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

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.

arXiv comment30 pages 19 figures. This paper completes the previous arXiv:1908.04447, added the definition of ideal detector and corrected few typos

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