## Definition and units of absorption coefficient µ
| ECE532 Biomedical Optics ©1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute |

Consider a chromophore idealized as a sphere with a particular geometrical size. Consider that this sphere blocks incident light and casts a shadow, which constitutes absorption. This description is of course an incorrect and schematicized version of the real situation. However, it does provide a simple concept which captures the essence of the **absorption coefficient**, the parameter we use to describe the effectiveness of absorption.

The size of the absorption shadow is called the **effective cross-section** (_{a} [cm^{2}]) and can be smaller or larger than the geometrical size of the chromophore (A [cm^{2}]), related by the proportionality constant called the **absorption efficiency** Q_{a} [dimensionless]:

The **absorption coefficient** µ_{a} [cm^{-1}] describes a medium containing many chromophores at a concentration described as a **volume density** _{a} [cm^{3}]. The absorption coefficient is essentially the cross-sectional area per unit volume of medium.

Experimentally, the units [cm^{-1}] for µ_{a} are inverse length, such that the product µ_{a}L is dimensionless, where L [cm] is a photon's pathlength of travel through the medium. The probability of survival (or transmission T) of the photon after a pathlength L is:

This expression for survival holds true regardless of whether the photon path is a straight line or a highly tortuous path due to multiple scattering in an optically turbid medium.

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