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.
Optical depth of a material, denoted τ, is given by:
where
Absorbance is related to optical depth by:
where A is the absorbance.
Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted τν and τλ respectively, are given by:
where
Spectral absorbance is related to spectral optical depth by:
where
Optical depth measures the attenuation of the transmitted radiant power in a material. Attenuation can be caused by absorption, but also reflection, scattering, and other physical processes. Optical depth of a material is approximately equal to its attenuance when both the absorbance is much less than 1 and the emittance of that material (not to be confused with radiant exitance or emissivity) is much less than the optical depth:
where
and according to Beer–Lambert law,
so:
Optical depth of a material is also related to its attenuation coefficient by:
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