# Absorbance

Author: the photonics expert Dr. Rüdiger Paschotta

Definition: the logarithm with base 10 of the inverse transmittance

Alternative term: optical density

Formula symbol: A

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

$$A = \lg \left( P_\rm{in} / P_\rm{out} \right)$$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 assumed 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 <$\alpha$>. The power transmission factor (transmittance) for a propagation length <$z$> is then <$\exp(-\alpha z)$>. Therefore, the absorbance can be calculated as

$$A = \lg \left( \exp (\alpha \;z) \right) = \alpha \;z/\ln 10 \approx \alpha \;z/2.303$$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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2024-03-23

What is the definition of absorbance if there is some absorption, some reflection, and some transmission?

The author's answer:

You may in principle define it such that it describes the decay of intensity only due to absorption. However, the term is not usually used in such a situation.