Correcting direction-dependent gains in the deconvolution of radio interferometric images

Astronomical imaging using aperture synthesis telescopes requires deconvolution of the point spread function as well as calibration of instrumental and atmospheric effects. In general, such effects are time-variable and vary across the field of view as well, resulting in direction-dependent (DD), time-varying gains. Most existing imaging and calibration algorithms assume that the corruptions are direction independent, preventing even moderate dynamic range full-beam, full-Stokes imaging. We present a general framework for imaging algorithms which incorporate DD errors. We describe as well an iterative deconvolution algorithm that corrects known DD errors due to the antenna power patterns (including errors due to the antenna polarization response) as well as pointing errors for high dynamic range full-beam polarimetric imaging. Using simulations we demonstrate that errors due to realistic primary beams as well as antenna pointing errors will limit the dynamic range of upcoming higher sensitivity instruments like the EVLA and ALMA and that our new algorithm can be used to correct for such errors. We show that the technique described here corrects for effects that can be described as approximate unitary operators in the interferometric measurement equation, such as those due to antenna pointing errors and non-azimuthally symmetric antenna power patterns. We have applied this algorithm to VLA 1.4 GHz observations of a field that contains two "4C" sources and have obtained Stokes I and V images with systematic errors that are one order of magnitude lower than those obtained with conventional imaging tools. Residual systematic errors that are seen at a level slightly above that of the thermal noise are likely due to selfcalibration instabilities that are triggered by a combination of unknown pointing errors and errors in our assumption of the shape of the primary beam of each antenna. We hope to present a more refined algorithm to deal with the fully general case in due course. Our simulations show that on data with no other calibration errors, the algorithm corrects pointing errors as well as errors due to known asymmetries in the antenna pattern.