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X-ray imaging is the oldest modern medical-imaging technique — Röntgen's discovery dates to 1895, and the first clinical radiograph followed within weeks. Despite the explosive growth of ultrasound and MRI, X-ray imaging remains the most widely used cross-sectional modality globally because of its speed, cost, and unique strength in visualising bone and high-contrast structures. Modern X-ray practice spans plain radiography, fluoroscopy, mammography, dental radiography, interventional angiography and computed tomography (CT), which uses computer reconstruction of many projection radiographs to build full 3-D tomographic images. This lesson rebuilds X-ray imaging from the production physics in the tube, through the attenuation of the beam in tissue, to the geometry of CT reconstruction and the dose considerations that govern its use.
Spec mapping: This lesson sits under AQA 7408 section 3.10.5 (X-ray imaging). It covers the production of X-rays in a vacuum tube via an electron beam accelerated through a high voltage onto a tungsten anode; the resulting bremsstrahlung (continuous) spectrum and the superimposed characteristic line spectrum; the role of tube voltage in determining the maximum photon energy (and therefore "hardness") and the role of tube current in determining intensity; X-ray attenuation in matter described by I = I_0 exp(-μx), with mass attenuation coefficient μ/ρ and half-value thickness x_½ = (ln 2)/μ; the use of contrast media (typically iodine-based, exploiting K-edge absorption); fluoroscopy as real-time radiography; computed tomography (CT) using rotating tube-detector geometry and Fourier-based or iterative reconstruction; and dose considerations including the millisievert dose per study and the ALARA (As Low As Reasonably Achievable) principle. (Refer to the official AQA specification document for exact wording.)
Synoptic links:
- Section 3.2.1.2 (photoelectric effect): the K-edge phenomenon used in iodinated contrast agents and the dominant attenuation mechanism at diagnostic X-ray energies is the photoelectric effect — directly linked to the quantum-physics work earlier in the course.
- Section 3.4 (electromagnetic spectrum): X-rays sit at energies 10²-10⁵ eV, wavelengths 10⁻⁸-10⁻¹¹ m. Comparing X-ray-imaging photon energies with the visible-light energies used in fibre-optic endoscopy is a textbook synoptic question.
- Section 3.8 (nuclear physics): radioactive decay shares the same exponential-decay mathematics (N = N_0 exp(-λt)) as X-ray attenuation (I = I_0 exp(-μx)). The half-value thickness for absorption is the spatial analogue of the half-life for radioactive decay.
A diagnostic X-ray tube is a sealed vacuum envelope containing two key electrodes:
Cathode — a heated tungsten filament (typically 2,000-2,500 K) that emits electrons by thermionic emission. Cathode current is typically 100-500 mA in radiography and 1-5 mA in fluoroscopy.
Anode — a target made of tungsten (atomic number Z = 74), often with a rhenium alloy and a copper backing for heat dissipation. The anode is held at a high positive potential of typically 50-150 kV relative to the cathode. Modern tubes use a rotating anode (spinning at 3,000-10,000 rpm) to spread the heat load over a larger area.
Electrons accelerated through the cathode-anode potential difference V_a strike the anode with kinetic energy eV_a. Two distinct production mechanisms operate:
As an electron decelerates near the tungsten nucleus, it radiates electromagnetic energy — bremsstrahlung, German for "braking radiation". The radiation is continuous in spectrum because the deceleration can be of any magnitude up to a maximum corresponding to complete kinetic-energy loss in a single interaction. The maximum photon energy is therefore
E_max = e V_a (and equivalently λ_min = hc / E_max)
For a 100 kV tube, E_max = 100 keV and λ_min ≈ 12.4 pm. Below E_max, the spectrum falls roughly linearly. Below about 20-30 keV, the spectrum is heavily attenuated by inherent filtration in the tube envelope and by deliberate aluminium filters — these low-energy photons would otherwise deposit dose in skin without contributing to the image.
