Efficient Data Acquisition and Parameter Estimation for Gamma-Ray Detectors and Other Sensors

Abstract

Gamma-ray detection is extensively used in areas such as astronomy, nuclear physics, and medical imaging. There are many different ways a gamma-ray can interact with a detector; for instance, it can transfer just a portion of its energy, or it can transfer all its energy, and in both cases produce a complex cascade of ionization events. The amount of information that can be extracted from each event signal depends on the way the data is acquired and the method utilized to estimate gamma-ray parameters. Parameters that can be estimated from the interaction event include the energy deposited, direction, position of interaction, and time of interaction. Energy, concentration, and distribution of the source can then be estimated from this data. We explored the use of Fisher information to quantify the amount of energy and timing information in digitized gamma-ray signals, and a related parameter called the Cramer-Rao lower bound to estimate the best resolution a detector can achieve. We developed an energy and timing estimation method based on maximum-likelihood. Based on the Fisher information analysis and maximum-likelihood estimation results, we developed a novel analog-to-digital conversion method for gamma-ray signals based on sigma-delta modulation that maintains statistical information on gamma-ray waveforms, but is less complex and less costly compared to conventional analog-to-digital converters. Lastly, we designed, built, and characterized a sigma-delta-modulation-based read-out electronics board for gamma-ray cameras. The novel read-out architecture allows to implement waveform digitization and acquisition in imaging systems with a large number of channels and with different types of sensors, such as photomultiplier tubes, avalanche photodiodes, and silicon photomultipliers.