Absorbance
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: the logarithm with base 10 of the inverse transmittance
Alternative term: optical density
Related: absorptionabsorption coefficientabsorptanceoptical densityreflectancetransmittancetransition cross-sectionsoptical attenuators
Units: (dimensionless number)
Formula symbol: A
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DOI: 10.61835/j1n Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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Definition of Absorbance
The absorbance e.g. of an optical filter or saturable absorber is the logarithm with base 10 of its inverse power transmission factor (transmittance):
$$A = \log_{10} \left( P_\textrm{in} / P_\textrm{out} \right)$$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, one should use the term attenuance.
Absorbance should not be confused with absorptance; both are dimensionless quantities, but the former is logarithmic.
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
$$A = \log_{10} \left( \exp (\alpha \;z) \right) = \alpha \;z/\ln 10 \approx \alpha \;z/2.303$$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.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is absorbance?
Absorbance is a measure of light attenuation in a material, defined as the base-10 logarithm of the ratio of incident to transmitted optical power: ($A = \log_{10}(P_\textrm{in} / P_\textrm{out})$).
How does an absorbance value relate to the attenuation factor?
The attenuation factor is 10 raised to the power of the absorbance. For example, an absorbance of 2 corresponds to a factor of 100.
What is the difference between absorbance and attenuance?
Absorbance specifically quantifies power loss due to absorption. Attenuance is a more general term that includes all optical power losses, for example also those from scattering and reflection.
How is absorbance related to the absorption coefficient?
For a material of length ($z$) with an absorption coefficient ($\alpha$), the absorbance is calculated as ($A = \alpha \cdot z / \ln 10$). This links the absorbance of a component to the intrinsic absorption properties of its material.
Suppliers
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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.