The VLA's resolution is generally diffraction-limited, and thus is set by the array configuration and frequency of observation. It is important to be aware that a synthesis array is "blind" to structures on angular scales both smaller and larger than the range of fringe spacings given by the antenna distribution. For the former limitation, the VLA acts like any single antenna – structures smaller than the diffraction limit (θ ∼ λ/B_max) are not seen – the resulting image will be smoothed to the resolution of the array. The latter limitation is unique to interferometers; it means that structures on angular scales significantly larger than the fringe spacing formed by the shortest baseline are not measured. No subsequent processing can partly or fully recover this missing information, which can only be obtained by observing in a more compact array configuration, by using the mosaicing method, or by utilizing data from an instrument such as a large single antenna or a compact array comprising smaller antennas which provides this information.

Table 2 summarizes the relevant information. This table shows the maximum and minimum antenna separations, the approximate synthesized beam size (full width at half-power) for the central frequency for each band, and the scale at which severe attenuation of large scale structure occurs.

These estimates of the synthesized beamwidth are for a uniformly weighted, untapered map produced from a full 12 hour synthesis observation of a source which passes near the zenith.

Footnotes:

1. B_max is the maximum antenna separation, B_min is the minimum antenna separation, θ_HPBW is the synthesized beam width (FWHM), and θ_LAS is the largest scale structure "visible" to the array.

2. The listed resolutions are appropriate for sources with declinations between −15 and 75 degrees. For sources outside this range, the extended north arm hybrid configurations (DnC, CnB, BnA) should be used, and will provide resolutions similar to the smaller configuration of the hybrid, except for declinations south of −30. No double-extended north arm hybrid configuration (e.g., DnB, or CnA) is provided.

3. The approximate resolution for a naturally weighted map is about 1.5 times the numbers listed for θ_HPBW. The values for snapshots are about 1.3 times the listed values.

4. The largest angular scale structure is that which can be imaged reasonably well in full synthesis observations. For single snapshot observations the quoted numbers should be divided by two.

5. For the C configuration an antenna from the middle of the north arm is moved to the central pad "N1". This results in improved imaging for extended objects, but may slightly degrade snapshot performance. Note that although the minimum spacing is the same as in D configuration, the surface brightness sensitivity and image fidelity to extended structure is considerably inferior to that of the D configuration.

The following figure is a graphical representation of the synthesized beamwidths for natural and robust weighting for the four main array configurations between 1 and 50 GHz. Also available are synthesized beamwidth figures for the low frequency (1–12 GHz) and the high frequency (12–50 GHz) receiver bands.

(click image to enlarge)

A project with the goal of doubling the longest baseline available in the A configuration by establishing a real-time fiber optic link between the VLA and the VLBA antenna at Pie Town was established in the late 1990s, and used through 2005. This link is no longer operational; the goal of implementing a new digital Pie Town link, now that EVLA construction is complete, remains unfunded.

The theoretical thermal noise expected for an image using natural weighting of the visibility data is given by:

where:

- SEFD is the "system equivalent flux density" (Jy), defined as the flux density of a radio source that doubles the system temperature. Lower values of the SEFD indicate more sensitive performance. For the VLA's 25-meter paraboloids, the SEFD is given by the equation SEFD = 5.62T_sys/η_A, where T_sys is the total system temperature (receiver plus antenna plus sky), and η_A is the antenna aperture efficiency in the given band.

- η_c is the correlator efficiency (~0.93 with the use of the 8-bit samplers).

- n_pol is the number of polarization products included in the image; n_pol = 2 for images in Stokes I, Q, U, or V, and npol = 1 for images in 'RCP' or 'LCP'.

- N is the number of antennas.

- t_int is the total on-source integration time in seconds.

- Δν is the bandwidth in Hz.

Figure 1 shows the SEFDs as a function of frequency used in the VLA exposure calculator for those Cassegrain bands currently installed on VLA antennas, and include the contribution to Tsys from atmospheric emission at the zenith. Table 3 gives the SEFD at some fiducial VLA frequencies.

Note that the theoretical rms noise calculated using equation 1 is the best limit possible. There are several factors that will tend to increase the noise compared with theoretical:

• For the more commonly-used "robust" weighting scheme, intermediate between pure natural and pure uniform weightings (available in the AIPS task IMAGR and CASA task clean), typical parameters will result in the sensitivity being a factor of about 1.2 worse than the listed values.
• Confusion. There are two types of confusion: (i) that due to confusing sources within the synthesized beam, which affects low resolution observations the most. Table 3 shows the confusion noise in D configuration (see Condon 2002, ASP Conf. 278, 155), which should be added in quadrature to the thermal noise in estimating expected sensitivities. The confusion limits in C configuration are approximately a factor of 10 less than those in Table 3; (ii) confusion from the sidelobes of uncleaned sources lying outside the image, often from sources in the sidelobes of the primary beam. This primarily affects low frequency observations.
• Weather. The sky and ground temperature contributions to the total system temperature increase with decreasing elevation. This effect is very strong at high frequencies, but is relatively unimportant at the other bands. The extra noise comes directly from atmospheric emission, primarily from water vapor at K-band, and from water vapor and the broad wings of the strong 60 GHz O₂ transitions at Q-band.
• Losses from the 3-bit samplers.  The VLA's 3-bit samplers incur an additional 10 to 15% loss in sensitivity above that expected -- i.e., the efficiency factor η_c = 0.78 to 0.83.

