Keywords: clic

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### SOLVE AMP PHASE

Commands `SOLVE AMPLITUDE` and `SOLVE PHASE` are used to derive the temporal variation of the gain through its amplitude and phase separately. One can either solve for the baseline gains or the antenna gains (with ) according to the mode selected with `SET AMPLITUDE ANTENNA BASELINE`.

In antenna mode, the averaged phase and amplitude closures and their standard deviation are computed, that allows to check for baseline-based errors, mostly in the form of amplitude decorrelation. The solutions are found by fitting directly the baseline-based quantities with the appropriate antenna-based combination (product of amplitudes, difference of phases).

Amplitude is mainly affected by variations of the antenna gain (pointing errors, defocussing, thermal and/or gravitational deformations), receiver gain and variation in the atmospheric absorption not accounted for in the atmospheric calibration (see sec. 4.8.1) in addition to decorrelation due to phase noise. For amplitude calibration, one should use `SET AMPLITUDE SCALED` prior to the `SOLVE` command so that the amplitude, which is on a temperature scale, is divided by the source flux. If the flux calibration is correct, the different sources should have the same values in K/Jy, which is actually the inverse of the antenna efficiency.

Figure 5: Example of `SOLVE AMPLITUDE /PLOT`.

Phase is affected by delay errors, in the form of baselines or time errors, atmospheric delays or drift in the receiver delay or phase (local oscillators). For the phase in particular, the atmospheric fluctuations introduce changes on a timescale that is usually smaller than the calibration period used for NOEMA. In order not to alias this fast varying component in the calibration, which would increase the final phase noise, it is important to keep in mind that the solution does not need to pass through the data points.

Figure 6: Example of SOLVE PHASE /PLOT.

Two mathematical functions can be fitted to the data: cubic splines (the knots spacing is controlled by the `SET STEP` command), which the default, or polynomials through the `/POLYNOM` degree option. It is possible to introduce breaks in the fuction or its derivatives with the `/BREAK` option.

Amplitude and phase calibration is done per IF (see section 2.1) by the combination of `SET POLARISATION` and `SET BAND` commands. In case of a polarized calibrator, the measured amplitude is:

| (20)

where is the parallactic angle and are the Stokes parameters. The (implicit) assumption of constant flux density for the calibrator breaks down if the linear polarisation fraction is more a few percents. In that case, one should use the average of both polarisation to perform the amplitude calibration (`SET POLARISATION BOTH`).

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