**Absorbance** is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)".^{ [1] } Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample".^{ [2] } The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms. What these uses of the term tend to have in common is that they refer to a logarithm of the ratio of a quantity of light incident on a sample or material to that which is detected after the light has interacted with the sample.

- History and uses of the term absorbance
- Beer-Lambert law
- Beer–Lambert law with non-scattering samples
- Absorbance for scattering samples
- Optics
- Mathematical definitions
- Absorbance of a material
- Spectral absorbance
- Relationship with attenuation
- Attenuance
- Attenuation coefficient
- Measurements
- Logarithmic vs. directly proportional measurements
- Instrument measurement range
- Method of measurement
- Shade number
- See also
- References

The term absorption refers to the physical process of absorbing light, while absorbance does not always measure only absorption; it may measure attenuation (of transmitted radiant power) caused by absorption, as well as reflection, scattering, and other physical processes.

The roots of the term absorbance are in the Beer–Lambert 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, , separating it into a scattering coefficient, , and an absorption coefficient, ,^{ [3] } 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. 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 absorbance rather than Napierian 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 response 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".^{ [2] } For decadic absorbance,^{ [4] } 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, or: . 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 materiel in the absence of scatter.^{ [5] }

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 use of the term "optical density" for absorbance is discouraged.

The **absorbance** of a material, denoted *A*, is given by^{ [1] }

where

- is the radiant flux
*transmitted*by that material, - is the radiant flux
*received*by that material, - 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.^{ [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 *A*_{ν} and *A*_{λ} respectively, are given by^{ [1] }

where

- Φ
_{e,ν}^{t}is the spectral radiant flux in frequency*transmitted*by that material, - Φ
_{e,ν}^{i}is the spectral radiant flux in frequency received by that material, *T*_{ν}is the spectral transmittance in frequency of that material,- Φ
_{e,λ}^{t}is the spectral radiant flux in wavelength*transmitted*by that material, - Φ
_{e,λ}^{i}is the spectral radiant flux in wavelength received by that material, *T*_{λ}is the spectral transmittance in wavelength of that material.

Spectral absorbance is related to spectral optical depth by

where

*τ*_{ν}is the spectral optical depth in frequency,*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.^{ [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

- Φ
_{e}^{t}is the radiant power transmitted by that material, - Φ
_{e}^{att}is the radiant power attenuated by that material, - Φ
_{e}^{i}is the radiant power received by that material, - Φ
_{e}^{e}is the radiant power emitted by that material,

that is equivalent to

where

*T*= Φ_{e}^{t}/Φ_{e}^{i}is the transmittance of that material,- ATT = Φ
_{e}^{att}/Φ_{e}^{i}is the*attenuance*of that material, *E*= Φ_{e}^{e}/Φ_{e}^{i}is the emittance of that material,

and according to Beer–Lambert law, *T* = 10^{−A}, so

and finally

Absorbance of a material is also related to its * decadic attenuation coefficient * by

where

*l*is the thickness of that material through which the light travels,*a*(*z*) is the*decadic attenuation coefficient*of that material at*z*.

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

*ε*is the*molar attenuation coefficient*of that material,*c*(*z*) is the molar concentration of that material at*z*.

If *c*(*z*) is uniform along the path, the relation becomes

The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged.^{ [1] }

The amount of light transmitted through a material diminishes exponentially as it travels through the material, according to the Beer–Lambert law (A=(ε)(l)). Since the absorbance of a sample is measured as a logarithm, it is directly proportional to the thickness of the sample and to the concentration of the absorbing material in the sample. Some other measures related to absorption, such as transmittance, are measured as a simple ratio so they vary exponentially with the thickness and concentration of the material.

Absorbance: −log_{10}(Φ_{e}^{t}/Φ_{e}^{i}) | Transmittance: Φ_{e}^{t}/Φ_{e}^{i} |
---|---|

0 | 1 |

0.1 | 0.79 |

0.25 | 0.56 |

0.5 | 0.32 |

0.75 | 0.18 |

0.9 | 0.13 |

1 | 0.1 |

2 | 0.01 |

3 | 0.001 |

Any real measuring instrument has a limited range over which it can accurately measure absorbance. An instrument must be calibrated and checked against known standards if the readings are to be trusted. Many instruments will become non-linear (fail to follow the Beer–Lambert law) starting at approximately 2 AU (~1% transmission). It is also difficult to accurately measure very small absorbance values (below 10^{−4}) with commercially available instruments for chemical analysis. In such cases, laser-based absorption techniques can be used, since they have demonstrated detection limits that supersede those obtained by conventional non-laser-based instruments by many orders of magnitude (detections have been demonstrated all the way down to 5 × 10^{−13}). The theoretical best accuracy for most commercially available non-laser-based instruments is attained in the range near 1 AU. The path length or concentration should then, when possible, be adjusted to achieve readings near this range.

