X-Ray Imaging

Spec mapping: OCR H556 Module 6.5 — Medical Imaging (production of X-rays in an X-ray tube by accelerated electrons striking a metal target; bremsstrahlung and characteristic line emission; the attenuation law $I = I_0 e^{-\mu x}$I=I0​e−μx; the linear attenuation coefficient $\mu$μ and its dependence on tissue type and photon energy; contrast media; intensifying screens and CCD / flat-panel detectors; radiation dose and lead shielding). Refer to the official OCR H556 specification document for exact wording.

X-rays were discovered in November 1895 by Wilhelm Röntgen, a German physicist working in Würzburg. Experimenting with Crookes tubes — evacuated glass tubes with a high voltage applied across two electrodes — he noticed that a fluorescent screen across the room was glowing, even though the tube was carefully shielded from visible light. Röntgen realised he had stumbled across an entirely new form of radiation: penetrating, invisible, capable of passing straight through wood, flesh and even thin metal. He called it "X-ray" as a deliberate placeholder, and within weeks he had produced the first X-ray photograph in history — an image of his wife's hand, complete with wedding ring.

The medical applications were immediate and obvious. Within a year, hospitals around the world were using X-rays to image broken bones and locate foreign bodies. Well over a century later, X-ray radiography remains one of the most widely used diagnostic tools in medicine — and the physical principles of its operation are the opening topic of Module 6.5 — Medical Imaging of the OCR A-Level Physics A specification (H556), a part of the syllabus that is unique to OCR and sets it apart from AQA and Edexcel Physics.

This lesson covers the generation of X-rays in an X-ray tube (bremsstrahlung plus characteristic-line emission), the exponential attenuation law $I = I_0 e^{-\mu x}$I=I0​e−μx, the half-value thickness, contrast media, image-forming detectors, and the safety-and-dose considerations that govern every clinical exposure.

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What Are X-Rays?

X-rays are electromagnetic waves — the same physical kind of thing as visible light, just at much higher frequency and correspondingly higher photon energy. The X-ray region of the electromagnetic spectrum runs from about 10 nm down to 0.01 nm, corresponding to photon energies from about 100 eV up to several hundred keV. For medical imaging, energies in the range 20–150 keV are standard:

• Mammography: ~20–30 keV (softer X-rays for fine tissue contrast).
• General radiography: ~50–100 keV.
• CT scanning: ~80–140 keV.
• Dental X-rays: ~60–70 keV.

The higher the photon energy, the more penetrating the X-ray. Low-energy X-rays are absorbed in superficial tissues; high-energy X-rays pass straight through the whole body with little absorption. A clinical X-ray has to balance penetration against image contrast — both depend on photon energy.

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The X-Ray Tube

X-rays are produced by accelerating electrons to high speed and then stopping them abruptly in a metal target. The standard device is an X-ray tube, an evacuated envelope containing a hot cathode (the electron source) and a tungsten anode (the target).

The essential components are:

• A heated cathode filament which thermionically emits electrons into the vacuum of the tube.
• A high voltage (typically 50–150 kV) applied between the cathode and the anode, accelerating the electrons.
• A metal target (anode) — almost always tungsten, chosen for its high melting point (it must survive being bombarded by an electron beam dissipating kilowatts of power) and its high atomic number (which boosts the X-ray production efficiency).
• An evacuated glass or metal envelope that prevents electron scattering by air molecules.

When an electron strikes the tungsten target, most of its kinetic energy is dissipated as heat — which is why the target must be actively cooled, and in modern tubes is mounted on a rapidly rotating disc to spread the thermal load. Only a small fraction — of order $1\%$1% — of the electron's kinetic energy is converted into X-ray photons, and that conversion proceeds through two physically distinct mechanisms.

Bremsstrahlung ("braking radiation")

As a fast electron passes near a tungsten nucleus, the intense Coulomb field deflects and decelerates it. An accelerating charge always emits electromagnetic radiation; in this case the emitted radiation lies in the X-ray band. The German word Bremsstrahlung ("braking radiation") describes the process exactly.

The key feature of bremsstrahlung is that the emitted photon can carry any energy from zero up to a maximum, which is reached when the electron gives up all its kinetic energy to a single photon. If the accelerating voltage is $V$V, the maximum photon energy is

$E_{\text{max}} = eV$Emax​=eV

and the corresponding minimum wavelength is

$\lambda_{\min} = \dfrac{hc}{eV}.$λmin​=eVhc​.

