Complex Gain Calibration

by Stephan W. Witz last modified Sep 21, 2016 by Tony Perreault

General Guidelines for Gain Calibration

Adequate gain calibration is a complicated function of source-calibrator separation, frequency, array scale, and weather. Since what defines adequate for some experiments is completely inadequate for others, it is difficult to define simple guidelines to ensure adequate phase calibration. However, some general statements remain valid most of the time. These are given below.

  • Under decent conditions with no thunderstorms or ionospheric storms, tropospheric effects dominate at frequencies higher than about 4 GHz; ionospheric effects dominate at frequencies lower than about 4 GHz.
  • Atmospheric (troposphere and ionosphere) effects are nearly always unimportant in the C and D configurations at L and S-bands, and in the D configuration at X and C-bands. For these cases, calibration need only be done to track instrumental changes—a couple of times per hour is usually sufficient.
  • If your target object has sufficient flux density to permit phase self-calibration, there is no need to calibrate more than once hourly at low frequencies or 15 minutes at high frequencies in order to track pointing or other effects that might influence the amplitude scale. The enhanced sensitivity of the VLA guarantees, for full-band continuum observations, that every field will have enough background sources to enable phase self-calibration at L and S-bands. At higher frequencies, the background sky is not sufficient, and only the flux of the target source itself will be available.
  • The smaller the source-calibrator angular separation, the better. In deciding between a nearby calibrator with an S code in the calibrator database, and a more distant calibrator with a P code, the nearby calibrator is usually the better choice. A detailed description of calibrator codes is available in the calibrator list.
  • In clear and calm conditions, most notably in the summer, phase stability often deteriorates dramatically after about 10AM due to small-scale convective cells set up by solar heating. Observers should consider a more rapid calibration cycle for observations between this time and a couple hours after sundown.
  • At high frequencies, and longer configurations, rapid switching between the source and nearby calibrator is often helpful. See Rapid Phase Calibration and the Atmospheric Phase Interferometer (API) (below).


Rapid Phase Calibration and the Atmospheric Phase Interferometer

For some objects, and under suitable weather conditions, the phase calibration can be considerably improved by rapidly switching between the source and calibrator. Source-calibrator observing cycles as short as 40 seconds can be used for very small source-calibrator separations. Observing efficiency declines, however, for very short cycle times, so it is important to balance this loss against a realistic estimate of the possible gain. Experience has shown that cycle times of 100 to 150 seconds at high frequencies have been effective for source-calibrator separations of less than 10 degrees. For the old VLA this was known as fast-switching; for the upgraded VLA, it is a loop of source-calibrator scans with short scan length. This technique stops tropospheric phase variations at an effective baseline length of ∼vat/2, where va is the atmospheric wind velocity aloft (typically 10 to 15 m/sec) and t is the total switching time. Short source-calibration scans have been demonstrated to result in images of faint sources with diffraction-limited spatial resolution on the longest baselines. Under average weather conditions, and using a 120 second cycle time, the residual phase at 43 GHz should be reduced to ≤ 30 degrees. Note that at a typical wind velocity in the compact D-configuration, this effective baseline length is the same as—or larger than—the longest baseline in the array and it is not worth the increased overhead of short cycle times. Under these circumstances, it is sufficient to calibrate every 5-10 minutes to track the instrumental changes. The fast switching technique will not work in bad weather (such as rain showers or when there are well-developed convection cells (thunderstorms)). It is also important to correctly specify the required tropospheric phase stability as measured by the Atmospheric Phase Interferometer at observe time (see below).

Further details can be found in VLA Scientific Memos # 169 and 173. These memos, and other useful information, can be obtained from References 9 and 10 in Documentation.  Also see the High Frequency Strategy guide for additional recommendations on observing at high frequencies.

An Atmospheric Phase Interferometer (API) is used to continuously measure the tropospheric contribution to the interferometric phase. The API uses an interferometer of two, 1.5 meter antennas, separated by 300 meters, observing an 11.7 GHz beacon from a geostationary satellite. The API data are heavily used for the dynamic scheduling of the VLA.

Characteristic seasonal averages are represented in Table 3.12.1 below:

Table 3.12.1: Seasonal API/wind values at the VLA

API (night)

API (median)

API (day)

Wind (night)

Wind (median)

Wind (day)

January 2.3 2.8 3.6 1.6 1.9 2.3
February 2.9 3.4 4.5 4.0 4.3 4.5
March 2.8 3.7 5.5 3.4 3.9 4.7
April 3.3 4.5 6.2 5.3 5.5 5.8
May 2.9 4.6 6.7 2.6 3.2 3.7
June 3.8 5.5 7.4 2.5 3.9 6.3
July 6.2 8.3 10.5 2.9 2.9 3.0
August 5.4 7.1 11.3 1.7 2.3 3.0
September 5.2 6.6 8.8 2.3 3.0 3.6
October 4.2 5.3 7.4 2.3 2.9 3.7
November 2.6 3.0 4.0 1.2 2.5 1.6
December 2.8 3.2 4.1 1.2 1.6 2.7

Day indicates sunrise to sunset values; night indicates sunset to sunrise values.