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Optical depth
From Wikipedia, the free encyclopedia
Optical depth is a measure of transparency, and is defined as the fraction of radiation (or light) that is scattered or absorbed on a path. One way of visualizing optical depth is to think of a fog. The fog between you and an object that is immediately in front of you has an optical depth of zero. As the object moves away, the optical depth increases until it reaches a large value and the object is no longer visible.
The optical depth expresses the quantity of light removed from a beam by scattering or absorption during its path through a medium. If I0 is the intensity of radiation at the source and I is the observed intensity after a given path, then optical depth τ is defined by the following equation:
In atmospheric sciences, one often refers to the optical depth of the atmosphere as corresponding to the vertical path from the Earth's surface to outer space; at other times the optical path is from the observer's altitude to outer space. Since τ refers to a vertical path, the optical depth for a slant path is τ' = mτ, where m is called the airmass factor, and for a plane-parallel atmosphere it is determined as m = 1 / cosθ, where θ is the zenith angle corresponding to the given path. Therefore
The optical depth of the atmosphere can be divided in several components, ascribed to Rayleigh scattering, aerosols, and gaseous absorption. The optical depth of the atmosphere can be measured with a sun photometer. See also: Beer's law.
Another example occurs in astronomy where the photosphere of a star is defined as the surface where its optical depth is 2/3. This means that each photon emitted at the photosphere suffers an average of less than one scattering before it reaches you. At the temperature at optical depth 2/3, the energy emitted by the star (the original derivation is for the sun) matches the observed total energy emitted.
Note that the optical depth of a given medium will be different for different colors (wavelengths) of lights.
For planetary rings, the optical depth is the proportion of light blocked by the ring when it lies between the source and the observer. This is usually obtained by observation of stellar occultations.