In general, the zenith atmospheric opacity to microwave radiation is very low - typically less than 0.01 at L, C and X-bands, 0.05 to 0.2 at K-band, and 0.05 to 0.1 at the lower half of Q-band, rising to 0.3 by 49 GHz. The opacity at K-band displays strong variations with time of day and season, primarily due to the 22 GHz water vapor line. Conditions are best at night, and in the winter. Q-band opacity, dominated by atmospheric O₂, is considerably less variable.

Observers should remember that clouds, especially clouds with large water droplets (read, thunderstorms!), can add appreciable noise to the system temperature. Significant increases in system temperature can, in the worst conditions, be seen at frequencies as low as 5 GHz.

Tipping scans can be used for deriving the zenith opacity during an observation. In general, tipping scans should only be needed if the calibrator used to set the flux density scale is observed at a significantly different elevation than the range of elevations over which the phase calibrator and target source are observed. However, the antenna tip capability is currently unavailable for the upgraded VLA -- it is hoped that this will again be available in the next year.

When the flux density calibrator observations are within the elevation range spanned by the science observing, elevation dependent effects (including both atmospheric opacity and antenna gain dependencies) can be accounted for by fitting an elevation-dependent gain term. See the following item.

• Antenna elevation-dependent gains. The antenna figure degrades at low elevations, leading to diminished forward gain at the shorter wavelengths. The gain-elevation effect is negligible at frequencies below 8 GHz. The antenna gains can be determined by direct measurement of the relative system gain using the AIPS task ELINT on data from a strong calibrator which has been observed over a wide range of elevation. If this is not possible, care should be taken to observe a primary flux calibrator at the same elevation as the target.

  Both CASA and AIPS allow the application of elevation-dependent gains and an estimated opacity generated from ground-based weather (e.g., through the tasks gencal and plotweather in CASA, and INDXR in AIPS).

• Pointing. The SEFD quoted above assumes good pointing. Under calm nighttime conditions, the antenna blind pointing is about 10 arcsec rms. The pointing accuracy in daytime can be much worse -- occasionally exceeding 1 arcminte, due to the effects of solar heating of the antenna structures. Moderate winds have a very strong effect on both pointing and antenna figure. The maximum wind speed recommended for high frequency observing is 15 mph (7 m/s). Wind speeds near the stow limit (45 mph) will have a similar negative effect at 8 and 15 GHz.

To achieve better pointing, "referenced pointing" is recommended, where a nearby calibrator is observed in interferometer pointing mode every hour or so. The local pointing corrections thus measured can then be applied to subsequent target observations. This reduces rms pointing errors to as little as 2 - 3 arcseconds (but more typically 5 to 7 arcseconds) if the reference source is within about 15 degrees (in azimuth and elevation) of the target source, and the source elevation is less than 70 degrees. At source elevations greater than 80 degrees (zenith angle < 10 degrees), source tracking becomes difficult; it is recommended to avoid such source elevations during the observation preparation setup.

Use of referenced pointing is highly recommended for all Ku, K, Ka, and Q-band observations, and for lower frequency observations of objects whose total extent is a significant fraction of the antenna primary beam. It is usually recommended that the referenced pointing measurement be made at 8 GHz (X-band), regardless of what band your target observing is at, since X-band is the most sensitive, and the closest calibrator is likely to be weak. Proximity of the reference calibrator to the target source is of paramount importance; ideally the pointing sources should precede the target by 20 or 30 minutes in Right Ascension (RA). The calibrator should have at least 0.3 Jy flux density at X-band and be unresolved on all baselines to ensure an accurate solution.

To aid VLA proposers there is an on-line guide to the exposure calculator; the exposure calculator provides a graphical user interface to these equations.

Special caveats apply for P-band (230 – 470 MHz) observing.  The listed SEFD in table 3 is from an observation taken far from the Galactic plane, where the sky brightness is about 30K.  At this band, Galactic synchrotron emission is very bright in directions near the Galactic plane.  The system temperature increase due to Galactic emission will degrade sensitivity by factors of two to three for observations in the plane, and by a factor of 5 or more at or near the Galactic center.   In addition, the antenna efficiency (currently about 0.31 for 300 MHz) will decline with both increasing and decreasing frequencies from the center of P-band.

The beam-averaged brightness temperature measured by a given array depends on the synthesized beam, and is related to the flux density per beam by:

where T_b is the brightness temperature (Kelvins) and Ω is the beam solid angle. For natural weighting (where the angular size of the approximately Gaussian beam is ∼ 1.5λ/B_max), and S in mJy per beam, the parameter F depends on the synthesized beam, therefore on the array configuration, and has the approximate value F = 190, 18, 1.7, 0.16 for A, B, C, and D configurations, respectively. The brightness temperature sensitivity can be obtained by substituting the rms noise, ΔI_m, for S. Note that Equation 2 is a beam-averaged surface brightness; if a source size can be measured the source size and integrated flux density should be used in Equation 2, and the appropriate value of F calculated. In general the surface brightness sensitivity is also a function of the source structure and how much emission may be filtered out due to the sampling of the interferometer. A more detailed description of the relation between flux density and surface brightness is given in Chapter 7 of Reference 1, listed in Documentation.

For observers interested in HI in galaxies, a number of interest is the sensitivity of the observation to the HI mass. This is given by van Gorkom et al. (1986; AJ, 91, 791):

where D is the distance to the galaxy in Mpc, and SΔV is the HI line area in units of Jy km/s.

