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The calculation of neutron reflectivity from raw time-of-flight dataincluding instrumental corrections as well as improved resolution calculationis presented. The theoretical calculations are compared to experimental datameasured on the vertical sample plane reflectometer D17 and the horizontalsample plane reflectometer FIGARO at the Institut Laue-Langevin, Grenoble,France (ILL). This article comprises the mathematical body of thetime-of-flight reflectivity data reduction software COSMOS which is used on D17and FIGARO.

Towards generalized data reduction on a chopper-based time-of-flight neutron reflectometer