Optical depth

Lore & Background

Optical depth is defined mathematically as τ = ln(Φ_e^i / Φ_e^t) = -ln T, where Φ_e^i is the incident radiant flux and Φ_e^t is the transmitted radiant flux, and T is the transmittance. A larger optical depth corresponds to a smaller amount of transmitted radiant power. Spectral optical depth, denoted τ_ν or τ_λ, uses spectral radiant flux in frequency or wavelength, respectively.

Reader's Guide

Optical depth is a fundamental concept in physics for quantifying how much a material attenuates radiant power, including effects from absorption, reflection, scattering, and other processes. It is dimensionless and not a length, though it increases with optical path length. In chemistry, a closely related quantity called absorbance (decadic absorbance) uses the common logarithm instead of the natural logarithm, and is related to optical depth by τ = A ln 10. The use of the term 'optical density' for optical depth is discouraged. Optical depth is approximately equal to attenuation when both the absorbance is much less than 1 and the emittance of the material is much less than the optical depth.

Did You Know?

• Optical depth is the natural logarithm of the ratio of incident to transmitted radiant power.
• Optical depth is dimensionless and is not a length.
• The term 'optical density' for optical depth is discouraged.
• Spectral optical depth can be defined in terms of frequency or wavelength.