Modern, nonlinear ballistic neutron guides are an attractive concept in neutron beam delivery and instrumentation, because they offer increased performance over straight or linearly tapered guides. However, like other ballistic geometries they have the potential to create significantly non-trivial instrumental resolution functions. We address the source of the most prominent optical aberration, namely coma, and we show that for extended sources the off-axis rays have a different focal length from on-axis rays, leading to multiple reflections in the guide system. We illustrate how the interplay between coma, sources of finite size, and mirrors with non-perfect reflectivity can therefore conspire to produce uneven distributions in the neutron beam divergence, the source of complicated resolution functions. To solve these problems, we propose a hybrid elliptic-parabolic guide geometry. Using this new kind of neutron guide shape, it is possible to condition the neutron beam and remove almost all of the aberrations, whilst providing the same performance in beam current as a standard elliptic neutron guide. We highlight the positive implications for a number of neutron scattering instrument types that this new shape can bring.
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