Absorbance

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

In spectroscopy, the absorbance A (also called optical density)^[2][3] is defined as:^[4]

$A_\lambda = \log_{10}(I_0/I)\,$,

where I is the intensity of light at a specified wavelength λ that has passed through a sample (transmitted light intensity) and I₀ is the intensity of the light before it enters the sample or incident light intensity (or power). Absorbance measurements are often carried out in analytical chemistry, since the absorbance of a sample is proportional to the thickness of the sample and the concentration of the absorbing species in the sample, in contrast to the transmittance I / I₀ of a sample, which varies exponentially with thickness and concentration.

Measuring absorbance

Absorptance^[5] (not absorbance) is defined as: The ratio of the radiant flux absorbed by a body to that incident upon it. Also called [absorption] factor. Compare absorptivity. Total absorptance refers to absorptance measured over all wavelengths. Spectral absorptance refers to absorptance measured at a specified wavelength.

Absorptance is explained, as it relates to absorbance, on the Color and Vision Research Laboratories, Institute of Ophthalmology, UCL, in this way:

Absorbance spectra are typically used to define photopigment spectra because their shape, when normalized (i.e., plotted as a fraction of the maximum absorbance), is independent of pigment optical density (pigment concentration). In contrast, the absorptance spectra, like the spectral sensitivity of the human subject, broadens as the optical density increases.^[6]

Outside the field of analytical chemistry, e.g. when used with the Tunable Diode Laser Absorption Spectroscopy (TDLAS) technique, the absorbance is often defined using the natural logarithm instead of the common logarithm, i.e. as

$A_\lambda = \ln(I_0/I)\,$,

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

Explanation

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]

Although absorbance does not have true units, it is quite often reported in "Absorbance Units" or AU (not to be confused with the Astronomical unit).

Absorbance vs transmittance

Absorbance	Transmittance (I / I0)	Percent transmittance (100 * I / I0)
0	1	100
0.1	0.79	79
0.25	0.56	56
0.5	0.32	32
0.75	0.18	18
0.9	0.13	13
1	0.1	10
2	0.01	1
3	0.001	0.1

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.

Shade number

Some filters, notably welding glass, are rated by shade number, which is 7/3 times the absorbance plus one:^[8]

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

See also

• Optical depth
• Beer-Lambert law
• Reflectivity
• Tunable Diode Laser Absorption Spectroscopy (TDLAS)
• Densitometry
• Neutral density filter

References

1. ^ Zitzewitz, Paul W. (1999). Glencoe physics. New York, N.Y.: Glencoe/McGraw-Hill. p. 395. ISBN 0-02-825473-2 
2. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "optical density".
3. ^ The Laser Guidebook, by Jeff Hecht, p79
4. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "absorbance".
5. ^ "Dictionary — Definition of absorptance, absorptance". Websters-online-dictionary.org. http://www.websters-online-dictionary.org/ab/absorptance,%20absorptance.html. Retrieved 2010-09-20. 
6. ^ http://www-cvrl.ucsd.edu/database/text/intros/intropig.htm
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, edited by J. W. Verhoeven, has appeared in Pure Appl. Chem. 68, 2223-2286 (1996).
8. ^ "How Many? A Dictionary of Units of Measurement by Russ Rowlett". Unc.edu. 2004-09-01. http://www.unc.edu/~rowlett/units/dictS.html. Retrieved 2010-09-20.