Calibration

Calibration is performed by fitting observed visibilities to a model visibility.

The scalar equation to be minimised is:

\[S = \sum_{t,f}^{}{\sum_{i,j}^{}{w_{t,f,i,j}\left| V_{t,f,i,j}^{\text{obs}} - J_{i}{J_{j}^{*}V}_{t,f,i,j}^{\text{mod}} \right|}^{2}}\]

The least squares fit algorithm uses an iterative substitution (or relaxation) algorithm from Larry D’Addario in the late seventies.

An extension of this approach using 2x2 antenna-based Jones matrices \(J_i\) and coherency matrices \(V_{t,f,i,j}\) has been adapted from the MWA RealTime System (Mitchell et at., 2008, IEEE JSTSP, 2, JSTSP.2008.2005327) and can be enabled with ska_sdp_func_python.calibration.solvers.solve_gaintable() option solver="jones_substitution":

\[S = \sum_{t,f}^{}{\sum_{i,j}^{}{w_{t,f,i,j}\left| V_{t,f,i,j}^{\text{obs}} - J_{i}V_{t,f,i,j}^{\text{mod}}J_{j}^{\dagger} \right|_F}^{2}}.\]

\(\left|A\right|_F^2\) is the squared Frobenius norm of matrix A, and within each solver iteration each Jones matrix undergoes independent optimisation relative to the others. Normal-equation-based solvers are also available, which carry out joint optimisation within each iteration. These are more computationally intensive but can have better convergence properties.

ska_sdp_func_python.calibration.chain_calibration Module

Functions to solve for and apply chains of antenna/station gain tables. See documentation for further information.

Functions

`apply_calibration_chain`(vis, gaintables[, ...])	Update the Visibility using the calibrated solutions in the form of GainTables.
`calibrate_chain`(vis, model_vis[, ...])	Calibrate using algorithm specified by calibration_context.
`create_calibration_controls`()	Create a dictionary containing default chain calibration controls.
`solve_calibrate_chain`(vis, model_vis[, ...])	Solve GainTables by fitting an observed visibility to a model visibility.

ska_sdp_func_python.calibration.ionosphere_solvers Module

Functions to solve for delta-TEC variations across the array

Functions

`solve_ionosphere`(vis, modelvis, xyz[, ...])	Solve for ionospheric delay as a function of station location.
`set_cluster_maps`(cluster_id)	Generate vectors to help convert between station and cluster indices.
`set_coeffs_and_params`(xyz, cluster_id[, ...])	Initialise coefficients and parameters.
`get_param_count`(param)	Return the total number of parameters across all clusters.
`apply_phase_distortions`(vis, param, coeff, ...)	Update visibility model with new fit solutions.
`build_normal_equation`(vis, modelvis, param, ...)	Build normal equations.
`cluster_design_matrix`(mdl_data, mask0, ant1, ...)	Generate elements of the design matrix for the current cluster.
`solve_normal_equation`(AA, Ab, param[, it])	Solve the normal equations and update parameters.
`update_gain_table`(gain_table, param, coeff, ...)	Add new solutions to gaintable.

ska_sdp_func_python.calibration.ionosphere_utils Module

Utilities to support ionospheric calibration and the generation of ionospheric phase screens.

Functions

`decompose_phasescreen`(x, y, r_0[, beta])	Generate eigenvectors for phase-screen pierce points.
`displace_phasescreen`(interpolated_screen, ...)	Distort interpolated phasescreen to maintain Kolmogorov statistics.
`interpolate_phasescreen`(input_screen)	Bilinear interpolation of a two dimensional phase screen.
`standardise_eigenvectors`(evec)	Fix arbitrary eigenvector signs.
`zern`(m, n, rho, phi)	Generate Zernike polynomial values.
`zern_array`(nm, x, y[, noll_order])	Generate an array of all Zernike polynomials up to a given degree.

ska_sdp_func_python.calibration.jones Module

Jones matrix related operations.

Functions

apply_jones(ej, cfs[, inverse, min_det])

Apply Jones matrix (or inverse).

ska_sdp_func_python.calibration.operations Module

Functions for calibration operations.

Functions

`apply_gaintable`(vis, gt[, inverse, use_flags])	Apply a GainTable to a Visibility. The corrected visibility is::.
`apply_antenna_gains_to_visibility`(vis, ...)	Apply antenna gains (Jones matrices) to a visibility array.
`concatenate_gaintables`(gt_list[, dim])	Concatenate a list of GainTables.
`multiply_gaintables`(gt, dgt[, time_tolerance])	Multiply two GainTables.

ska_sdp_func_python.calibration.solvers Module

Functions to solve for antenna/station gain.

Functions

`solve_gaintable`(vis[, modelvis, gain_table, ...])	Solve a gain table by fitting an observed visibility to a model visibility.
`solve_antenna_gains_itsubs_matrix`(gain, gwt, ...)	Solve for the antenna gains using full matrix expressions.
`solve_antenna_gains_itsubs_nocrossdata`(gain, ...)	Solve for the antenna gains using full matrix expressions,
`solve_antenna_gains_itsubs_scalar`(gain, gwt, ...)	Solve for the antenna gains.

ska_sdp_func_python.calibration.alternative_solvers Module

Alternative functions to solve for antenna/station gain.

Functions

`solve_with_alternative_algorithm`(solver, ...)	Solve this row (time slice) of the gain table.
`jones_sub_solve`(vobs, vmdl, wgt, ant1, ant2, ...)	Solve this time and frequency slice of the gain table
`normal_equation_solve`(vobs, vmdl, wgt, ant1, ...)	Solve this time and frequency slice of the gain table
`normal_equation_solve_with_presumming`(vobs, ...)	Solve this time and frequency slice of the gain table

ska_sdp_func_python.calibration.solver_utils Module

Utility functions used by solvers. Based on the Yandasoft algorithm.

Functions

`gen_cdm`(gXi, gYi, dXYi, dYXi, gXj, gYj, ...)	Generate Complex Diff matrix for baseline i-j.
`gen_coherency_products`(Som, Smm, vobs, vmdl, ...)	Accumulate jones_substitution products for antenna ant.
`gen_pol_matrix`(gXi, gYi, dXYi, dYXi, gXj, ...)	Generate the 4x4 gain matrix for baseline i-j.
`update_design_matrix`(A, dv, wobs, wmdl, gX, ...)	Update design matrix for a set of visibilities.