The principle behind tracer location using PEPT is extremely simple. Each positron annihilation results in a pair of back-to-back γ-rays. Detection of these enables a line to be drawn between the detected points, along which the tracer must lie. It is obvious that in principle two such lines are sufficient to locate the tracer.
In practice, there are a number of sources of inaccuracy:
- Each emitted positron will travel a certain distance before it encounters an electron, so the source of the γ-rays may not lie within the tracer particle. Unless the system under investigation is of very low density this error is trivially small.
- The emitted γ-rays are not quite 180° apart but depart from a straight line by about 0.5°, in order to conserve momentum. Again, the error which comes from this is trivially small in all feasible geometries.
- The detectors in the PEPT camera, whether of the large-area position-sensitive type or made up of discrete blocks, do not give the exact position of each detected event, but the discretised position, e.g. the centre of the block which detects the event. This results in an intrinsic spatial resolution for each type of camera, which is limited by the size and geometric arrangement of the detector elements, and is a significant contributor to uncertainty in location.
- The emitted γ-rays can be scattered by the material of interest and the material of the container and any internal or external hardware such as stirrers, blades or motors. This can result in spurious lines being drawn between detected events, a source of “noise” in the locating process. The magnitude of the effect is very situation-specific.
The effects of all of the factors listed above are mitigated by the use of many events (typically 50-100 lines) for each location and a very robust location algorithm which iteratively eliminates the outlying lines and converges on a most likely location.
Roughly speaking, if the imaging system has a spatial resolution w, and N events are used to determine a single location, the expected uncertainty in location is w/√N. Typical values of w=6mm and N=50 give an uncertainty of around 1mm.