A lens-reflector antenna comprises a hemispherical dielectric lens with a planar reflector. Beam scanning may be achieved by moving a primary feed around the fixed lens or by rotating the lens reflector with respect to a fixed feed. Truncation of the reflector and obstruction of the aperture by mechanical supports introduce scanning loss. These effects are analysed through a numerical technique where the spherical wave expansion method is used to populate an effective aperture matrix in the near field, which is then modified to account for shadowing effects. The results are verified by a measurement campaign using a scale model and by comparison with the commercial EM solver FEKO.