Editing Absorbance (section)

==Mathematical definitions==

===Absorbance of a material===
The '''absorbance''' of a material, denoted {{mvar|A}}, is given by<ref name="GoldBook">{{GoldBookRef|title=Absorbance|file=A00028|accessdate=2015-03-15}}</ref>

<math display="block">A = \log_{10} \frac{\Phi_\text{e}^\text{i}}{\Phi_\text{e}^\text{t}} = -\log_{10} T,</math>

where

* <math display="inline">\Phi_\text{e}^\text{t}</math> is the [[radiant flux]] {{em|transmitted}} by that material,
* <math display="inline">\Phi_\text{e}^\text{i}</math> is the [[radiant flux]] {{em|received}} by that material, and
* <math display="inline">T = \Phi_\text{e}^\text{t}/\Phi_\text{e}^\text{i}</math> is the [[transmittance]] of that material.

Absorbance is a [[dimensionless]] quantity. Nevertheless, the '''absorbance unit''' or '''AU''' is commonly used in [[ultraviolet–visible spectroscopy]] and its [[high-performance liquid chromatography]] applications, often in derived units such as the milli-absorbance unit (mAU) or milli-absorbance unit-minutes (mAU×min), a unit of absorbance integrated over time.<ref>{{cite web |author= GE Health Care |title= ÄKTA Laboratory-Scale Chromatography Systems - Instrument Management Handbook |date= 2015 |publisher= GE Healthcare Bio-Sciences AB |location= Uppsala |url= https://cdn.gelifesciences.com/dmm3bwsv3/AssetStream.aspx?mediaformatid=10061&destinationid=10016&assetid=16189 |archive-url= https://web.archive.org/web/20200315013424/https://cdn.gelifesciences.com/dmm3bwsv3/AssetStream.aspx?mediaformatid=10061&destinationid=10016&assetid=16189 |archive-date= 2020-03-15 }}</ref>

Absorbance is related to [[optical depth]] by

<math display="block">A = \frac{\tau}{\ln 10} = \tau \log_{10} e \,,</math>

where {{mvar|τ}} is the optical depth.

===Spectral absorbance===
'''Spectral absorbance in frequency''' and '''spectral absorbance in wavelength''' of a material, denoted {{math|''A{{sub|ν}}''}} and {{math|''A{{sub|λ}}''}} respectively, are given by<ref name=GoldBook />

<math display="block">\begin{align}
A_\nu &= \log_{10} \frac{\Phi_{\text{e},\nu}^\text{i}}{\Phi_{\text{e},\nu}^\text{t}} = -\log_{10} T_\nu\,, \\
A_\lambda &= \log_{10} \frac{\Phi_{\text{e},\lambda}^\text{i}}{\Phi_{\text{e},\lambda}^\text{t}} = -\log_{10} T_\lambda\,,
\end{align}</math>

where

* <math display="inline">\Phi_{\mathrm{e},\nu}^t</math> is the [[Radiant flux|spectral radiant flux in frequency]] {{em|transmitted}} by that material;
* <math display="inline">\Phi_{\mathrm{e},\nu}^i</math> is the spectral radiant flux in frequency {{em|received}} by that material;
* <math display="inline">T_\nu</math> is the [[Transmittance|spectral transmittance in frequency]] of that material;
* <math display="inline">\Phi_{\mathrm{e},\lambda}^t</math> is the [[Radiant flux|spectral radiant flux in wavelength]] {{em|transmitted}} by that material;
* <math display="inline">\Phi_{\mathrm{e},\lambda}^i</math> is the spectral radiant flux in wavelength {{em|received}} by that material; and
* <math display="inline">T_\lambda</math> is the [[Transmittance|spectral transmittance in wavelength]] of that material.

Spectral absorbance is related to spectral optical depth by

<math display="block">\begin{align}
A_\nu &= \frac{\tau_\nu}{\ln 10} = \tau_\nu \log_{10} e \,, \\
A_\lambda &= \frac{\tau_\lambda}{\ln 10} = \tau_\lambda \log_{10} e \,,
\end{align}</math>

where
* {{mvar|τ{{sub|ν}}}} is the spectral optical depth in frequency, and
* {{mvar|τ{{sub|λ}}}} is the spectral optical depth in wavelength.

Although absorbance is properly unitless, it is sometimes reported in "absorbance units", or AU. Many people, including scientific researchers, wrongly state the results from absorbance measurement experiments in terms of these made-up units.<ref>{{cite journal |doi=10.1021/jz4006916 |title=How to Make Your Next Paper Scientifically Effective |journal=J. Phys. Chem. Lett. |date=2013 |volume=4 |pages=1578–1581 |issue=9|last1=Kamat |first1=Prashant |last2=Schatz |first2=George C. |pmid=26282316 |doi-access=free }}</ref>