The output of an antenna that scans an incoherent source distribution is ‘smoothed’, that is, it contains fewer rapid variations with angle than the true source distribution. This is because the antenna rejects or reduces high spatial frequency components of the source spectrum. Source spectrum components passed by the antenna can be restored to their correct value by data-processing but such techniques usually yield a non-physical approximation to the source distribution. In a new technique that enhances angular resolution, the best mean square match to the restored source data is determined, and the minimum amount of extrapolated data added to guarantee a physical approximation to the sources surveyed by the antenna