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This article is about a quantitative expression related to the physical process of absorption. For a discussion of the process of absorption itself, see .
"Optical density" redirects here. "Optical density" can also refer to .
In , absorbance or decadic absorbance is the
of the ratio of incident to transmitted
through a material, and spectral absorbance or spectral decadic absorbance is the common logarithm of the ratio of incident to transmitted
through a material. Absorbance is , 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. In , a closely related quantity called "" is used instead of absorbance: the
of the ratio of incident to transmitted radiant power through a material. The optical depth equals the absorbance times ln(10).
refers to the physical process of absorbing light, while absorbance does not always measure absorption: it measures
(of transmitted radiant power). Attenuation can be caused by absorption, but also reflection, scattering, and other physical processes.
Absorbance of a material, denoted A, is given by
{\displaystyle A=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} }^{\mathrm {i} }}{\Phi _{\mathrm {e} }^{\mathrm {t} }}}\right)=-\log _{10}T,}
Φet is the
transmitted
Φei is the radiant flux recei
of that material.
Absorbance is related to
{\displaystyle A={\frac {\tau }{\ln 10}},}
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
{\displaystyle A_{\nu }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\nu }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\nu }^{\mathrm {t} }}}\right)=-\log _{10}T_{\nu },}
{\displaystyle A_{\lambda }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {t} }}}\right)=-\log _{10}T_{\lambda },}
Φe,νt is the
transmitted
Φe,νi is the spectral radiant flux in frequency recei
Φe,λt is the
transmitted
Φe,λi is the spectral radiant flux in wavelength recei
Tλ is the
of that material.
Spectral absorbance is related to spectral optical depth by
{\displaystyle A_{\nu }={\frac {\tau _{\nu }}{\ln 10}},}
{\displaystyle A_{\lambda }={\frac {\tau _{\lambda }}{\ln 10}},}
τν is the spectral optica
τλ is the spectral optical depth in wavelength.
Although absorbance is properly unitless, it is sometimes reported in "arbitrary units", or AU. Many people, including scientific researchers, wrongly state the results from absorbance measurement experiments in terms of these made-up units.
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 [] when both the absorbance is much less than 1 and the emittance of that material (not to be confused with
or ) is much less than the absorbance. Indeed,
{\displaystyle \Phi _{\mathrm {e} }^{\mathrm {t} }+\Phi _{\mathrm {e} }^{\mathrm {att} }=\Phi _{\mathrm {e} }^{\mathrm {i} }+\Phi _{\mathrm {e} }^{\mathrm {e} },}
Φet is the radiant power transmit
Φeatt is the radiant power attenua
Φei is the radiant power recei
Φee is the radiant power emitted by that material,
that is equivalent to
{\displaystyle T+ATT=1+E,}
T = Φet/Φei is the transmitta
ATT = Φeatt/Φei is the attenuance
E = Φee/Φei is the emittance of that material,
and according to , T = 10-A, so
{\displaystyle ATT=1-10^{-A}+E\approx A+E\quad {\text{if}}\ A\ll 1,}
and finally
{\displaystyle ATT\approx A\quad {\text{if}}\ E\ll A.}
Absorbance of a material is also related to its
{\displaystyle A=\int _{0}^{l}a(z)\,\mathrm {d} z,}
l is the thickness of that material through whi
a(z) is the decadic attenuation coefficient of that material at z,
and if a(z) is uniform along the path, the attenuation is said to be a linear attenuation and the relation becomes:
{\displaystyle A=al.}
Sometimes the relation is given using the
of the material, that is its attenuation coefficient divided by its :
{\displaystyle A=\int _{0}^{l}\varepsilon c(z)\,\mathrm {d} z,}
ε is the molar attenuation coefficient
c(z) is the molar concentration of that material at z,
and if c(z) is uniform along the path, the relation becomes:
{\displaystyle A=\varepsilon cl.}
The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged.
The amount of light transmitted through a material diminishes
as it travels through the material, according to Beer–Lambert law. 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: -log10(Φet/Φei)
Transmittance: Φet/Φei
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,
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 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 . 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
{\displaystyle A_{\lambda }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {t} }}}\right)\!.}
The absorbance spectrum is plotted on a graph of absorbance vs. wavelength.
will do all this automatically. To use this machine, solutions are placed in a small
and inserted into the holder. The machine is controlled through a computer and, once you "blank" it, will automatically display 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 .
Some filters, notably
glass, are rated by shade number, which is 7/3 times the absorbance plus one:
{\displaystyle SN={\frac {7}{3}}A+1,}
{\displaystyle SN={\frac {7}{3}}(-\log _{10}T)+1,}
where SN is the shade number.
So, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units) the shade number would be 8.
Zitzewitz, Paul W. (1999). Glencoe Physics. New York, N.Y.: Glencoe/McGraw-Hill. p. 395.  .
, , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "".
