Calibration

Corrupting and Calibrating Visibilities

For simulations to be useful, they must include the propagation and instrumental effects that corrupt radio signals. These corruptions mainly fall into two classes. First, we have direction independent effects (DIEs), which include receiver gains and phase errors induced by the troposphere. Then, we have direction dependent effects (DDEs). These effects vary across the sky; the primary beam gain is an example of such an effect. Calibration is covered in this lecture

Radio interferometry measurement equation

For a sky containing sources s={s₁, s₂, ...}, the visibilities observed by baseline pq are given by:

V_pq = G_p (Σ_s E_sp X_spq E_sq^H) G_q^H

where G represents all direction independent effects, E represents all the direction dependent effects and X is the sky coherency.

Complex receiver gains

This section demonstrates the calibration principle in a very simple way. We will simulate an observation of a central point source, then fake some gain variations on the observation and examine the difference. Finally we will solve for these gain drifts and remove them.

In this case, the RIME reduces to:

V_pq = G_p X_pq G_q^H

We will again use turbo-sim.py to simulate a point source at the phase centre, but this time we add gain errors. The figure bellows shows the gains for each antenna.

Now lets see how good our G-Jones calibration was.

No G Err	With G Err	After G Cal
That is pretty good!

Direction Dependent Effects

The single component model we have been using thus far is not adequate to illustrate DDE effects, so lets use something a bit more interesting. Find the sky model here)

This is a 2 square degree field containing 102 sources.

This is the plan for this section:

1. Create an empty MS
2. Simulate the sky model into MS (into DATA column)
   2.1. Add noise
   2.2. Add pointing errors (analytic WSRT cos3 beam)
3. Calibrate
   3.1. Do a G calibration with the primary beam.
   3.2. Do a G calibration without the primary beam.
   3.3. Do a G+dE Calibration without the primary beam (dEs will only be applied to sources with I>0.05)

Screenshots of the simulation TDL options are below.

Sim TDL P1	Sim TDL P2

Screenshots of the calibration TDL options are below.

Cal TDL P1	Cal TDL P2	Cal TDL (dE)

Lets look at the visibilities. The last two results are with E-Jones turned off.

Simulated visibilities	G With beam	G without beam	G+dE without beam