Optical depth

In physics, optical depth or optical thickness, is the natural logarithm of the ratio of incident to transmitted radiant power through a material, and spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.

In chemistry, a closely related quantity called "absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a material, that is the optical depth divided by ln 10.

Mathematical definitions

Optical depth

Optical depth of a material, denoted τ, is given by:

where

Optical depth (astrophysics)

Optical depth in astrophysics refers to a specific level of transparency. Optical depth and actual depth, and respectively, can vary widely depending on the absorptivity of the astrophysical environment. Indeed, is able to show the relationship between these two quantities and can lead to a greater understanding of the structure inside a star.

Optical depth is a measure of the extinction coefficient or absorptivity up to a specific 'depth' of a star's makeup.

The assumption here is that either the extinction coefficient or the column number density N is known. These can generally be calculated from other equations if a fair amount of information is known about the chemical makeup of the star. From the definition, it is also clear that large optical depths correspond to higher rate of obscuration. Optical depth can therefore be though of as the opacity of a medium.

The extinction coefficient can be calculated using the transfer equation. In most astrophysical problems, this is exceptionally difficult to solve since solving the corresponding equations requires the incident radiation as well as the radiation leaving the star. These values are usually theoretical.