Complex Gain Calibration

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

• Tropospheric effects dominate at wavelengths shorter than 20 cm, ionospheric effects dominate at wavelengths longer than 20 cm.
• 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. Hence, for these cases, calibration need only be done to track instrumental changes - a couple of times per hour is generally 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 (L/S/C bands) or 15 minutes at high frequencies (K/Ka/Q bands) in order to track pointing or other effects that might influence the amplitude scale.  The newly-enhanced sensitivity of the VLA now guarantees, for full-band continuum observations, that every field will have enough background sources to enable phase self-calibration at L and S bands, and probably also at C-band.  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 Key to 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).
• Use Figure 1 below to estimate how much time is minimally needed for each gain calibrator scan.  For instance, a 1 Jy calibrator and 4 MHz total bandwidth requires at least 30 seconds on source

Figure 1 - minimum time required on a gain calibrator scan as a function of bandwidth and calibrator flux for the rather extreme case of upper Q-band.  Durations derived from this plot will definitely be sufficient for all other bands.

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. However, observing efficiency declines 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 just a loop of source-calibrator scans with short scan length. This technique "stops" tropospheric phase variations at an "effective" baseline length of ∼v_at/2 where v_a is the atmospheric wind velocity aloft (typically 10 to 15 m/sec), and t is the total switching time. It has been demonstrated to result in images of faint sources with diffraction-limited spatial resolution on the longest VLA 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, however, that for the compact D-configuration, and a typical wind velocity, 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 also not work in bad weather (such as rain showers, or when there are well-developed convection cells - most notably, thunderstorms). It is also important to specify correctly 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.  See also the High Frequency Observing 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 using an interferometer comprising two 1.5 meter antennas separated by 300 meters, observing an 11.7 GHz beacon from a geostationary satellite. The API data can be used to estimate the required calibration cycle times when using fast switching phase calibration, and in the worst case, to indicate to the observer that high frequency observing may not be possible with current weather conditions.

Characteristic seasonal averages are represented below:

Note: day indicates sunrise to sunset values; night indicates sunset to sunrise values.