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24.2 Production and use of X-rays

Syllabus
9702–2028–2029
Topic
24.2
Level
A2

Learning objectives

24.2.1That X-rays are produced by electron bombardment of a metal target and• explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum wavelength of X-rays produced from the accelerating p.d.24.2.2The use of X-rays in imaging internal body structures• understand the use of X-rays in imaging internal body structures, including an understanding of the term contrast in X-ray imaging24.2.3I = I0e–µx for the attenuation of X-rays in matter• recall and use I = I0e–µx for the attenuation of X-rays in matter24.2.4Computed tomography (CT) scanning produces a 3D image of an internal• understand that computed tomography (CT) scanning produces a 3D image of an internal structure by first combining multiple X-ray images taken in the same section from different angles to obtain a 2D image of the section, then repeating this process along an axis and combining 2D images of multiple sections

Electron bombardment of a metal target produces X-rays with a minimum wavelength

Electrons emitted by a heated cathode accelerate through a large p.d. V toward a metal target. Rapid deceleration and atomic interactions at the target produce X-ray photons.

maximumelectronkineticenergy=eVmaximumphotonenergy=hfmax=hc/λmin=eVmaximum electron kinetic energy=eV maximum photon energy=hf_max=hc/λ_min=eV

For V=58 kV, λmin=hc/eV=(6.63×10⁻³⁴)(3.00×10⁸)/[(1.60×10⁻¹⁹)(58×10³)]=2.14×10⁻¹¹ m=21.4 pm.

Most electron energy becomes thermal energy, so the target needs a high melting point and heat removal; tungsten is commonly suitable.

The minimum wavelength is the rare limit where one photon receives all eV. Increasing V decreases λmin; tube current mainly changes the number/intensity of X-rays, not this limit.

X-ray contrast comes from differences in transmitted intensity

Send X-rays through the body and detect the transmitted beam. Different structures absorb/attenuate different fractions, so the detector records different transmitted intensities and forms an internal image.

Contrast is the difference in detector response or degree of blackening between image regions. Greater difference in transmitted intensity gives greater contrast.

Bone has a much larger attenuation coefficient than many soft tissues, so fewer X-rays reach the detector behind bone. Bone and soft tissue therefore give good contrast; tissues with similar μ give poor contrast.

On traditional film, more transmitted X-rays produce greater blackening; digital displays may map detector signal to brightness differently, but contrast still comes from signal differences.

Do not define contrast as brightness alone. It is a difference between regions produced by different attenuation/transmission through their material and thickness.

Calculate X-ray attenuation through one or several material layers

I=I0e(−μx)μ=−ln(I/I0)/x;x=−ln(I/I0)/μI=I₀e^(−μx) μ=−ln(I/I₀)/x; x=−ln(I/I₀)/μ

I/I₀ is the transmitted fraction. If 80% is absorbed, 20%=0.20 remains and belongs on the left of the exponential equation.

For muscle μ=0.22 cm⁻¹ and 80% absorption: 0.20=e^(−0.22x), so x=−ln(0.20)/0.22=7.3 cm.

Forsuccessivelayers:I/I0=e(−μ1x1)e(−μ2x2)…=e[−Σ(μixi)]For successive layers: I/I₀=e^(−μ₁x₁)e^(−μ₂x₂)…=e^[−Σ(μᵢxᵢ)]

Equal thickness x through materials with μ=3.0 and 0.22 cm⁻¹ gives I/I₀=e^(−3.22x). If I/I₀=0.13, x=0.63 cm.

Add μx exponents, not transmitted fractions. Keep μ and x in reciprocal units and distinguish fraction transmitted from fraction absorbed=1−I/I₀.

CT builds a 3D volume from many-angle X-ray projections of many sections

Choose one thin body section. An X-ray source and detectors acquire many transmission projections through that same section from different angles.

A computer combines the angular attenuation data to reconstruct a two-dimensional map/image of that section.

Repeat the angular scan for successive sections along an axis, then combine/stack the reconstructed 2D section images to produce a three-dimensional representation.

manyanglesofonesection→onereconstructed2Dslicemanyadjacent2Dslices→one3Dvolumemany angles of one section → one reconstructed 2D slice many adjacent 2D slices → one 3D volume

Compared with one projection radiograph, CT separates overlapping structures and gives 3D localization, but multiple X-ray exposures generally increase ionising-radiation dose.

Different angles create one slice; different positions create different slices. A single rotating projection is not itself the final 3D image.