This is the Duane–Hunt law. An X-ray tube operated at 100 kV gives

$$\begin{aligned} E_{\text{max}} &= 100\,\text{keV}, \\ \lambda_{\min} &= \dfrac{(6.63 \times 10^{-34})(3.00 \times 10^{8})}{(1.60 \times 10^{-19})(1.00 \times 10^{5})} \\ &\approx 1.24 \times 10^{-11}\,\text{m} \approx 12.4\,\text{pm}. \end{aligned}$$Emax​λmin​​=100keV,=(1.60×10−19)(1.00×105)(6.63×10−34)(3.00×108)​≈1.24×10−11m≈12.4pm.​

Photons of any energy below $eV$eV are also produced; the bremsstrahlung spectrum is continuous from $0$0 up to $eV$eV, falling off smoothly. Low-energy photons dominate in number; high-energy photons dominate in penetration.

Characteristic X-rays

Superimposed on the continuous bremsstrahlung spectrum are sharp peaks at specific discrete energies — the characteristic X-rays. They arise when a fast tube electron collides with an inner-shell electron of a tungsten atom and ejects it. The resulting hole in (say) the K-shell is then filled by an electron dropping down from a higher shell (L, M, …), emitting a photon whose energy equals the difference between the two atomic levels.

Because atomic energy levels are quantised, the emitted photon energies are sharp and characteristic of the target element — hence "characteristic" X-rays. Tungsten's strong K-line at about 59 keV and L-lines around 8–11 keV are standard features of every clinical X-ray spectrum.

The characteristic photon energies depend only on the atomic number of the target, not on the tube voltage — provided the tube voltage is high enough to liberate the relevant inner-shell electron in the first place.

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The X-Ray Spectrum

A typical medical X-ray spectrum therefore consists of:

• A continuous bremsstrahlung component extending from zero up to the maximum energy $eV$eV.
• Sharp characteristic lines at energies set by the target atom's inner-shell transitions (the K and L lines for tungsten).
• A truncated low-energy tail. Photons below about 20 keV contribute only to patient dose — they are absorbed in skin and superficial tissues without ever reaching the detector — and so are deliberately removed by an aluminium filter placed in the beam path. The filtered spectrum is what actually reaches the patient.

flowchart LR
    HV["Cathode-anode<br/>HT supply<br/>~ 50–150 kV"]
    Cath["Hot cathode<br/>thermionic e⁻ emission"]
    Beam["Accelerated electron beam"]
    Anode["Tungsten anode<br/>(rotating, cooled)"]
    Brem["Bremsstrahlung<br/>continuous spectrum<br/>up to E_max = eV"]
    Char["Characteristic lines<br/>K-shell, L-shell"]
    Filt["Al filter<br/>removes < 20 keV"]
    Spec["Filtered clinical spectrum"]
    HV --> Cath
    Cath --> Beam
    Beam --> Anode
    Anode --> Brem
    Anode --> Char
    Brem --> Filt
    Char --> Filt
    Filt --> Spec

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Attenuation of X-rays in Matter

As X-rays pass through matter they are attenuated: some photons are absorbed (by the photoelectric effect or, at higher energies, by pair production), others are scattered out of the beam (by Compton scattering). For a monoenergetic beam of intensity $I_0$I0​ passing through a thickness $x$x of a uniform material, the transmitted intensity follows the exponential law

$I = I_0\, e^{-\mu x}$I=I0​e−μx

where $\mu$μ is the linear attenuation coefficient of the material, with units of m$^{-1}$−1 (or, more commonly, cm$^{-1}$−1). This is the direct spatial analogue of the radioactive decay law $N = N_0 e^{-\lambda t}$N=N0​e−λt that we met in Lesson 2 — with the distance travelled through the medium replacing time.

The attenuation coefficient depends on two things:

• The material — specifically its density $\rho$ρ and atomic number $Z$Z. Denser materials and higher-$Z$Z materials attenuate more strongly.
• The photon energy $E$E. At diagnostic energies, higher-energy X-rays are less attenuated than lower-energy X-rays.

