thumb|Aerosol Optical Depth (AOD) at 830 nm measured with the same LED sun photometer from 1990 to 2016 at Geronimo Creek Observatory, Texas. Measurements made at or near solar noon when the Sun is not obstructed by clouds. Peaks indicate smoke, dust and smog. Saharan dust events are measured each summer.

In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material.

Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material.

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 optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.<math display="block">\tau = \ln\!\left(\frac{\Phi_\mathrm{e}^\mathrm{i{\Phi_\mathrm{e}^\mathrm{t\right) = -\ln T</math>where

  • <math display="inline">\Phi_\mathrm{e}^\mathrm{i}</math> is the radiant flux received by that material;
  • <math display="inline">\Phi_\mathrm{e}^\mathrm{t}</math> is the radiant flux transmitted by that material;
  • <math display="inline">T</math> is the transmittance of that material.

The absorbance <math display="inline">A</math> is related to optical depth by:<math display="block">\tau = A \ln{10}</math>

Spectral optical depth

The spectral optical depth in frequency (denoted <math>\tau_\nu</math>) or in wavelength (<math>\tau_\lambda</math>) of a material is given by:<math display="block">\tau = Q_\text{e} \left[\frac{9\pi L^2 H N}{16\rho_l^2}\right]^{1/3}</math>where:

  • Q<sub>e</sub> is the extinction efficiency
  • L is the liquid water path
  • H is the geometrical thickness
  • N is the concentration of droplets
  • ρ<sub>l</sub> is the density of liquid water

So, with a fixed depth and total liquid water path, <math display="inline">\tau \propto N^{1/3}</math>.