Comparison of beam position calculation methods for application in digital acquisition systems

摘要

We review beam position monitors adopting the perspective of an analogue-to-digital converter in a sampling data acquisition system. From a statisticaltreatment of independent data samples we derive basic formulae of positionuncertainty for beam position monitors. Uncertainty estimates only rely on afew simple model parameters and have been calculated for two "practical" signalshapes, a square pulse and a triangular pulse. The analysis has been carriedout for three approaches: the established signal integration androot-sum-square ap- proaches, and a least-square fit for the models of directproportion and straight-line. The latter approach has not been reported in theliterature so far. The straight-line fit provides the most robust estimator since it does notrequire baseline restoration, it is immune to signal offsets, and its standarddeviation is smallest. Consequently, of the analysed estimators it promises thehighest fidelity of results. The fit approach represents a simple, natural wayto analyse beam position monitor data which can be easily implemented inhardware and offers potential for new applications.