KAHIBARO
32.2. Projection Angles
Table of Contents
Number of projections
In SPECT, a complete acquisition consists of several projections, each acquired at a different camera angle around the patient or phantom. The number of projections determines how finely you sample the object in angle, and it has a strong impact on both image quality and scan time.
In a GATE simulation you typically specify the number of projections in your motion or acquisition loop. Conceptually, you choose an integer $N_{\text{proj}}$ that tells GATE how many distinct camera positions will be simulated over a full or partial rotation.
You usually combine three ingredients when you plan the number of projections: the total rotation angle (for example, 180 degrees or 360 degrees), the desired angular resolution, and the available statistics per projection. For a fixed total number of emitted photons, if you increase $N_{\text{proj}}$, each projection will receive fewer counts. This improves angular sampling but increases the noise in individual projections.
The choice of $N_{\text{proj}}$ is therefore a trade‑off between angular sampling and per‑projection statistics. In a simulation, you can study this trade‑off explicitly by running the same geometry and source with different numbers of projections while keeping total activity or total simulated time constant.
A simple way to think about the number of projections is to relate it to the intrinsic spatial resolution of the gamma camera and the size of the object. For larger objects or high‑resolution collimators, a larger number of projections is often beneficial. For preliminary tests or debugging, however, you might select a small number, such as 8 or 16 projections, to reduce computation time. Once the setup is correct, you can increase $N_{\text{proj}}$ to values typical of clinical protocols, for example 60 or more projections over a full rotation, depending on the application.
In GATE, the number of projections usually appears in your control logic, for example a loop index that moves the detector through successive angles and launches a simulation segment at each position. The exact implementation details belong to the more general SPECT acquisition scripting, but when you set or change the number of projections, keep in mind how it will modify angular sampling and photon statistics across your dataset.
For a fixed total number of simulated photons, increasing the number of projections improves angular sampling but increases noise per projection because each view receives fewer counts.
Angular step
The angular step is the angular distance between two consecutive projection angles. If you perform a total rotation of $\Theta_{\text{tot}}$ degrees with $N_{\text{proj}}$ projections that are evenly spaced, the angular step $\Delta \theta$ is given by
$$
\Delta \theta = \frac{\Theta_{\text{tot}}}{N_{\text{proj}}}.
$$
In a typical SPECT acquisition you choose $\Theta_{\text{tot}}$ and $N_{\text{proj}}$, and then compute $\Delta \theta$ from this relation. For example, if you want a full 360 degree rotation with 60 projections, the angular step is 6 degrees. If you simulate a 180 degree acquisition with 30 projections, the angular step is also 6 degrees.
The table below shows a few common combinations of total rotation, number of projections, and the corresponding angular step:
| Total rotation $\Theta_{\text{tot}}$ | Number of projections $N_{\text{proj}}$ | Angular step $\Delta \theta$ |
|---|---|---|
| 180° | 30 | 6° |
| 180° | 60 | 3° |
| 360° | 60 | 6° |
| 360° | 120 | 3° |
In GATE, you use the angular step to update the detector orientation between projections. Conceptually, if $\theta_0$ is the starting angle, the $k$‑th projection angle is
$$
\theta_k = \theta_0 + k \, \Delta \theta, \quad k = 0, 1, \ldots, N_{\text{proj}} - 1.
$$
You can implement this rule in Python by changing the rotation of the detector head for each projection. The coordinate system and the rotation axis depend on your scanner geometry, but the idea is always to apply a consistent angular increment.
The angular step directly influences the sampling of the sinogram. If $\Delta \theta$ is too large, some structures in the object may be undersampled in angle, which leads to artifacts or loss of resolution in reconstructed images. If $\Delta \theta$ is small, angular sampling improves, but you need either more total counts or longer simulation time to keep the noise level acceptable, since the counts are distributed across more projections.
In practice, you choose an angular step to match clinical or experimental protocols you want to emulate, or to explore how angular sampling affects image quality. In GATE simulations this means adjusting $\Delta \theta$ together with the number of projections and the total rotation, checking that the resulting set of projection angles covers the desired angular range without gaps or overlaps.
For evenly spaced projections, the angular step must satisfy
$$
\Delta \theta = \frac{\Theta_{\text{tot}}}{N_{\text{proj}}}.
$$
Choosing a smaller $\Delta \theta$ (more projections for the same total rotation) improves angular sampling but reduces counts per projection if total statistics are kept constant.
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