Typical linear attenuation coefficients at 100 keV:

Material	$\mu$μ (cm$^{-1}$−1)
Air	$\sim 2 \times 10^{-4}$∼2×10−4
Water (soft tissue)	$\sim 0.17$∼0.17
Muscle	$\sim 0.18$∼0.18
Fat	$\sim 0.17$∼0.17
Bone	$\sim 0.40$∼0.40
Lead	$\sim 60$∼60

Bone attenuates about $2$2–$3$3 times more strongly than soft tissue — enough to make bones stand out clearly as bright (less-exposed) regions on a radiograph. Lead is enormously more attenuating still, which is why it is the shielding material of choice in X-ray rooms.

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Half-Value Thickness

By direct analogy with the half-life in radioactive decay, the half-value thickness $x_{1/2}$x1/2​ is the thickness of material that reduces the X-ray intensity to half its initial value. Setting $I = I_0/2$I=I0​/2 in the attenuation law:

$$\begin{aligned} \tfrac{1}{2} I_0 &= I_0\, e^{-\mu x_{1/2}}, \\ \tfrac{1}{2} &= e^{-\mu x_{1/2}}, \\ \mu x_{1/2} &= \ln 2, \\ x_{1/2} &= \dfrac{\ln 2}{\mu}. \end{aligned}$$21​I0​21​μx1/2​x1/2​​=I0​e−μx1/2​,=e−μx1/2​,=ln2,=μln2​.​

Typical half-value thicknesses at 100 keV:

Material	$x_{1/2}$x1/2​
Water / soft tissue	~4 cm
Bone	~1.7 cm
Lead	~0.12 mm

A lead sheet of just 1 mm reduces 100 keV X-ray intensity by a factor of about $2^{8.3} \approx 320$28.3≈320. Practical X-ray shielding uses lead sheets a few millimetres thick, with correspondingly vast attenuation factors. The 0.5 mm lead apron worn by a radiographer behind a shielded screen reduces the operator's dose to a negligible level — the inverse-square fall-off of intensity with distance from the tube provides the rest of the protection.

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Worked Example 1: Attenuation through soft tissue

An X-ray beam of intensity $I_0$I0​ passes through 12 cm of soft tissue ($\mu = 0.17$μ=0.17 cm$^{-1}$−1). What fraction of the beam emerges?

Solution.

$$\begin{aligned} \mu x &= 0.17 \times 12 = 2.04, \\ \dfrac{I}{I_0} &= e^{-2.04} \approx 0.13. \end{aligned}$$μxI0​I​​=0.17×12=2.04,=e−2.04≈0.13.​

About 13% of the beam passes through; the other 87% is absorbed by the tissue, delivering the dose that is the inevitable cost of diagnostic X-ray imaging.

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Worked Example 2: Bone-versus-soft-tissue contrast

At 80 keV, $\mu_\text{tissue} = 0.19$μtissue​=0.19 cm$^{-1}$−1 and $\mu_\text{bone} = 0.50$μbone​=0.50 cm$^{-1}$−1. A 2 cm thickness of bone is embedded in 10 cm of soft tissue (so the beam traverses 8 cm of tissue plus 2 cm of bone). What fraction of the beam emerges (a) through 10 cm of tissue alone, and (b) through the tissue–bone–tissue path?

Solution.

(a) Pure tissue:

$\dfrac{I}{I_0} = e^{-(0.19)(10)} = e^{-1.90} \approx 0.15.$I0​I​=e−(0.19)(10)=e−1.90≈0.15.

(b) Tissue 8 cm + bone 2 cm:

$$\begin{aligned} \mu x &= (0.19)(8) + (0.50)(2) = 1.52 + 1.00 = 2.52, \\ \dfrac{I}{I_0} &= e^{-2.52} \approx 0.080. \end{aligned}$$μxI0​I​​=(0.19)(8)+(0.50)(2)=1.52+1.00=2.52,=e−2.52≈0.080.​

The contrast ratio (tissue-only / tissue + bone) is $0.15 / 0.080 \approx 1.9$0.15/0.080≈1.9. This $\approx 2{:}1$≈2:1 intensity ratio is exactly what makes the bone visible on the radiograph: regions behind the bone receive less exposure and appear brighter on a positive print (or darker on a negative).

