Abstract text (incl. figure legends and references)

Energetic electrons do not deposit their energy locally at their Point of Entry (PoE) into the detector volume but statistically produce three-dimensional trajectories by multiple scattering. The energy deposition happens along these trajectories, typically extending over several pixels. The output of the pixelated semiconductor-based detector system is a binned two-dimensional projection of the energy deposition. However, to get images with a high spatial resolution, not the energy deposition into the detector volume is of interest but the precise PoE of the primary electrons into the detector volume.

We developed a convolutional neural network (CNN) whose output is a frame-wise probability map. The probability map describes the probability that each physical pixel contains a PoE map with values between zero and one. The CNN has no fully-connected layers and, therefore, applies to different physical detector sizes without retraining. The modular design of the CNN also enables the fast adaptation to different primary energies and physical pixel sizes via transfer learning.

For a primary energy of 300 keV, a modulation transfer function (MTF) of 0.77 at a Nyquist frequency of 0.5 is obtained from a slanted edge [1, 2]. For comparison, the MTF obtained using conventional state-of-the-art PoE reconstruction methods is below 0.4 at a Nyquist frequency of 0.5 [2]. The MTF is constant up to a rate of 0.04 e - /pix/frame and decreases slowly for higher rates. Therefore, the CNN can provide a precise reconstruction even with higher electron rates.

Moreover, the CNN can be expanded by a super-resolution module to enable probability maps with subpixel resolution of a factor of four by four. The super-resolution shows its full power for primary energies below 120 keV. For these energies, the energy depositions in the pixel structure are dominated by systematic effects like diffusion and repulsion and not by stochastic effects like multiple scattering. Therefore, a more precise reconstruction of the PoE is possible.

Using the presented CNN to reconstruct the PoE of individual primary electrons frame-wise enables a high spatial resolution, which can be extended to subpixel resolution for lower primary energies. Application examples will be provided.

[1] B. Eckert et al., Electron Imaging Reconstruction for Pixelated Semiconductor Tracking Detectors Using the Approach of Convolutional Neural Networks, submitted to IEEE, Transaction on Nuclear Science (2021)

[2] International Organization for Standardization, Photography - Electronic Still Picture Imaging-Resolution and Spatial Frequency Responses, ISO 12233:2017, ISO (2017)