High Dynamic Range Imaging with the VLA We firmly believe the upgraded VLA to be the finest cm-wave interferometer of Earth. But how good is it? We have proof of its sub-microJy sensitivity, but how good an imager is it? Can we make an image with a believable fidelity of many millions? In an attempt to answer this question, I have attempted some deep imaging of bright point sources at high frequencies while in the A-configuration. High frequencies are preferred for this basic test, since we don't want to be limited by pointing offsets. An initial short test using 3C273 at K-band was disappointing. Although it gave great images (both in polarization and in total intensity), the large (18 arcsecond jet) was undersampled by the array, leading to difficulties in deconvolution. Further, the source has considerable sub-arcsecond structure from its 'inner' jet, and has highly polarized (about 7%) nuclear emission. Both are bad things -- as discussed below. A better test object is 3C84, which is stronger (31 Jy from the nucleus), almost completely unpolarized, and has much smaller and constrained structure on the milliarcsecond scale. Further, its more northern declination enable better u-v coverage than 3C273 (which is at a dreadful declination of +02 degrees). Debra generously gave me 6 hours to do this test, under ideal weather conditions, on the last weekend of the A-configuration. Because the theoretical dynamic range, with the much time for 3C84 at Ku band is a whopping 20 million or so -- which we *know* we can't possibly reach -- I split the time between Ku and K bands. Two frequencies at the opposite ends of each band were chosen. The 8-bit system was utilized. The goal is to better understand what our limiations are. Four databases resulted, centered at 14.65, 17.488, 21.53, and 25.5 GHz. 3C84 was observed 69 times, each of 100 to 110 seconds length -- a total of 2.0 hours per tuning. Each of these four tunings spanned 1024 MHz, with 2 MHz channel resolution and eight subbands. The integration time was 1 second, to allow careful editing. In addition to 3C84, 3C48, 3C147, and a local pure point-source calibrator, J0303+4716, were observed, to enable proper flux, bandpass, and polarization calibration. The data were carefully edited and calibrated, with delay calibration for each subband done each second, normalized bandpass calibration done on each scan (3C84 is strong enough to permit this), and a full channel polarization solution enabled by the long 6 hour track and high SNR. (I won't report on these solutions here, but they are a wonder to view!). The observations of 3C84 from the four databases were then split off with the basic calibration applied. 3C84 has an almost perfectly flat spectrum (total integrated intensity). A single subband from each of the four tunings was utilized to generate a model of 3C84 using the usual self-calibration methods -- typical dynamic ranges for these were a few hundred thousand. As is always the case, various oddities were found along the way. Because of the most important of these (the strange slow 'wobble'), I elected to utilize for these tests only the 21.53 GHz database -- this one (taken with the 'BD' IF pair) is nearly free of any 'wobbles', and had all 27 antennas operating. I utilized my 'best' model from this band to generate closure corrections, utilizing the entire 6-hour duration to protect (as best one can) from permanently imprinting the model into the data. Closure corrections were generated in two ways, the the results compared: 1) BLCAL This utilized the entire subband and provides a single closure correction, applied to the entire subband. 2) BLCHN This is Eric's experimental channel based closure calculator -- 3C84 is strong enough to make this feasible. The solutions were found to be very constant across each subband (to a level better than 1 part in 10^4) for nearly every baseline. The subsequent imaging tests showed no difference in the results between databases generated these two ways. Hence, all the results below come from BLCAL corrections. To explore how the rms noise reduces with time and bandwidth, and with and without closure corrections, images were made with a wide range of integration times and bandwidths. The images were 512 x 512, with 10 milliarcsecond cell size, and uniform weight. The 'natural' beam is 70 milliarcseconds. In the table below, the 'rms noise' values were determined from a band across the top of the image, utilizing about 10% of the total pixels. This location is important, as discussed below. To show the remarkable accuracy with which the VLA can measure visibilities, I attach two (u,v) plots, showing the amplitude as a function of baseline length. In order to show the high SNR and relative accuracy, the data shown are integrated over an entire subband (128 MHz), and over 35 seconds. The first plot: UVCOV-NOBL.pdf shows the amplitudes without 'closure' corrections applied. The offset 'clumps' are individual baselines, and its obvious on physical grounds that these points belong with the others. Similar offsets are seen in phase. The result of applying the closure corrrections from the best model are shown in UVCOV-BL.pdf. A remarkable improvement, clearly in the right direction (but not necessarily right!). Note that 3C84 is clearly slightly resolved (by 1 to 2% on baselines to 2.5 million wavelengths) -- and that the resolution is seen in all position angles. An important point for later. So, below is a table showing how the noise in the empty field declines with integration time and bandwidth. The bandwidth involved was increased in