Production and use of X-rays

Section: Medical Physics | Syllabus: Cambridge A Level Physics (9702)

Production and Use of X-rays

X-rays are high-energy electromagnetic radiation with wavelengths typically between 10^-8 m and 10^-13 m. They are widely used in medical imaging due to their ability to penetrate soft tissue while being absorbed by denser materials like bone.

Production of X-rays

X-rays are produced in an X-ray tube by the bombardment of a metal target with high-speed electrons.

How X-rays are Produced

A heated cathode emits electrons by thermionic emission
Electrons are accelerated towards a metal anode (target) by a high potential difference (typically 30-150 kV)
When electrons strike the metal target (usually tungsten), X-rays are produced

X-rays are produced by two mechanisms:

Bremsstrahlung (braking radiation): Electrons decelerate rapidly when they interact with target atoms, emitting X-ray photons with a continuous range of energies
Characteristic X-rays: Electrons knock out inner-shell electrons from target atoms; when outer electrons fall to fill the vacancy, X-rays of specific wavelengths are emitted

Figure: X-ray Tube

Cross-section of an X-ray tube showing:

Cathode: Heated filament that emits electrons by thermionic emission
Anode (target): Metal target (usually tungsten) attached to rotating anode
Evacuated glass tube: Contains cathode and anode in vacuum
High voltage supply: Accelerates electrons from cathode to anode (30-150 kV)
Lead shielding: Absorbs stray X-rays except through exit window
Oil reservoir: Cooling system (less than 1% of electron energy becomes X-rays; rest becomes heat)

Figure: X-ray Spectrum

Graph of relative intensity vs wavelength showing:

Continuous spectrum (Bremsstrahlung): Smooth curve starting at minimum wavelength _min, rising to a peak, then decreasing
Characteristic peaks: Sharp spikes superimposed on continuous spectrum at specific wavelengths (depend on target material)
Minimum wavelength: Cut-off at _min = hc/eV (when electron loses all KE in one collision)
Higher accelerating voltage shifts the curve left (shorter _min) and increases intensity

Minimum Wavelength of X-rays

The maximum energy of an X-ray photon equals the kinetic energy gained by an electron accelerated through the p.d.

Maximum photon energy: E_max = eV

Since E = hf = (hc/λ), the minimum wavelength is:

_min = (hc/eV)

where e = electron charge, V = accelerating p.d., h = Planck constant, c = speed of light Effect of Changing Tube Parameters

Increasing accelerating p.d.: decreases minimum wavelength, increases maximum photon energy, shifts spectrum to higher energies
Increasing tube current: increases number of X-ray photons (intensity) but does not change minimum wavelength

X-ray Imaging and Contrast

Contrast The difference in visibility (degree of darkening) between two areas in an X-ray image. Good contrast allows different structures to be distinguished clearly.

Contrast depends on the relative absorption of X-rays by different tissues. Bone absorbs X-rays strongly (appears white), air absorbs very little (appears black), and soft tissues appear as shades of grey.

Contrast Enhancement

Soft tissues often have similar absorption properties, making them difficult to distinguish. A contrast medium can be used to improve visibility:

Barium meal: Barium sulfate suspension swallowed to image the digestive tract
Iodine compounds: Injected intravenously to image blood vessels

These substances have high linear attenuation coefficients, making the structures they fill appear clearly on the X-ray image.

Attenuation of X-rays

As X-rays pass through matter, their intensity decreases exponentially due to absorption and scattering.

I = I_0 e^-μ x

where I = transmitted intensity, I_0 = incident intensity, μ = linear attenuation coefficient (cm^-1), x = thickness of material

The linear attenuation coefficient μ depends on:

The density of the material (denser materials absorb more)
The atomic number of the material (higher Z absorbs more)
The energy of the X-ray photons (lower energy photons are absorbed more easily)

Half-Value Thickness (x_1/2) The thickness of material required to reduce the X-ray intensity to half its original value. x_1/2 = (ln 2/μ) = (0.693/μ)

Computed Tomography (CT) Scanning

Conventional X-ray images are 2D projections of 3D structures, providing no depth information. Computed Tomography (CT) overcomes this limitation by producing 3D images.

CT Scanning A technique that produces a 3D image of internal structures by combining multiple X-ray images taken from different angles. How CT Scanning Works

An X-ray tube rotates around the patient, taking images from many different angles in the same plane (section)
Detectors measure the transmitted X-ray intensity at each angle
A computer combines these measurements to create a 2D cross-sectional image (slice) of that section
The patient moves through the scanner and the process is repeated for multiple adjacent sections
The multiple 2D slices are combined to form a 3D image of the internal structure

Figure: CT Scanner Setup

Cross-section of CT scanner showing:

X-ray tube: Rotates around the patient (often through 360°)
Detector array: Ring of detectors on opposite side from X-ray tube, also rotates
Patient table: Moves patient through the scanner between rotations
Narrow X-ray beam: Passes through one "slice" of the patient at a time

Multiple measurements at different angles are combined by computer to reconstruct a 2D cross-sectional image. Multiple slices are stacked to create a 3D image.

Feature	Conventional X-ray	CT Scan
Image type	2D shadow image	3D cross-sectional image
Soft tissue contrast	Poor	Better
Radiation dose	Lower	Higher (multiple exposures)
Cost	Lower	Higher

Advantages of CT over Conventional X-rays

Provides depth information (3D imaging)
Better contrast between soft tissues
Can view cross-sections at any angle
Can detect smaller abnormalities

Worked Examples

Worked Example: Minimum X-ray Wavelength

Question: Calculate the minimum wavelength of X-rays produced by a tube operating at 150 kV.

Solution

_min = (hc/eV) = 6.63 × 10^-34 × 3.00 × 10^81.60 × 10^-19 × 150 × 10^3

_min = 1.989 × 10^-252.40 × 10^-14 = 8.29 × 10^-12 m

Worked Example: X-ray Attenuation

Question: For bone, the linear attenuation coefficient for 150 keV X-rays is 0.6 cm^-1. Calculate the half-value thickness.

Solution

x_1/2 = (ln 2/μ) = (0.693/0.6) = 1.2 cm

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Production and use of X-rays