Bands

For observations taken with the 8-bit samplers,  each receiver can tune to two different frequencies, each 1.024 GHz wide,  within the same frequency band. Right-hand circular (RCP) and left-hand circular (LCP) polarizations are received for both frequencies, except for the low-band receiver (50 – 500 MHz), which provides linear polarization (X and Y).  Each of these four data streams follows the VLA nomenclature, and are known as IF (for "Intermediate Frequency" channel) "A", "B", "C", and "D". IFs A and B provide RCP (or Y when applicable), IFs C and D provide LCP (or X when applicable).  IFs A and C are always at the same frequency, as are IFs B and D (but note that the A and C IFs  frequency is usually different from the B and D frequency). We normally refer to these two independent data streams as "IF pairs" – i.e., the 'A/C' pair and the 'B/D' pair.   In 8-bit mode, a maximum of 1.024 GHz can be correlated for each IF pair (see the WIDAR Section), for a total maximum bandwidth of  2.048 GHz.  To distinguish this 8-bit system from the 3-bit system, these IF pairs are denoted A0/C0 and B0/D0.

With the 3-bit samplers, more options are available.  This system provides four (R,L) polarization pairs, each 2048 MHz wide.  The A/C IF pair provides two sampled pairs, labelled A1/C1 and A2/C2, and the B/D IF pair provides two sampled pairs, labelled B1/D1 and B2/D2.

For more details on the 8-bit and 3-bit samplers see the VLA Samplers section.

The tuning ranges, along with default frequencies for continuum applications, are given in Table 4 below.

Notes:

1.  Listed here are the nominal band edges.  For all bands, the receivers can be tuned to frequencies outside this range, but at the cost of diminished performance.  Contact VLA staff for further information.

2. The 4-band system is currently under development. Observing time may be requested through the RSRO program.

3. The default setup for P-band will provide  16 subbands from the A0/C0 IF pair, each 16 MHz wide, to cover the frequency range 224 – 480 MHz. The channel resolution is 125 kHz. 

4. The default frequency set-up for L-band comprises two 512 MHz IF pairs (each comprising 8 contiguous subbands of 64 MHz) to cover the entire 1 – 2 GHz of the L-band receiver.

Tuning Restrictions

In general, for all frequency bands except Ka, if the total span of the two independent IF pairs of the 8-bit system (defined as the frequency difference between the lower edge of one IF pair and the upper edge of the other) is less than 8.0 GHz, there are no restrictions on the frequency placements of the two IF pairs. For K, Ka and Q bands (the only bands where a span greater than 8 GHz is possible), there are special rules:

• At Ka band, the low frequency edge of the A0/C0 IF pair must be greater than 32.0 GHz. There is no restriction on the B0/D0 frequency, unless the B0/D0 band overlaps the A0/C0 band when the latter is tuned at or near the 32.0 GHz limit.  In this case, the Observation Preparation Tool (OPT) may not allow the requested frequency setups.  Users wanting to use such a frequency setup are encouraged to contact the NRAO Helpdesk for possible tuning options.
• At K and Q bands, if the frequency span is greater than 8.0 GHz, the B0/D0 frequency must be lower than the A0/C0 frequency.

For the 3-bit system the maximum frequency span permitted for the A1/C1 and A2/C2 IF pairs is about 5000 MHz.  The same restriction applies to B1/D1 and B2/D2.  The tuning restrictions given above for the separation and location of the 8-bit pairs A0/C0 and B0/D0 also apply to the 3-bit pairs, with A0/C0 replaced by A1/C1 and A2/C2, and B0/D0 replaced by B1/D1 and B2/D2.

The 8-bit Set consists of four 8-bit samplers running at 2.048 GSamp/sec.  The four samplers are arranged in two pairs, each pair providing 1024 MHz bandwidth in both polarizations.  The two pairs are denoted A0/C0 and B0/D0.  Taken together, the four samplers offer a maximum of 2048 MHz coverage with full polarization. The frequency spans sampled by the two pairs need not be adjacent.  Some restrictions apply, depending on band, as described in the section on Frequency Bands and Tunability.

The 3-bit Set consists of eight 3-bit samplers running at 4.096 GSamp/sec.  The eight samplers are arranged as four pairs, each pair providing 2048 MHz bandwidth in both polarizations.  Two of these pairs, denoted A1/C1 and A2/C2 cannot span more than 5000 MHz (lower edge of one to the higher edge of the other). The same limitation applies to the second pair, denoted B1/D1 and B2/D2.  The tuning restrictions are described in the section on  Frequency Bands and Tunability.

Which set to use?

• S, L, and 4/P-band observations, whether line or continuum, should use the 8-bit sampler set.
• C and X-band continuum observations should use 3-bit samplers in order to exploit the full 4 GHz bandwidth: in spite of the 15% reduction in sensitivity that comes with 3-bit (at equal bandwidth to the 8-bit samplers; see below for details) and the reduced effective bandwidth after removing RFI this still provides superior overall sensitivity. For more details we refer to EVLA memo 166.
• Ku, K, Ka, and Q band continuum observations should use the 3-bit samplers for maximum bandwidth.
• Wide-band spectral line searches requiring more than 2 GHz span should use the 3-bit samplers.
• Spectral-line observations which fit within two (possibly disjoint) 1 GHz bands should use the 8-bit set.
• Simultaneous continuum and high resolution spectral line observation can use mixed 3-bit and 8-bit samplers. The 3 bit samplers in this case will be set up to deliver the continuum data, while the 8-bit samplers will be for the spectral line data. The mix mode can be used in C and the higher frequency bands.
  

