Figure 1 — CT image versus a conventional radiograph.
Tomographic reconstruction may be thought of as an advanced form of triangulation Features buried within a sample detected by conventional projection radiography can be localised in 2 dimensions but not in three: the position along the path travelled by the X-ray beam from the source to the detector cannot be determined. However, if we make 2 measurements at different viewing angles, we can use the process of triangulation to begin to estimate the position of the object within the sample. For example in Figure 2a, if we acquire and image though a section of a sample containing two discrete objects, we obtain a profile of the attenuation of the X-ray beam by the objects. If we then back project this data (project the data back along a line corresponding to the direction in which the data was acquired), what we obtain is a shadow image representing attenuation at this viewing angle. We can then repeat this process at 90o to the first measurement and calculate a second back projection (Figure 2b). By combining these two back projections, we can begin to localise the objects in our sample (Figure 2c). Positional accuracy is even further enhanced y making additional radiographs from more viewing angles and triangulating. In essence, a CT image is the result of triangulating hundreds of images acquired at different viewing angles.
Figure 2 — Schematic illustrations of back projection.
The resulting 2D cross sectional images are a quantitative map of the linear X-ray attenuation coefficient (i.e. the extent to which incident X-rays are removed as the X-ray beam propagates through the sample) at each pixel. A key feature that allows CT to be used to study materials is that the linear attenuation coefficient is proportional to material density. CT imaging therefore probes the distribution of material density within samples in 3 dimensions.