00 Foundations
Buildup factor
Broad-beam transmission I = B I₀ e^{−μx} includes scatter that narrow-beam law omits.
Listen
Listen · English
Simulation
Buildup factor — Change the numbers; the scene follows.
Where it works
Linear accelerator
Isocenter
At isocenter, on the central axis through the patient (or a phantom in the same place).
Open this machineFormula
Variables
Results
I_broad
Broad-beam intensity
55.7825
I_narrow
Narrow-beam intensity
22.313
I/I₀
Broad transmission
0.5578
Curve
Explanation
What it means
A narrow-beam (good-geometry) measurement rejects scatter, so I/I₀ = e^{−μx}. In a wall, a patient, or a broad therapy field, scattered photons still reach the point of interest and the observed transmission is larger by the buildup factor B ≥ 1. B grows with optical thickness μx, field size and decreasing energy. Shielding TVLs are tabulated as broad-beam values for this reason. This is a working relation in Radiation physics.
Where it is used
Clinically it sits on the Linear accelerator — Isocenter. At isocenter, on the central axis through the patient (or a phantom in the same place). Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.
Linear accelerator · Open this machineHow to use it
Enter I₀, μ, x and B (1 for narrow beam). Typical concrete B at 3–4 TVL of 6 MV is 2–10. Compare the narrow-beam result (B=1) with the broad-beam result. Change one input and watch the curve and the simulation follow.
Symbols
- I₀Incident intensity100
- μLinear attenuation0.05 cm⁻¹
- xThickness30 cm
- BBuildup factor2.5
Worked example
A typical case from the default values: I₀ = 100 (Incident intensity); μ = 0.05 cm⁻¹ (Linear attenuation); x = 30 cm (Thickness); B = 2.5 (Buildup factor). Substituting into the relation gives I_broad = 55.7825; I_narrow = 22.313; I/I₀ = 0.5578. These are teaching numbers — align them with your machine.
Typical values give
- I_broad = 55.7825
- I_narrow = 22.313
- I/I₀ = 0.5578
Where it comes from
The displayed formula is the working relation. Broad-beam transmission I = B I₀ e^{−μx} includes scatter that narrow-beam law omits. Usual reference: Attix / NCRP 151. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Attix / NCRP 151
Assumptions & limits
B is an input, not computed from a Berger or GP buildup table. Does not distinguish coherent, Compton or fluorescence. Use tabulated B or TVL for a named spectrum and material.
Pitfalls
Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. B is an input, not computed from a Berger or GP buildup table. Does not distinguish coherent, Compton or fluorescence. Use tabulated B or TVL for a named spectrum and material.
Keep this
Photons do not deposit dose; the electrons they set in motion do. B is an input, not computed from a Berger or GP buildup table. Does not distinguish coherent, Compton or fluorescence. Use tabulated B or TVL for a named spectrum and material.
In this specialty