Complex Gain Calibration

General Guidelines for Complex Gain Calibration

Adequate complex gain calibration (tracking amplitude and phase fluctuations as a function of time) is a complicated function of source-calibrator separation, frequency, array scale (configuration), 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—three or four times per hour is usually sufficient for tracking the system gains.
If your target object has sufficient flux density to permit phase self-calibration, there is no need to calibrate more than a couple of times per hour 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.
In principle, the smaller the source-calibrator angular separation, the better (even if the closer calibrator is weaker). However, the final choice will depend on the observing frequency. If deciding between a nearby calibrator with an S code in the calibrator database, and a more distant calibrator with a P code, for low frequencies (L-band and below) the nearby calibrator is usually the better choice (low frequency strategy). For higher frequencies it is advisable to use the further away but higher quality P-code calibrator (high frequency strategy). A detailed description of calibrator codes is available in the calibrator list.
Phase stability often deteriorates dramatically after about 10AM due to small-scale convective cells set up by solar heating, even in clear and calm conditions, especially in the summer. Observers should consider a more rapid calibration cycle for observations between this time and a couple of hours after sundown.
At high frequencies, and longer configurations, rapid switching between the source and nearby calibrator is needed to track tropospheric phase fluctuations if the target cannot be self-calibrated. 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. This is represented in the Observation Preparation Tool as 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. 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 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 shown in Table 3.12.1 below:

**Table 3.12.1: Seasonal API/wind values at the VLA**
Month	API (night) [deg]	API (median) [deg]	API (day) [deg]	Wind (night) [m/s]	Wind (median) [m/s]	Wind (day) [m/s]
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.

Other Issues that Affect Complex Gain (Amplitude)

There are other instrumental effects that cause fluctuations in gain over time for VLA observations - we describe three of them here. Note that all of these effects are to the gain amplitude, not phase.

Gain Curves

The VLA antennas have elevation-dependent gain variations which are important to account for at the four highest frequency bands. Gain curves are determined by VLA staff per antenna and per band, and the necessary corrections can be applied to the visibility data in both AIPS and CASA. Additionally, atmospheric opacity will also cause an elevation-dependent gain which is also particularly notable at these four highest frequency bands. We currently do not have an atmospheric opacity monitoring procedure; users should utilize the appropriate tasks available in both AIPS and CASA to estimate and correct for the opacity using ground-based weather data. If your complex gain calibrator is near your target source, and the flux density scale calibrator is also observed at a similar elevation, then most of this elevation-based gain will be calibrated correctly during normal calibration. Note also that a good procedure for removing elevation-based gain dependencies uses the AIPS task ELINT. This task will generate a 2^nd order polynomial gain correction utilizing your own calibrator observations. This will remove both the antenna and opacity gain variations, and has the decided advantage of not utilizing opacity models or possibly incorrect antenna gain curves. Use of this procedure is only practical if your observations span a wide range in elevation.

Antenna Pointing Offsets

Another important gain variation effect at the four highest frequency bands is that due to antenna pointing offsets. Daytime observations on sunny days can suffer pointing errors, primarily in elevation, of up to one arcminute. This effect can be largely removed by utilizing the referenced pointing procedure which determines the pointing offset of a nearby calibrator. This offset is then applied to subsequent target source observations. It is recommended that this local offset be determined at least hourly, more often during sunrise or sunset, utilizing an object within 15 degrees of the target source—preferentially at an earlier right ascension. Studies show that the maximum pointing error will be reduced to about 7 arcseconds or better if proper referenced pointing is utilized.

Electronic Gain Variations

The VLA's post-amplifiers are not temperature stabilized and exhibit significant gain (amplitude) changes between night and day, particularly at the four highest frequency bands. Changes as large as 30% have been seen between night and day in calm, clear conditions. These gain changes, and others caused by possible changes in attenuator settings, are monitored and can be removed by application of the internal calibration signal, whose results are recorded in the switched power table in both AIPS and CASA. These corrections are not applied by the calibration pipeline—users who wish to correct for these gain changes must utilize the appropriate tasks in AIPS or CASA. For the most accurate flux density bootstrapping, this table must be applied to the visibility data before calibration.