The influence of background on neutron polariser optimisation

The optimisation of neutron spin filter polarisers is of current interest. A commonly used ‘quality factor’ is the maximisation of τp2. We discuss the optimisation of measurements of the spin-flip and non-spin-flip cross sections to equal precision when using two 3He polarising filters, where the correct quality factor for such measurements is τ2p4/(1+p4). Here, τ and p are the transmission and polarisation of an initially unpolarised beam. We explore the sensitivity of this criterion to background, and find that it gives a good estimate of optimum thickness unless the background is independent of both the polariser and the analyser.