We consider a troublesome form of non-isoplanatism in synthesis radio telescopes: non-coplanar baselines. We present a novel interpretation of the non-coplanar baselines effect as being due to differential Fresnel diffraction in the neighborhood of t
he array antennas. We have developed a new algorithm to deal with this effect. Our new algorithm, which we call W-projection, has markedly superior performance compared to existing algorithms. At roughly equivalent levels of accuracy, W-projection can be up to an order of magnitude faster than the corresponding facet-based algorithms. Furthermore, the precision of result is not tightly coupled to computing time. W-projection has important consequences for the design and operation of the new generation of radio telescopes operating at centimeter and longer wavelengths.
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 and 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 and that our new algorithm can be used to correct for such errors. 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. 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.
