Cambridge A-Level Physics 9702 – Production and Use of X‑rays
Production and Use of X‑rays
Learning Objective
By the end of this lesson you should be able to:
Explain how X‑rays are produced in an X‑ray tube.
Describe how X‑rays are used to image internal body structures.
Define “contrast” in X‑ray imaging and identify the factors that affect it.
Discuss the role of contrast agents.
1. How X‑rays are Produced
In a conventional X‑ray tube electrons are accelerated from a heated cathode (filament) towards a metal anode (target) by a high voltage \$V\$. Two main processes generate X‑rays:
Bremsstrahlung (braking radiation) – when high‑speed electrons are decelerated in the electric field of the nuclei in the target, a continuous spectrum of X‑ray photons is emitted. The maximum photon energy is given by
\$E_{\text{max}} = eV,\$
where \$e\$ is the elementary charge.
Characteristic radiation – if an incident electron ejects an inner‑shell electron from a target atom, an outer‑shell electron falls to fill the vacancy, emitting a photon with energy equal to the difference between the two energy levels. This produces sharp lines (e.g., \$K{\alpha}, K{\beta}\$) specific to the target material.
Suggested diagram: Cross‑section of an X‑ray tube showing the cathode, focusing cup, anode target, and emitted X‑ray beam.
2. Components of an X‑ray Tube
Component
Function
Cathode (filament)
Heats to emit electrons via thermionic emission.
Focusing cup
Shapes the electron beam and directs it toward the anode.
Anode (target)
High‑Z material (e.g., tungsten) where X‑rays are produced.
Glass envelope
Maintains a vacuum to prevent electron scattering.
High‑voltage power supply
Provides the accelerating potential \$V\$ (typically 40–150 kV).
3. X‑ray Imaging of the Human Body
When an X‑ray beam passes through the body, different tissues attenuate the beam to different extents. The transmitted intensity \$I\$ is described by the exponential attenuation law:
\$I = I_0 \, e^{-\mu x},\$
where \$I_0\$ is the incident intensity, \$\mu\$ is the linear attenuation coefficient (depends on material composition and photon energy), and \$x\$ is the thickness of the material.
After passing through the patient, the remaining X‑rays expose a detector (film or digital sensor). Areas that attenuate more appear lighter (more exposure) or darker depending on the detection method.
4. Contrast in X‑ray Imaging
Contrast is the difference in image density (or pixel value) between adjacent structures. It allows us to distinguish one tissue from another.
4.1 Factors Influencing Contrast
Material density (\$\rho\$) – denser tissues (bone) have larger \$\mu\$ and thus higher attenuation.
Atomic number (\$Z\$) – higher \$Z\$ increases photoelectric absorption, especially at lower photon energies.
Thickness (\$x\$) – thicker regions attenuate more, increasing contrast up to a point.
Photon energy – lower‑energy X‑rays increase contrast (more photoelectric effect) but also increase patient dose.
4.2 Quantitative Measure of Contrast
The contrast \$C\$ between two regions with intensities \$I1\$ and \$I2\$ can be expressed as:
\$C = \frac{|I1 - I2|}{I1 + I2} \times 100\%.\$
5. Use of Contrast Agents
When natural differences in \$\mu\$ are insufficient (e.g., soft‑tissue imaging), contrast agents containing high‑Z elements (iodine, barium) are introduced to increase attenuation locally.
Contrast Agent
Typical Use
Key Property
Iodine‑based (e.g., iohexol)
Angiography, CT scans of blood vessels
High atomic number (Z = 53) – strong photoelectric absorption
Barium sulfate suspension
Gastro‑intestinal tract studies
Insoluble, high density, coats mucosal surfaces
Gadolinium (used in MRI, not X‑ray)
Reference – illustrates that contrast agents are modality‑specific
Paramagnetic, enhances magnetic resonance signal
6. Optimising Image Quality
Balancing contrast against other image quality factors is essential:
Resolution – ability to distinguish fine detail; limited by detector pixel size and focal spot size.
Noise – statistical fluctuations in photon number; reduced by increasing exposure but raises dose.
Patient dose – must be kept as low as reasonably achievable (ALARA principle).
7. Summary Checklist
Know the two mechanisms of X‑ray production: bremsstrahlung and characteristic radiation.
Understand the exponential attenuation law and its dependence on \$\mu\$, \$x\$, and photon energy.
Define contrast and be able to calculate it using the provided formula.
Identify the main factors that affect contrast: density, atomic number, thickness, and photon energy.
Explain why and how contrast agents are used in clinical imaging.
Recall the trade‑off between contrast, resolution, noise, and patient dose.