Methods and constraints for the correction of the error beam pick-up in single dish radio observations

The beam pattern of a single dish radio telescope is given by the main beam and additional components at larger angles, usually called error beam or s tray pattern. The latter have relatively small peak amplitudes (typ. below -25 dB), depending on the rms surface error of the primary reflector. Howev er, because of their large angular extent, they are sensitive to extended s ources; and a significant fraction of the observed intensity can result fro m error beam pick-up. For (sub-)mm observations suffering from error beam p ick-up we introduce a new temperature scale for the corrected data, the cor rected main beam brightness temperature T-mb,T-c, which provides a better a pproximation to the intensity detected by the main beam than the commonly u sed antenna temperature and main beam brightness temperature. We consider t wo different correction methods. The first method uses complementary observ ations obtained with a smaller telescope. Smeared to the angular resolution of the error beam pattern they provide an estimate of the error beam Dick- up in the observations of the large telescope. For the second method! the e rror beam pick-up is de-convolved from the observed map in Fourier space. T he requirements for both correction methods and their advantages and limita tions are discussed in detail. Both correction methods require additional o bservations, unless the full spatial extent of the emission is observed. We find that the deconvolution method is attractive for the correction of ful ly sampled maps with an angular extent much larger than the error beam patt ern. For smaller maps and more sparsely sampled observations, the subtracti on method is favorable, because the additional observations with a small te lescope are less time consuming.