Mathematical modelling and study of the encoding readout scheme for position sensitive detectors

TL;DR

This paper introduces a graph-based mathematical model for encoding readout schemes in position-sensitive detectors, enabling systematic construction and optimization of schemes with proven prototypes tested on MRPC detectors.

Contribution

It presents a novel graph model for encoding schemes, translating the construction problem into a graph theory problem and providing a more general approach.

Findings

Maximum of n(n-1)/2+1 strips processed with n channels for odd n

Maximum of (n(n-2))/2+2 strips processed with n channels for even n

Prototype encoding scheme verified with MRPC detectors

Abstract

Encoding readout methods based on different schemes have been successfully developed and tested with different types of position-sensitive detectors with strip-readout structures. However, how to construct an encoding scheme in a more general and systematic way is still under study. In this paper, we present a graph model for the encoding scheme. With this model, encoding schemes can be studied in a more systematic way. It is shown that by using an encoding readout method, a maximum of n(n-1)/2+1 strips can be processed with n channels if n is odd, while a maximum of (n(n-2))/2+2 strips can be processed with n channels if n is even. Furthermore, based on the model, the encoding scheme construction problem can be translated into a problem in graph theory, the aim of which is to construct an Eulerian trail such that the length of the shortest subcycle is as long as possible. A more general approach to constructing the encoding scheme is found by solving the associated mathematical problem. In addition, an encoding scheme prototype has been constructed, and verified with MRPC detectors.