Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)".
Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample".
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.
The term
absorption
Absorption may refer to:
Chemistry and biology
* Absorption (biology), digestion
**Absorption (small intestine)
*Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials
*Absorption (skin), a route by which ...
refers to the physical process of absorbing light, while absorbance does not always measure only absorption; it may measure
attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable att ...
(of transmitted radiant power) caused by absorption, as well as reflection, scattering, and other physical processes.
History and uses of the term absorbance
Beer-Lambert law
The roots of the term absorbance are in the
Beer–Lambert law
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 t ...
. 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
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a ci ...
(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,
, 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
Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating fie ...
, 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).
Beer–Lambert law with non-scattering samples
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
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 Inter ...
or
absorptivity of the attenuating species;
is the optical path length; and
is the concentration of the attenuating species.
Absorbance for scattering samples
For samples which scatter light, absorbance is defined as "the negative logarithm of one minus absorptance (absorption fraction:
) as measured on a uniform sample".
For decadic absorbance,
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.
Optics
In
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
, absorbance or decadic absorbance is the ''
common logarithm
In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered i ...
'' of the ratio of incident to ''transmitted''
radiant power
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 spe ...
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
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
, 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.
Mathematical definitions
Absorbance of a material
The absorbance of a material, denoted ''A'', is given by
:
where
:
is the
radiant flux
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 Spec ...
''transmitted'' by that material,
:
is the
radiant flux
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 Spec ...
''received'' by that material,
:
is the
transmittance
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 th ...
of that material.
Absorbance is a
dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
quantity. Nevertheless, the absorbance unit or AU is commonly used in
ultraviolet–visible spectroscopy
UV spectroscopy or UV–visible spectrophotometry (UV–Vis or UV/Vis) refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible regions of the electromagnetic spectrum. Being relativel ...
and its
high-performance liquid chromatography
High-performance liquid chromatography (HPLC), formerly referred to as high-pressure liquid chromatography, is a technique in analytical chemistry used to separate, identify, and quantify each component in a mixture. It relies on pumps to pa ...
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.
Absorbance is related to
optical depth
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 ...
by
:
where ''τ'' is the optical depth.
Spectral absorbance
Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted ''A''
ν and ''A''
λ respectively, are given by
:
:
where
: Φ
e,νt is the
spectral radiant flux in frequency ''transmitted'' by that material,
: Φ
e,νi is the spectral radiant flux in frequency received by that material,
: ''T''
ν is the
spectral transmittance in frequency of that material,
: Φ
e,λt is the
spectral radiant flux in wavelength ''transmitted'' by that material,
: Φ
e,λi 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.
Relationship with attenuation
Attenuance
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 when both the absorbance is much less than 1 and the emittance of that material (not to be confused with
radiant exitance
In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on wheth ...
or
emissivity
The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is n ...
) is much less than the absorbance. Indeed,
:
where
: Φ
et is the radiant power transmitted by that material,
: Φ
eatt is the radiant power attenuated by that material,
: Φ
ei is the radiant power received by that material,
: Φ
ee is the radiant power emitted by that material,
that is equivalent to
:
where
: ''T'' = Φ
et/Φ
ei is the transmittance of that material,
: ATT = Φ
eatt/Φ
ei is the ''attenuance'' of that material,
: ''E'' = Φ
ee/Φ
ei is the emittance of that material,
and according to
Beer–Lambert law
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 t ...
, , so
:
and finally
:
Attenuation coefficient
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
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 Inter ...
'' of the material, that is its attenuation coefficient divided by its
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
:
:
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.
Measurements
Logarithmic vs. directly proportional measurements
The amount of light transmitted through a material diminishes
exponentially
Exponential may refer to any of several mathematical topics related to exponentiation, including:
*Exponential function, also:
**Matrix exponential, the matrix analogue to the above
* Exponential decay, decrease at a rate proportional to value
*Exp ...
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.
Instrument measurement range
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.
Method of measurement
Typically, absorbance of a dissolved substance is measured using
absorption spectroscopy
Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating fie ...
. 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. 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.
A
UV-Vis spectrophotometer will do all this automatically. To use this machine, solutions are placed in a small
cuvette
A cuvette ( French: cuvette = "little vessel") is a small tube-like container with straight sides and a circular or square cross section. It is sealed at one end, and made of a clear, transparent material such as plastic, glass, or fused quartz. ...
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
High-performance liquid chromatography (HPLC), formerly referred to as high-pressure liquid chromatography, is a technique in analytical chemistry used to separate, identify, and quantify each component in a mixture. It relies on pumps to pa ...
.
Shade number
Some filters, notably
welding
Welding is a fabrication (metal), fabrication process that joins materials, usually metals or thermoplastics, by using high heat to melt the parts together and allowing them to cool, causing Fusion welding, fusion. Welding is distinct from lower ...
glass, are rated by shade number (SN), which is 7/3 times the absorbance plus one:
:
or
:
For example, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units), its shade number would be 8.
See also
*
Absorptance 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.
Mathematical definitio ...
*
Tunable Diode Laser Absorption Spectroscopy Tunable diode laser absorption spectroscopy (TDLAS, sometimes referred to as TDLS, TLS or TLAS) is a technique for measuring the concentration of certain species such as methane, water vapor and many more, in a gaseous mixture using tunable diode l ...
(TDLAS)
*
Densitometry
Densitometry is the quantitative measurement of optical density in light-sensitive materials, such as photographic paper or photographic film, due to exposure to light.
Overview
Optical density is a result of the darkness of a developed picture ...
*
Neutral density filter
In photography and optics, a neutral-density filter, or ND filter, is a filter that reduces or modifies the intensity of all wavelengths, or colors, of light equally, giving no changes in hue of color rendition. It can be a colorless (clear) or ...
*
Mathematical descriptions of opacity When an electromagnetic wave travels through a medium in which it gets attenuated (this is called an "opaque" or " attenuating" medium), it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to ...
References
{{Authority control
Spectroscopy
Optical filters
Logarithmic scales of measurement