Towards a detailed resolution smearing kernel for time-of-flight neutron reflectometers

In this article a `detailed' form of the resolution kernel used to analyse data from reactor-based time-of-flight (TOF) neutron reflectometers is derived. In contrast to monochromatic neutron reflectometers, where the resolution kernel is close to Gaussian, TOF neutron reflectometers can have trapezoidal resolution kernels. This is a consequence of the disc chopper systems used to pulse the beam having a wavelength uncertainty that is rectangular in shape. The effect of using the detailed and approximate kernels is compared, with the main effects occurring where the width of the kernel is approximately the same as the width of the features in the reflectivity curve, i.e. around the critical edge and at high Q_z. The difference between the two kernels is greatest when the wavelength and angular components are of different sizes.