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From Theory to RealityConsider 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 absorbs and scatters, 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, , 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: Integrating the function over the layer: 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.

