Research work

The dominant time-varying direction dependent effect in interferometric imaging using El-Az mount antennas is due to the rotation of the projected antenna Primary Beam (PB) on the sky with time. This azimuthally-asymmetric PB also varies significantly with frequency. For wide-band continuum imaging, the rotation of the PB with time and scaling with frequency together constitute the dominant time- and frequency-varying direction dependent (DD) gains. The effects of ignoring these variable gains leads to errors that are significantly higher than the thermal noise limit of modern wide-band radio telescopes (like the EVLA).

Following are some intial results from that test the WB A-Projection algorithm to correct for the frequency dependence of the PB (the related paper is in prepration).

The blue curve shows the spectrum (covering the frequency range of 1.0 -- 2.0 GHz) of a unit point source located at the ~33% point of the PB at the reference frequency. The image was made using the classical imaging algorithm. The red curve shows the spectrum of the same source, but when imaged using the wide-band A-Projection (WB A-Projection ;ApJ, 2013,Vol.770, No. 2, 91 ; [astro-ph]) algorithm. The gain variation as a function of frequency is markedly reduced. The residual frequency variation correspond to about 5% flux variation across the frequency range.

The animations show the simulated PB for the EVLA at L-Band as a function of frequency (along the animation axis). The entire animation covers a frequency range of 1 GHz (Frame 30) to 2 GHz (Frame 1). The left panel shows the PB as a function of frequency when imaging is done using the classical imaging algorithms. The right panel shows the effective PB as a function of frequency when imaging is done using the WB A-Projection algorithm. Notice that while the PB in the left panels varies significantly with frequency, the main-lobe of the PB in the right panels is largely independent of the frequency and corresponds to the PB at the reference frequency.

This animation shows the PB-spectra through the 2D PBs shown in the panels above. The blue curve correspond to the frequency-dependent PB as seen by the classical imaging algorithm. The green curve correspond to the effective PB when imaging is done using the WB A-Projection. Each pair of curve correspond to a direction along a vertical slice of the 2D PB, starting at the center of the beam. This shows that the WB A-Projection algorithm has effectively projected-out the frequency dependence of the PB.

The animation below shows a deep image of the 3C147 field using the EVLA at L-Band (using a single 128MHz-wide spectral window) in the background (in gray scale). Also shown as an overlay is the contour plot of the EVLA Primary Beam pattern rotating on the sky as a function of the Parallactic Angle (PA) -- or equivalently, as a function of time.

PB is rotationally asymmetric, more so beyond the main-lobe. Its rotation with PA results in time and direction dependent gain variations. The resulting deconvolution errors are seen around the sources in the first sidelobe of the PB. Similar, but of smaller magnitude, errors are also present around sources near the half-power point in the mainlobe of the PB (seen more clearly in the Stokes-I image via the link below).

Images on this link show the improvements in Stokes-I and -V images after corrections for the PB effects is applied using the A-Projection algorithm.

The algorithm to correct for antenna pointing and primary beam effects during imaging was applied to a VLA C-array observation at 1.4GHz (data courtesy Matthews & Uson). The field has two "4C" sources located on either side of the pointing center at roughly the half-power point of the primary beam. Rotation of antenna power pattern on the sky leads to a low level direction dependent error in the Stokes-I image. The Stokes-V power pattern varies much more strongly across the field of view leading to strong direction dependent instrumental Stokes-V error.

The images in the first row below are made using the convectional deconvolution algorithm. Instrumental Stokes-V is clearly visible in the image in the right panel. The peak flux is about 10x higher than the noise limit (~0.1mJy/beam).

The images in the second row were made using the AWProject algorithm. The effects of rotating azimuthally asymmetric primary beams with polarization squint are corrected during image deconvolution. Improvements in imaging performance are clearly visible in both images. There is mild improvement in the Stokes-I image. Improvements in the Stokes-V image are more dramatic. Since we don't expect intrinsic Stokes-V flux for these sources, Stokes-V image should be noise-like. After PB corrections, it is indeed consistent with pure noise.

Stokes-I image before correction	Stokes-V image before correction

Stokes-I image after correction	Stokes-V image after correction

Algorithm to correct for antenna pointing errors and primray beam effects during imaging is reported as EVLA Memo #100 .

Errors in the observed visibilities can be classified as direction dependent and direction independent effects. Since direction dependent effects change arcoss the field of view, they must be corrected during imaging.

Antenna primary beams are usually not azimuthally symmetric due to blockages from feed/feed-legs, etc. As a result, for El-Az mount antennas, sources close to the null and those in the sidelobes experience large gain variations as a function of feed Parallactic angle. As result, these sources are poorly deconvolved and in-beam dynamic range is limited by the PSF sidelobes due to these sources.

Using appropriate Fourier plane filters as part of the forward (data to image) and inverse (image to data) transforms, large scale Primary Beam effects like the VLA polarization squint, antenna pointing errors, etc. can be corrected for a full beam polarimetric imaging experiment. In the example below we used a model for the VLA illumination pattern to construct the Fourier plane filters and correct for the polarization squint, pointing offsets and the effects of rotating primary beam sidelobes for a typical L-band VLA observation.

VLA Aperture Illumination pattern @1.4GHz (Courtesy W.Brisken, EVLA Memo #58 )	Primary Beam projected on the sky as a function of time

Algorithm to solve for antenna based pointing errors is reported as EVLA Memo #84 .

Here is the link to our paper on Adaptive Scale Pixel(Asp)-model deconvolution which is an adaptive scale sensitive algorithm. The algorithm is implemented as a Glish client in AIPS++ and is currently been incorporated in the imager tool.

• Deconvolution of the telescope Point Spread Function (PSF) is necessary for even moderate dynamic range imaging with interferometric telescopes. The process of deconvolution can be treated as a search for a model image such that the residual image is consistent with the noise model. For any search algorithm, a parameterized function representing the model such that it fundamentally separates signal from noise will give optimal results. In general, spatial correlation length (a measure of the scale of emission) is a stronger separator of the signal from the noise, compared to the strength of the signal alone. Consequently scale sensitive deconvolution algorithms result into more noise-like residuals.

  Shown below is an example of the performance of the Adaptive Scale Pixel (Asp) deconvolution algorithm. The first image below is the Dirty Image for a complex source. The image was deconvolved using the Asp-Clean algorithm and the restored image is shown in the second panel below. The residual image, shown in the third panel is consistent with random noise with no correlated features larger than the resolution element.

  The Dirty Image	The restored image	The residual image

We (Cornwell, Golap & Bhatnagar) developed a new, faster but more memory demanding algorithm for wide field imaging which corrects for the w-term. The algorithm, called "w-projection" is described in EVLA Memo #67 .

In 2002, I worked on identifying the source of runtime inefficiencies of AIPS++. It was then measured to be significantly slower than expected for the standard calibration and image deconvolution algorithms.

The fixes were found were related to algorithmic/conceptual problems as well implementation issues. This work is mostly reported in the AIPS++ memo 258 on benchmarking, and Gridding performance evaluation.

I made minor contributions to the algorithm for RFI excision in synthesis imaging without a reference signal reported in EVLA Memo #86.

Read this note for the analysis of some details that may impact the usefullness of the above algorithm.

I was partly involved in the supervision of the thesis work of P. Chandra on the study of the early evolution of extra Galactic SNe using the GMRT in the 1.4GHz band.
SN 1993J at metre wavelengths.
Synchrotron aging and the radio spectrum of SN 1993J.