KAHIBARO
28.2. Energy Selection
Table of Contents
511 keV photopeak
In PET, almost all useful coincidence events come from the two 511 keV photons produced when a positron annihilates with an electron. When these photons are fully absorbed in a scintillation crystal, the measured energy is close to 511 keV and forms a characteristic peak in the detected energy spectrum, called the 511 keV photopeak.
In a GATE PET simulation, you usually observe this photopeak in either singles or coincidence energy spectra after digitization. The raw energy deposition in a crystal is first summed over hits, then blurred by the detector energy resolution. Because of this finite resolution, the photopeak is not a single line at 511 keV but a broadened peak with a width that is often characterized by the full width at half maximum, FWHM. For a detector with energy resolution $R$ at 511 keV, you often express it as a percentage:
$$
R = \frac{\text{FWHM}}{E_0} \times 100\%
$$
with $E_0 = 511 \,\text{keV}$.
For PET energy selection, the 511 keV photopeak is the primary feature of interest. You must always take detector energy resolution into account, because the measured peak is broadened and not exactly at 511 keV for every event.
In simulated spectra, you may also see a continuum below 511 keV from Compton scattered photons, both those that scatter in the patient or phantom and those that scatter inside the detector before being absorbed. These events deposit less than 511 keV and populate lower energies. Identifying the photopeak means locating the local maximum around 511 keV and understanding how much of the spectrum below it is scatter.
In practice, you often begin by plotting a histogram of detected energies from singles or coincidence data and visually identify the photopeak region. Because you control the detector model and blurring in GATE, you can predict approximately where the peak should appear and what width it should have given your specified resolution.
PET energy windows
Energy selection in PET is implemented by defining an energy window around the 511 keV photopeak. The goal is to keep as many true, unscattered annihilation photons as possible and reject as many scattered photons as possible. This selection is applied to the energy of singles before forming coincidences, or to the energies in coincidence events, depending on your digitizer chain.
An energy window is usually defined by a lower and an upper energy threshold. For a nominal 511 keV photopeak, common clinical-like settings are for example 350 to 650 keV, or 400 to 600 keV. The lower threshold removes most scattered photons that lost a significant amount of energy, and the upper threshold removes events with abnormally high reconstructed energy, for example from pile up or multiple interactions summed together.
In GATE you typically configure the PET energy window as part of the digitizer. Singles that do not pass the energy window are discarded and do not contribute to coincidence formation. This has a direct impact on the number of random, scatter, and even true coincidences. A narrower window reduces scatter more effectively but also reduces sensitivity because some true events fall into the tails of the photopeak and are rejected.
You can think of the trade off in terms of accepted fraction of true events versus rejected scatter. If $N_\text{true}$ is the number of true events before energy selection and $N_\text{true,win}$ is the number that fall inside the window, then the true acceptance is
$$
f_\text{true} = \frac{N_\text{true,win}}{N_\text{true}}
$$
Similarly, for scatter events $N_\text{scat}$ and $N_\text{scat,win}$ the scatter acceptance is
$$
f_\text{scat} = \frac{N_\text{scat,win}}{N_\text{scat}}
$$
Ideal energy selection would give a high $f_\text{true}$ and a low $f_\text{scat}$, but in practice both depend on detector resolution and on how much scattering occurs in the object.
When choosing PET energy windows, always:
- Place the window around the 511 keV photopeak.
- Set a lower threshold high enough to reject most scattered photons.
- Avoid an excessively narrow window that removes too many true events, especially with poor energy resolution.
In a PET coincidence analysis workflow, energy selection is typically applied early. After running a simulation and producing singles or coincidence ROOT files, you can reproduce the same energy window in analysis by selecting events with energies between $E_\text{low}$ and $E_\text{high}$. This allows you to study how different energy windows affect sensitivity, scatter fraction, and count rates without rerunning the full simulation, as long as you initially saved events over a broad energy range.
As you explore PET performance metrics, it is useful to systematically vary the PET energy window and measure how the number of true, scattered, and random coincidences changes. In a GATE based study, you can quantify how tighter energy selection improves image quality indicators, at the cost of reduced statistics and longer acquisition or simulation times needed to achieve a given level of noise.
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