"How to Make Your Next Paper Scientifically Effective". J. Phys. Chem. Lett. (4): . 2013. :.
Reusch, William. .
Reusch, William. .
Russ Rowlett (). . Unc.edu.
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Absorbance
The technique of absorbance is as old as the first alchemists. They sought to identify and understand their elixirs by looking at the color and opacity of solutions as different reagents were mixed, heated, and stirred.
Today it remains the most widely used spectroscopic technique for studying liquids and gases due to its simplicity, accuracy, and ease of use. An absorbance spectrum can be used as a qualitative tool to identify or “fingerprint” substances, or as a quantitative tool to measure the concentration of a molecule in solution.
The most common image of an absorbance measurement is a solution in a cuvette, measured in transmission with a dual-beam spectrometer – the classic introductory chemistry lab experiment. In practice, however, absorbance measurements can take many forms. They work equally well for gases as for liquids, and have found their way into consumer products and industrial applications alike. Samples no longer need to fit into the standard 1 cm pathlength cuvette, as flow cells, dip probes, micropipetters, folded gas cells, and micro-cuvettes allow the sampling optic to be customized to the sample.
Modular spectroscopy has provided infinitely more flexibility to choose the wavelength range and resolution needed, and to move between sampling optics quickly and easily for measurements in the lab or field. With our wide range of spectrometers, light sources, and accessories, we can help you to create a flexible system to measure a wide range of solutions and concentrations. Are you ready to think outside the cuvette? Read on.
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Advantages
Non-destructive: Unless the sample is photo-sensitive, the measurement can be repeated without altering the sample. Can be performed in-situ or within process flows.
Quantitative: Allows determination of solution concentration or the extinction coefficient of a substance.
Accurate: Can quantify absorbance to within 0.001 absorbance units when implemented properly.
Applications
Other Common Applications
Kinetics: reaction monitoring, endpoint detection, protein and DNA thermodynamics, enzyme kinetics, on-line thermal cycling of biological particles
Quality & process control: pharmaceutical and textile manufacturing, particle size analysis, ethylene production, polymer processing
Chemical analysis: fluorophore characterization, phenol determination, column liquid chromatography, trace detection of metals
Research: analysis of freshwater and marine environments, characterization of liquid crystals, study of eye tissues, photostability studies of compounds in various environments
Environmental monitoring: SO2 detection as a predictor of volcanic activity, fenceline monitoring near chemical plants, airborne pollution monitoring in cities, prediction of red tide events, soil contamination analysis, ozone monitoring
Food testing: analysis of composition in dairy products, determining solids content in fruit, predicting odor and flavor suitability in wines
Biomedical: reading microtiter plates and labs-on-a-chip, analysis of nucleic acids and proteins, clinical and in-vitro blood diagnostics
What Is Absorbance?
When light is incident on a sample in a cuvette, it can be transmitted, absorbed, or scattered. This is often written as T + A + S = 1. Transmission is the light that passes through the sample without interacting with it. Light that encounters a molecule or particle can be either absorbed or scattered. Elastic scattering occurs when the interaction changes the direction of light, but not its wavelength or energy.
When an absorption measurement is made, however, it is assumed that scatter is zero, in which case all light not transmitted to the detector is absorbed by the sample, i.e., T + A = 1.
This is true for the ideal case of an infinitely dilute solution of infinitely small particles in a transparent solvent. Luckily, it is also reasonably accurate in practice for a wider range of absorbing substances, solvents and concentrations. Absorbance occurs when the light encountering the molecule in the solvent matches the frequency of molecular vibrations or transitions in electronic energy-level states within the molecule. The chance of this happening is dependent on the cross section of the molecule for a particular energy level transition, and determines how absorptive a molecule is in solution. The more concentrated the solution, the greater the chance that a photon travelling through the solution will be absorbed. In fact, the probability of absorption increases linearly with both the pathlength and concentration of the solution, a relationship which has been quantified in the Beer-Lambert Law, also known as Beer’s Law.
What Is Beer’s Law?
Beer’s Law (also called the Beer-Lambert law) says that the absorbance of a solution will depend directly on the concentration of the absorbing molecules and the pathlength traveled by light through the solution.
A(λ) is the absorption of the solution as a function of wavelength
ε(λ) is the molar absorptivity or extinction coefficient of the absorbing molecule as a function of wavelength (in L/mol·cm)
c is the concentration of the solution (in mol/L)
l is the pathlength traveled by light through the solution (in cm)
But how can we determine the amount of light absorbed? By measuring the transmission through the sample. Provided the sample has low scatter (as with a relatively dilute, clean solution), almost all of the light not absorbed will be transmitted. Transmission is the ratio of incident intensity, I0 to transmitted intensity, I, and will decrease with increasing path length or concentration.
By taking the negative log10 of each side of this equation, we get a linear absorbance equation that is useful for calculations from measurements.
