Novel methods for measuring the optical parameters of the water Cherenkov detector

In this paper, novel methods are presented to measure the optical properties of muon detectors (MDs) in the Large High-Altitude Air Shower Observatory (LHAASO), which can also be used by other experiments. Each MD consists of a cylindrical water Cherenkov detector, with a Tyvek liner containing pure water, and a photomultiplier tube (PMT) mounted on the top. The time distribution of the photons collected by the PMT in the water Cherenkov detector have an approximately exponential distribution, and their decay factor is determined by the photon absorption length in the water, the reflectivity of the inner Tyvek surface, the mean reflecting step length of photons reflected by the inner surface, and the ratio of reflectional Tyvek area to the total inner surface area. By considering the principles of photon propagation in the water Cherenkov detector, we have developed novel methods to measure the water absorption length, the Tyvek reflectivity, and the mean step length of photons. The step length of photons can be determined by measuring the time distribution of the reflected photons hitting the PMT after multiple photons with single wavelength are generated in the tank, with slightly different ratios of the inner Tyvek to the total inner area. The water absorption length and Tyvek reflectivity can be measured simultaneously by the PMT by changing the height of the water, while the step length and Tyvek reflectivity in air can also be measured simultaneously. The proposed novel methods are supported by deduction of formulae and verified by GEANT4 simulations and the prototype experiment.