Summary

The complex time-dependent gains for each antenna/spwid are determined from the ratio of the data column (raw data), divided by the model column, for the specified data selection. The gains can be obtained for a specified solution interval for each spectral window, or by a spline fit to all spectral windows simultaneously. Any specified prior calibrations (e.g., bandpass) will be applied on the fly.

Introduction

The fundamental calibration to be done on your interferometer data is to calibrate the antenna-based gains as a function of time, using gaincal. Systematic time-dependent complex gain errors are almost always the dominant calibration effect, and a solution for them is almost always necessary before proceeding with any other calibration solve. Traditionally, this calibration type has been a catch-all for a variety of similar effects, including: the relative amplitude and phase gain for each antenna/polarization, phase and amplitude drifts in the electronics of each antenna, amplitude response as a function of elevation (gain curve), and tropospheric amplitude and phase effects. In CASA, it is possible to handle many of these specific effects separately, as available information, circumstances, and required accuracy warrant, but if accuracy is not paramount it is still possible to solve for the net effect using a quick-and-dirty gaincal. In fact, gaincal is often used for an initial exploration of a dataset, to find data problems, etc. Also, a provisional gaincal solution can be used as prior calibration to optimize bandpass calibration.  Such gaincal solutions are typically discarded.

It is best to have determined a (constant or slowly-varying) bandpass from the frequency channels by solving for the bandpass, and to include any other ancillary calibration that may be available via gencal (e.g., gaincurve, antenna position corrections, opacity, etc.).

See Solving for Calibration for more information on the task parameters gaincal shares with all solving tasks, including data selection, general solving properties and arranging prior calibration. Also see the rerefant task documentation for the behavior of reference antenna application. Below we describe parameters unique to gaincal, and those common parameters with unique properties.

Gain calibration types: gaintype

The gaintype parameter selects the type of gain solution to compute. For complex gain calibration, the choices are 'T', 'G', and 'GSPLINE'. The gaincal task also supports rudimetary delay solutions using 'K' and 'KCROSS'.

Polarization-dependent sampled gain (gaintype='G')

Generally speaking, gaintype='G' can represent any multiplicative polarization- and time-dependent complex gain effect downstream of the polarizers. (Polarization- and time-independent effects upstream of the polarizers may also be treated implicitly with G.) Multi-channel data (per spectral window) will be averaged in frequency before solving (use calibration type B to solve for frequency-dependent effects within each spectral window).

Polarization-independent sampled gain (gaintype='T')

At high radio frequencies (>10 GHz), it is often the case that the most rapid time-dependent gain errors are introduced by the troposphere, and are polarization-independent. It is therefore unnecessary to solve for separate time-dependent solutions for both polarizations, as is the case for gaintype='G'. Thus gaintype='T' is available to calibrate such tropospheric effects, differing from G only in that a single common solution for both polarizations is determined. In cases where only one polarization is observed, gaintype='T' is adequate to describe the time-dependent complex multiplicative gain calibration entirely. For the dual-polarization case, it is necessary to ensure that the two polarizations are, in fact, coherent by using a prior G or (unnormalized) bandpass calibration. 

Spline gains (gaintype='GSPLINE')

At high radio frequencies, where tropospheric phase fluctuates rapidly, it is often the case that there is insufficient signal-to-noise to obtain robust G or T solutions on timescales short enough to track the variation. In this case it is desirable to solve for a best-fit functional form for each antenna using the GSPLINE solver. This fits a time-series of cubic B-splines to the phase and/or amplitude of the calibrator visibilities.

The combine parameter can be used to combine data across spectral windows, scans, and fields. Note that if you want to use combine='field', then all fields used to obtain a GSPLINE amplitude solution must have models with accurate relative flux densities. Use of incorrect relative flux densities will introduce spurious variations in the GSPLINE amplitude solution.

The GSPLINE solver requires a number of unique additional parameters, compared to ordinary G and T solving. The sub-parameters are:

The duration of each spline segment is controlled by splinetime. The splinetime will be adjusted automatically such that an integral number of equal-length spline segments will fit within the overall range of data.

Phase splines require that cycle ambiguities be resolved prior to the fit; this operation is controlled by npointaver and phasewrap. The npointaver parameter controls how many contiguous points in the time-series are used to predict the cycle ambiguity of the next point in the time-series, and phasewrap sets the threshold phase jump (in degrees) that would indicate a cycle slip. Large values of npointaver improve the SNR of the cycle estimate, but tend to frustrate ambiguity detection if the phase rates are large. The phasewrap parameter may be adjusted to influence when cycles are detected. Generally speaking, large values (>180 degrees) are useful when SNR is high and phase rates are low. Smaller values for phasewrap can force cycle slip detection when low SNR conspires to obscure the jump, but the algorithm becomes significantly less robust. More robust algorithms for phase-tracking are under development (including traditional fringe-fitting).

