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. 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 , is given by:where is the radiant flux transmitted by that material; is the radiant flux received by that material; is the transmittance of that material. The absorbance is related to optical depth by: Spectral optical depth Spectral optical depth in frequency and spectral optical depth in wavelength of a material, denoted and respectively, are given by: where is the spectral radiant flux in frequency transmitted by that material; is the spectral radiant flux in frequency received by that material; is the spectral transmittance in frequency of that material; is the spectral radiant flux in wavelength transmitted by that material; is the spectral radiant flux in wavelength received by that material; is the spectral transmittance in wavelength of that material. Spectral absorbance is related to spectral optical depth by: where is the spectral absorbance in frequency; is the spectral absorbance in wavelength. Relationship with attenuation Attenuation 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 attenuation 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 Φet is the radiant power transmitted by that material; Φeatt is the radiant power attenuated by that material; Φei is the radiant power received by that