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Absorbance

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Logarithm of ratio of incident to transmitted radiant power through a sample

This article is about a quantitative expression. For the process itself, seeAbsorption (electromagnetic radiation).

"Optical density" redirects here. For other uses, seeRefractive index,Nucleic acid quantitation, andNeutral-density filter.

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Inspectroscopy,absorbance (abbreviated asA)^[1] is a logarithmic value which describes the portion of a beam oflight which does not pass through a sample. While name refers to theabsorption of light, other interactions of light with a sample (reflection, scattering) may also contributeattenuation of the beam passing through the sample. The term "internal absorbance" is sometimes used to describe beam attenuation caused by absorption, while "attenuance" or "experimental absorbance" can be used to emphasize that beam attenuation can be caused by other phenomena.^[2]

History and uses of the term absorbance

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Beer-Lambert law

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The roots of the term absorbance are in theBeer–Lambert law (or Beer's law). As light moves through a medium, it will become dimmer as it is being "extinguished".Pierre Bouguer recognized that this extinction (now often called attenuation) was not linear with distance traveled through the medium, but related by what we now refer to as an exponential function.

If $I_{0}$ is the intensity of the light at the beginning of the travel and $I_{d}$ is the intensity of the light detected after travel of a distance $d {\displaystyle d}$ , the fraction transmitted, $T {\displaystyle T}$ , is given by

$T={\frac {I_{d}}{I_{0}}}=\exp(-\mu d)\,,$

where $\mu$ is called anattenuation constant (a term used in various fields where a signal is transmitted though a medium) or coefficient. The amount of light transmitted is falling off exponentially with distance. Taking the natural logarithm in the above equation, we get

$-\ln(T)=\ln {\frac {I_{0}}{I_{d}}}=\mu d\,.$

For scattering media, the constant is often divided into two parts,^[3] $\mu =\mu _{s}+\mu _{a}$ , separating it into a scattering coefficient $\mu _{s}$ and an absorption coefficient $\mu _{a}$ , obtaining

$-\ln(T)=\ln {\frac {I_{0}}{I_{s}}}=(\mu _{s}+\mu _{a})d\,.$

If a size of a detector is very small compared to the distance traveled by the light, any light that is scattered by a particle, either in the forward or backward direction, will not strike the detector. (Bouguer was studying astronomical phenomena, so this condition was met.) In such case, a plot of $-\ln(T)$ as a function of wavelength will yield a superposition of the effects of absorption and scatter. Because the absorption portion is more distinct and tends to ride on a background of the scatter portion, it is often used to identify and quantify the absorbing species. Consequently, this is often referred to asabsorption spectroscopy, and the plotted quantity is called "absorbance", symbolized as $\mathrm {A}$ . Some disciplines by convention use decadic (base 10) absorbance rather than Napierian (natural) absorbance, resulting in: $\mathrm {A} _{10}=\mu _{10}d$ (with the subscript 10 usually not shown).

Absorbance for non-scattering samples

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Within a homogeneous medium such as a solution, there is no scattering. For this case, researched extensively byAugust Beer, the concentration of the absorbing species follows the same linear contribution to absorbance as the path-length. Additionally, the contributions of individual absorbing species are additive. This is a very favorable situation, and made absorbance an absorption metric far preferable to absorption fraction (absorptance). This is the case for which the term "absorbance" was first used.

A common expression of the Beer's law relates the attenuation of light in a material as: $\mathrm {A} =\varepsilon \ell c$ , where $\mathrm {A}$ is theabsorbance; $\varepsilon$ is themolar attenuation coefficient orabsorptivity of the attenuating species; $\ell$ is the optical path length; and $c {\displaystyle c}$ is the concentration of the attenuating species.

Absorbance for scattering samples

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For samples which scatter light, absorbance is defined as "the negative logarithm of one minus absorptance (absorption fraction: $\alpha$ ) as measured on a uniform sample".^[4] For decadic absorbance,^[2] this may be symbolized as $\mathrm {A} _{10}=-\log _{10}(1-\alpha )$ . If a sample both transmits andremits light, and is not luminescent, the fraction of light absorbed( $\alpha$ ), remitted( $R {\displaystyle R}$ ), and transmitted( $T {\displaystyle T}$ ) add to 1: $\alpha +R+T=1$ . Note that $1-\alpha =R+T$ , and the formula may be written as $\mathrm {A} _{10}=-\log _{10}(R+T)$ . For a sample which does not scatter, $R=0$ , and $1-\alpha =T$ , yielding the formula for absorbance of a material discussed below.

Even though this absorbance function is very useful with scattering samples, the function does not have the same desirable characteristics as it does for non-scattering samples. There is, however, a property calledabsorbing power which may be estimated for these samples. Theabsorbing power of a single unit thickness of material making up a scattering sample is the same as the absorbance of the same thickness of the material in the absence of scatter.^[5]

Optics

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Inoptics,absorbance ordecadic absorbance is thecommon logarithm of the ratio of incident totransmittedradiant power through a material, andspectral absorbance orspectral decadic absorbance is the common logarithm of the ratio of incident totransmittedspectral radiant power through a material. Absorbance isdimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero.