This explains why absorbance is a dimensionless number that scales with concentration on a log scale. A perfectly transparent sample (T = 100%) will have an absorbance value of zero, while a perfectly opaque sample (T = 0%) will have an absorbance value of infinity. When units are specified, absorbance is usually described in terms of absorbance units (AU) or optical density (OD). The linearity of absorbance makes it conveniently additive.
For example, if one sample has an absorbance of 0.5 AU and another has an absorbance of 0.3 AU, then putting both samples in the light path in tandem will yield an absorbance of 0.8 AU. Similarly, if two different substances are present in the same sample, then the total absorbance will equal the sum of their individual absorbance values at that wavelength. It is important to keep in mind that many factors can affect the validity of Beer’s Law. Before using it to calculate the concentration of a solution or extinction coefficient of a substance, it is best to validate the relationship by measuring a set of standard solutions and plotting a calibration curve. The sweet spot for measuring absorbance with best accuracy is between 0.5 and 1.0 absorbance units, so aim to work in this range when choosing the pathlength of your sample cell, and create a calibration curve using concentrations across this range.
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Technical Notes:
Featured Products for Absorbance in Gases:
This high-resolution spectrometer is configured for UV absorbance in the sample setup. We use Grating #H7 set for 200-300 nm, with a 5 um slit as entrance aperture and a detector collection lens for increased sensitivity.
Deuterium source produces continuous output from ~215-400 nm
Cuvette holder for 10-cm pathlength cuvettes
Cylindrical quartz cell with T has volume of 28.2 mL
QP455-025-XSR-BX
Pair of extreme solarization-resistant patch cord assemblies, 455 um diameter, 0.25 m length
Spectroscopy software
Featured Products for Absorbance in Solutions:
General-purpose spectrometer is preconfigured for 200-850 nm and has a 25 um slit and order-sorting filter
DH2000-BAL
Balanced deuterium tungsten halogen light source provides illumination from 215-2000 nm
This sturdy cuvette holder accepts 1 cm pathlength cuvettes
A quartz cuvette is recommended for UV applications in particular
QP450-2-XSR
Two 450 um extreme solarization-resistant optical fibers will transmit and receive light in this setup
Absorbance Standards (optional)
NIST-traceable photometric absorbance standards for 200-450 nm (STAN-ABS-UV) and 400-900 nm (STAN-ABS-VIS) ranges
Spectroscopy software
What light source should I use for illumination?
What is the best sampling optic for my measurement?
What spectrometer should I use for detection?
Are there any integrated systems I can use?
Why do I need a reference measurement?
Do I need an absorbance standard?
Why is stray light important?
How do I use Beer's Law to calculate concentration or extinction coefficient?
Why isn't my calibration curve linear?
What's the difference between relative and absolute absorbance?
Collimated light through a sample
If diffuse illumination is combined with collimated detection (using a lens for light gathering), the result is a relative absorbance measurement. That is, the absorbance reading for a specific sample will depend on the specific instrument used. Our direct-attach and integrated cuvette holders provide diffuse illumination to the cuvette via light focused directly from a bulb. Transmission dip probes and flow cells are also relative absorbance sampling optics.
Collimated illumination combined with collimated detection results in absolute absorbance measurements, which are independent of the instrument used to make the measurement. Any of our cuvette holders which use a fiber and collimating lens combination provide collimated illumination, as the light exiting the fiber does so with a well-defined range of angles, allowing proper collimation. Be aware, however, that making adjustments to the position of the collimating lens in these cuvette holders will affect collimation of the incident light.
Relative absorbance systems work very well for determining concentration when used with a calibration curve. They are not suitable, however, for determining extinction coefficients, as the exact optical pathlength is not known. Absolute absorbance sampling optics:
CUV-ALL (1 cm cuvettes)
CUV-UV (1 cm cuvettes)
CUV-UV-10 (10 cm cuvettes)
CUV-VAR (1 – 10 cm pathlength)
CUV-TLC-50F (1 cm cuvettes)
Relative absorbance sampling optics:
(1 cm cuvettes)
ISS-UV-VIS (1 cm cuvettes)
CUV-FL-DA (1 cm cuvettes)
USB-ISS-VIS (1 cm cuvettes)
USB-ISS-UV (1 cm cuvettes)
USB-ISS-T (12 mm round test tubes)
All dip probes
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How do I take the best dark measurement?
How do I take the best reference measurement?
How do I make repeatable measurements?
How do I measure very low concentrations or low absorbance?
How do I measure very high concentrations or high absorbance?
Is there an easy way to make kinetics measurements in the software?
Should I correct for electrical dark?
Should I use the non-linearity correction?
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High-sensitivity Spectrometer for Absorbance
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Extended Range Spectrometer for UV-NIR applications
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Application-ready Spectrometer for the UV-VIS with Enhanced Sensitivity
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