Instrumental Polarization

Shows the effects of instrumental polarization using a WSRT data set.

Uses modifications to the standard Siamese/example-sim.py and Siamese/OMS/wsrt_beams.py to include a slight ellipticity for X and Y but in opposite directions. We expect this will lead to different polarized response depending on the position on the sky.

The modified sources are attached.

Using example-sim.py

To show the effects across the field of view, use a grid of sources. All simulations in this log use example the same sky model settings, so that comparisons are valid.

Compile options for the sky model are show in the image below.

To use the new beam model calculation, enable the E Jones and use the Siamese.OMS.wsrt_beams model, with a Beam Ellipticity of 0.01. It is only slight but is enough to lead to different X and Y beam patterns for off axis sources.

Compile time options shown.

Once compiled, can see what is happening by opening up the tree in the left meqbrowser panel, as shown in the image below. Expanding to a sufficient level, you can see the calculation of the elliptical beam with the 0.01 ellipticity added.

It is also useful to bring up the inspector:E bookmark to look at the data as it is simulated, then slick simulate MS.

Created an image with the settings shown below. Images all Stokes parameters, even though we used unpolarized sources as input.

To look in detail, use more pixels in the image. I have used 128 pixel images to make the purr log portable. When I viewed this log, there seemed to be an error actually displaying the image of the fits data in the HTML, but load in ds9/kvis to look.

The main image is in Stokes I as expected, since we had unpolarized input. However, there is some leakage into Stokes Q. We can see the effect from the position in the grid of the source.

If the two model beams are 90 degree offset ellipses, there is no difference in the beam response at the phase centre, or on the diagonals. The vertical and horizontal arms show the strongest leakage since the beam pattern is the most different in these positions.

As well as elliptical beam with instrumental polarisation, add period pointing errors to E. Use the options show below and compile.

Use inspector:E bookmark to check the simulated data is as expected. Shows the periodic pointing error, seen in the images of the bookmark.

Simulate MS.

Image with the same options as before, still have leakage into Q. The effect from the pointing errors is quite small, difficult to see the difference from just the elliptical beams performed above.

Compare difference, run again without pointing errors and subtract from data (see image below).

Runtime options: take as input previous pointer error included data in MODEL_DATA and output to SUBTRACTED_DATA.

There was an error imaging my custom column SUBTRACTED_DATA, saying it didn't know what type of data it was. I re-ran the subtraction above but put the output in CORRECTED_DATA and the imaging was fine.

Make the image of CORRECTED_DATA to see difference.

Small residuals in Stokes I image from 1 Jy sources. Around 10^-5. Even smaller residuals in Stokes Q image, around 10^-7. The histograms of these look fairly noise-like.

Having non-identical beams for each polarization leads to leakage into other Stokes components.

The influence of pointing errors is quite small with the 10 arcsecond level used. This indicates that the WSRT beam model central maximum probably doesn't change greatly with these small fluctuations in direction.