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Attenuation: linear/mass coefficients & HVL

Transmitted intensity I/I0 falls exponentially with absorber thickness as I = I0 e^(-mu x). The thickness at which I/I0 = 0.5 is the half-value layer, HVL = 0.693/mu. A higher attenuation coefficient (denser or higher-Z absorber, or lower photon energy) gives a steeper curve and a smaller HVL than a lower coefficient.

Exponential attenuation and the half-value layer Transmitted intensity I/I0 falls exponentially with absorber thickness as I = I0 e^(-mu x). The thickness at which I/I0 = 0.5 is the half-value layer, HVL = 0.693/mu. A higher attenuation coefficient (denser or higher-Z absorber, or lower photon energy) gives a steeper curve and a smaller HVL than a lower coefficient. I / I₀ 1.0 0.5 0 HVL (high μ) HVL (low μ) absorber thickness x I = I₀ e^(−μx) monoenergetic, narrow beam at HVL, I/I₀ = 0.5 HVL = 0.693/μ ( = ln2 / μ ) lower μ higher energy, lower Z, less dense → larger HVL higher μ lower energy, higher Z, denser → smaller HVL
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