Light scattering from nanostructures is an essential ingredient in several optical technologies, and experimental verification of simulations of light scattering is important. In particular, solar cells may benefit from light-trapping due to scattering. However, light that is successfully trapped in an absorbing media such as e.g. Si necessarily escapes direct detection. We present in this paper a technique for direct measurement and analysis of light scattering from nanostructures on a surface, exemplified with aperiodic patterns of Ag strips placed on a GaAs substrate. By placing the structures on the flat face of a half-cylinder, the angular distribution of light scattered into the azimuth plane can be directly detected, including directions above the critical angle that would be captured if the substrate had the form of a slab. Modelling of the scattered light by summing up contributions from each strip agrees with the experimental results to a very detailed level, both for scattering backward and into the substrate.