Major Characteristics of each Set

The 8-bit samplers are warranted for observations at 4/P-band, L-band, and S-band. The full analog bandwidth from the receivers fits within the 2048 MHz span covered by the samplers.

For the 3-bit samplers users need to be aware of the following issues:

• Sensitivity: compared to the 8-bit system, the sensitivity of  the 3-bit samplers is worse by ~15% (at equal bandwidth). Alternatively, a given continuum noise level, requiring on-source  integration time T with the 8-bit (two bands of 1GHz), requires  0.33T with the 3-bit (4 bands of 2GHz, assuming the bandwidth is available from the front end.)
• Resonances: each of the eight 3-bit samplers on an antenna has a resonance about 3 MHz wide.  Each resonance is independent of all others, so there is no correlated signal between antennas.  The resonance degrades the spectrum in its narrow frequency range, but has little effect on continuum observing.  Bandpass solutions will be affected, but can be interpolated over. Spectral-line calibration and  images at  the affected frequencies will show significant loss in sensitivity. The resonances are easily seen in autocorrelation spectra, and it is recommended that users, especially spectral-line users, utilize these to locate the compromised frequencies.
• Amplitude Calibration: The traditional method for both 8- and 3-bit systems is to observe a flux-density calibrator, use self-cal to determine the antenna amplitude calibration factors (gains), and transfer the gains to the phase calibrator and target. For 3-bit samplers this procedure gives results good to  5%, between elevations of 20-70degrees. (Expect worse at the upper edge of Q-band and/or during bad weather). The switched power data can be used to correct for system gain variations and works well for the 8-bit samplers.  For 3-bit samplers, the Pdif depends on the Psum,  i.e. Pdif is non-linear, and its application will bias the resulting visibilities by 5 to 10%.  The origin of this effect is understood, but we have not yet determined how best to compensate for it.  Because of this, we do not recommend use of the 'Psum' and 'Pdif' data to calibrate visibilities from the 3-bit samplers. We do, however, recommend that the 'Requantizer Gains' in the switched power data be applied to remove gain changes. For more information about the switched power, and 'Psum' and 'Pdif, see EVLA memo 145.

Setting up the 8-bit or 3-bit Samplers

Either set requires an initial scan for each individual LO (frequency) tuning, during which power levels are optimized.

For the 8-bit system, a 'dummy scan' of 1 minute duration is sufficient for each tuning.  This  is usually done while the antennas are slewing at the start of an observing file, as the pointing direction of the antennas is not critical.

For the 3-bit system, the requirements are more demanding, see the section on 3-bit set-up. The minimum setup time is 1 minute for each tuning, to adjust the power levels and bandpass slopes across the 2GHz samplers.  These values are retained and applied if the tuning is re-encountered in the same observation.  In addition, every time the LO setup is changed, whether or not it is new (e.g. changing from 8-bit X-band reference pointing back to target),  a scan of 30 seconds is needed to re-set the subband gains (requantizers) in the correlator.  For better amplitude calibration at high frequencies, the 3-bit initial setup should be near the elevation of the target, so do it after the first 8-bit setup described above. For 3-bit observing without 8-bit (e.g. C or X-band, without reference pointing), the power variation with elevation is small so the 3-bit setup can be done at any elevation.

For settings that use a mix of 3-bit and 8-bit samplers, the guidelines to set up the 3-bit samplers should be followed.


Other issues

The overhead for setup of 3-bit samplers can eat into observing time, especially for projects with many different LO settings, and/or sources all over the sky, accompanied by a band change, reference pointing, and requantizer reset for each direction. The impact is most severe for short scheduling blocks.

Polarization testing conducted so far indicates no degradation of performance by using the 3-bit samplers.

Acknowledgements

NRAO is grateful to Professor Rob Ivison for supporting the upgrade of some of the 3-bit samplers on the VLA via a grant from the European Research Council.  For observations using the 3-bit samplers between May 2015 and March 2018 we encourage users to include the following text in the Acknowledgments section of their publications:

"We acknowledge funding towards the 3-bit samplers used in this work from ERC Advanced Grant 321302, COSMICISM."

The default integration times for the various array configurations are as follows:

Observations with the 3-bit (wideband) samplers must use these integration times. Observations with the 8-bit samplers may use shorter integration times, but these must be requested and justified explicitly in the proposal, and obey the following restrictions:

Note that integration times as short as 5 msec and data rates as high as 300 MB/s can be supported for some observing, though any such observing is considered Resident Shared Risk Observing (RSRO). For these short integration times and high data rates there will be limits on bandwidth and/or number of antennas involved in the observation. Those desiring to utilize such short integration times and high data rates should consult with NRAO staff.

The maximum recommended integration time for any EVLA observing is 60 seconds. For high frequency observations with short scans (e.g., fast switching, as described in Rapid Phase Calibration and the Atmospheric Phase Interferometer (API)), shorter integration times may be preferable.

Observers should bear in mind the data rate of the VLA when planning their observations. For N_ant antennas and integration time Δt, the data rate^† is:

Here N_chpol is the sum over all subbands of spectral channels times polarization products:

where N_chan,i is the number of spectral channels in subband i, and N_polprod,i is the number of polarization products for subband i (1 for single polarization [RR or LL], 2 for dual polarization [RR & LL], 4 for full polarization products [RR, RL, LR, LL]). This formula, combined with the maximum data rates given above, imply that observations using the maximum number of channels currently available (16384) will be limited to minimum integration times of ~2 seconds for standard observations, and 0.8 seconds for shared risk observations.

