02 Imaging

HVL and attenuation

Compute μ, HVL, and transmitted intensity through thickness x.

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Simulation

HVL and attenuation — Change the numbers; the scene follows.

Where it works

Radiography room

X-ray tube

At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here.

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Formula

I = I_0 e^{-\mu x},\quad \mathrm{HVL}=\frac{\ln 2}{\mu}

Variables

I₀ · Incident intensitya.u.μ · Linear attenuation coeff.cm⁻¹x · Thicknesscm

Results

I
Transmitted intensity
47.2367a.u.
I/I₀
Transmission
0.4724
HVL
Half-value layer
4.621cm

Curve

Explanation

I = I_0 e^{-\mu x},\quad \mathrm{HVL}=\frac{\ln 2}{\mu}

What it means

Under narrow-beam geometry, intensity falls exponentially: I = I₀ e^{−μx}. The half-value layer ln2/μ is the thickness that halves the beam — a practical measure of quality (hardness) for kV x-ray beams. This is a working relation in Diagnostic imaging.

Where it is used

Clinically it sits on the Radiography room — X-ray tube. At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here. Diagnostic equations live on the tube, the detector, and the patient: magnification, air kerma, CTDI, and why bone lights up at 70 kV. They turn a technique chart into physics you can defend.

Radiography room · Open this machine

How to use it

Diagnostic HVL is specified in mm Al (must exceed a regulatory minimum at each kVp). First HVL < second HVL because beams are polyenergetic (hardening). Change one input and watch the curve and the simulation follow.

Symbols

I₀Incident intensity100 a.u.
μLinear attenuation coeff.0.15 cm⁻¹
xThickness5 cm

Worked example

A typical case from the default values: I₀ = 100 a.u. (Incident intensity); μ = 0.15 cm⁻¹ (Linear attenuation coeff.); x = 5 cm (Thickness). Substituting into the relation gives I = 47.2367 a.u.; I/I₀ = 0.4724; HVL = 4.621 cm. These are teaching numbers — align them with your machine.

Typical values give

I = 47.2367a.u.
I/I₀ = 0.4724
HVL = 4.621cm

Where it comes from

The displayed formula is the working relation. Compute μ, HVL, and transmitted intensity through thickness x. Usual reference: Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg

Assumptions & limits

Monoenergetic narrow-beam model. Broad-beam shielding needs buildup. For polyenergetic beams use an effective μ or tabulated HVLs.

Pitfalls

kVp is not the same as effective energy. CTDI is not patient dose — SSDE and organ dose come after. Do not quote DLP as if it were effective dose without a k-factor. Monoenergetic narrow-beam model. Broad-beam shielding needs buildup. For polyenergetic beams use an effective μ or tabulated HVLs.

Keep this

Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Monoenergetic narrow-beam model. Broad-beam shielding needs buildup. For polyenergetic beams use an effective μ or tabulated HVLs.

In this specialty

Diagnostic imaging