Half-value layer (HVL) is the thickness of a material required to reduce the air kerma of an X-ray or gamma-ray beam to half its original value. HVL is most accurately measured under narrow-beam geometry, as broad-beam setups allow scatter to reach the detector, leading to an underestimation of attenuation unless corrected.

Calculation

Monoenergetic beams
For monoenergetic beams HVL is directly related to linear attenuation coefficient (µ):
HVL = 0.693 / μ.

This formula can be derived from the Beer-Lambert Law:
I_x = I₀ e^{-μ x}

To find HVL, set x = HVL and I_x = 0.5 I₀

• 0.5 I₀ = I₀ e^{-μ HVL}

• 0.5 = e^{-μ HVL}

• ln(0.5) = -μ HVL

• -0.693 = -μ HVL

• HVL = 0.693 / μ

Polyenergetic beams
HVL for polyenergetic beams is determined experimentally rather than through a simple formula. The attenuation curve is measured by passing the X-ray beam through increasing thicknesses of material, plotting intensity vs. thickness, and finding the point where intensity drops to 50%.

Application

• HVL is particularly useful for characterizing polyenergetic X-ray beams (such as those used in diagnostic radiology), where individual linear attenuation coefficients (μ) vary with energy. Unlike linear and mass attenuation coefficients, which are strictly energy-dependent and ideal for monoenergetic beams, HVL provides a practical summary of a beam’s overall penetrability.

• HVL serves as a surrogate measure of beam quality or X-ray spectrum penetrability. A lower HVL suggests a beam with a lower mean photon energy and greater attenuation per unit thickness. HVL is conventionally measured in millimeters of aluminum for diagnostic X-rays.

Beam hardening

As an X-ray beam passes through a filter or tissue, beam hardening occurs: lower-energy photons are preferentially absorbed via the photoelectric effect, increasing the average energy of the remaining photons. As a result, each subsequent HVL is larger than the first (1st HVL < 2nd HVL < 3rd HVL), since higher-energy photons require thicker material to be attenuated by half.

See also

• Beam hardening

• Linear attenuation coefficient

• Beer-Lambert Law

• Kerma

• Exposure