KAHIBARO
37.5. Photodetectors
Table of Contents
PMTs
Photomultiplier tubes, or PMTs, are vacuum photodetectors that convert faint bursts of optical photons into electrical pulses with large gain. In GATE, they are not modeled at the detailed level of dynodes and electron trajectories. Instead, you typically represent a PMT by a sensitive surface or volume placed after an optical interface and by a statistical model of photon detection and signal generation.
The first step is geometric. You place a volume that represents the photocathode or the front face of the PMT, in contact with the scintillator or with an optical window. Optical surfaces between the scintillator and the photocathode determine reflection, refraction, and transmission. These surfaces are defined elsewhere in the course, so here you only need to know that the PMT will detect only those optical photons that cross into its sensitive region.
Quantum efficiency is the key parameter that links incoming optical photons to photoelectrons. In GATE, this is handled through the optical properties of the photocathode material or surface. You typically specify a wavelength dependent quantum efficiency, so that only a fraction of the photons with a given wavelength are converted to primary electrons. The Monte Carlo engine then samples for each photon whether it is detected or lost. The actual internal multiplication of electrons in the dynode chain is not tracked; instead you model it statistically.
PMTs provide large gain, often of the order of $10^6$ to $10^7$, which turns a few photoelectrons into a measurable pulse. In GATE based simulations, this gain is usually not represented as individual electrons but as a proportional scaling of the detected photon count into an energy or charge signal later in the digitizer chain. You can add energy and time blurring there to mimic the combined effect of gain fluctuations, transit time spread, and electronic noise.
One important aspect for optical simulations is the time response of the PMT. The arrival time of the first detected photons and the distribution of detection times influence timing resolution. PMT transit time spread is usually modeled as an additional Gaussian time smearing applied in the digitizer. You choose a standard deviation that matches the PMT timing specification and apply this smearing to each detected hit time. The resulting distribution of detection times contributes to the coincidence timing resolution in applications such as PET.
The spectral sensitivity of PMTs must match the scintillator emission spectrum. In GATE, this is captured by using consistent wavelength dependent properties for the scintillator light yield and for the PMT quantum efficiency. Photons outside the sensitive range of the PMT will usually be lost, so defining realistic spectra is crucial if you want to estimate detection efficiency. Angular dependence of the photocathode response can also be approximated through the reflectivity and transmission of the optical surface.
PMTs are typically used as large area detectors. In simulations, you may either model a separate PMT for each crystal or couple multiple crystals to a common PMT. The second case is common in older gamma cameras, where position information is reconstructed from the ratio of signals in several PMTs. In GATE, this type of light sharing is reproduced by allowing optical photons to travel from a scintillator block to several PMT photocathodes. The number of photons detected in each PMT provides the basis for position reconstruction in the digitizer and in the later data analysis.
You should also be aware of saturation and nonlinearity effects. Real PMTs show a reduced gain at very high light levels. In most basic simulations, you can ignore this and treat the detector as linear, but for high precision work you might introduce a nonlinear transfer function in the digitizer, which maps the number of detected photons to a measured amplitude. This function can be defined to match measured calibration data.
PMTs are sensitive to magnetic fields and require high voltage. These engineering constraints are not directly simulated in GATE. For medical physics applications, you mainly care about the resulting performance parameters: detection efficiency, timing resolution, and spatial resolution. PMT models in GATE should therefore be tuned to reproduce these macroscopic performance figures rather than internal device physics.
Important PMT modeling points:
- Define a photocathode region and appropriate optical surfaces so that only transmitted photons can be detected.
- Use a realistic, wavelength dependent quantum efficiency to convert optical photons into detected events.
- Apply gain and timing models at the digitizer level to reproduce energy resolution and transit time spread, instead of simulating internal electron multiplication.
SiPMs
Silicon photomultipliers, or SiPMs, are solid state photodetectors composed of many microcells, each operated in Geiger mode. In GATE, SiPMs are treated in a similar way to PMTs at the macroscopic level: photons that reach the sensitive silicon surface may be detected with a probability equal to the photon detection efficiency, and the detailed avalanche processes are not tracked. However, SiPMs have distinctive characteristics that you should represent in your simulation model when possible.
