The Optimization of Neutron Polarizing Transmission Filter Thickness

For a neutron polarizing transmission filter the transmitted neutron beam polarization and intensity are determined by the filter thickness. It is possible to trade off polarization for intensity and vice versa. Thus, there is an optimum filter thickness which minimizes the errors in scattering cross sections measured on an instrument using such filters. Formulae expressing the errors in measured neutron scattering cross sections are given in terms of the polarization and transmission of the filters which enable the calculation of optimum filter thickness for any given filter type once the relationship between polarization and transmission is known. Formulae for optimum counting times in each polarization state are also presented. The optimum filter thickness for different types of measurements is discussed. An analysis of the effect of instrumental background on the optimization is also presented.