KAHIBARO
28.1. Coincidence Events
Table of Contents
Detector pair
In PET, a coincidence event links two detector elements that detect photons within a short time window. Each coincidence is defined by a detector pair, which is usually represented by the positions or identifiers of the two detectors that registered the photons.
In GATE PET simulations, singles are the individually processed detector events after digitization. The coincidence sorter examines these singles and pairs them if their detection times fall within the coincidence time window you have configured. The result is a list of coincidence events. For each coincidence, the output typically includes the identifiers of the two detectors, for example ring ID, module ID, and crystal ID for each side. From these, you can reconstruct the two 3D detection positions.
Once you know the positions of the two detectors in a coincidence pair, you can construct a line of response, or LOR, which is the straight line connecting the two detection points. The annihilation event that produced the coincidence photons is assumed to lie somewhere along this line. Later chapters on LORs and PET reconstruction use these detector pairs as the basic geometric input.
It is useful to keep track of how detector pairs are indexed. Some outputs store the full 3D coordinates of each detection. Others store only integer IDs that you must convert back to positions using your known scanner geometry. Consistency between your geometry definition and your coincidence analysis code is essential so that detector pairs map to correct spatial locations in the scanner.
In PET analysis, every coincidence event is fundamentally defined by a pair of detector locations, and these two points define the line of response used for image reconstruction.
Energy
Each coincidence is composed of two photons that have passed through the digitizer chain. For every side of the detector pair, GATE records an energy value that represents the measured energy in that detector element after all digitization effects such as energy summation, blurring, and thresholds.
In ideal PET, both photons from positron annihilation have an energy of 511 keV. However, in a realistic simulation, the recorded energies differ from 511 keV because of several effects. First, the photons can undergo Compton scattering in the patient, in detector components, or in shielding before reaching the scintillation crystal. This reduces the energy deposited in the detector. Second, even for unscattered photons, the detector has finite energy resolution, which is modeled in the digitizer as Gaussian blurring. Third, part of the energy may escape the crystal after a Compton interaction, especially near crystal edges, which also leads to measured energies below 511 keV.
For coincidence events, you can use the recorded energies on each side to select which events you consider valid. A typical PET analysis applies an energy window around the 511 keV photopeak for each photon, for example requiring that both recorded energies lie between a lower and an upper threshold. This reduces the number of scattered coincidences but also removes some true events. The exact energy window is chosen based on scanner performance and the trade off between sensitivity and noise.
When you examine coincidence output from GATE, you often find separate branches or fields for the energy of the first detector and the second detector in the pair, as well as an event level identifier. You can create histograms of these energies, check that the 511 keV peak is present, and tune your energy window. Later in this course, you will use coincidence energy to classify true, scattered, and random coincidences and to compute PET performance metrics.
Energy selection for coincidence events is usually implemented as a photopeak window around 511 keV for each photon, and this is one of the main tools to reduce scattered coincidences in PET.
Time
Time information is central to defining coincidence events in PET. Every single event produced by the digitizer carries a detection time. The coincidence sorter uses these times to decide whether two singles should be grouped into one coincidence. If the absolute time difference between two singles is smaller than the coincidence time window you configured, they are considered a coincidence pair.
Let the detection times of two singles be $t_1$ and $t_2$. The time difference is often defined as $\Delta t = t_1 - t_2$ or as its absolute value $|\Delta t|$, depending on the analysis. In GATE, each coincidence event usually stores the two detection times and sometimes the time difference. The criterion used by the sorter can be expressed as:
Two singles form a coincidence if their detection times satisfy
$$|\Delta t| = |t_1 - t_2| \leq \Delta t_{\text{window}}$$
where $\Delta t_{\text{window}}$ is the coincidence time window configured in the digitizer.
The choice of the coincidence time window directly affects the number and type of coincidence events. A narrow window reduces random coincidences because it is less likely that two unrelated singles fall within the allowed time difference. However, if the window is too narrow compared to the detector timing resolution, some true coincidences will be lost. A wide window increases sensitivity but also increases the fraction of randoms.
In time of flight PET, the same time information is used not only to decide whether two singles belong together, but also to estimate the position of the annihilation along the LOR. Even in non TOF PET, studying the distribution of time differences for coincidence events can help you understand detector timing performance, validate your digitizer settings, and optimize the coincidence window.
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