Typically, absorbance of a dissolved substance is measured using absorption spectroscopy. This involves shining a light through a solution and recording how much light and what wavelengths were transmitted onto a detector. Using this information, the wavelengths that were absorbed can be determined.^{ [8] } First, measurements on a "blank" are taken using just the solvent for reference purposes. This is so that the absorbance of the solvent is known, and then any change in absorbance when measuring the whole solution is made by just the solute of interest. Then measurements of the solution are taken. The transmitted spectral radiant flux that makes it through the solution sample is measured and compared to the incident spectral radiant flux. As stated above, the spectral absorbance at a given wavelength is

The absorbance spectrum is plotted on a graph of absorbance vs. wavelength.^{ [9] }

A UV-Vis spectrophotometer will do all this automatically. To use this machine, solutions are placed in a small cuvette and inserted into the holder. The machine is controlled through a computer and, once it has been "blanked", automatically displays the absorbance plotted against wavelength. Getting the absorbance spectrum of a solution is useful for determining the concentration of that solution using the Beer–Lambert law and is used in HPLC.

Some filters, notably welding glass, are rated by shade number (SN), which is 7/3 times the absorbance plus one:^{ [10] }

or

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

The **Beer–Lambert law**, also known as **Beer's law**, the **Lambert–Beer law**, or the **Beer–Lambert–Bouguer law** relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics, for photons, neutrons, or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation.

In physics, the **cross section** is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted *σ* (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

In optics, the **refractive index** of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

In physics, **optical depth** or **optical thickness** is the natural logarithm of the ratio of incident to *transmitted* radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. **Spectral optical depth** or **spectral optical thickness** is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.

**Radiometry** is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct from quantum techniques such as photon counting.

The **reflectance** of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic structure of the material to the electromagnetic field of light, and is in general a function of the frequency, or wavelength, of the light, its polarization, and the angle of incidence. The dependence of reflectance on the wavelength is called a *reflectance spectrum* or *spectral reflectance curve*.

In physics, **Planck's law** describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.

In optics, a **Fabry–Pérot interferometer** (**FPI**) or **etalon** is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. *Etalon* is from the French *étalon*, meaning "measuring gauge" or "standard".

**Transmittance** of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.

In radiometry, **radiance** is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation, and to quantify emission of neutrinos and other particles. The SI unit of radiance is the watt per steradian per square metre. It is a *directional* quantity: the radiance of a surface depends on the direction from which it is being observed.

In radiometry, **irradiance** is the radiant flux *received* by a *surface* per unit area. The SI unit of irradiance is the watt per square metre (W⋅m^{−2}). The CGS unit erg per square centimetre per second (erg⋅cm^{−2}⋅s^{−1}) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called *radiant flux*.

The term **quantum efficiency** (**QE**) may apply to **incident photon to converted electron (IPCE) ratio** of a photosensitive device, or it may refer to the TMR effect of a Magnetic Tunnel Junction.

In radiometry, photometry, and color science, a **spectral power distribution** (**SPD**) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term *spectral power distribution* can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.

In radiometry, **radiant flux** or **radiant power** is the radiant energy emitted, reflected, transmitted, or received per unit time, and **spectral flux** or **spectral power** is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.

**Absorption cross section** is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc. In honor of the fundamental contribution of Maria Goeppert Mayer to this area, the unit for the two-photon absorption cross section is named the "GM". One GM is 10^{−50} cm^{4}⋅s⋅photon^{−1}.