two ways: within the subband, and across the subbands. I made the images with 2, 8, 32 and 128 MHz 'chunks' with 1 subband (subband 4 was selected), and with all 8 subbands. And, for each of these eight combinations, images were made with 1 second, 100 seconds, and the full 2 hours (~7200 seconds) integrations. All rms values are in mJy/beam. The peak of the image is 31050 mJy/beam. Int. Time No BL correction BL correction ------------------------------------------------------------------ 1 subband 8 subbands 1 subband 8 subbands ------------------------------------------------------------------- subband BW = 2 MHz ------------------------------------------------------------------- 1 sec. 8.28 3.26 8.23 3.18 100 sec. 1.51 0.69 1.04 0.37 7200 sec. 0.21 0.091 0.116 0.043 --------------------------------------------------------------------- subband BW = 8 MHz --------------------------------------------------------------------- 1 sec 3.94 1.77 3.83 1.64 100 sec. 1.26 0.60 0.46 0.192 7200 sec. 0.186 0.093 0.064 0.025 --------------------------------------------------------------------- subband BW = 32 MHz --------------------------------------------------------------------- 1 sec. 2.40 1.04 2.20 0.841 100 sec. 1.12 0.589 0.380 0.123 7200 sec. 0.176 0.091 0.045 0.0170 ---------------------------------------------------------------------- subband BW = 128 MHz --------------------------------------------------------------------- 1 sec. 1.46 0.733 1.17 0.497 100 sec. 1.06 0.535 0.205 0.086 7200 sec. 0.161 0.075 0.034 0.0146 --------------------------------------------------------------------- So the maximum 'dynamic range' (as defined above) is a spiffy 2.12 million. But is this meaningful? Some Observations: 1) Closure corrections help a lot, and start to become important at a dynamic range of about 10,000. 2) The non-closure corrected images show little improvement with increasing subband bandwidth. (Note the rms for 2, 8, 32 and 128 MHz subband BW for the 100 and 7200 seconds integration -- almost no change with increasing BW). This is not surprising -- the closure errors are constant over these bandwidths. 3) Both BL and non-BL images improve with time, with the Bl-corrected images fairly close to the ideal square-root improvement in BW and time. The noise is the area chosen for the rms calculation remains noise-like (mostly). See below. But of course, the calculation is a cheat. More relevant is the rms noise in an area immediately adjacent to the nuclear core emission. So I selected an area in the 'worst place', and found that the rms noise bottoms out at about 0.075 mJy/beam for all combinations of time and bandwidth. (DR ~ 400,000:1). The rms noise decreases away from the nucleus. My 512 x 512 image size was chosen to minimize computing time. I made a 2K x 2K image for the full BW full time case -- the rms noise is the corners was a 91 microJy/beam -- close to the expected -- for a 'DR' of 3.4 million. To show the map appearances, I include two greyscale images: 3C84-70mas-NoBL.pdf is the 70 mas resolution image with no closure corrections, for the full-time full bandwidth, all-IF case. 3C84-70mas-BL.pdf is the same case, with the closure corrections applied. The rms noise (in the upper regions) is more than 5 times lower. The closure-corrected image clearly shows the problem -- a 'stippled' region which does not change with increased integration time or bandwidth. It is my contention that this is due to an inadequate model utilized in the self-calibration, and closure correction, process. 3C84 is well known to have small-scale (about 40 milliarcseconds) structure north and south of the core. (See Craig's 22 GHz VLBA image taped to his door). The VLA, in A-configuration at K band, clearly 'sees' these extensions, but not with enough resolution to enable an adequate model. To illustrate this, I include a super-resolved deconvolution, using a 20 milliarcsecond restoring beam to show where 'CLEAN' tries to put its components. (3C84-21-20mas.pdf). The north and south extensions are real -- these are equivalent to those shown in Criag's image, although my map has them about equal, while Craig's (surely more correct!) has a fairly strong asymmetry. However, the four 'objects' forming a box are certainly not correct. These are in fact CLEAN's attempt to describe the clear resolution shown in the visiblity plot -- the upper envelope of the visibility plot clearly tells us there is a ~100 milliarcsecond 'disk-like' structure present. We don't have the baseline coverage to clearly identify the details -- CLEAN's attempt is plausible, but probably not right. (I tried VTESS, but that was even less plausible). At this point, I'm open to suggestions. If anybody (who has read this far down) wants to have a try with these data, I'll put the compressed (128 MHz BW, 35 second average) version into my ftp area. Other version (less integration, small BW) can also be moved, for people who want to try their hand. As for the origin of the closure corrections -- these are surely the 'D*D' terms, which we make no attempt to measure or correct. For an unpolarized source, this contribution, of about 0.1% amplitude, is constant in parallactic angle, so acts like a simple offset. The corrections we determine are of the correct magnitude. A final note of interest: The 'Q' and 'U' maps are very much worse than either I or V -- about ten times noisier. The origin of this is also easy to identify -- for an unpolarized object the 'RL' and 'LR' signals are due to D*I terms -- much larger than D*D. And, the leakage signals rotate with parallactic angle as well.