These data rates are challenging for data transfer, as well as data analysis. Currently data may either be downloaded via ftp within the Science Operations Centers, or mailed on hard drives for those not in the same building as the archive. The Archive Access Tool allows some level of frequency averaging to decrease data set sizes before ftp, for users whose science permits; note that the full spectral resolution will be retained in the NRAO archive for all observations.

Higher time resolutions and data rates are possible in principle but will be considered only through the Resident Shared Risk program.

^†Note: The data rate formula given above does not account for the auto-correlations delivered by WIDAR. Precise data rate values can be obtained through the use of the General Observing Setup Tool (GOST), or the Resource Catalog of the Observation Preparation Tool.

The very wide bandwidths of the upgraded Very Large Array mean that RFI (radio-frequency interference) will be present in a far larger fraction of VLA observations than in observations made with the old systems.  Considerable effort has gone into making the VLA's new electronics as linear as possible, so that the effects of any RFI will remain limited to the actual frequencies at which the RFI exists.   Non-linear effects, such as receiver saturation, should occur only for those very unlikely, and usually very brief, times when the emitter is within the antenna primary beam.

RFI is primarily a problem within the low frequency bands (C, S, L, and the low-band system), and is most serious to the D configuration.  With increasing frequency and increasing resolution comes an increasing fringe rate, which is often very effective in reducing interference to tolerable levels.

The bands within the tuning range of the VLA which are allocated exclusively to radio astronomy are 1400-1427 MHz, 1660-1670 MHz, 2690-2700 MHz, 4990-5000 MHz, 10.68-10.7 GHz, 15.35-15.4 GHz, 22.21-22.5 GHz, 23.6-24.0 GHz, 31.3-31.8 GHz, and 42.5-43.5 GHz. No external interference should occur within these bands.

RFI seen in VLA data can be internal or external.  Great effort has been expended to eliminate all internally-generated RFI.  Nevertheless, some internal RFI remains, which we are working hard to eliminate.   Nearly all such internally-generated signals are at multiples of 128 MHz.  So far as we know, all such internal signals are unresolved in frequency, and hence will affect only a single channel.

Radio frequency interference of external origin will be an increasing problem to astronomical observations. Table 7 lists some of the sources of external RFI at the VLA site that might be observed within the VLA's expanded tuning range within L and S bands. Figure 3 shows a raw power cross-power spectrum at L-band. Figure 4 shows a similar plot for the lower half of S-band.

The three last entries in the table deserve extra discussion.  These are all satellite transmissions, whose severity is a strong function of the angular offset between the particular satellite and the antenna.  It appears that significant degradation can occur if the antennas are within ~10 degrees of the satellite.  The great majority of the satellites are along the 'Clarke Belt' -- the zone of geosynchronous satellites.  As seen from the VLA, this belt is at a declination of about -5.5 degrees.  There are dozens -- probably hundreds -- of satellites 'parked' along this belt, transmitting in many bands:  S, C, Ku, K, and Ka at a minimum.  Observations of sources in the declination rate of +5 to -15 degrees can expect to be significantly degraded due to satellite transmission.  The Sirius digital radio system (and probably the satellites in the 2178 -- 2195 MHz band) comprises three satellites in a 24-hour, high eccentricity orbit with the apogee above the central U.S.  For the Sirius system, the orbit is arranged such that each of the three satellites spends about eight hours near an azimuth of 25 degrees and an elevation of 65 degrees.  The corresponding region in astronomical coordinates is between declinations 50 to 65 degrees, and hour angles between -1 and -2 hours.  Observations at S-band within that area may -- or may not -- be seriously affected.  The most reliable way to judge the seriousness of the satellite emissions is to inspect the switched power table data, particularly in those subbands where there is little RFI.

VLA staff periodically observes the entire radio spectrum, with the VLA,  from 1.0 through 50.0 GHz with 125 kHz channel resolution to monitor the ever-changing RFI spectrum.  Plots from this program, accompanied with tables of identified sources are available at the RFI section of the VLA Observing Guide. Users concerned about the precise frequencies of strong RFI, and the likelihood of being affected, are encouraged to peruse these plots.

Although most of the stronger sources of RFI are always present, it is very difficult to reliably predict their effect on observations.  Besides the already noted dependence on frequency and array configuration, there is another significant dependency on sky location for those satellites in geostationary orbit.  For these transmitters, (for example, the frequency range from 3.8 to 4.2 GHz), the effect on observing varies dramatically on the declination of the target source.  Sources near zero declination will be very strongly affected, while observations north of the zenith may well be nearly unaffected, especially at the highest resolutions.

Also available are total-power plots of all RFI observations made by the interference protection group, from 1993 onwards at http://www.vla.nrao.edu/cgi-bin/rfi.cgi. For general information about the RFI environment, contact the head of the IPG (Interference Protection Group) by sending e-mail to nrao-rfi@nrao.edu.

The VLA electronics (including the WIDAR correlator) have been designed to minimize gain compression due to very strong RFI signals, so that in general it is possible to observe in spectral windows containing RFI, provided the spectra are well sampled to constrain Gibbs ringing, and spectral smoothing (such as Hanning) is applied.  Both AIPS and CASA provide useful tasks which automatically detect and flag spectral channels/times which contain strong RFI.

