# Absorbance

Definition: the logarithm with base 10 of the inverse transmittance

Alternative term: optical density

German: Extinktion

Formula symbol: A

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Author: Dr. RĂ¼diger Paschotta

The absorbance e.g. of an optical filter or saturable absorber is the logarithm with base 10 of its inverse power transmission factor (transmittance):

For example, an absorbance of 3 means that the optical power is attenuated by the factor 10^{3} = 1000.
That would correspond to an attenuation by 30 decibels and a transmittance of 10^{−3}.

It is usually assume that any optical power losses are caused by absorption and not e.g. by scattering.
Otherwise, should use the term *attenuance*.

Absorbance should not be confused with *absorptance*, which is a dimensionless quantity.

If several absorbing devices are used in series, their absorbance values can simply be added. The absorbance of a homogeneously doped laser crystal, for example, is proportional to its length and the doping concentration.

An alternative term, which however is ambiguous, is *optical density*.

Absorbance values often depend on the optical wavelength.

Note that optical attenuation e.g. of a neutral density filter may not be entirely resulting from absorption, but at least partially from reflection; the term *absorbance* is then questionable.

## Relation to the Absorption Coefficient

The absorption per unit length is often quantified with an absorption coefficient α.
The power transmission factor (transmittance) for a propagation length *z* is then exp(−α *z*).
Therefore, the absorbance can be calculated as

In some cases, one uses a *decadic absorption coefficient*, which is smaller by the factor ln 10, so that the absorbance is simply that coefficient times the optical path length.

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See also: absorption, absorption coefficient, absorptance, optical density, reflectance, transmittance, transition cross sections, optical attenuators

and other articles in the category general optics

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