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 a
Cambridge A-Level Physics 9702 – Production and Use of X‑rays
Production and Use of X‑rays
Objectives
Explain how X‑rays are produced in an X‑ray tube.
Describe the interaction of X‑rays with matter.
Understand the principle of computed tomography (CT) scanning.
Explain how a 3‑D image is reconstructed from multiple X‑ray projections.
1. Production of X‑rays
An X‑ray tube consists of a heated cathode that emits electrons by thermionic emission and an anode made of a high‑Z material (usually tungsten). When a high potential difference \$V\$ (typically 30–150 kV) is applied, electrons are accelerated towards the anode and decelerate rapidly upon impact. Two processes generate X‑rays:
Bremsstrahlung (braking radiation) – deceleration of electrons in the electric field of the nucleus produces a continuous spectrum of X‑ray energies up to a maximum photon energy \$E_{\max}=eV\$.
Characteristic radiation – electrons knock out inner‑shell electrons of the anode atoms; outer‑shell electrons fill the vacancy, emitting photons with discrete energies characteristic of the anode material.
2. Interaction of X‑rays with Matter
The intensity \$I\$ of an X‑ray beam after passing through a material of thickness \$x\$ is described by the exponential attenuation law:
\$I = I_0 e^{-\mu x}\$
where \$I_0\$ is the initial intensity and \$\mu\$ is the linear attenuation coefficient, which depends on photon energy and the atomic number of the material.
3. Computed Tomography (CT) Scanning
CT scanning creates a three‑dimensional (3‑D) representation of an object’s internal structure. The process can be divided into two main stages:
3.1. Acquisition of 2‑D Projections
The X‑ray source and detector rotate around the object, acquiring many projections (X‑ray images) of the same thin slice from different angles (typically 0° to 360°).
Each projection records the line integral of the attenuation coefficient \$\mu\$ along the X‑ray path.
3.2. Reconstruction of a 2‑D Slice
Mathematically, the set of projections \$p(\theta, s)\$ (where \$\theta\$ is the rotation angle and \$s\$ is the detector position) is related to the slice image \$f(x,y)\$ by the Radon transform:
Reconstruction algorithms (e.g., filtered back‑projection) invert this transform to obtain \$f(x,y)\$, a 2‑D map of \$\mu\$ for that slice.
3.3. Stacking Slices to Form a 3‑D Image
The patient/table moves incrementally along the longitudinal axis (the “z‑axis”).
For each new position, the above acquisition and reconstruction steps are repeated, producing a series of contiguous 2‑D slices.
These slices are stacked and interpolated to generate a volumetric dataset, which can be displayed as cross‑sections in any plane or rendered as a 3‑D model.
4. Advantages of CT over Conventional Radiography
Feature
Conventional X‑ray
CT Scan
Dimensional information
2‑D projection only
True 3‑D reconstruction
Contrast resolution
Limited, overlapping structures
High, can differentiate tissues of similar density
Quantitative data
Qualitative
Attenuation coefficients (Hounsfield units)
Geometric distortion
Significant for thick objects
Minimised by slice‑by‑slice acquisition
5. Safety Considerations
Use the lowest possible tube voltage and current that yields adequate image quality (ALARA principle).
Shielding with lead aprons and walls reduces exposure to staff and other patients.
Limit scan length and number of slices to minimise dose.
6. Summary Flowchart (Suggested diagram)
Suggested diagram: Flowchart showing (1) X‑ray generation, (2) rotation and acquisition of multiple projections of a slice, (3) reconstruction of the slice, (4) translation to next slice, (5) stacking to produce a 3‑D image.