Resolution

by Stephan W. Witz last modified Jun 22, 2017 by Emmanuel Momjian

Resolution

The VLA's resolution is generally diffraction-limited, and thus is set by the array configuration and the observing frequency. Like all synthesis arrays, the VLA is sensitive only to structures on a range of angular scales between the diffraction limit (the smallest angular scale detectable) and a "Largest Angular Scale" (which depends on the fringe spacing formed by the shortest baselines in the configuration). For emission structures smaller than the diffraction limit (θ ∼ λ/Bmax), the VLA acts like a single-dish instrument—the resulting image is smoothed to the resolution of the array. For emission structures larger than the detectable range, the VLA is simply blind to the emission; this is a limitation unique to interferometers. No subsequent processing can fully recover the missing information from these large scales. It can only be obtained by observing in a more compact VLA array configuration or with data from an instrument that is sensitive to the missing angular scales, such as a large single dish or a compact array of smaller antennas.

Table 3.1.1 displays the VLA's resolution and the scale at which severe attenuation of large-scale structure occurs. This table shows the maximum and minimum antenna separations, the approximate synthesized beam size (full width at half-power; the resolution element) for the central frequency for each band, and the largest angular scale of detectable emission.

Table 3.1.1: Configuration Properties
ConfigurationABCD
Bmax (km1) 36.4 11.1 3.4 1.03
Bmin (km1) 0.68 0.21 0.0355 0.035
Band Synthesized Beamwidth θHPBW(arcsec)1,2,3
74 MHz (4) 24 80 260 850
350 MHz (P) 5.6 18.5 60 200
1.5 GHz (L) 1.3 4.3 14 46
3.0 GHz (S) 0.65 2.1 7.0 23
6.0 GHz (C) 0.33 1.0 3.5 12
10 GHz (X) 0.20 0.60 2.1 7.2
15 GHz (Ku) 0.13 0.42 1.4 4.6
22 GHz (K) 0.089 0.28 0.95 3.1
33 GHz (Ka) 0.059 0.19 0.63 2.1
45 GHz (Q) 0.043 0.14 0.47 1.5
Band Largest Angular Scale θLAS(arcsec)1,4
74 MHz (4) 800 2200 20000 20000
350 MHz (P) 155 515 4150 4150
1.5 GHz (L) 36 120 970 970
3.0 GHz (S) 18 58 490 490
6.0 GHz (C) 8.9 29 240 240
10 GHz (X) 5.3 17 145 145
15 GHz (Ku) 3.6 12 97 97
22 GHz (K) 2.4 7.9 66 66
33 GHz (Ka) 1.6 5.3 44 44
45 GHz (Q) 1.2 3.9 32 32
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.
Notes:
1. Bmax is the maximum antenna separation, Bmin is the minimum antenna separation, θHPBW is the synthesized beam width (FWHM), and θLAS is the largest angular scale structure visible to the array.
2. The listed resolutions are appropriate for sources with declinations between −15 and +75 degrees.
3. The approximate resolution for a naturally weighted map is about 1.5 times the numbers listed for θHPBW. 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.