![]() | This article may be too technical for most readers to understand.(July 2025) |
In spectroscopy, absorbance is a logarithmic value which describes the portion of a beam of light which does not pass through a sample. While name refers to the absorption of light, other interactions of light with a sample (reflection, scattering) may also contribute attenuation 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. [1]
The roots of the term absorbance are in the Beer–Lambert law (or Beer's law). As light moves through a medium, it will become dimmer as it is being "extinguished". 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 is the intensity of the light at the beginning of the travel and is the intensity of the light detected after travel of a distance , the fraction transmitted, , is given by
where is called an attenuation 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
For scattering media, the constant is often divided into two parts, [2] , separating it into a scattering coefficient and an absorption coefficient , obtaining
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 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 as absorption spectroscopy, and the plotted quantity is called "absorbance", symbolized as . Some disciplines by convention use decadic (base 10) absorbance rather than Napierian (natural) absorbance, resulting in: (with the subscript 10 usually not shown).
Within a homogeneous medium such as a solution, there is no scattering. For this case, researched extensively by August 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: , where is the absorbance; is the molar attenuation coefficient or absorptivity of the attenuating species; is the optical path length; and is the concentration of the attenuating species.
For samples which scatter light, absorbance is defined as "the negative logarithm of one minus absorptance (absorption fraction: ) as measured on a uniform sample". [3] For decadic absorbance, [1] this may be symbolized as . If a sample both transmits and remits light, and is not luminescent, the fraction of light absorbed (), remitted (), and transmitted () add to 1: . Note that , and the formula may be written as . For a sample which does not scatter, , and , 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 called absorbing power which may be estimated for these samples. The absorbing 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. [4]
In optics, absorbance or decadic absorbance is the common logarithm of the ratio of incident to transmitted radiant power through a material, and spectral absorbance or spectral decadic absorbance is the common logarithm of the ratio of incident to transmitted spectral radiant power through a material. Absorbance is dimensionless, 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.
The absorbance of a material, denoted A, is given by [5]
where
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. [6]
Absorbance is related to optical depth by
where τ is the optical depth.
Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted Aν and Aλ respectively, are given by [5]
where
Spectral absorbance is related to spectral optical depth by
where
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. [7]
Absorbance is a number that measures the attenuation 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 with radiant exitance or emissivity) is much less than the absorbance. Indeed,
where
This is equivalent to
where
According to the Beer's law, T = 10−A, so
and finally
Absorbance of a material is also related to its decadic attenuation coefficient by
where
If a(z) is uniform along the path, the attenuation is said to be a linear attenuation, and the relation becomes
Sometimes the relation is given using the molar attenuation coefficient of the material, that is its attenuation coefficient divided by its molar concentration:
where
If c(z) is uniform along the path, the relation becomes
The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged. [5]
Absorbance is a widely used measurement in quantitative absorption spectroscopy. While the attenuation of a light beam can be also be described by transmittance (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. [8]
For quantitative purposes, absorbance is often measured on a sample solution held in a cuvette, 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. [8] 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. [9]
Some filters, notably welding glass, are rated by shade number (SN), which is 7/3 times the absorbance plus one: [10]
For example, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units), its shade number would be 8.
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