Geometrically, you usually represent a SiPM as a small rectangular or square area coupled directly to a crystal, sometimes through an optical glue or a light guide. You define an optical surface between the crystal and the SiPM and assign optical properties that approximate the real interface, including reflectivity and refractive indices. Since SiPMs are pixelated, in many detectors you simulate an array of SiPM pixels, each associated with a separate optical surface and sensitive volume. This enables you to study light sharing, spatial resolution, and edge effects.
Photon detection efficiency, often abbreviated PDE, is the SiPM equivalent of PMT quantum efficiency, but it includes several factors in one value: quantum efficiency, Geiger probability, and fill factor. In GATE, you typically define the PDE as a wavelength dependent property of the SiPM material or surface. Each incoming photon is then accepted or rejected based on this probability. A realistic PDE curve is essential to predict the number of fired microcells and the resulting energy resolution.
Because SiPMs consist of many microcells, they show saturation when many photons arrive within the same recovery time. There is a finite number of cells, so the detected signal cannot grow linearly forever. Basic optical simulations in GATE often ignore cell level saturation and treat the detector as linear if the number of detected photons is well below the number of cells. For more advanced work, you can approximate saturation by applying a nonlinear mapping from detected optical photons to signal amplitude in the digitizer. For example, if $N_{\text{cells}}$ is the number of microcells and $N_{\gamma}$ is the number of photons that reach the SiPM, you may use an analytical expression of the form
$$
N_{\text{fired}} = N_{\text{cells}} \left( 1 - e^{ - \frac{\text{PDE} \cdot N_{\gamma}}{N_{\text{cells}}} } \right),
$$
then convert $N_{\text{fired}}$ into an energy or charge signal.
SiPMs also exhibit dark counts, optical cross talk, and afterpulsing. These noise processes introduce extra pulses that are not directly related to the scintillation light. GATE does not generate dark counts by default; instead, you can approximate their impact at the digitizer or analysis stage by adding a random background of low amplitude signals or by introducing additional noise into the energy and time measurements. For many medical imaging simulations, you focus on the dominant contribution of scintillation photons and incorporate noise implicitly into the energy and timing resolution parameters.
Timing performance of SiPMs is a key reason for their use in time of flight PET. SiPMs can provide very fast response, with small transit time spread. In GATE, optical photons propagate through the scintillator with finite speed, and their arrival times at the SiPM surface are simulated explicitly. You then apply an additional timing jitter that represents the intrinsic time resolution of the SiPM and the associated electronics. A common approach is to sample a Gaussian smearing for each detected photon or for each summed signal, then take an effective detection time such as the first photon time or a weighted mean. The combination of scintillator decay time, optical transport, and SiPM jitter determines your overall timing resolution.
The coupling between the scintillator and SiPM is often more direct than for PMTs. This can improve light collection efficiency but also makes the simulation sensitive to surface treatment. You might define different optical properties for polished, ground, or wrapped crystal surfaces and experiment with reflectors or air gaps to see how the number and distribution of photons at each SiPM pixel change. In GATE, these effects are controlled through material properties and optical surfaces rather than explicit SiPM settings.
SiPM arrays are commonly used as position sensitive detectors in both PET and SPECT. When you simulate an array, you obtain separate photon counts or signals for each pixel. The distribution of counts across the array can be analyzed to estimate interaction positions in the scintillator volume, either by simple center of gravity calculations or by more advanced methods. GATE itself records the optical photon hits at each sensitive volume; you implement the reconstruction logic in your digitizer configuration or in your data analysis scripts.
Temperature dependence, gain variations, and nonuniformity across SiPM pixels are system level effects that you may choose to include or ignore depending on your goals. If they are important, you can assign different PDE values or gain factors to different SiPM volumes, or introduce pixel dependent energy blurring. This allows you to reproduce measured maps of detector response and to investigate calibration strategies.
Key SiPM modeling aspects:
- Represent the SiPM as a pixelated sensitive surface coupled to the crystal and define realistic optical interfaces.
- Use a wavelength dependent photon detection efficiency to convert optical photons into fired cells, and consider using a saturation model when many photons are expected.
- Include timing jitter and energy blurring at the digitizer stage to capture the combined effect of SiPM response and electronics, which is essential for time of flight and energy resolution studies.
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