Measurement of Absorption
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 , in the form of a collimated beam. The radiant power transmitted through the layer,, is detected. If , there is no loss of radiant power and therefore no attenuation. If however the medium absorbs some quantity of radiant power, , then , and (Figure 1B). In the case of material that both absorbs and scatters (Figure 1C), the scattered radiant power is given by , and .
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, , is the fraction of incident power transmitted through the layer:
The absorptance, , is the fraction of incident radiant power that is absorbed ():
The absorption coeﬃcient (with units of ) is the absorptance per unit distance
which, for an inﬁnitesimally thin layer can be expressed as:
Rearranging this expression and taking the limit as yields:
Assuming that the absorption coeﬃcient is constant over the layer of thickness and integrating gives
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.