Extracting astronomy data from frequency channels in which the RFI is present is much more difficult. Testing of algorithms which can distinguish and subtract RFI signals from interferometer data is ongoing.

The 3-bit samplers will be more susceptible to RFI signals than the 8-bit samplers, since the latter have more 'levels' within which these strong signals can be accommodated.  However, since the RFI power at the bands where the 3-bit samplers will most commonly be used (C, X, Ku, K, Ka, and Q) is nearly always less than the total noise power, we do not expect problems when wide-band 3-bit observing is done in these bands.

Calibration of VLA data when strong RFI is present within a subband can be difficult.  Careful editing of the data, using newly available programs within CASA and AIPS, will be necessary before sensible calibration can be done.  The use of spectral smoothing (typically, Hanning), prior to editing and calibration, is strongly recommended when RFI is present within a subband.

Identification and removal of RFI is always more effective when the spectral and temporal resolutions are high.  However, the cost of higher spectral and temporal resolution is in database size and, especially, in computing time.  A good strategy is to observe with high resolution, then average down in time and frequency once the editing is completed.

The continuum subarray option offers two 1 GHz baseband pairs with the 8-bit samplers in up to 3 subarrays, with the same spectral channel and polarization product options as are available for wideband observing. The setup for each subarray is completely independent, in terms of observing frequency, polarization products, and integration times.

When using three subarrays, there are some restrictions on the number of antennas in each subarray. The Baseline Board in the correlator treats each set of 4 antennas independently, using a separate column of correlator chips. With 8 such columns, the correlator can handle up to 8x4= 32 antennas. The correlator configuration software requires that a given column not be split across subarrays. This does not matter when using only two subarrays, but forces some subtle restrictions when using three. For instance, one cannot observe with 9 antennas in each of 3 subarrays, because 9 antennas requires three columns (two with 4 antennas each, and one with 1 antenna); three subarrays of 9 antennas each would require 3x3= 9 columns, one more than are actually available. Splitting the array into 10, 9, and 8 antennas is allowed, since the first two subarrays use 3 columns each, while the third uses only two.

The following table gives four examples of how correlator resources can be split into multiple subarrays. Antennas in each subarray are color-coded: red for subarray 1, green for subarray 2 (if present), and blue for subarray 3 (if present).  The last column gives the number of antennas in each subarray (e.g., in the setup shown in the first row, subarray 1 has 10 antennas; subarray 2 has 9 antennas; and subarray 3 has 8 antennas). In all cases a total of 27 antennas are used.  [The columns are numbered in reverse order (C7 to C0) to match the numbering scheme used on the actual Baseline Boards.]

In preparation for observing, the a-priori position must be known to within the antenna primary beam, except perhaps for mosaicing observations. In the special case of using the phased VLA as a VLBI element, the a-priori position must be accurate to within the synthesized beam of the array.

In post-processing, target positions are typically determined from an image made after phase calibration, i.e. correcting the antenna and atmospheric phases as determined on the reference source. The accuracy of the calibration determines the  accuracy of the positions in the image. (Note that phase self-calibration imposes the assumed position of the model, i.e.,  makes  the position indeterminate. Therefore, an absolute position cannot be determined after self-calibration, but relative positions between features within a self-calibrated image are valid.)

It may help to think of astrometry in 2 steps, narrow and wide-field.

In narrow-field astrometry, the target is close to the phase tracking center and the antennas nod every few minutes between the target and a calibrator. Under good conditions of phase stability, accurate antenna positions, (so-called 'baselines'), a strong target, a close calibrator with accurately known position, and rapid switching, the accuracy can approach 1-2% of the synthesized beam, with a floor of ~2 mas. Even under more typical conditions, 10% of the beam is readily achieved.

Astrometric calibrators are marked 'J2000  A' in the VLA calibrator list, and have an accuracy of ~2 mas. Other catalogs from the USNO and the VLBA are also useful, but offsets may exist between the VLA and VLBA centroids, arising from extended structure in the particular source, and the different resolutions of the arrays.

For studies of proper motion and parallax, the absolute accuracy of a calibrator may be less important than its stability over time. Close or in-beam calibrators with poor a-priori positions can be used, and tied to the ICRF reference frame in the same or separate observations.

Phase stability can be assessed in real time from the Atmospheric Phase Interferometer (API) at the VLA site, which uses observations of a geostationary satellite at ~12GHz. Dynamic scheduling uses the API data to run a project under suitable conditions, specified by the user. Note that  VLBI projects using the phased VLA will typically be fixed date, not dynamically scheduled.

The widefield case is to determine the positions of targets within the primary beam, referenced to a calibrator within the beam or close by. In addition to the previous effects, there are distortions as a function of position in the field, from small errors in the Earth orientation parameters (EOP) used at correlation time, differential aberration, and phase gradients across the primary beam.  With no special effort, the errors build up to roughly ~1 synthesized beam at a separation of ~10^4 beams from the phase tracking center.  Not all these errors are fully understood, and accurate recovery of positions over the full primary beam in the wideband, widefield  case is a research area. These effects are handled somewhat differently in the post-processing packages. Check with VLA staff for more details.

The VLA Calibrator List contains information on 1860 sources sufficiently unresolved and bright to permit their use as calibrators, and is also available within the Observation Preparation Tool.

