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

Abstract

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.

A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry

“…Implementations of algorithms such as MS-CLEAN and MS-MFS are inefficient in memoryuse, and other approaches may be required for large image sizes. For wide-field imaging, the time variation of the antenna primary beams must be taken into account during imaging, and wide-band methods combined with algorithms for directiondependent corrections (Bhatnagar et al 2008, or Smirnov 2011. For full-Stokes wide-band imaging, where a Taylor-polynomial in frequency is not the most appropriate basis function to model Stokes Q, U, V emission, wide-band imaging with other flux models must be tried.…”

“…A brute-force polynomial-division using more series coefficients will yield a more accurate solution. Note however, that such a correction will not be accurate if there are time-dependent variations in the primary-beam, and will require integration with the AW-Projection algorithm discussed in Bhatnagar et al (2008).…”

“…Bhatnagar et al (2008) describe an algorithm for the correction of time-variable and wide-field instrumental effects for narrow-band interferometric imaging. For wide-field wide-band imaging, these algorithms must be extended to include the frequency dependence of the instrument.…”

First LOFAR observations at very low frequencies of cluster-scale non-thermal emission: the case of Abell 2256

“…The entire FOV, to an attenuation factor of 0.15 compared to the beam center, was then imaged and cleaned using Casapy with w-projection (Cornwell et al 2005; 768 w-planes were used in total. Ideally, to create flux corrected wide-field images, the time-variable direction dependent effects need to be taken into account (e.g., Bhatnagar et al 2008). This functionality is still under development for LOFAR data.…”

Revisiting the radio interferometer measurement equation

“…This has been a serious dynamic range limitation at the VLA, but some recent developments promise to alleviate the problem. Uson & Cotton (2008) describe a CLEAN-like algorithm (implemented in the Obit package) that corrects these artefacts during deconvolution; the RIME-derived AW-projection method of Bhatnagar et al (2008) can correct them during imaging. Note that both methods rely on an a priori beam model, and have, to date, been only been applied to VLA data, for which the Brisken simulations provide a very detailed beam model.…”