3️⃣ Beam Intensity & Penetrability, Inverse Square, Filtration & HVL

Inverse square law – statement

The intensity of radiation from a point source is inversely proportional to the square of the distance from the source: I₂ = I₁ × (D₁² / D₂²).

Inverse square law – practical effect

If you double the SID, the intensity at the image receptor becomes one-fourth; if you halve the distance, intensity becomes four times greater.

Exposure maintenance (mAs–distance) formula

To keep the same receptor exposure when changing SID: mAs₂ = mAs₁ × (D₂² / D₁²). As distance increases, mAs must increase by the square of the distance ratio.

Tube output (beam intensity)

The amount of radiation produced by the tube per unit time at a given distance from the source; depends on kVp, mAs, filtration, and distance.

Effect of kVp on tube output

Increasing kVp increases beam intensity (more photons reach the detector) and increases beam quality (more penetrating photons).

Effect of mAs on tube output

Increasing mAs increases beam intensity in direct proportion (twice the mAs gives roughly twice the output) but does not change photon energy.

Effect of filtration on tube output

Adding filtration removes low-energy photons, decreasing overall intensity but increasing average beam energy and reducing patient skin dose.

Filter – definition

An absorbing material (usually aluminum) placed in the x-ray beam to remove low-energy photons that would be absorbed by the patient and not contribute to the image.

Units of filtration

Filtration is expressed in millimeters of aluminum equivalent (mm Al/eq), meaning the thickness of aluminum that would produce the same attenuation.

Minimum total filtration requirement

For general diagnostic x-ray tubes operating above 70 kVp, the total filtration (inherent plus added) must be at least 2.5 mm aluminum equivalent.

Inherent vs added filtration

Inherent filtration comes from the tube and housing (glass envelope, oil, tube window); added filtration consists of metal sheets and collimator components placed in the beam.

Compensating filter – definition

A specially shaped filter (such as a wedge or trough) placed in the beam to even out receptor exposure when one part of the field is much thicker or denser than another.

Beam hardening – definition

The increase in average photon energy (beam quality) as low-energy photons are removed by filtration or by passing through tissue; the beam becomes more penetrating but less intense overall.

Half-value layer (HVL)

The thickness of a specified absorber required to reduce the x-ray beam intensity to one-half of its original value; used as a measure of beam quality.

Effect of increasing beam quality on HVL

As beam quality (average energy) increases, the HVL increases because a thicker absorber is needed to cut the intensity in half.

Effect of increasing kVp on interactions and image (review chart)

When kVp increases: fewer photons are attenuated and more are transmitted; the probability of both PE and Compton per photon decreases, but relatively more interactions are Compton; patient dose per mAs decreases, receptor exposure increases, occupational dose increases, and contrast resolution decreases (image becomes more gray).

Effect of increasing tissue atomic number (Z) on interactions and image (review chart)

When tissue atomic number increases: more photons are attenuated, more photons undergo photoelectric effect, patient dose increases, receptor exposure decreases, occupational dose decreases, and contrast resolution increases (more subject contrast).