The simulated data was analyzed following the same steps adopted in the analysis of experimentally measured data [
6]. In each module, we selected pixels with more than 120 keV of deposited energy to avoid possible noise contribution. Compton events were identified as the ones where exactly two pixels fired in a module and the sum of their energies corresponded to the energy of the incident gamma.
Since the single-side readout detector matrices simulated in this study could not provide the depth-of-interaction information, Compton scattering of 511 keV gammas resulted in an ambiguous detector response for
°. In events where two pixels fire with comparable energies, one cannot determine which one acted as the scatterer and which as the absorber. To reconstruct Compton scattering angle
, the pixel with the lower deposited energy is considered the scatterer, i.e., the one where the recoil electron is absorbed, since 511 keV gammas predominately scatter forward. To check this assumption, we compared the reconstructed scattering angle
with the true scattering angle
known from the simulation. This is shown in
Figure 4 for GAGG detector. It can be seen how
is assigned to
and the ambiguity for scattering angles
° is visible. We quantify this effect in
Table 2 and
Table 3, for GAGG and LYSO configurations, respectively. The study showed that up to approximately 60% of events were correctly reconstructed for the theta ranges of interest. The tables also show the percentage of correctly reconstructed angles in two ranges of interest,
and
, and it is higher in the latter case. It is also clear that this percentage depends on the event topology, growing with increasing inter-pixel distance,
d. This is expected since the backward Compton scattering results in the lower energy of the scattered gamma, which, on the other hand, has a shorter absorption length.
Finally, the Compton scattering angle,
, is calculated according to Compton scattering kinematics:
where
and
are the energies of the incoming and the scattered gammas, respectively. The recoil energy of the electron deposited inside the pixel is then
=
.
To reconstruct the azimuthal scattering angle
in each module, the distances
and
between the first and second fired pixels in
x and
y directions, respectively, were calculated (
Figure 5). Angle
could then be obtained by using the formula: