KAHIBARO
31.2. Collimator
Table of Contents
Parallel-hole collimator
In a gamma camera, the collimator is the front component that decides which photons are allowed to reach the scintillation crystal. For beginners, it helps to think of it as a heavy metal plate with many long, narrow holes. Photons that travel almost straight along the hole axis pass through, while photons that come from other directions are absorbed by the collimator material. This converts an essentially directionless photon field into a direction-selective system, which is what creates an image.
In GATE, a parallel-hole collimator is usually modeled as a relatively thin but dense volume placed directly in front of the detector crystal. Because it consists of many repeated holes and septa, you rarely build each individual hole explicitly as a separate volume in a beginner simulation. Instead, there are two main approaches.
The first approach is to approximate the collimator as a uniform slab of material and handle geometric response later in analysis. This is useful only for very simplified or non-imaging studies and is generally not appropriate if your goal is to study realistic image formation or angular response.
The second and more realistic approach is to explicitly model the repeated hole pattern using repeated or parameterized volumes. Here, you create a base hole cell and repeat it in two dimensions to cover the detector area. Each repeat contains both the hole and the surrounding septa, or you build the pattern as two interlocking volume types for holes and septa. This is closer to what is actually used in clinical gamma cameras and is what you should aim for in an imaging focused GATE simulation.
A parallel-hole collimator is called “parallel-hole” because the axes of all the holes are parallel to each other and perpendicular to the crystal surface. This means that, in a basic geometry, the collimator can be represented by holes aligned along the global z axis, with the gamma camera detecting photons coming roughly along that axis from the patient or phantom.
Clinically, different parallel-hole collimators are used for different radionuclides and clinical tasks, such as low-energy high-resolution (LEHR), low-energy high-sensitivity (LEHS), or medium-energy collimators. The names reflect tradeoffs between spatial resolution and sensitivity. When you build a gamma camera in GATE, you usually start by choosing one such design and translating its nominal parameters, for example hole diameter and length, into your geometry configuration.
Hole geometry
The key parameters that define hole geometry are hole shape, hole size, hole length, and the pattern in which the holes are arranged. These geometric choices control the two most important performance quantities of a collimator: spatial resolution and sensitivity.
Clinical collimators often use hexagonal holes, because hexagons pack efficiently and provide good symmetry. For beginners, however, square or circular holes are easier to build in GATE. Square holes can be made with simple boxes and regular repetitions, while circular holes are typically approximated using cylindrical tubes or Boolean operations.
For each hole, you need at least an in-plane dimension and a length. In GATE, it is convenient to define:
Hole length $L$
Hole width or diameter $d$
Collimator thickness $t$ (often equal to $L$ for straight, non-tapered holes)
The effective spatial resolution at a distance $z$ from the collimator face, which we can call $R(z)$, can be approximated for a simple parallel-hole collimator by a relation of the form
$$
R(z) \approx d \left(1 + \frac{z}{L}\right),
$$
where $d$ is the hole diameter or width and $L$ is the hole length. This shows that longer holes improve resolution, because for a fixed $z$ the factor $z / L$ becomes smaller. At the same time, longer holes reduce the number of photons that reach the crystal, so the sensitivity decreases.
Sensitivity $S$ of a parallel-hole collimator is approximately proportional to the solid angle of acceptance of a hole. For simple designs, and ignoring septal penetration, you can remember that:
Smaller holes and longer holes improve resolution but reduce sensitivity.
Larger holes and shorter holes improve sensitivity but worsen resolution.
In GATE, you implement the hole geometry by combining the base hole shape and its repetition. A typical gamma camera head might have hundreds of thousands of holes, but you never define all of them manually. Instead, you define a basic unit cell of size $p_x \times p_y$ that contains one hole of size $d_x \times d_y$ in the center and septa on all sides. Then, you repeat this unit cell across the detector face using parameterized or replicated volumes, which is much more efficient and less error prone.
It is important to align the holes correctly relative to the crystal. For a head whose crystal normal is the positive z direction, you place the collimator so that the holes are aligned along the same direction, and their exit plane is in contact with the crystal entrance face. Incorrect alignment will give physically meaningless angular acceptance.
You should also ensure that the collimator thickness matches the physical design you intend to simulate. If you are modeling a low-energy collimator, the thickness can be relatively modest. For medium or high energy radionuclides, the collimator may need to be significantly thicker to reduce septal penetration. That choice will be discussed further when considering the material and septa, but the hole length and hole geometry must be consistent with it.
Septa
Septa are the walls between neighboring holes, typically made of a high density, high atomic number material such as lead or tungsten. They are responsible for stopping photons that approach at large angles or that try to pass from one hole to another. In a GATE geometry, septa occupy all the space that is not part of a hole in the collimator volume.
The main septal parameter is the septal thickness, which is the minimum distance between adjacent holes. If the hole pitch is $p$ and the hole diameter or width is $d$, then the septal thickness $s$ is
$$
s = p - d.
$$
This simple relation helps you design a consistent pattern. In a real collimator, the pitch and hole shape determine how septa connect in a grid or honeycomb structure. When you build the geometry in GATE, you usually define the unit cell so that its external size is the pitch in each direction, and then you carve out the hole inside that cell. What remains is the septal material.
From a physics perspective, septal thickness must be large enough to stop photons that might otherwise pass through diagonal paths or from neighboring holes. If the septa are too thin for the photon energy you simulate, septal penetration and septal scatter become significant. This produces image artifacts such as loss of contrast, image blur, and additional background.
For a simple rule of thumb, you can relate septal thickness and attenuation length in the collimator material. If $\mu$ is the linear attenuation coefficient of the septal material at the photon energy of interest, the fraction of photons transmitted through a septum of thickness $s$ is
$$
T = e^{-\mu s}.
$$
To limit septal penetration, you want $T$ to be very small, which means that $s$ should be several attenuation lengths. In practice, collimator manufacturers choose combinations of septal thickness and hole length that achieve acceptable penetration for the radionuclides in question. When reproducing an existing collimator in GATE, try to obtain these nominal parameters from technical documentation.
In beginner simulations, you might not explicitly tune septal thickness using detailed analytical calculations. However, you should still ensure that:
Septa are made of a dense material such as lead or tungsten.
Septal thickness is not unrealistically small for the photon energy you simulate.
Hole and septal dimensions are consistent, with $s = p - d$.
In GATE, septa can be implemented in several ways. One approach is to define a large lead plate and then subtract holes using Boolean operations. Another, more scalable method uses a repeated pattern where each unit cell is primarily lead and includes a carved out cavity for the hole. Replication in x and y produces the full collimator.
Because collimators have many small features, your choice of step size and production cuts in the collimator region can affect both accuracy and performance. For example, if you choose very small production cuts in the collimator, transport can become slow due to many short steps in a dense material. On the other hand, overly coarse settings can misrepresent septal scatter. It is good practice to assign a separate region to the collimator and check that your physics and cut settings are reasonable, without going into the detailed physics configuration that is handled in other chapters.
When you combine hole geometry and septa correctly in GATE, and place the collimator in front of the crystal, you obtain a gamma camera model that can reproduce key imaging characteristics such as spatial resolution and angular response, which are essential in SPECT simulations.
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