The Simulations Themselves

The simulations were done entirely within AIPS, using UVSIM to produce the data sets, UVMOD to replace the uv data by random noise, and UVSUB to add in the model. Since we are primarily interested in the effects of uv-coverage, systematic errors (e.g. calibration and pointing errors) which could muddy the waters were not included. However, the deconvolution routines, being intrinsically non-linear, might lead to different results for different signal-to-noise ratios, so the simulations do include random, thermal noise. The parameters of the simulations were as follows:

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Frequency: all simulations were carried out at a nominal frequency of 1.42 GHz. This is basically irrelevant but leads to more concrete source sizes, resolutions, etc. This choice also facilitates the comparison of these simulations with previous work, which has all been carried out at this nominal frequency.

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Configurations: the uv-coverage is that of the C, CS (as in 1997), C-2, and CS-2 configurations, for a long synthesis (HA= $\pm4\rm\,hours$) and a 6-minute snapshot (HA= $0.0-0.1\rm\,hours$). The source was taken to be at $\delta=60^\circ$. The integration time was 30 seconds, and the source was observed continuously, i.e. no time was removed to simulate calibrator scans.

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Thermal noise: Gaussian noise with rms 8.3 mJy per 30s visibility was added independently to every baseline, simulating the VLA's thermal noise at 20cm as given in the Observational Status Summary. Unless otherwise noted, all simulations of a given configuration were carried out using the same noise realization. The tests described in § show that this does not affect the results.

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Models: ideally the simulations should span the range of sources which might be imaged with the C/CS configuration, concentrating on those sources which in size and complexity might be expected to be most sensitive to the possible shortcomings of CS configuration, as outlined in the introduction. I took this to mean that the sources should be very complex, reasonably strong, and characteristic of typical sources imaged by the VLA. Unfortunately each suite of simulations takes quite a bit of time, so only a few sources could be used. Here I chose two of the best images yet made with the VLA, based on four-configuration observations of the supernova remnant Cassiopeia A (Cas A; donated by Rick Perley) at 20cm and the radio galaxy Cygnus A (Cyg A; donated by Chris Carilli) at 6cm. These were both VTESS models made at very high resolution (1.3 arcsec for Cas A; 0.5 arcsec for Cyg A).

• Source size: Cas A was simulated ``as-is,'' with a diameter of roughly 6 arcmin. Cyg A is intrinsically about 2 arcmin long; for the simulations the Cyg A model was used both ``as-is'' and scaled up in size by factors of 2 and 2.8. The model images are shown in Figure . According to the 1997 Observational Status Summary, C configuration should be sensitive to structure on size scales ranging from 12.5 to 420 arcsec; the additional short spacings of CS should therefore not be necessary for imaging these sources. Holdaway (1994) explored a wider range of source sizes, but only for Cas A.
• Source flux (SNR): The flux densities of the sources were also scaled (see Tables 1-4), ranging from the high-flux case where the thermal noise was completely swamped by sidelobes of the source, to the low-flux case where the off-source residual sidelobes were slightly under the thermal noise. The even-lower-SNR case was covered exhaustively by Rupen (1997).

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Imaging and Deconvolution: There are many different ways of weighting the data when Fourier transforming, and several important variations in deconvolving the resulting images. For instance, it might be argued that large, bright sources would be best deconvolved with some variety of MEM, while faint, small ones should be subjected to CLEAN; and in practice big, bright objects are likely to be worked on for many days in order to obtain the best possible images, with several versions of those images produced to best match the desired science. Simulations, involving many data sets and no direct scientific return, cannot practically be subjected to the same scrutiny as real data. My approach here has been to adopt a single, simple way of making the images, which seems not too different from what typical observers might actually do for at least a first stab at the processing. In particular, all images were made using the AIPS task IMAGR with the following parameters:

• Map size: $256\times256$ $\left(4\times4\rm\,arcsec\right)$ pixels
• Weighting: Briggs' robustness of 0 (roughly mid-way between natural and uniform weighting, Briggs 1995), no taper. This led to an increase in the expected noise (compared to natural weighting) of about 20% for the long observations, and 12.5% for the snapshots, a figure basically independent of the configuration.
• Deconvolution: CLEAN, as implemented in AIPS' IMAGR, with a single circular (Cas A) or rectangular (Cyg A) box enclosing the true extent of the source plus an additional 10-20 pixels on each side. The number of iterations used was the same for all configurations in a given suite of simulations (see Tables 1-4), and was chosen as the point where the recovered flux had settled down to the final (asymptotic) value. This is a fairly deep CLEAN. For the cognoscenti, the GAIN was 0.1 (to subtract only 10% of a peak at a time), FACTOR$=-1$ (to force more major cycles), and MINPA=151 (to set the minimum patch size for minor cycles), all in hopes of making CLEAN a bit more robust.

The choice of deconvolution method is one of the main sources of uncertainty in the results of these simulations - the resulting CLEAN models differ from the truth images in ways characteristic of well-known CLEAN instabilities (see below), and one would expect changes in the deconvolution algorithm to lead to changes in the fidelity of the maps. Some comparisons with VTESS are given below (§).

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Convolving to a Common Resolution: As discussed below, the available measures of image quality vary considerably with the resolution, and to compare configurations one must compare images made at the same resolution. Holdaway (1998, priv. comm.) does this using one of Dan Briggs' very pretty programs in SDE, which figures out how to weight the uv-data to give any (reasonable) desired beam size. Unfortunately this is not yet available in AIPS, and in the interests of simplicity³ I simply convolved the CLEAN images (with residuals restored) to a common Gaussian beam using CONVL. This will introduce some errors because the residuals do not have the same point-spread-function as the CLEAN components, but for the deep CLEANs considered here this should be a small effect. At any rate the fidelity seems reasonably robust to minor differences in the restoring beams.

These simulations are summarized in Tables 1-4, with a few sample contour plots of the resulting images and difference maps (simulations-truth) shown in Figures -. In all cases IMAGR recovered the proper total flux density was recovered to within 1%; the case of VTESS is covered below (§). The contour plots are not terribly informative, except to show that these four configurations all produce images which appear visually to be of similar (and reasonable) quality. Even the snapshots, although rather `blotchy,' recover the main, and even some of the subtler, features of the sources. The difference maps basically illustrate the tendency of CLEAN to produce a mottled structure⁴, as well as (in the case of snapshot observations of Cas A) the alternating positive/negative ripple characteristic of CLEAN when applied to a large, bright disk. For Cas A in particular one might expect MEM to do a better job, and the two deconvolution algorithms are compared for a few sample simulations in § below.

In sum, there are no major, obvious differences between images made with C or CS configuration of small or moderate-size sources: as expected, any differences due to the change in intermediate baselines are subtle. I therefore turn next to quantitative measurements of the image quality.