KAHIBARO
18.2 Creating Singles
Table of Contents
Energy
In GATE, singles represent detector events that have already passed through the digitizer chain. Creating singles is therefore not done by hand, but by configuring the digitizer so that raw hits are transformed into realistic energy, position, and time measurements. For energy, this starts from the sum of deposited energy in the sensitive volume, then applies detector effects.
The digitizer typically first groups hits that belong to the same detector channel and event. Within a crystal or pixel, the energy deposits from all steps are summed into a single value, often called the measured energy. This summation is crucial, because the detector electronics do not distinguish individual microscopic interactions; they respond to the total light or charge produced.
After energy summation, energy blurring is applied to mimic finite energy resolution. In a simple Gaussian model, the measured energy $E_\text{meas}$ is sampled from a normal distribution centered on the deposited energy $E_\text{dep}$ with a standard deviation $\sigma(E_\text{dep})$ that depends on energy. A common parameterization uses the relative full width at half maximum (FWHM) at a reference energy, for example at 511 keV for PET or 140 keV for Tc-99m. The connection between FWHM and the Gaussian standard deviation is:
For a Gaussian peak:
$$\text{FWHM} = 2.355 \,\sigma$$
so
$$\sigma = \frac{\text{FWHM}}{2.355}.$$
If the detector has a relative energy resolution $R$ at an energy $E_0$, then its FWHM at that energy is $R \times E_0$, and $\sigma$ follows directly. In GATE, you configure such parameters when you add the energy blurring step to the digitizer. The singles then store the blurred energy, not the ideal deposited energy; this is what you will later use to build spectra and apply energy windows.
After blurring, energy thresholds are applied. A lower threshold removes events whose measured energy is too small to be detected reliably, for example below electronic noise or below a scatter rejection level. An upper threshold can also be set to exclude extremely high energy deposits that are outside the useful range for a given modality. Only events with energy inside the configured energy window survive to become singles. By adjusting blurring parameters and thresholds, you control both the realism of the singles and the balance between sensitivity and noise in your simulated detector data.
Position
The position recorded in singles represents the detector channel that produced the signal, not the microscopic location of each interaction. In hits, you have precise interaction coordinates; in singles, you typically have crystal, pixel, or channel coordinates, sometimes with additional information like module or ring identifiers.
When the digitizer groups hits, it uses the volume hierarchy and readout configuration to map them to a specific detector element. For example, many PET scanners have a hierarchy with rings, modules, and crystals. The digitizer can translate this hierarchy into integer IDs stored in each single, such as crystal ID, module ID, and ring ID. These IDs uniquely identify the spatial channel in which the energy was recorded.
In some configurations, the position stored in the singles is the nominal center of the detector element, such as the crystal center. This means that the recorded spatial resolution is limited by the detector segmentation. In other configurations, especially for continuous crystals or pixelated detectors with position reconstruction, the digitizer can apply spatial blurring, which adds a Gaussian displacement to the ideal position to mimic limited intrinsic and readout resolution.
The singles output can therefore contain both discrete identifiers and continuous coordinates. A typical situation looks like this:
| Quantity | Role in singles |
|---|---|
| Crystal / pixel ID | Identifies the detection element |
| Module / ring ID | Higher level location, scanner geometry indexing |
| Position (x, y, z) | Reconstructed or element-center coordinates |
| Position blurring | Models intrinsic and electronic spatial resolution |
When you create singles through the digitizer configuration, you decide which of these quantities are written. For later analysis, you often reconstruct the physical position of detection from IDs and geometry, or directly use the recorded coordinates if they are provided. For coincidence sorting and line of response building, consistent and correctly configured positions in singles are essential, since they define the endpoints of each coincidence pair in PET and the projection bin in SPECT or CT-like setups.
Time
The time stored in singles represents the detection time of the event as seen by the electronics, which is derived from the underlying interaction times stored in hits. Similar to energy and position, the digitizer transforms microscopic information into a realistic, macroscopic timestamp.
For each detector channel, hits have time stamps that correspond to the physical time of each interaction. The digitizer selects or combines these times to obtain one representative time per single, for example the time of the first interaction or a light collection timing model. This ideal detection time is then blurred to simulate finite timing resolution of the detector and readout.
Timing blurring is usually modeled as a Gaussian smearing around the ideal time, with a standard deviation determined by the detector timing resolution. If your detector has a coincidence timing resolution $\Delta t_\text{FWHM}$, the Gaussian standard deviation of the time blurring is:
Timing resolution conversion:
If timing FWHM is $\Delta t_\text{FWHM}$, then
$$\sigma_t = \frac{\Delta t_\text{FWHM}}{2.355}.$$
In GATE, you specify this timing blur in the digitizer configuration. The singles then carry blurred time values that reflect realistic detector performance. These times are important for several reasons. In PET, they are used by the coincidence sorter to identify pairs of singles that occur within a coincidence time window, thereby forming coincidence events. In time of flight PET, the time difference between two singles in a pair is directly related to the position of the annihilation along the line connecting the detectors. In SPECT or CT-like acquisitions, time can be used to relate detected events to acquisition phases or gantry angles.
When you create singles, you must also ensure that the simulation includes a proper time structure for the source and acquisition. The total acquisition time, activity, and rate of events influence the distribution of detection times. By controlling both the source time structure and the digitizer timing configuration, you obtain singles whose time stamps are suitable for coincidence sorting, dead time models, or time-dependent studies in your GATE simulations.
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