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optical thickness[′äp·tə·kəl ′thik·nəs]
The optical thickness τ of a medium is a dimensionless quantity that characterizes the attenuation of optical radiation in the medium. The attenuation results from the joint action of light absorption and light scattering. The effects of radiation amplification caused by multiple scattering are not taken into account.
For an optically homogeneous medium, τ = ∊l, where ∊ is the medium’s volume extinction coefficient—which is equal to the sum of the absorption and scattering coefficients—and l is the geometric length of the path of the light ray in the medium. In a heterogeneous medium, in which ∊ depends on the coordinates, τ = ∫ ∊ dl, the integration being carried out along the path of the light ray. The modified Bouguer-Lambert-Beer law, which takes into account the scattering as well as the absorption of light, is written in terms of optical thickness as F = F0e-τ, where F0 and F are the radiation flux incident on the medium in the form of a parallel beam of rays and the flux emerging from the medium in the same direction, respectively. A layer of a substance for which τ > 1 is often said to be optically thick, and a layer with τ < 1 to be optically thin; this demarcation, however, is arbitrary.
The relation between the optical thickness of a layer of a medium and the layer’s transmittance T is τ = –In T. The layer’s specular optical density D = —log T is, in terms of r, D = 0.434τ. In general, τ is a function of the frequency v, or of the wavelength λ, of the radiation: τ = τ(ν) = τ*(λ). A single value of the optical thickness, however, is often used when only one radiation frequency is involved—that is, τ is the optical thickness for a monochromatic radiation flux.
The concept of optical thickness is widely used for the description of processes of light scattering and absorption in, for example, the study of turbid mediums and the theory of radiative transfer. With respect to radiative transfer, the concept finds particular application in astrophysics and the physics of the earth’s atmosphere.