Accurate flux densities can be obtained by observing one of 3C286, 3C147, 3C48 or 3C138 during the observing run. Not all of these are suitable for every observing band and configuration - consult the VLA Calibrator Manual for advice. Over the last several years, we have implemented accurate source models directly in AIPS and CASA for much improved calibration of the amplitude scales. Models are available for 3C48, 3C138, 3C147, and 3C286 for L, S, C, X, Ku, K, Ka, and Q bands.

Since the standard source flux densities are slowly variable, we monitor their flux densities when the array is in its D configuration. As the VLA cannot accurately measure absolute flux densities, the values obtained must be referenced to assumed or calculated standards, as described in the next paragraph. Table 8 shows the flux densities of these sources in January 2012 at the standard VLA bands.  The flux density scale for the VLA, from 1 through 50 GHz, is based on emission models of the planet Mars, which is then calibrated to the CMB dipole using WMAP (Wilkinson Microwave Anisotropy Probe) observations (see Perley and Butler, 2013, for details).  The source 3C286 (=J1331+3030) is known to be non-variable, and has thus been adopted as the prime flux density calibrator source for the VLA. The adopted polynomial expression for the spectral flux density for 3C286 is:

[display]\log(S) = 1.2515 - 0.4605 \log(f) - 0.1715 \log^2(f) + 0.0336 \log^3(f)[/display]

where S is the flux density in Jy, and f is the frequency in GHz.

The absolute accuracy of our flux density scale is estimated to be about 2%.   With care, the internal accuracy in flux density bootstrapping is better than 1% at all bands except Q-band, where pointing errors limit bootstrap accuracy to perhaps 3%.   Note that such high internal accuracies are only possible in long-duration observations where the antenna gains curves and atmospheric opacity can be directly measured, and where there is good elevation overlap between the target source(s) and the flux density standard calibrator.

The sources 3C48, 3C147, and 3C138 are all slowly variable.  VLA staff monitor these variations on timescale of a year or two, and suitable polynomial coefficients are determined for them which should allow accurate flux density bootstrapping. These coefficients are updated approximately every other year, and are used in the AIPS task SETJY and in the CASA task setjy.

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, and the necessary corrections are applied to the visibility data when these data are downloaded from the archive. In addition to this, atmospheric opacity will also cause an elevation-dependent gain which is particularly notable at these four highest frequency bands.   At the current time, we do not have an atmospheric opacity monitoring procedure, so users should utilize the appropriate tasks available in both AIPS and CASA to estimate and correct for the opacity using ground-based weather data.  Correction of these gain dependencies, plus regular calibration using a nearby phase calibrator, should enable good amplitude gain calibration for most users.  Note that extraordinary attenuation by clouds can only be (approximately) corrected for by regular observation of a nearby calibrator.

A better procedure for removing elevation gain dependencies uses the AIPS task ELINT.  This task will generate a 2nd 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 outdated antenna gain curves.  Use of this procedure is only practical if your observations span a wide range in elevation.

By far the most important gain variation effect is that due to pointing.  Daytime observations on sunny days can suffer pointing errors of up to one arcminute (primarily in elevation).  This effect can be largely removed by utilizing the 'referenced pointing' procedure.  This determines the pointing offset of a nearby calibrator, which is then applied to subsequent target source observations.  It is recommended that this local offset be determined at least hourly, utilizing an object within 15 degrees of the target source -- preferentially at an earlier HA.  Studies show that the maximum pointing error will be reduced to about 7 arcseconds, or better.  VLA staff continue to work on improving this essential methodology.

The VLA's post-amplifiers are not temperature stabilized, and exhibit significant gain 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 will be removed with excellent accuracy by application of the internal calibration signal, whose results are recorded in the switched power table (SY table, in AIPS).  These corrections are not applied by default -- 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.  Gain bootstrapping better than 1% can be accomplished for the 8-bit sampler system after application of the switched power data.  For the 3-bit system there is an additional complication, as the values of the switched power data are sensitive to the total power, as well as the system gain.  VLA staff are currently working on a methodology to remove the total power dependency.  Not applying the switched power data will reduce bootstrapping accuracy to perhaps 10%, and possibly worse, if the observation of the flux density calibrator is not close in time to the local phase/amplitude calibrator.

For projects requiring imaging in Stokes Q and U, the instrumental polarization should be determined through observations of a bright calibrator source spread over a range in parallactic angle. The phase calibrator chosen for the observations can also double as a polarization calibrator provided it is at a declination where it moves through enough parallactic angle during the observation (roughly Dec 15deg to 50deg for a few hour track). The minimum condition that will enable accurate polarization calibration from a polarized source (in particular with unknown polarization) is three observations of a bright source spanning at least 60 degrees in parallactic angle (if possible schedule four scans in case one is lost). If a bright unpolarized unresolved source is available (and known to have very low polarization) then a single scan will suffice to determine the leakage terms. The accuracy of polarization calibration is generally better than 0.5% for objects small compared to the antenna beam size. At least one observation of 3C286 or 3C138 is required to fix the absolute position angle of polarized emission. 3C48 also can be used for this at frequencies of ~3 GHz and higher, or 3C147 at frequencies abover ~10 GHz.  The table below shows the measured fractional polarization and intrinsic angle for the linearly polarized emission for these four sources in December 2010.  Note that 3C138 is variable -- the polarization properties are known to be changing significantly over time, most notably at the higher frequencies.  See Perley and Butler (2013b) for details.

More information on polarization calibration strategy can be found in the VLA Observing Guide.

