a variety of physical characteristics. For instance, the reflectivity of an element as a function of wavelength, along with characteristics of the incident radiation, determines its color and brightness. The brightness of an element at some observing distance and at one wavelength is referred to as monochromatic apparent spectral radiance. The monochromatic apparent spectral radiance of any element is given according to Eq. (6) by

where N* is substituted explicitly for Nq(\ - Tr). The subscript / indicates that the radiance is associated with a specific uniform landscape feature. In the early literature the subscript t (for target) was used instead of I because of the applicability of Eq. (12) and contrast to the seeing of military targets.

A scenic element is always seen against some background, such as the sky or another landscape feature. The apparent and inherent background radiance are related by an expression similar to Eq. (12)

bNr = TrbN0+N* Subtracting Eq. (13) from Eq. (12) yields the relation oNr -hNr) = Tr(,N0 -bN0)

Thus, radiance differences are transmitted along any path with the same attenuation as that experienced by each image-forming ray.

The image-transmitting properties of the atmosphere can be separated from the optical properties of the object by the introduction of the contrast concept. The inherent spectral contrast, C0, of a scenic element is, by definition,

The corresponding definition for apparent spectral contrast at some distance r is

If Eq. (14) is divided by the apparent radiance of the background hNr and combined with Eqs. (15) and (16), the result can be written as

Substituting Eq. (13) for bNr and rearranging yields

bN0Tr

The right-hand member of Eq. (18) is an expression for the contrast transmittance, rn of the path of sight. Equation (18) is the law of contrast reduction by the atmosphere expressed in the most general form. It should be emphasized that Eq. (18) is completely general and applies rigorously to any path of sight regardless of the extent to which the scattering and absorbing properties of the atmosphere or the distribution of lighting exhibit nonuniformities from point to point.