Page updated: April 10, 2020
Author: Collin Roesler
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Measurement of Absorption

0.1 From Theory to Reality

Consider a scenario where the goal is to measure the absorption spectrum of a thin layer of material (Figure 1A). The incident radiant power is given by Φo, in the form of a collimated beam. The radiant power transmitted through the layer,Φt, is detected. If Φt = Φo, there is no loss of radiant power and therefore no attenuation. If however the medium absorbs some quantity of radiant power, Φa, then Φt < Φo, and Φo = Φt + Φa (Figure 1B). In the case of material that absorbs and scatters, the scattered radiant power is given by Φb, and Φo = Φt + Φa + Φb.


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Figure 1: Figure 1. Diagrammatic representation of theoretical attenuation by a thin layer of A. non-attenuating, B. absorbing, and C. absorbing and scattering material. The thickness of the layer is given by Δx.

To quantify the absorbed radiant power only, it is necessary to measure both the transmitted and scattered radiant power. This is a requirement for an absorption meter. Consider first a nonscattering material. The measured dimensionless transmittance, T, is the fraction of incident power transmitted through the layer:

T = Φt Φo.

The absorptance, A, is the fraction of incident radiant power that is absorbed (1 T):

A = Φa Φo = Φo Φt Φo .

The absorption coefficient, a(m1), is the absorptance per unit distance

a = A Δx

which, for an infinitesimally thin layer can be expressed as:

a = ΔΦ Φ Δx = ΔΦ ΦΔx,.

Rearranging this expression and taking the limit as Δx 0 yields:

aΔx = limΔx0 ΔΦ Φ

Integrating the function over the layer:

0xadx = ΦoΦt dΦ (Φ ax|0x = lnΦ| ΦoΦt ax = [ln(Φt) ln(Φo)] = ln Φt Φo a = 1 xln Φt Φo

This equation provides a guide toward designing instruments to accurately measure absorption. The Level 2 pages beginning at Benchtop Spectrometry of Solutions give the specifics on techniques to measure absorption by dissolved and particulate constituents in seawater.

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