Quantify beam hardening with practical HVL tools. Model exponential attenuation or fit two measured points. Choose units, export reports, and validate dose planning quickly.
X‑ray attenuation through a filter is often modeled as an exponential:
I = I₀ · e^(−μx)
I₀ is unattenuated intensity, I is transmitted intensity.μ is the linear attenuation coefficient.x is filter thickness along the beam path.
The Half‑Value Layer (HVL) is the thickness that halves intensity:
HVL = ln(2) / μ
For two measured points (x₁,I₁) and (x₂,I₂):
μ = ln(I₁/I₂) / (x₂ − x₁)
Practical tip: HVL is spectrum‑dependent, so compare only like‑for‑like setups.
| Filter material | kVp label | Thickness (mm) | Measured intensity (a.u.) | Transmission (I/I₀) |
|---|---|---|---|---|
| Aluminium | 80 kVp | 0 | 100 | 1.00 |
| Aluminium | 80 kVp | 2 | 62 | 0.62 |
| Aluminium | 80 kVp | 4 | 41 | 0.41 |
| Aluminium | 80 kVp | 6 | 33 | 0.33 |
Example values are illustrative only. Use your measured detector readings.
Half‑value layer (HVL) is the thickness of a chosen absorber that reduces beam output to 50%. For diagnostic beams, the absorber is usually aluminum and HVL is reported in mm Al as a compact indicator of penetration, filtration, and spectrum hardness.
Higher HVL generally means a “harder” beam with fewer low‑energy photons. This often reduces superficial dose for a given detector signal, but it can also shift image contrast and may require technique adjustments (mAs) to keep receptor exposure consistent. It also supports dose optimization.
Under narrow‑beam conditions, attenuation can be approximated by I = I0 · e−μx. Solving for 50% transmission gives HVL = ln(2)/μ, and for 10% transmission gives TVL = ln(10)/μ. These conversions let you move between μ, HVL, and TVL quickly.
HVL is ideally measured with narrow‑beam geometry to limit scatter reaching the detector. Broad‑beam setups can increase detected signal via scatter, changing the apparent “half” point. For trending, keep distance, collimation, and filtration setup unchanged.
HVL rises with increasing kVp because the spectrum shifts to higher photon energies. It also rises with greater total filtration (inherent + added). Generator waveform (ripple) can alter effective energy, so identical kVp values do not always produce identical HVLs across systems.
Many quality‑control tables link required HVL to kVp and show a near‑linear rise across operating ranges. As a commonly cited benchmark, tables often list about 2.5 mm Al HVL at 90 kVp, with HVL increasing at higher kVp for the same filtration. Use references appropriate to your jurisdiction and protocol. For low‑kVp dental units, accepted minimum HVLs are typically smaller.
Record baseline output without test filters, then add aluminum in steps and measure air kerma (or exposure) each time. Compute transmission (I/I0) and find the thickness where transmission equals 0.5. If the half point lies between two steps, linear interpolation is commonly applied.
Report HVL together with kVp, total filtration, geometry, detector type, and distances. If you have multiple layers, homogeneity factor (HVL1/HVL2) summarizes beam hardening; values closer to 1 indicate a more uniform spectrum. Tracking HVL over time can reveal filtration changes or tube aging.
A higher HVL usually indicates a more penetrating, more heavily filtered beam with higher effective energy.
Yes. HVL can be defined for any absorber, but diagnostic beam quality is most often referenced to aluminum for consistency.
Geometry, scatter, added filtration, tube aging, and generator waveform can all shift the measured HVL. Keep the setup consistent and repeat the test.
Homogeneity factor is HVL1 divided by HVL2. It reflects spectrum hardening; values closer to 1 suggest a more uniform beam.
For narrow‑beam attenuation, HVL = ln(2)/μ. Knowing either HVL or μ lets you compute the other directly.
TVL is the thickness that reduces intensity to one‑tenth. It is commonly used for shielding designs that target decade reductions.
Either is acceptable if you use consistent units and minimize extra scatter. Air kerma is common in modern QC; exposure appears in older protocols.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.