If the bombarding electron carries enough energy to knock out a K-shell electron of a tungsten atom, an outer-shell electron will fall into the resulting vacancy, emitting a characteristic photon whose energy equals the difference between the two shell binding energies. Tungsten K-edge energy is about 69.5 keV; the principal characteristic Kα and Kβ lines fall at ~59 keV and ~67 keV respectively. These show as discrete spikes superimposed on the bremsstrahlung continuum.
A diagnostic X-ray tube is operated at 120 kV. Calculate (a) the maximum kinetic energy of electrons reaching the anode in joules, (b) the maximum X-ray photon energy in keV, and (c) the corresponding minimum wavelength.
(a) KE_max = eV = 1.60 × 10⁻¹⁹ × 120 × 10³ = 1.92 × 10⁻¹⁴ J.
(b) E_max = 120 keV (by definition: a 120 kV potential delivers 120 keV to each electron, and an electron giving up all its energy in a single bremsstrahlung interaction produces a 120 keV photon).
(c) λ_min = hc / E_max = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (1.92 × 10⁻¹⁴) = 1.04 × 10⁻¹¹ m (≈ 10 pm).
The radiation lies well into the X-ray region of the electromagnetic spectrum and is much shorter in wavelength than visible light (~500 nm).
When an X-ray beam of intensity I_0 enters a uniform thickness x of a material with linear attenuation coefficient μ, the transmitted intensity is
I = I_0 exp(-μ x)
μ has units of m⁻¹ (or cm⁻¹). It depends on the photon energy, on the material's density, and on the material's effective atomic number. At diagnostic energies (typically 30-150 keV), the dominant attenuation mechanism in soft tissue is Compton scattering (energy-dependent only weakly; depends mostly on electron density); in higher-Z materials such as bone and iodine, photoelectric absorption becomes dominant — and it scales as roughly Z³/E³, which is why bone (Z_eff ≈ 13) and iodine (Z = 53) appear so much more opaque than soft tissue (Z_eff ≈ 7).
To compare materials independent of density, the mass attenuation coefficient is defined:
μ/ρ (units m² kg⁻¹ or cm² g⁻¹)
For the same photon energy, μ/ρ depends only on chemistry, not density. Air and water have very different μ values but only modestly different μ/ρ. The transmitted intensity through a mass per unit area σ = ρx is
I = I_0 exp[-(μ/ρ) σ]
The thickness that halves the beam intensity is
x_½ = (ln 2) / μ ≈ 0.693 / μ
The mathematics is identical to nuclear half-life. Two half-value thicknesses reduce intensity to a quarter; three to an eighth; ten to about 0.1%.
| Material | μ at 80 keV (cm⁻¹, approx.) | x_½ at 80 keV (cm, approx.) |
|---|---|---|
| Air | ~2 × 10⁻⁴ | ~3,500 |
| Soft tissue | ~0.18 | ~3.8 |
| Bone (cortical) | ~0.40 | ~1.7 |
| Iodine contrast | depends on concentration | — |
| Lead | ~15 | ~0.05 |
Values are illustrative textbook ranges; the exact value depends on photon spectrum and composition.
A monoenergetic 80 keV X-ray beam traverses 10.0 cm of soft tissue with linear attenuation coefficient 0.18 cm⁻¹. Calculate (a) the fraction of beam intensity transmitted, and (b) the half-value thickness.
(a) I/I_0 = exp(-μx) = exp(-0.18 × 10.0) = exp(-1.80) = 0.165 or 16.5%.
(b) x_½ = (ln 2)/μ = 0.693/0.18 = 3.85 cm.
Ten centimetres of tissue is therefore about 2.6 half-value thicknesses — consistent with the transmitted fraction (1/2)^2.6 ≈ 0.165.
Iodine has a K-edge at 33.2 keV — a sharp jump in the photoelectric absorption coefficient as the photon energy crosses the K-shell binding energy. X-ray tubes are tuned so that a substantial fraction of their bremsstrahlung spectrum sits just above the iodine K-edge, making iodine an exceptionally efficient absorber for diagnostic imaging. Iodinated contrast media (typically tri-iodinated benzene rings such as iohexol or iopamidol) are injected intravenously for CT angiography and intra-luminally for fluoroscopic gastrointestinal studies. The contrast appears bright (heavily attenuated, low transmission) on the image.
