Optimization With Simulated Annealing and Experimental Study of a Discretized Position Circuit (DPC) Network Using an Array of SiPMs

Arrays of tens or even hundreds of silicon photomultipliers (SiPMs) coupled to scintillators to build compact and robust position-sensitive radiation detectors are becoming ubiquitous in nuclear medicine devices. In order to reduce the number of read-out electronic channels, and still be able to keep position information, multiplexing the SiPM signals with 2-D resistor networks is fairly common. Good results are obtained with the discretized positioning circuit (DPC) configuration. Even though it is a simple topology with a minimum number of discrete components, it yields good peak/valley ratios. However, it has the disadvantage that the network is asymmetric in
$X$
and
$Y$
directions, leading to different paths for the signal to reach the output depending on the position of the event. This causes the pulse shape to be also dependent on the position of the interaction in the detector, and creates a distortion (pincushion or barrel) of the position determined with center of energy algorithms. This effect can be partially remedied by a nonhomogeneous choice of resistors in the network, but finding the best resistor values, in the case of large SiPM aggregations is very time consuming. We have developed a framework to optimize resistor values in DPC configurations to minimize position distortion and then impose that every SiPMs see an impedance to ground as similar as possible. We solved the DPC circuit and employed a simulated annealing algorithm to explore thousands of resistor combinations. The best combinations found in the computer were implemented in the laboratory confirming the results of the simulated annealing algorithm. In addition, we have verified that the optimized DPC network preserves the pulse shape to the extent that pulse shape discrimination makes it possible to disentangle two different scintillator layers (phoswich) of LYSO and GSO.