# Linear attenuation coefficient

Last revised by Raymond Chieng on 23 May 2023

Linear attenuation coefficient (µ) is a constant that describes the fraction of attenuated incident photons in a monoenergetic beam per unit thickness of a material 1. It includes all possible interactions including coherent scatter, Compton scatter and photoelectric effect 1. Its complement is the transmitted portion of the beam. It is expressed numerically in units of cm-1.

Linear attenuation coefficient increases with increasing atomic number and increasing physical density of the absorbing material. It decreases with increasing photon energy (except at K-edges) 1.  Muscle tissue has higher linear attenuation coefficient when compared to fat tissue for the same energy photon beam 4.

###### Calculating µ

The intensity of the beam at distance x (cm) within a material is calculated using the following equation 2:

Ix=I0.e−μx

Where Ix is the intensity at depth of x cm, I0 is the original intensity, and µ is the linear attenuation coefficient​.

Rearrange and take the log of both sides gives the equation for µ.

μ = ln(Io/Ix)/x

###### Variants

The mass attenuation coefficient is a normalization of the linear attenuation coefficient per unit density of a material producing a value that is constant for a given element or compound (i.e. it is independent of the density of the material) 1,3. It is expressed in cm2/g (square centimeters per gram).