Deriving the angular response function for backscattering sensors

We derived the angular response function (W) for scattering sensors that automatically satisfies the normalization criterion and its corresponding weight (W). W's, derived for two commercial sensors, HydroScat-6 (HOBI Labs) and ECO-BB (Sea-Bird Inc.), agrees well with the Monte Carlo simulation and direct measurements. The backscattering measured for microbeads of known sizes agrees better with Mie calculation when the derived W was applied. We deduced that the reduction of W with increasing attenuation coefficient is related to path length attenuation and showed that this theoretically derived correction factor performs better than the default methods for the two commercial backscattering sensors. The analysis conducted in this study also leads to an estimate of uncertainty budget for the two sensors. The major uncertainty for ECO-BB is associated with its angular response function because of its wide field of view, whereas the main uncertainty for the HydrScat-6 is due to attenuation correction because of its relatively long path length.