# Absorbance

"Optical density" redirects here. "Optical density" can also refer to index of refraction.[1]

In spectroscopy, the absorbance (also called optical density[2][3]) of a material is a logarithmic ratio of the amount of radiation falling upon a material to the amount of radiation transmitted through the material.[4][5] Absorbance measurements are often carried out in analytical chemistry.

In physics, the term spectral absorbance is used interchangeably with spectral absorptance or absorptivity. In this case it has a slightly different meaning: the fraction of radiation absorbed at specific wavelengths.

A closely related term is the transmittance.[6]

## Detailed explanation

Absorbance at a certain wavelength of light ($\lambda$), denoted $A_\lambda$, is a quantitative measure expressed as[2]

$A_\lambda = \log_{10} \frac{I_0}{I},$

i.e., as an unsigned logarithmic ratio between $I_0$, the radiation falling upon a material (the intensity of the radiation before it passes through the material or incident radiation) and $I$, the radiation transmitted through a material (the intensity of the radiation that has passed through the material or transmitted radiation). As such, absorbance is closely related to transmittance T:[6]

$A_\lambda = \log_{10} \left( T^{-1} \right) = -\log_{10} T.$

Outside the field of analytical chemistry (e.g. when used in biology and tunable diode laser absorption spectroscopy) the absorbance is often defined using the natural logarithm instead of the common logarithm, i.e. as

$A_\lambda = \ln \frac{I_0}{I}.$

The term absorption refers to the physical process of absorbing light, while absorbance refers to the mathematical quantity. Also, absorbance does not always measure absorption: if a given sample is, for example, a dispersion, part of the incident light will in fact be scattered by the dispersed particles, and not really absorbed. However, in such cases, it is recommended that the term "attenuance" (formerly called "extinction") be used, which accounts for losses due to scattering and luminescence.[7]

See the Beer-Lambert law for a more complete discussion.

Although absorbance is properly unitless, it is sometimes reported in "absorbance units", or AU. However, many people, including scientific researchers, wrongly state the results from absorbance measurement experiments in terms of these arbitrary units.[8]

## Logarithmic vs. directly proportional measurements

The amount of light transmitted through a material diminishes exponentially as it travels through the material. 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 thickness and concentration of the material.

Absorbance Transmittance ($I/I_0$)
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

## 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 in the range near 1 AU. The path length or concentration should then, when possible, be adjusted to achieve readings near this range.

## How to measure absorbance

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.[9] 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 intensity of whatever light source is in use is referred to as I0. Then the intensity that makes it through the solution sample, I, is measured and compared to I0. As stated above, the absorbance at a given wavelength is

$A_\lambda = \log_{10} \frac{I_0}{I}.$

The absorbance spectrum is plotted on a graph of absorbance vs. wavelength.[10]

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 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 HPLC.

Some filters, notably welding glass, are rated by shade number, which is 7/3 times the absorbance plus one:[11]

shade number $= \frac{7}{3}A + 1$

or

shade number $= \frac{7}{3}(- \log_{10} T) + 1$

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

## Similar terms

Many similar terms are used to describe concepts relating to absorbance and some terms may have differing interpretation or usage in different disciplines.

While A and OD are measured on the same scale by the same instruments, they are practically very different measurements.[citation needed] Where the sample contains any particles the amount of light reaching the detector will be affected by scattering of light by those particles, not only by the absorbance of the dissolved chemicals. The scattering affect will have a different effect on the amount of light reaching the detector depending on the architecture of the individual instrument. Absorbance is an absolute unit. Two instruments (properly calibrated) will provide the same reading of Absorbance from the same sample, provided it contains no particles. Where the sample contains any particles it is incorrect to refer to the result as Absorbance - it is Optical Density. It is incorrect to report OD results to anybody who doesn't have access to the very same instrument. It should first be converted into an absolute unit using a locally produced calibration curve.

### Absorptance

Absorptance refers to a directly proportional ratio. Absorptance is the ratio of the radiation absorbed by a surface to that incident upon it. Total absorptance refers to absorptance measured over all wavelengths. Spectral absorptance refers to absorptance measured at a specified wavelengths.[12]

Absorptance is a simple ratio, whereas absorbance is a logarithmic ratio. This difference means that the two different measures are often used for different applications.

### Absorption factor

Same as Absorptance.[citation needed]

### Absorptivity

In physics, the term spectral absorbance is used interchangeably with absorptivity, meaning the fraction of radiation absorbed at a given wavelength. In chemistry, absorptivity usually refers to Molar absorptivity, which is the constant $\epsilon$ used in the Beer-Lambert law, $A=\epsilon c l$, where $A$ is the absorbance, $c$ is the concentration of the solution, and $l$ is the path length.[5]

### Mnemonic

A mnemonic to remember the difference between absorbance and absorptance is that absorbance has no t, or not t, meaning it measures all that is not transmitted.

## References

1. ^ Zitzewitz, Paul W. (1999). Glencoe physics. New York, N.Y.: Glencoe/McGraw-Hill. p. 395. ISBN 0-02-825473-2.
2. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "optical density".
3. ^ Laser Guidebook, by Jeff Hecht, p79
4. ^
5. ^ a b "Dictionary — Definition of absorptance". Websters-online-dictionary.org. Retrieved 2011-11-21.
6. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Trnasmittance".
7. ^ International Union of Pure and Applied Chemistry (IUPAC) Glossary of terms used in photochemistry. Recommendations 1988 (Braslavsky, S. E. & Houk, K. N., eds) Pure Appl. Chem. 60, 1055-1106 (1988). An updated version, y J. W. Verhoeven, has appeared in Pure Appl. Chem. 68, 2223-2286 (1996).
8. ^ "How to Make Your Next Paper Scientifically Effective". J. Phys. Chem. Lett. (4): 1578−1581. 2013. doi:10.1021/jz4006916.
9. ^ Reusch, William. "Visible and Ultraviolet Spectroscopy". Retrieved 2014-10-29.
10. ^ Reusch, William. "Empirical Rules for Absorption Wavelengths of Conjugated Systems". Retrieved 2014-10-29.
11. ^ "How Many? A Dictionary of Units of Measurement by Russ Rowlett". Unc.edu. 2004-09-01. Retrieved 2010-09-20.
12. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "absorbance".