The **linear attenuation coefficient**, **attenuation coefficient**, or **narrow-beam attenuation coefficient** characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient value that is large represents a beam becoming 'attenuated' as it passes through a given medium, while a small value represents that the medium had little effect on loss. The SI unit of attenuation coefficient is the reciprocal metre (m^{−1}). **Extinction coefficient** is another term for this quantity, often used in meteorology and climatology. Most commonly, the quantity measures the exponential decay of intensity, that is, the value of downward *e*-folding distance of the original intensity as the energy of the intensity passes through a unit thickness of material, so that an attenuation coefficient of 1 m^{−1} means that after passing through 1 metre, the radiation will be reduced by a factor of *e*, and for material with a coefficient of 2 m^{−1}, it will be reduced twice by *e*, or *e*^{2}. Other measures may use a different factor than *e*, such as the *decadic attenuation coefficient* below. The **broad-beam attenuation coefficient** counts forward-scattered radiation as transmitted rather than attenuated, and is more applicable to radiation shielding.

The **mass attenuation coefficient**, or **mass narrow beam attenuation coefficient** of a material is the attenuation coefficient normalized by the density of the material; that is, the attenuation per unit mass. Thus, it characterizes how easily a mass of material can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation, sound, or any other beam that can be attenuated. The SI unit of mass attenuation coefficient is the square metre per kilogram. Other common units include cm^{2}/g and mL⋅g^{−1}⋅cm^{−1}. **Mass extinction coefficient** is an old term for this quantity.

**Absorptance** of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power. This should not be confused with absorbance and absorption coefficient.

The **near-infrared (NIR) window** defines the range of wavelengths from 650 to 1350 nanometre (nm) where light has its maximum depth of penetration in tissue. Within the NIR window, scattering is the most dominant light-tissue interaction, and therefore the propagating light becomes diffused rapidly. Since scattering increases the distance travelled by photons within tissue, the probability of photon absorption also increases. Because scattering has weak dependence on wavelength, the NIR window is primarily limited by the light absorption of blood at short wavelengths and water at long wavelengths. The technique using this window is called NIRS. Medical imaging techniques such as fluorescence image-guided surgery often make use of the NIR window to detect deep structures.

In chemistry, the **molar absorption coefficient** or **molar attenuation coefficient** is a measurement of how strongly a chemical species absorbs, and thereby attenuates, light at a given wavelength. It is an intrinsic property of the species. The SI unit of molar absorption coefficient is the square metre per mole, but in practice, quantities are usually expressed in terms of M^{−1}⋅cm^{−1} or L⋅mol^{−1}⋅cm^{−1}. In older literature, the cm^{2}/mol is sometimes used; 1 M^{−1}⋅cm^{−1} equals 1000 cm^{2}/mol. The molar absorption coefficient is also known as the **molar extinction coefficient** and **molar absorptivity**, but the use of these alternative terms has been discouraged by the IUPAC.

- 1 2 3 4 IUPAC ,
*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " Absorbance ". doi : 10.1351/goldbook.A00028 - 1 2 IUPAC ,
*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " decadic absorbance ". doi : 10.1351/goldbook.D01536 - ↑ "Light scattering by small particles. By H. C. Van de Hulst. New York (John Wiley and Sons), London (Chapman and Hall), 1957. Pp. Xiii, 470; 103 Figs.; 46 Tables. 96s".
*Quarterly Journal of the Royal Meteorological Society*.**84**(360): 198–199. 1958. Bibcode:1958QJRMS..84R.198.. doi:10.1002/qj.49708436025.^{[ verification needed ]} - ↑ Bertie, 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. - ↑ 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. - ↑ GE Health Care. ÄKTA Laboratory-Scale Chromatography Systems - Instrument Management Handbook. GE Healthcare Bio-Sciences AB, Uppsala, 2015. https://cdn.gelifesciences.com/dmm3bwsv3/AssetStream.aspx?mediaformatid=10061&destinationid=10016&assetid=16189
- ↑ Kamat, Prashant; Schatz, George C. (2013). "How to Make Your Next Paper Scientifically Effective".
*J. Phys. Chem. Lett*.**4**(9): 1578–1581. doi: 10.1021/jz4006916 . PMID 26282316. - ↑ Reusch, William. "Visible and Ultraviolet Spectroscopy" . Retrieved 2014-10-29.
- ↑ Reusch, William. "Empirical Rules for Absorption Wavelengths of Conjugated Systems" . Retrieved 2014-10-29.
- ↑ Russ Rowlett (2004-09-01). "How Many? A Dictionary of Units of Measurement". Unc.edu. Archived from the original on 1998-12-03. Retrieved 2010-09-20.

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