Optical depth
Dimensionless measure of radiant power attenuation through a material.
Optical depth, also referred to as optical thickness, is a dimensionless physical quantity that quantifies how much radiant power is attenuated when traveling through a material. It is formally defined as the natural logarithm of the ratio of incident radiant power to transmitted radiant power. Consequently, a larger optical depth corresponds to a smaller fraction of the original radiant power being transmitted. This quantity is not a length, but it increases monotonically with the optical path length, approaching zero as that path length shrinks to nothing. The term "optical density" is discouraged for this concept. In chemistry, a closely related measure called absorbance or decadic absorbance is used instead, which employs the common logarithm of the same power ratio; this absorbance equals the optical depth divided by the natural logarithm of ten due to the different logarithmic bases.
Optical depth measures attenuation, which can arise from absorption, reflection, scattering, or other processes. When both the absorbance is much less than one and the material’s emittance is much less than the optical depth, the optical depth approximates the attenuation. The relationship between optical depth and the material’s attenuation coefficient is given by the integral of that coefficient along the path length; if the coefficient is uniform, the optical depth is simply the product of the coefficient and the thickness. Alternatively, it can be expressed using the attenuation cross section and number density of the material.
In atomic physics, the spectral optical depth of an atomic cloud is derived from quantum-mechanical properties, including the transition dipole moment, atom number, beam frequency, and natural linewidth. In atmospheric science, the optical depth often refers to the vertical path from Earth’s surface to outer space, or from an observer’s altitude to space. For a slant path, it equals the vertical optical depth multiplied by the relative airmass, which for a plane-parallel atmosphere is the secant of the zenith angle. The total atmospheric optical depth can be split into components from Rayleigh scattering, aerosols, and gaseous absorption, and is measured with a sun photometer. For a plane-parallel cloud layer, the optical depth depends on the extinction efficiency, liquid water path, droplet concentration, and liquid water density. In astronom
- field
- Physics
- known_for
- Measuring attenuation of radiant power through a material
- related_quantity
- Absorbance (decadic absorbance) in chemistry
Lore & Background
Optical depth is a dimensionless quantity that measures how much a material attenuates transmitted radiant power, defined as the natural logarithm of the ratio of incident to transmitted flux. It increases monotonically with the path length through the material and approaches zero as that path length approaches zero. A larger optical depth indicates less transmitted power. The closely related term "absorbance" or "decadic absorbance" uses the common logarithm instead, making it equal to the optical depth divided by a factor due to the different logarithm bases. Optical depth is not a length, and the term "optical density" for this quantity is discouraged. The quantity can be specified for a particular wavelength or frequency, called spectral optical depth. Attenuation responsible for optical depth can arise from absorption, reflection, scattering, or other processes. The optical depth of a material is approximately equal to its attenuation when both the absorbance and the emittance of the material are very small. The Beer–Lambert law relates optical depth to the attenuation coefficient integrated along the path; if the coefficient is uniform, the optical depth is simply the product of that coefficient and the path length. Alternatively, it can be expressed using the attenuation cross section and number density of the material. In atmospheric science, the total atmospheric optical depth is the sum of components from Rayleigh scattering, aerosols, and gaseous absorption, and is measured with a sun photometer. For a plane-parallel cloud layer, the optical depth depends on the extinction efficiency, liquid water path, geometrical thickness, droplet concentration, and liquid water density. In astronomy, the photosphere of a star is defined as the surface where the optical depth equals 2/3, meaning each photon emitted there undergoes on average less than one scattering before reaching an observer.
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.
More in Optics And Photonics 1-24
Spotted an error? Know more?
This is a living reference — every entry is fact-audited, and reader corrections feed straight into our audit queue. Suggest an edit · See this site's audit record