  3D-localization of gamma sources has the potential to improve the outcome of
radio-guided surgery. The goal of this paper is to analyze the localization
accuracy for point-like sources with a single coded aperture camera. We both
simulated and measured a point-like $^{241}$Am source at $17$ positions
distributed within the field of view of an experimental gamma camera. The setup
includes a 0.11mm thick tungsten sheet with a MURA mask of rank $31$ and
pinholes of $0.08$mm in diameter and a detector based on the photon counting
readout circuit Timepix3. Two methods, namely an iterative search (ISL)
including either a symmetric Gaussian fitting or an exponentially modified
Gaussian fitting (EMG) and a center of mass method were compared to estimate
the 3D source position. Considering the decreasing axial resolution with
source-to-mask distance, the EMG improved the results by a factor of $4$
compared to the Gaussian fitting based on the simulated data. Overall, we
obtained a mean localization error of $0.77$mm on the simulated and $2.64$mm on
the experimental data in the imaging range of $20$mm to $100$ mm. This paper
shows that despite the low axial resolution, point-like sources in the
nearfield can be localized as well as with more sophisticated imaging devices
such as stereo cameras. The influence of the source size and the photon count
on the imaging and localization accuracy remains an important issue for further
research. The acquired datasets and the localization methods of this research
are publicly available on GitHub at "https://zenodo.org/records/11449544".
