Mean Free Path - Mean Free Path in Radiography

Mean Free Path in Radiography

In gamma-ray radiography the mean free path of a pencil beam of mono-energetic photons is the average distance a photon travels between collisions with atoms of the target material. It depends on the material and the energy of the photons:

where μ is the linear attenuation coefficient, μ/ρ is the mass attenuation coefficient and ρ is the density of the material. The Mass attenuation coefficient can be looked up or calculated for any material and energy combination using the NIST databases

In X-ray radiography the calculation of the mean free path is more complicated, because photons are not mono-energetic, but have some distribution of energies called spectrum. As photons move through the target material they are attenuated with probabilities depending on their energy, as a result their distribution changes in process called Spectrum Hardening. Because of Spectrum Hardening the mean free path of the X-ray spectrum changes with distance.

Sometimes one measures the thickness of a material in the number of mean free paths. Material with the thickness of one mean free path will attenuate 37% (1/e) of photons. This concept is closely related to Half-Value Layer (HVL); a material with a thickness of one HVL will attenuate 50% of photons. A standard x-ray image is a transmission image, a minus log of it is sometimes referred as number of mean free paths image.