Barium sulphate (Z = 56, K-edge 37.4 keV) is used for gastrointestinal contrast where the agent is administered orally or rectally and is not absorbed.
graph LR
A["Beam I_0<br/>at x = 0"] --> B["Tissue, μ"]
B --> C["I = I_0 exp(-μx)"]
C --> D["After 1 half-value layer<br/>I = I_0 / 2"]
D --> E["After 2 HVL<br/>I = I_0 / 4"]
E --> F["Exponential<br/>decay"]
style C fill:#3498db,color:#fff
style F fill:#27ae60,color:#fff
Fluoroscopy uses a continuous (or pulsed) low-current X-ray beam (typically 1-5 mA at 70-120 kV) to produce a real-time image, displayed on a digital flat-panel detector or — historically — on an image intensifier coupled to a TV camera. Fluoroscopy supports:
Because the beam is continuous for procedures lasting minutes to hours, fluoroscopy is a higher-dose modality than plain radiography. Operators wear lead aprons and thyroid shields; modern systems use pulsed acquisition and aggressive automatic exposure control to keep doses ALARA.
A plain radiograph is a 2-D projection of a 3-D object — all the structures along each ray sum into one pixel value, and overlap obscures detail. CT solves this by acquiring many projections from different angles around the patient and reconstructing the underlying 3-D distribution of attenuation coefficient by computer.
The CT scanner geometry is a ring of X-ray tube and detector array that rotates rapidly (about 360° in 0.25-0.5 s in modern scanners) around a table that translates slowly through the gantry. Each rotation acquires a fan-beam (or cone-beam, in volumetric scanners) projection from every angle. Reconstruction algorithms — filtered back-projection is the classical method; modern scanners use iterative reconstruction (e.g. ASIR, IMR) for lower dose — solve the Radon-transform inversion to produce a 3-D voxel grid of attenuation coefficients.
Typical CT image properties:
CT is the highest-dose routine X-ray study. Typical doses:
| Study | Effective dose (mSv) |
|---|---|
| Chest radiograph | ~0.02 |
| Mammogram | ~0.4 |
| Head CT | ~2 |
| Chest CT | ~7 |
| Abdomen / pelvis CT | ~10 |
| Coronary CT angiogram | ~5-10 |
| Annual UK natural background | ~2.7 |
Values are typical clinical estimates; actual dose depends on scanner, technique and patient size. The ALARA principle governs all clinical X-ray practice: every exposure should be justified, optimised and limited to what is medically necessary. CT dose has fallen substantially over the past decade with iterative reconstruction, tube-current modulation, kV reduction for selected studies, and routine audit.
A monoenergetic X-ray beam of incident intensity I₀ passes through 3.0 cm of soft tissue (linear attenuation coefficient μ_s = 0.20 cm⁻¹) followed immediately by 2.0 cm of cortical bone (μ_b = 0.50 cm⁻¹). Use the Beer-Lambert law I = I₀ exp(−μx).
(a) Intensity after the soft-tissue layer alone.
I₁ = I₀ exp(−μ_s × x_s) = I₀ exp(−0.20 × 3.0) = I₀ exp(−0.60)
exp(−0.60) = 0.5488
So I₁ = 0.549 I₀ — about 54.9% of the incident intensity survives 3 cm of soft tissue.
(b) Intensity after both layers.
For sequential layers, the surviving intensity multiplies:
I₂ = I₀ exp(−μ_s x_s − μ_b x_b) = I₀ exp(−0.60 − 1.00) = I₀ exp(−1.60)
exp(−1.60) = 0.2019
So I₂ = 0.202 I₀ — only about 20.2% of the incident intensity reaches the detector behind the bone, against 54.9% in the unobstructed-by-bone region. The contrast ratio between the two regions on the detector is 0.549 / 0.202 ≈ 2.7, which is what produces the bright-bone, dark-soft-tissue appearance of a plain radiograph.
(c) Half-value thickness of bone.
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