High sensitivity linear polarization imaging may be limited by time dependent instrumental polarization, which can add low levels of spurious polarization near features seen in total intensity and can scatter flux throughout the polarization image, potentially limiting the dynamic range. Preliminary investigation of the EVLA's new polarizers indicates that these are extremely stable over the duration of any single observation, strongly suggesting that high quality polarimetry over the full bandwidth will be possible.

The accuracy of wide field linear polarization imaging will be limited, likely at the level of a few percent at the antenna half-power width, by angular variations in the antenna polarization response. Algorithms to enable removable of this angle-dependent polarization are being tested, and observations to determine the antenna polarizations have begun. Circular polarization measurements will be limited by the beam squint, due to the offset secondary focus feeds, which separates the RCP and LCP beams by a few percent of the FWHM. The same algorithms noted above to correct for antenna-induced linear polarization can be applied to correct for the circular beam squint. Measurement of the beam squints, and testing of the algorithms, is ongoing.

Ionospheric Faraday rotation of the astronomical signal is always notable at 20 cm. The typical daily maximum rotation measure under quiet solar conditions is 1 or 2 radians/m², so the ionospherically-induced rotation of the plane of polarization at these bands is not excessive - 5 degrees at 20 cm. However, under active conditions, this rotation can be many times larger, sufficiently large that polarimetry is impossible at 20 cm with corrrection for this effect. The AIPS program TECOR has been shown to be quite effective in removing large-scale ionospherically induced Faraday Rotation. It uses currently-available data in IONEX format. Please consult the TECOR help file for detailed information. Ionosphere correction can also be performed in CASA using the task gencal; consult the calibration chapter of CASA Cookbook for more details.

The two-dimensional geometry of the VLA allows a snapshot mode whereby short observations can be used to image relatively bright unconfused sources. This mode is ideal for survey work where the sensitivity requirements are modest.

Single snapshots with good phase stability of strong sources should give dynamic ranges of a few hundred. Note that because the snapshot synthesized beam contains high sidelobes, the effects of background confusing sources are much worse than for full syntheses, especially at 20 cm and longer wavelengths in the D configuration. For instance, at 20 cm a single snapshot will give a limiting noise of about 0.2 mJy. This level can be reduced by taking multiple snapshots separated by at least one hour. The deconvolution of the data is necessary to remove the effects of background sources. Before considering snapshot observations at 20 cm, users should first determine if the goals desired can be achieved with the existing "Faint Images of the Radio Sky at Twenty-centimeters survey (FIRST, http://www.cv.nrao.edu/first/)" (B configuration), or the NRAO VLA Sky Survey (NVSS, http://www.cv.nrao.edu/nvss/) (D configuration, all-sky) surveys.

Observations at low elevation in the C and D configurations will commonly be affected by shadowing. It is strongly recommended that all data from a shadowed antenna be discarded. This will automatically be done during filling (CASA tasks importasdm and importevla) when using the default inputs. AIPS task UVFLG can be used to flag VLA data based on shadowing, although it will only flag based on antennas in the dataset, and is ignorant of antennas in other sub-arrays. The CASA task flagdata can also be used to flag data based on shadowing.

Cross-talk is an effect in which signals from one antenna are picked up by an adjacent antenna, causing an erroneous correlation. This effect is important at low frequencies in compact configurations.  Careful examination of the visibilities is necessary to identify and remove this form of interference. The affected data would show time-variable high-amplitude points.

Any single VLA configuration will allow accurate imaging of a range of spatial scales determined by the shortest and longest baselines. For extended and structured objects, it may be required to obtain observations in multiple array configurations. It is advisable that the frequencies used be the same for all configurations to be combined. The ideal combination of arrays results in a uv-plane with all cells equally filled by uv-points. To first order, this can be achieved by using the beam sizes of the individual arrays to inversely scale the on-source integration time. This approach is equivalent to achieving the same surface brightness sensitivity for all arrays on all scales. For the VLA, observations in the different configurations generate beam sizes that decrease by factors of 3, i.e. C configuration generates a 3 times smaller beam than D configuration, B 3 times smaller than C, and A three times smaller than B. Thus, on-source integrations would increase by about an order of magnitude between each array. Such a drastic increase is very expensive and, in fact, not necessary since some spatial scales are common to more than a single array, which is equivalent to some uv-cells being filled more than others. The best way to fill the uv plane depends on many factors, such as declination of the source, LST time of the observation, and bandwidth.

For the VLA, experience shows that a factor of about 3 in on-source integration time for the different array configurations works well for most experiments.

E.g., 20min on-source time in D, 1h in C, 3h in B, and 9h in A should produce a decent map. Using large bandwidths and multi-frequency synthesis will broaden all uv tracks radially and one may need even less array configurations or shorter integration times between the different arrays.

Objects larger than the primary antenna pattern may be mapped through the technique of interferometric mosaicing.  The VLA has no limit on the number of pointings for each mosaic. Typically hexagonal, rectangular, or individual pointing patterns are used and the overlap regions will result in an improved rms over each individual pointing. Given the many, potentially short observations, it is important to obey the data rate limits outlined in the Time Resolution and Data Rates Section. On-the-fly (OTF) mosaics, i.e. dumping the data while moving the telescopes across the source, is also available.

Time-variable structures (such as the nuclei of radio galaxies and quasars) cause special, but manageable, problems. See the article by Mark Holdaway in reference 2 (Documentation) for more information.

Guidelines for mosaicing with the VLA are given in the VLA Observing Guide.