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Worked Example 3: Half-value thickness of lead

Find the half-value thickness of lead at 100 keV, given $\mu_\text{Pb} = 60$μPb​=60 cm$^{-1}$−1, and hence the thickness of lead required to reduce the beam intensity by a factor of $10^6$106.

Solution.

$x_{1/2} = \dfrac{\ln 2}{\mu} = \dfrac{0.693}{60} \approx 0.0116\,\text{cm} = 0.12\,\text{mm}.$x1/2​=μln2​=600.693​≈0.0116cm=0.12mm.

To reduce intensity by a factor of $10^6$106 we need

$$\begin{aligned} e^{-\mu x} &= 10^{-6}, \\ \mu x &= 6 \ln 10 \approx 13.8, \\ x &= \dfrac{13.8}{60} \approx 0.23\,\text{cm} = 2.3\,\text{mm}. \end{aligned}$$e−μxμxx​=10−6,=6ln10≈13.8,=6013.8​≈0.23cm=2.3mm.​

A lead sheet about 2.3 mm thick attenuates a 100 keV beam by a million-fold — entirely consistent with the few-millimetre lead linings of clinical X-ray rooms.

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Contrast Media

Some parts of the body — stomach, intestines, arteries, bladder — have attenuation very close to that of surrounding tissue. X-rays pass through them almost identically, giving poor contrast and invisible boundaries on the radiograph. To make these structures visible, doctors use contrast media: substances that contain elements with high atomic number, so that they attenuate X-rays much more strongly than soft tissue.

Two classical contrast agents:

• Barium sulfate ($\mathrm{BaSO}_4$BaSO4​). Barium has $Z = 56$Z=56, comparable to the target element of an X-ray tube. A "barium meal" drunk by the patient coats the stomach and intestines, making them appear bright on the radiograph. Barium sulfate is insoluble and chemically inert, so it passes harmlessly through the digestive system.
• Iodine compounds. Iodine has $Z = 53$Z=53, again strongly attenuating. Injectable iodine-based contrast agents are used to outline blood vessels (angiography), the urinary tract and various other soft-tissue structures. Modern iodine-based agents are organic molecules chosen for low toxicity and rapid clearance.

Contrast media exploit the strong dependence of the photoelectric cross-section on atomic number ($\sigma \propto Z^{4}$σ∝Z4 approximately) and work best at photon energies just above the K-shell absorption edge of the contrast element.

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Forming the Image: Detectors

In Röntgen's day the image was formed on a photographic film. Modern radiographs are formed on a flat-panel digital detector consisting of an array of photodiodes coupled to a scintillator (or directly sensitive to X-rays). Each pixel records the intensity of the transmitted beam; the image is stored digitally and displayed on a monitor.

A bridge technology between film and flat-panel was the intensifying screen: phosphor plates (calcium tungstate or rare-earth phosphors) sandwiching a photographic film. The phosphor emits visible-light photons when struck by an X-ray, and the film records the visible light. Because each X-ray photon liberates many visible photons, the patient dose required to produce a given film density is reduced — typically by a factor of 30–50 compared with film alone. Older clinical departments still use this technology; modern departments are almost entirely digital.

Charge-coupled devices (CCDs) and complementary metal-oxide-semiconductor (CMOS) sensors, coupled to a thin scintillating layer (e.g. caesium iodide doped with thallium), now dominate. They give live-update digital imaging at high resolution and low dose, and can be integrated with computer image-processing pipelines for windowing, edge enhancement and automatic measurement.

The fundamental imaging geometry is simple: the X-ray source is approximately a point, the patient sits between source and detector, and the recorded image is a shadow projection of the patient's internal structure. This simplicity is both the strength and the weakness of plain X-ray radiography. It is cheap, fast and universally available. But it loses all depth information — overlapping structures superimpose — and it cannot resolve small contrast differences in soft tissue. These limitations are precisely what motivate the CT scanner in the next lesson.

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Radiation Dose and Safety

X-rays are ionising and carry a small but real risk of inducing cancers and genetic damage. Doses are quoted in sieverts (Sv), which weight the deposited energy per unit mass of tissue by the biological effectiveness of the radiation type. For X-rays the weighting factor is 1, so 1 Sv = 1 J kg$^{-1}$−1.

Typical effective doses for clinical procedures: