Work in progress: Direction dependent corrections
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
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 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
This animation shows the PB-spectra through the 2D
PBs shown in the panels above.
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
Shown below are results from VLA L-band simulations. The first sidelobe was included in the imaging. Stokes-I and -V images are corrected for VLA polarization squint and PB rotation on the sky. The images on left are not corrected for antenna pointing errors.
|Stokes-I before pointing correction||Stokes-I image after pointing correction|
|Stokes-V before pointing correction||Stokes-V image after pointing correction|
|Peak residual and RMS for this image
is ~50μJy and ~10μJy respectively
|Peak residual and RMS for this image
is ~5μJy and ~1μJy respectively
Algorithm to solve for antenna based pointing errors is reported as EVLA Memo #84 .
We analyzed the effect of antenna based pointing errors on the imaging dynamic range and fidelity and present an algorithm to solve for these errors using a model for the sky brightness distribution. For a typical L-band eVLA simulation with typical pointing errors for the VLA antennas, the RMS noise can be reduced by a factor of ∼10 using this algorithm. The improvement in the image fidelity is even larger. The formulation given here can be further extended to include other direction dependent effects - specially for application to mosaicing observation. Extension of this work for such, more sophisticated solvers is in progress.
|Pointing error solution||Residuals: Before correction||Residuals: After correction|
|Antenna pointing errors as a function of time (continuous lines). Dashed lines show the residual pointing errors after Pointing Selfcal||Residual image before pointing correction. The peak and RMS noise in the image is ~250μJy/beam and ~15μJy respectively.||Residual image after pointing correction. The peak and RMS noise in the image is ~5μJy/beam and ~1μJy respectively.|
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 .
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 the result is not tightly coupled to computing time.
|Tangent Plane imaging||UV-plane Facet imaging||W-projection imaging|
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.
|Improvements in the AIPS++ runtime performance (red vs. green curves)|
|Improvements in imager performance||Improvements in calibrater performance|
|The x-axis represents N where the image size in pixels is NxN. The y-axis is the total runtime in seconds per major cycle.||The x-axis represents the number of solution intervals and the y-axis is the total runtime in seconds.|
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.
GMRT related work
|Plot of fractional complex leakage for all GMRT antennas on the complex plane. C03LX and C03RX (open circles) are from correlations of R- and L-channel of C03 with X-channel of other linear antennas. Similarly for C03LY and C03RY (triangles). This also shows that one of the linearly polarized antennas is leakier than the others and L-channel of C03 is noisier than its R-channel.||Poincare sphere representation of polarization states. Linear states map to the equator, and purely circular states to the poles. Closure phase between three coherent but non-identical antennas represented by the points I,J and K is equal to half the solid angle of IJK.|