Single- and multi-band delay (gaintype='K')

With gaintype='K' gaincal solves for simple antenna-based delays via Fourier transforms of the spectra on baselines to (only) the reference antenna. This is not a global fringe fit but will be useful for deriving delays from data of reasonable SNR. If combine includes 'spw', multi-band delays solved jointly from all selected spectral windows will be determined, and will be identified with the first spectral window id in the output caltable. When applying a multi-band delay table, a non-trivial spwmap is required to distribute the solutions to all spectral windows (fan-out is not automatic).

After solving for delays, a subsequent bandpass is recommended to describe higher-order channel-dependent variation in the phase and amplitude.

Cross-hand delays (gaintype='KCROSS')

With gaintype='KCROSS', gaincal solves for a global cross-hand delay. This is used only when doing polarimetry. Use parang=T to apply prior gain and bandpass solutions. This mode assumes that all cross-hand data (per spw) share the same cross-hand delay residual, which should be the case for a proper gain/bandpass calibration. See sections on polarimetry for more information on use of this mode.

 

Solution normalization: solnorm, normtype

Nominally, gain solution amplitudes are implicitly scaled in amplitude to satisfy the the effective amplitude ratio between the visiibility data and model (as pre-corrected or pre-corrupted, respectively, by specified prior calibrations). If solnorm=True, the solution amplitudes will be normalized so as to achieve an effective time- and antenna-relative gain calibration that will minimally adjust the global amplitude scale of the visibility amplitudes when applied.  This is desirable when the model against which the calibration is solved is in some way incomplete w.r.t. the net amplitude scale, but a antenna- and time-relative calibration is desired, e.g., amplitude-sensitive self-calibration when not all of the total flux density has been recovered in the visibility model.  The normalization factor is calculated from the power gains (squared solution amplitudes) for all antennas and times (per spw) according to the the setting of normtype.  If normtype='mean', (the default), the square root of the mean power gain is used to normalize the amplitude gains.  If normtype='median', the median is used instead, which can be useful to avoid biasing of the normalization by outlier amplitudes.  The default for solnorm is solnorm=False, which means no normalization.

 

Robust solving:  solmode, rmsthresh

Nominally (solmode=''), gaincal performs an iterative, steepest-descent chi-squared minimization for its antenna-based gain solution, i.e., minimizaiton of the L2 norm.  Visibility outliers (i.e., data not strictly consistent with the assumption of antenna-based gains and the supplied visibility model within the available SNR) can significantly distort the chi-squared gradient calculation, and thereby bias the resulting solution.  For an outlier on a single baseline, the solutions for the antennas in that baseline will tend to be biased in the direction of the outlier, and all other antenna solutions in the other direction (by a lesser amount consistent with the fraction of normal, non-outlying baselines to them).  It is thus desirable to dampen the influence of such outliers, and solmode/rmshresh provide a mechanism for achieving this.  These options apply only to gaintype='G' and 'T', and will be ignored for other options.

Use of solmode='L1' invokes an approximate form of minimization of the aggregate absolute deviation of visibilities with respect to the model, i.e., the L1 norm.  This is achieved by accumulating the nominal chi-squared and its gradient using weights divided by (at each iteration of the steepest descent process) the current per-baseline absolute residual (i.e., the square-root of each baseline's chi-square contribution).  (NB:  It is not possible to analytically accumulate the gradient of L1 since the absolute value is not differentiable.)   To avoid an over-reliance on baselines with atypically small residuals at each interation, the weight adjustments are clamped to a minimum (divided) value, and the steepest descent convergence is repeated three times with increasingly modest clamping. The net effect is to gently but effectively render the weight of relative outliers to appropriately damped influence in the solution.

Using solmode='R' invokes the normal L2 solution, but attempts to identify outliers (relative to apparent aggregate rms) upon steepest descent convergence, flag them, and repeat the steepest descent.  Since outliers will tend to bias the rms calculation initially (and thus possibly render spuriously large rms residuals for otherwise good data), outlier detection and re-covergence is repeated with increasingly aggressive rms thresholds, a sequence specifiable in rmsthresh.  By default (rmsthresh=[]) invokes a sequence of 10 thresholds borrowed from a traditional implementation found in AIPS: [7.0,5.0,4.0,3.5,3.0,2.8,2.6,2.4,2.2,2.5].  Note that the lower threshold values are likely to cull visibilites not formally outliers, but merely with modestly large residuals still consistent with gaussian statistitics, and thereby unnecessarily decrease net effective sensitivity in the gain solution (cf normal L2), especially for larger arrays where the number of baselines likely implies a larger number of visibility residuals falling in the modest wings of the distribution.  Thus, it may be desirable to set rmsthresh manually to a more modest sequence of thresholds.  Optimization of rmsthresh for modern arrays and conditions is an area of ongoing study.

Use of solmode='L1R' combines both the L1 and R modes described above, with the iterative clamped L1 loop occuring inside the R outliner excision threshold sequence loop.