3.2 Data reduction & Analysis
3.2.3 Peeling and Atmospheric Modelling
Although self-calibration greatly improved on the main calibration imaging results, the final im- age still suffers from artifacts around bright sources which inflate the noise level of the image and restrict the quality of the resulting scientific analysis. One of the major sources of visibility phase
Figure 3.5: 2D schematic showing the four calibration regimes discussed by Lonsdale (2005) that depend on the field-of-view of the telescope and the antenna spacings. The array is represented by three antennas at ground level, each with their own field-of-view (red, green, and blue regions, respectively). The antennas observe the same source through the ionosphere which is shown by the grey bubbles. Top left (regime 1): Compact array of small antennas with narrow primary beams. Top right (regime 2): Extended array of small antennas with narrow primary beams.
Bottom left (regime 3): Compact array of large antennas with wide fields-of-view. Bottom right (regime 4): Extended array of large antennas with wide fields-of-view. See text for details.
Source: Intema et al. (2009).
errors is the ionosphere, with severe atmospheric conditions potentially causing amplitude errors as well (Jacobson and Erickson, 1992). Lonsdale (2005) identified four ionospheric calibration regimes defined by the size of the array and the individual fields-of-view of the antennas. These regimes are schematically outlined in Figure 3.5. In regimes 1 and 2 (top left and right panels respectively) the antennas have a narrow primary beam compared to the large scale ionospheric structure and thus they probe a fairly constant ionospheric electron density. In regimes 3 and 4 (bottom left and right panels respectively), the antennas have a large primary beam and therefore
experience variations in ionosphere structure across their fields-of-view. For the compact arrays in regimes 1 and 3, the ionospheric variations across the antennas can be approximated by a gra- dient. However, these variations across the array differ significantly from a gradient and can in fact be quite complex in the case of the extended arrays in regimes 2 and 4, where each antenna views the source through a wholly different portion of the ionosphere. The phase variations in- troduced to the visibilities become more complex as one moves from regime 1 to regime 4, with the latter being the most complicated case where each antenna requires its own phase correction that changes across its primary beam, i.e. in this case the ionosphere is a direction-dependent effect. Self-calibration cannot account for this as it produces only a single phase correction per antenna (Pearson and Readhead, 1984).
There are several proposed and existing methods to deal with direction-dependent iono- spheric calibration in radio data reductions, e.g. direction-dependent modifications to the stan- dard self-calibration schemes (Schwab, 1984; Subrahmanya, 1991), field-based calibration (Cot- ton et al., 2004), RIME-based mathematical schemes (Smirnov, 2011), clustered calibration (Kazemi et al., 2013), non-linear Kalman filters (Tasse, 2014), and Bayesian techniques (Lochner et al., 2015). Solving for atmospheric phase errors in a direction-dependent way is the main pur- pose of the SPAM package, which is designed to work in the fourth Lonsdale regime. It uses source peeling of bright sources within the target field (e.g. Noordam, 2004) and use of a single or multi-layered phase screen to model the phase errors (see Intema et al., 2009, for full details on the algorithms involved).
SPAM’s peeling process is fully automated. In essence, bright sources in the field-of-view are identified and a measurement for the atmospheric phase structure is made by phase calibrat- ing on these sources over short time intervals. A virtual phase screen (or multiple screens) is imposed at a set height above the Earth’s surface and all peeled source–antenna pair phase mea- surements from the peeling process are mapped onto this screen. This is then fit with a set of optimised Karhunen-Lo´eve base functions which represents the stochastic ionosphere as a linear combination of orthogonal functions. The fitted ionospheric model will reproduce the phases in the measured directions, but when applied on-the-fly during imaging, will also predict the direction-dependent phase corrections for arbitrary viewing directions.
After self-calibration is complete, we completed the following direction-dependent SPAM recipe:
1. First bright sources in the model-subtracted self-calibrated data are identified using the primary beam facets, and peeled. Depending on the quality of the precedingSC3image, sources with fluxes above 0.02–0.04 Jy are identified as peeling candidates in our reduc- tions. Each source is visually checked to ensure they are suitable candidates for further peeling processing. Sources that are too extended or appear to be heavily influenced by artifacts are excluded from the fitting procedure.
2. An ionospheric model is then fit to the selected peeled source phases. For our datasets, the model used between four and ten peeled sources for this initial ionospheric fit.
3. Instrumental phase effects are then removed and the ionospheric model is re-fit before automatic flagging procedures are applied.
4. The model phase solutions, peeling amplitude solutions, and delays are combined to pro- duce a set of peeling solutions which replace the model solutions. The uv-data is then imaged to produce the first peeling result,SP1. Our images show a major improvement in phase errors around the more extended, bright sources in the field, compared to the SC3images, with the map noise being reduced by up to 25% in areas affected by strong sidelobes.
5. Bandpass phase solutions and amplitude calibration solutions are determined before outlier flagging is performed. Once the solutions are applied, the data is re-imaged to produce imageSP1A. Small improvements in amplitude errors around bright sources are evident, although the map noise is largely unchanged.
6. Automatic flagging of baseline-dependent problems, which appear in the image as strip- ing, is performed before subtracting the primary beam sources and applying baseline- and residual amplitude-based flagging. The data is then re-calibrated against the peeling solu- tions and re-imaged to produce imageSP1B. For some of our datasets, this image appeared
marginally worse than the previousSP1Aimage in terms of the noise level, however am- plitude errors were slightly reduced around the brightest sources.
7. Steps 1 to 6 are then repeated to create imagesSP2,SP2A, andSP2B. This second round of peeling improves on the first round by fitting ionospheric phase solutions to between 12 and 20 sources for each of our datasets, with identified source fluxes as low as 10 mJy. For the brightest sources the second round of peeling shows a flux measurement change of up to 2%.
The SP1B and SP2B images for ACT-CL J0014.9−0056 are shown in the top right and bottom left panels of Figure 3.4, respectively. The first round of peeling reduces the visible sidelobes of most of the bright sources, in particular the extended source to the North-East. For the majority of our clusters, the second round of peeling produced a good image with which to finalise the reduction process. However for clusters ACT-CL J0014.9−0056 and ACT-CL J0045−0152, additional rounds of self-calibration and peeling were performed due to source shape errors introduced during the final round of peeling and in an attempt to further reduce sidelobes that affected the central part of the image. In the case of ACT-CL J0014.9−0056, the final post-peeling image that lead to the best quality image after primary beam and flux scale corrections (see§3.2.4),SP4, is shown in the bottom middle panel of Figure 3.4. The final post- peeling images for our cluster sample have a rms noise in the range 30−87µJy beam−1. The target rms from our observing proposal was 40µJy for each of our clusters.