Image processing for X-ray and electron detection based on neural networks for pixelated semiconductor detectors

The analysis of large data sets in physics experiments profits from recent advances in machine learning techniques based on neural networks. The strength of this approach relies on the existence of validated calibration data called ground truth and reliably tested numerical simulations. Especially in recent years, the widespread use of neural networks gained momentum because of the continuous supply of software and a substantial increase in computer processing power. This continuous increase also impacts applications based on neural networks in analyzing data acquired by pixelated semiconductor detectors.
The user at a beamline experiment expects the event parameters such as the position of the radiation in terms of the point of entry on subpixel level and the amplitude, which describes the energy deposition, the number of photons, or the number of electrons. In electron microscopy, energetic electrons produce three-dimensional tracks in the detector volume and do not deposit their energy locally at their point of entry. The energy deposition happens along these tracks, typically extending over several pixels. However, the user is not interested in the tracks of the primary electrons but in the precise point of entry. In crystallography experiments, the online indexing of the Laue diffraction patterns enables new opportunities. That means all sensor and electronics artifacts need to be analyzed and corrected in real-time.
Four different methods based on neural networks are developed for different event rates on the detectors to precisely determine the point of entry and the intensity of the radiation on the detector. The developed methods enable the reconstruction of positional information and intensity images in real-time at high frame rates. For further physics analyses, no additional detector corrections need to be performed. For X-rays, subpixel resolution has been achieved of less than 10 % of the pixel dimensions. For 300 keV electrons in transmission electron microscopy (TEM), the point of entry in the detector was determined precisely (40 µm) although they produce a track of more than 450 µm in the silicon.
Crucial for the development and testing of the neural networks are large data sets containing, on the one hand, the unanalyzed raw data of the detector system and, on the other hand, the associated exact entry points of the primary radiation, e.g., by simulations. The requirement for the unanalyzed dataset is a physically accurate description of the signal formation in the individual pixels.
For this purpose, the primary particles' behavior in the detector volume and the signal response of the individual pixels are physically described and modeled. The results are implemented in a Monte Carlo simulation. Numerous measurements have verified the Monte Carlo data.
Finally, the newly developed neural networks are compared with the previously used methods in terms of parameters such as spatial precision and analysis speed based on simulated data and performed measurements. We have executed a series of measurements with a transmission electron microscope at different electron intensities and energies to test and verify the developed methods. The results based on the use of neural networks are in good agreement with the precisely known points of entry from the TEM and the simulated data. An X-ray data set with 1.3 keV X-rays yielded a position resolution of better than 3 µm - again, in good agreement with experimental data from an X-ray microscope. The performance of the developed algorithms paves the way to real-time data analysis and data reduction.
In this sense, this work provides a basis and fundamental understanding for future advanced data analysis applications for pixelated semiconductor detector systems.