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Absorption coefficient Table of
contents

 

Absorption coefficient, ambiguity

Absorption coefficient, and absorbance

Absorption coefficient, and refractive index

Absorption coefficient, chlorophyll-specific

Absorption coefficient, concentration-specific

Absorption coefficient, decadic

Absorption coefficient, definition

Absorption coefficient, dispersions

Absorption coefficient, mass-specific

Absorption coefficient, mass-specific, aquatic sciences

Absorption coefficient, molar

Absorption coefficient, natural

Absorption coefficient, of

Absorption coefficient, particle mass-specific

Absorption coefficient, particulate media

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Absorption coefficient, ambiguity

Hu Chuanmin 2002

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Absorption coefficient, and absorbance

Hu Chuanmin 2002

See also Braslavsky SE 2007

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Absorption coefficient, and refractive index

For a homogeneous material, the absorption coefficient is related to the imaginary part of the complex refractive refractive index, m", of the material as follows:

 a(λ) = 4π m"(λ) / λ  (1)

where λ is the wavelength of light in vacuum.

See also Eq. 2 in Refractive index.

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Absorption coefficient, chlorophyll-specific

Absorption coefficient, mass-specific, aquatic sciences

 ■ Absorption coefficient, mass-specific

 ■ Absorption coefficient, concentration-specific

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Absorption coefficient, concentration-specific

Absorption coefficient, a, of light in a medium is related to the concentration in that medium of the light-absorption agent, as well as to optical properties of the agent. Hence, by normalizing a to the concentration of that agent, one should be able to focus on the effect of those properties on light absorption by the medium. This leads to the concept of the concentration-specific absorption coefficient, exemplified by the mass-specific absorption coefficient and the molar absorption coefficient.

 ■ Absorption coefficient, mass-specific

 ■ Absorption coefficient, molar

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Absorption coefficient, decadic

The absorption coefficient is generally expressed by solving Eq. 3 in Absorption coefficient, definition by using the natural logarithm scale. However, the decimal logarithm scale is sometimes used instead. This latter approach leads to the decadic absorption coefficient, a10 (for example, Litjens RAJ et al 1999, Quickenden TI and Irvin 1980). The decadic absorption coefficient, a10, is related to the absorption coefficient, a, as follows:

 a10 = a / ln10  (2)

Thus, it is important to understand which definition of the absorption coefficient is used in a publication, because each leads to a different numerical value although the units (for example, m-1) may be the same.

 ■ Absorption coefficient, natural

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Absorption coefficient, definition

Absorption coefficient of light in a medium is customarily denoted by a [length-1] and defined by the following equation:

 a = - (1 / z) ln[Φ(z) / Φ(0)]  (1)

where Φ [power] is the power of light in a collimated beam, z [length] is the distance. Notation "[power]" means the unit of power, for example, Watt. The above equation is a solution of the following equation (the Lambert law for absorption):

 Φ(z) = Φ(0) e -az  (2)

which is a solution of a differential equation describing the loss of power of light propagating in a homogenous medium:

 (z) = -(z) dz  (3)

The inverse of the absorption coefficient is referred to as the absorption length. It is the average distance a photon can travel in a medium before being absorbed.

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Absorption coefficient, dispersions

As noted by Duysens LNM 1956, the absorption coefficient spectrum of a dispersion of pigmented particles may differ from the absorption coefficient spectrum of the pigment solution. This pigment packaging (for example, Finlay JC and Foster 2004 - red blood cells, and Morel A and Bricaud 1981 - phytoplankton) causes a flattening of the absorption spectrum of the dispersion as compared to that of the pigment solution.

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Absorption coefficient, mass-specific

The mass-specific absorption coefficient [length2 mass-1] is defined as follows:

 am = a / Cmv  (1)

where a is the absorption coefficient, and Cmv [mass length-3] is the mass-per-volume concentration of a light absorbing agent. That agent can be dissolved in the medium, and/or dispersed as particles.

Absorption coefficient, mass-specific, aquatic sciences

 ■ Absorption coefficient, concentration-specific

 ■ Absorption coefficient, dispersions

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Absorption coefficient, mass-specific, aquatic sciences

In aquatic sciences, the mass-specific absorption coefficients include the particle mass-specific absorption coefficient, ap*, (for example, Wozniak SB et al 2010) and the chlorophyll-specific absorption coefficient, achl*, (for example, Bricaud A et al 1995) and are typically expressed in m2 g-1 and m2 mg-1, respectively.

Absorption coefficient, mass-specific

 ■ Absorption coefficient, concentration-specific

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Absorption coefficient, molar

The molar absorption coefficient, usually expressed in dm3 moles-1 cm-1 in the spectroscopic literature (for example, Braslavsky SE 2007), is defined as follows:

 aM = a / CM  (1)

where a is the absorption coefficient defined by Eq 1 in Absorption coefficient, definition and CM [moles dm-3] is the molar concentration of the light absorbing agent.

Given that the volume per unit mass of a medium is temperature dependent, the concentration-specific absorption coefficients also depend on temperature. For example, the mass of 1 mole of water (H20) is ~18.01528 g / mole (a constant). However, the specific density of water changes. At 5 °C, it is 1000 g dm-3, while at 25 °C it is ~997.1 g dm-3. Hence, at 5 °C the molar concentration of water is (1000 / 18.01528 ) moles / dm-3 = ~55.5084 moles / dm-3, while at 25 °C it is ~55.3475 moles / dm-3.

 ■ Absorption coefficient, mass-specific

 ■ Absorption coefficient, concentration-specific

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Absorption coefficient, natural

Absorption coefficient, definition

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Absorption coefficient, of

water, see Absorption coefficient of water

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Absorption coefficient, particle mass-specific

Absorption coefficient, mass-specific, aquatic sciences

 ■ Absorption coefficient, concentration-specific

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Absorption coefficient, particulate media

Absorption coefficient, dispersions

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CITATION:
Jonasz M. 2006. Absorption coefficient (www.mjcopticaltech.com/Publications/AbsCf.php).
Published: 13-Jan-2006

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