Algebraic methods for reconstruction of coordinates in cathode strip chambers

Abstract

Many types of detectors, such as cathode strip chambers, provide a possibility to reconstruct track positions by induced strip charges. There are two main types of algebraic methods for this purpose: center of gravity methods and little-known differential methods. In the differential methods, the coordinate is calculated by a ratio whose numerator and denominator are linear combinations of differences of strip charges. Instead of strip charges, one can also use increasing functions of strip charges. Only special cases of these methods have appeared in the literature. A consistent description of these methods is not yet presented. The center of gravity methods can also be improved. The comparative performance of the general differential methods and the center of gravity methods is unknown. This paper fills this gap. Many new generalized formulas for both types of methods are derived. Their performance is studied with a simplified simulation of a detector.