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# Absorbance

Author: the photonics expert

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 103 = 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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## Questions and Comments from Users

2024-03-23

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