Half-value layer

Last revised by Lachlan McKay on 25 Feb 2024

Half-value layer (HVL) is the thickness of a material required to reduce the air kerma of an x-ray or gamma ray to half its original value. It applies to narrow beam geometry only, as with broad-beam geometry, a greater amount of scatter will reach the detector, overestimating the degree of attenuation. It is used to quantify polyenergetic beams instead of linear and mass attenuation coefficients used for monoenergetic beams. 

It is a surrogate measure of the penetrability of an x-ray spectrum, also referred to as beam quality. A lower HVL indicates low photon energy. HVL is conventionally measured in millimeters of aluminum. After filtration by one HVL, the subsequent HVL will be higher as the filtered photons have higher energy (thicker material is required to attenuate half of the penetrating beams). This is because the lower energy photons are preferentially absorbed via the photoelectric effect. The result of this is that the 1st HVL < 2nd HVL.

It is related to linear attenuation coefficient (μ) with the following formula (see below for derivation):

  • HVL = 0.693 / μ

Derivation from equation for linear attenuation coefficient, Ix = I0.e-μx

  • To find HVL, let x = HVL and Ix = 0.5I0

    0.5I0 = I0.e-μ.HVL

    0.5 = e-μ.HVL

    Ln(0.5) = -μ.HVL

    -0.693 = -μ.HVL

    HVL = 0.693/μ

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