Mathematical definitions

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Absorbance of a material

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Theabsorbance of a material, denotedA, is given by^[6]

$A=\log _{10}{\frac {\Phi _{\text{e}}^{\text{i}}}{\Phi _{\text{e}}^{\text{t}}}}=-\log _{10}T,$

where

${\textstyle \Phi _{\text{e}}^{\text{t}}}$ is theradiant fluxtransmitted by that material,
${\textstyle \Phi _{\text{e}}^{\text{i}}}$ is theradiant fluxreceived by that material, and
${\textstyle T=\Phi _{\text{e}}^{\text{t}}/\Phi _{\text{e}}^{\text{i}}}$ is thetransmittance of that material.

Absorbance is adimensionless quantity. Nevertheless, theabsorbance unit orAU is commonly used inultraviolet–visible spectroscopy and itshigh-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.^[7]

Absorbance is related tooptical depth by

$A={\frac {\tau }{\ln 10}}=\tau \log _{10}e\,,$

whereτ is the optical depth.

Spectral absorbance

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Spectral absorbance in frequency andspectral absorbance in wavelength of a material, denotedA_ν andA_λ respectively, are given by^[6]

${\begin{aligned}A_{\nu }&=\log _{10}{\frac {\Phi _{{\text{e}},\nu }^{\text{i}}}{\Phi _{{\text{e}},\nu }^{\text{t}}}}=-\log _{10}T_{\nu }\,,\\A_{\lambda }&=\log _{10}{\frac {\Phi _{{\text{e}},\lambda }^{\text{i}}}{\Phi _{{\text{e}},\lambda }^{\text{t}}}}=-\log _{10}T_{\lambda }\,,\end{aligned}}$

where

${\textstyle \Phi _{\mathrm {e} ,\nu }^{t}}$ is thespectral radiant flux in frequencytransmitted by that material;
${\textstyle \Phi _{\mathrm {e} ,\nu }^{i}}$ is the spectral radiant flux in frequencyreceived by that material;
${\textstyle T_{\nu }}$ is thespectral transmittance in frequency of that material;
${\textstyle \Phi _{\mathrm {e} ,\lambda }^{t}}$ is thespectral radiant flux in wavelengthtransmitted by that material;
${\textstyle \Phi _{\mathrm {e} ,\lambda }^{i}}$ is the spectral radiant flux in wavelengthreceived by that material; and
${\textstyle T_{\lambda }}$ is thespectral transmittance in wavelength of that material.

Spectral absorbance is related to spectral optical depth by

${\begin{aligned}A_{\nu }&={\frac {\tau _{\nu }}{\ln 10}}=\tau _{\nu }\log _{10}e\,,\\A_{\lambda }&={\frac {\tau _{\lambda }}{\ln 10}}=\tau _{\lambda }\log _{10}e\,,\end{aligned}}$

where

τ_ν is the spectral optical depth in frequency, and
τ_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.^[8]

Relationship with attenuation

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Attenuance

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Absorbance is a number that measures theattenuation of the transmitted radiant power in a material. Attenuation can be caused by the physical process of "absorption", but also reflection, scattering, and other physical processes. Absorbance of a material is approximately equal to its attenuance^{[clarification needed]} when both the absorbance is much less than 1 and the emittance of that material (not to be confused withradiant exitance oremissivity) is much less than the absorbance. Indeed,

$\Phi _{\mathrm {e} }^{\mathrm {t} }+\Phi _{\mathrm {e} }^{\mathrm {att} }=\Phi _{\mathrm {e} }^{\mathrm {i} }+\Phi _{\mathrm {e} }^{\mathrm {e} }\,,$

where

${\textstyle \Phi _{\mathrm {e} }^{\mathrm {t} }}$ is the radiant power transmitted by that material,
${\textstyle \Phi _{\mathrm {e} }^{\mathrm {att} }}$ is the radiant power attenuated by that material,
${\textstyle \Phi _{\mathrm {e} }^{\mathrm {i} }}$ is the radiant power received by that material, and
${\textstyle \Phi _{\mathrm {e} }^{\mathrm {e} }}$ is the radiant power emitted by that material.

This is equivalent to

$T+\mathrm {ATT} =1+E\,,$

where

${\textstyle T=\Phi _{\mathrm {e} }^{\mathrm {t} }/\Phi _{\mathrm {e} }^{\mathrm {i} }}$ is the transmittance of that material,
${\textstyle \mathrm {ATT} =\Phi _{\mathrm {e} }^{\mathrm {att} }/\Phi _{\mathrm {e} }^{\mathrm {i} }}$ is theattenuance of that material,
${\textstyle E=\Phi _{\mathrm {e} }^{\mathrm {e} }/\Phi _{\mathrm {e} }^{\mathrm {i} }}$ is the emittance of that material.

