• Outline
• Glossary
• 8. Calibration
  • Previous: 8.4 3GC Calibration
  • Next: 9. Pracrical Advice for Reducing a Data Set and Recognizing Errors

Import standard modules:

Import section specific modules:

8.5 Further Reading and References

We summarize all the references and the further reading material which we have already mentioned in a dispersed manner througout the chapter here. We started the chapter by showing that calibration is usually performed by using the Levenberg-Marquedt gradient method in Sec. 8.1 ➞. The relevant references and further reading material for Sec. 8.1 ➞ is given in the following summary block:

Calibration as a least squares problem

• GPU accelerated nonlinear optimization in radio interferometric calibration ⤴
• Radio interferometric gain calibration as a complex optimization problem ⤴

In Sec. 8.2 ➞ we discussed 1GC calibration, which is when we use the calibration solutions we obtained from a calibrator observation to correct our target field observation. The relevant external material associated with this section can be found in the following summary block:

1GC

• Interferometry and synthesis in radio astronomy ⤴
  
• Synthesis imaging in radio astronomy II ⤴

We then described the method of self-calibration (2GC calibration) in Sec. 8.3 ➞, which entails using the field that we are observing to also calibrate the observation. Some of the most important articles that pertain to 2GC calibration can be found below:

2GC

• A phase sensitive interferometer technique for the measurement of the Fourier transforms of spatial brightness distributions of small angular extent ⤴
• The measurement of the angular diameter of radio stars ⤴
• The mapping of compact radio sources from VLBI data ⤴
• Adaptive calibration of radio interferometer data ⤴
• A new method for making maps with unstable radio interferometers ⤴
• The almost serendipitous discovery of self-calibration ⤴
• Image formation by self-calibration in radio astronomy ⤴

We ended the chapter by briefly looking at 3GC calibration (see Sec 8.4 ➞). In wide-field observations we can no longer afford to ignore direction dependent effects, i.e. effects like pointing error. The 3GC calibration algorithms can in general be divided into physics-based and heuristic approaches (depending on whether a physical model that can accurately describe the direction dependent effect exists or not). The approaches belonging to these two broad categories are summarized below:

3GC: Physics-based approaches

• Pointing-selfcal: GSF:LF: dead link: [EVLA Memo 84. Solving for the antenna based pointing errors ⤴](www.aoc.nrao.edu/evla/geninfo/memoseries/evlamemo84.ps)
• Kalman filter: Nonlinear Kalman filters for calibration in radio interferometry ⤴
• Primary beam: Incorporation of antenna primary beam patterns in radio-interferometric data reduction to produce wide-field, high-dynamic-range images ⤴

3GC: Heuristic-only approaches

• Peeling: LOFAR calibration challenges ⤴
• Differential gains: Revisiting the radio interferometer measurement equation-II. Calibration and direction-dependent effects ⤴
• Clustered calibration: Clustered calibration: an improvement to radio interferometric direction-dependent self-calibration ⤴

Correcting for a direction dependent effect is tricky in its own right, some of the approaches that are used to accomplish this is summarized below:

3GC: Correcting for a known direction dependent effect

• Facetting: Radio-interferometric imaging of very large fields-The problem of non-coplanar arrays ⤴
• AW-projection: Correcting direction-dependent gains in the deconvolution of radio interferometric images ⤴

We also briefly mentioned the developments which have been made with regards to the calibration solver itself (see Sec 8.4 ➞); some of the most recent developments in this regard can be found below:

Solver Development

• Eigendecomposition: Gain calibration methods for radio telescope arrays ⤴
• SAGEcal: Radio interferometric calibration using the SAGE algorithm ⤴
• Robust calibration: Robust radio interferometric calibration using the t-distribution ⤴
• StEFCal: Fast gain calibration in radio astronomy using alternating direction implicit methods: Analysis and applications ⤴
• Riemann-Manifold: Radio interferometric calibration using a Riemannian manifold ⤴
• Blind Calibration: Blind calibration for radio interferometry using convex optimization ⤴
• Complex Optimization: Radio interferometric gain calibration as a complex optimization problem ⤴
• Kalman filter: Nonlinear Kalman filters for calibration in radio interferometry ⤴

Good literature reviews on 3GC can be found in:

3GC: Literature reviews

• Revisiting the radio interferometer measurement equation-II. Calibration and direction-dependent effects ⤴
• Advances in calibration and imaging techniques in radio interferometry ⤴

Next: 9. Practical Advice for Reducing a Data Set and Recognizing Errors