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 stray pattern. The latter have relatively small peak amplitudes (typ. below -25 dB), depending on the rms surface error of the primary reflector. However, because of their large angular extent, they are sensitive to extended sources; and a significant fraction of the observed intensity can result from error beam pick-up. For (sub-)mm observations suffering from error beam pick-up we introduce a new temperature scale for the corrected data, the corrected main beam brightness temperature T-mb,T-c, which provides a better approximation to the intensity detected by the main beam than the commonly used antenna temperature and main beam brightness temperature. We consider two different correction methods. The first method uses complementary observations 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 error beam pick-up is de-convolved from the observed map in Fourier space. The requirements for both correction methods and their advantages and limitations are discussed in detail. Both correction methods require additional observations, unless the full spatial extent of the emission is observed. We find that the deconvolution method is attractive for the correction of fully sampled maps with an angular extent much larger than the error beam pattern. For smaller maps and more sparsely sampled observations, the subtraction method is favorable, because the additional observations with a small telescope are less time consuming.