According to the Beer's law,T = 10^−A, so

$\mathrm {ATT} =1-10^{-A}+E\approx A\ln 10+E,\quad {\text{if}}\ A\ll 1,$

and finally

$\mathrm {ATT} \approx A\ln 10,\quad {\text{if}}\ E\ll A.$

Attenuation coefficient

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Absorbance of a material is also related to itsdecadic attenuation coefficient by

$A=\int _{0}^{l}a(z)\,\mathrm {d} z\,,$

where

l is the thickness of that material through which the light travels, and
a(z) is thedecadic attenuation coefficient of that material atz.

Ifa(z) is uniform along the path, the attenuation is said to be alinear attenuation, and the relation becomes $A=al.$

Sometimes the relation is given using themolar attenuation coefficient of the material, that is its attenuation coefficient divided by itsmolar concentration:

$A=\int _{0}^{l}\varepsilon c(z)\,\mathrm {d} z\,,$

where

ε is themolar attenuation coefficient of that material, and
c(z) is the molar concentration of that material atz.

Ifc(z) is uniform along the path, the relation becomes

$A=\varepsilon cl\,.$

The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged.^[6]

Use in Analytical Chemistry

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Absorbance is a widely used measurement in quantitativeabsorption spectroscopy. While the attenuation of a light beam can be also be described bytransmittance (the ratio of transmitted incident light), the logarithmic formulation of absorbance is convenient for sample quantification: under conditions where the Beer's law is valid, absorbance will be linearly proportional to sample thickness and the concentration of the absorptive species.^[9]

For quantitative purposes, absorbance is often measured on a sample solution held in acuvette, where the solution is sufficiently dilute that the linear relationship of the Beer's law holds. The cuvette provides a known and consistent path length for the light beam passing through the sample.^[9] Measuring first the absorbance of the cuvette and a "blank" solution containing no analyte, differences in absorbance between samples can be used to quantity the analyte. Spectrometers generally measure absorbance separately for a range of wavelength: this data is then plotted as absorbance vs. wavelength.^[10]

Shade number

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Some filters, notablywelding glass, are rated by shade number (SN), which is 7/3 times the absorbance plus one:^[11]

${\begin{aligned}\mathrm {SN} &={\frac {7}{3}}A+1\\&={\frac {7}{3}}(-\log _{10}T)+1\,.\end{aligned}}$

For example, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units), its shade number would be 8.

References

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^Lawrence, Eleanor. "A".Henderson's Dictionary of Biological Terms. p. 1.ISBN 0-470-21446-5.
^^a ^bBertie, John E. (2006). "Glossary of Terms used in Vibrational Spectroscopy". In Griffiths, Peter R (ed.).Handbook of Vibrational Spectroscopy.doi:10.1002/0470027320.s8401.ISBN 0471988472.
^Van de Hulst, H. C. (1957).Light Scattering by Small Particles. New York: John Wiley and Sons.ISBN 9780486642284.{{cite book}}:ISBN / Date incompatibility (help)
^IUPAC,Compendium of Chemical Terminology, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "decadic absorbance".doi:10.1351/goldbook.D01536
^Dahm, Donald; Dahm, Kevin (2007).Interpreting Diffuse Reflectance and Transmittance: A Theoretical Introduction to Absorption Spectroscopy of Scattering Materials.doi:10.1255/978-1-901019-05-6.ISBN 9781901019056.
^^a ^b ^cIUPAC,Compendium of Chemical Terminology, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "Absorbance".doi:10.1351/goldbook.A00028
^GE Health Care (2015)."ÄKTA Laboratory-Scale Chromatography Systems - Instrument Management Handbook". Uppsala: GE Healthcare Bio-Sciences AB. Archived fromthe original on 2020-03-15.
^Kamat, Prashant; Schatz, George C. (2013)."How to Make Your Next Paper Scientifically Effective".J. Phys. Chem. Lett.4 (9):1578–1581.Bibcode:2013JPCL....4.1578K.doi:10.1021/jz4006916.PMID 26282316.
^^a ^bHam, Bryan M.; MaHam, Aihui (2024).Analytical chemistry: a toolkit for scientists and laboratory technicians (2nd ed.). Hoboken, New Jersey: John Wiley & Sons, Inc. pp. 235–237.ISBN 978-1-119-89445-2.
^Reusch, William."Empirical Rules for Absorption Wavelengths of Conjugated Systems". Retrieved2014-10-29.
^Russ Rowlett (2004-09-01)."How Many? A Dictionary of Units of Measurement". Unc.edu. Archived fromthe original on 1998-12-03. Retrieved2010-09-20.

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Spectroscopic	NMR Circular dichroism Dual-polarization interferometry Absorbance Fluorescence Fluorescence anisotropy
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