Properties of the Center of Gravity as an Algorithm for Position Measurements: Two-Dimensional Geometry

TL;DR

This paper analyzes the properties of the center of gravity algorithm for 2D position measurements, exploring discretization effects, detector array geometries, and methods to eliminate errors through crosstalk, with simulations for calorimeter applications.

Contribution

It provides analytical tools and proofs showing how certain crosstalk spreads can eliminate discretization errors in the center of gravity method for various detector geometries.

Findings

Discretization errors can be eliminated with specific crosstalk spreads.

Analytical tools for different detector array geometries are developed.

Simulations demonstrate improved energy and position reconstruction.

Abstract

The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular, hexagonal, and triangular detectors are analytically studied, and tools are given to simulate their discretization properties. Special signal distributions free of discretized error are isolated. It is proved that some crosstalk spreads are able to eliminate the center of gravity discretization error for any signal distribution (ideal detectors). Simulations, adapted to the CMS em-calorimeter and to a triangular detector array, are provided for energy and position reconstruction algorithms with a finite number of detectors.