Calibration

Corrupting and Calibrating Visibilities

For simulations to be useful, they must include the propergation and instrumental effects that corrupt radio signals. These corruptions mainly fall into two classes. First, we have direction independent effects (DIEs), which include reciever 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.

The general measurement equation of a radio interferometer can be written as:
V_{pq} = \mathbf{G}_p(\sum _s \mathbf{E}_{sp} X_{spq} \mathbf{E}_{sq}^H)\mathbf{G_q^H}
where G represents all direction independent effects, E represents all the direction dependent effects and X is the sky coherency. This is the equation we will be solving when we are calibrating.

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} = \mathbf{G}_p X_{pq} \mathbf{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. sim_gain The figure bellows shows the gains for each antenna. sim_vis_insp

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 edeqaute 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:

Create an empty MS
Simulate the sky model into MS (into DATA column)
2.1. Add noise
2.2. Add pointing errors (analytic WSRT cos3 beam)
Do a G calibration
Do a G+dE Calibration (dEs will only be applied to surces with I>0.05)