# Imaging limitations

The technique of Synthesis Imaging is affected by a number of limitations. Here, we outline some arising from the array geometry: the field of view such that bandwidth- and time-smearing effects are held below a specified value, and the smallest/largest usefully detectable angular structures. Other limitations, such as propagation effects through the neutral atmosphere or the ionosphere and instrumental effects are not treated here. For more information on aperture-synthesis imaging in general, refer to

- the various European Radio Interferometry Schools (linked from EVN Meetings page)
- transcripts from the various NRAO Synthesis Imaging Summer Schools, e.g., "Synthesis Imaging in Radio Astronomy", eds. R.A. Perley, F.R. Schwab, and A.H. Bridle (1988, ASP Conf. Ser. v6); "Synthesis Imaging in Radio Astronomy II", eds. G.B. Taylor, C.L. Carilli, and R.A. Perley (1999, ASP Conf. Ser. v180)
- lectures in "VLBI and the VLBA", eds. J.A. Zensus, P.J. Diamond, and P.J. Napier (1995, ASP Conf. Ser. v82)
- "Interferometry and Synthesis in Radio Astromony", A.R. Thompson, J.M. Moran, G.W. Swenson (multiple editions)

## Field of View (FoV) Limitations

For VLBI the undistorted FoV is always much smaller than the primary beam of the individual participating antennas. The two main effects responsible for this are bandwidth smearing and time smearing. Of these, time smearing usually places the most severe limitations on the FoV. Both are discussed below. There is also a separate EVN Field of View Guide that discusses these issues in more detail.

## Bandwidth Smearing

Bandwith smearing arises because the telescopes observe over a finite
frequency band (i.e., the larger the bandwidth, the higher the sensitivity).
Averaging the visibilities over frequency range is
equivalent to averaging over a short * radial * cut in the
uv-plane. If the response of the interferometer varies appreciably
over this area or cut through the uv-plane, then structure
corresponding to this variation will be reduced in amplitude or
"smeared out" altogether.

Rapidly varying components in the uv-plane correspond to sources that are located far from the phase centre. The effect of bandwidth smearing on the final image is thus to radialy smear sources located far from the phase centre. The observed peak for the smeared source is reduced (compared to the true peak) but the total flux of the source is conserved.

The effects of bandwidth smearing can be minimised (at the expense of computer processing time and disk space) by not averaging in frequency. The number of frequency points per subband used in the correlation will of course set an fundamental level of BW-smearing, but any subsequent frequency averaging will in turn further reduce the unsmeared FoV.

Here we tabulate the radial distance from the phase-centre for which bandwidth smearing is limited to a 10% reduction in the response to a point source for a sampling of frequency-channel widths for typical "short" (2500 km) and "long" (10000km) EVN baselines. Note that BW-smearing FoV is independent of frequency when expressed as an angle on the sky.

channel BW | B = 2500 km | B = 10000 km | comment |
---|---|---|---|

256 MHz | 77.3 mas | 19.3 mas | full spanned BW for 2 Gbps |

32 MHz | 0.619" | 0.155" | single subband BW for 2 Gbps |

0.5 MHz | 39.6" | 9.9" | typical continuum frequency-channel width |

The FoV Guide contains a more detailed table, keyed by the observing subband bandwidth and number of frequency points per SB in the correlation, along with the formulae by which the FoV values were computed.

## Time Smearing

Whereas BW-smearing involved averaging radially in the uv-plane, in time smearing the averaging is along the elliptical tracks in the uv-plane. The effect of time-smearing is also stronger on longer baselines, since these sweep through the uv-plane more quickly than do shorter baselines. Time-smearing is a much more complicated process than bandwidth smearing, being dependent on the source position and baseline orientation. The total flux density of a smeared component is not conserved. The effects of time-smearing also scale directly with increasing observing frequency. We assume an observing frequency of 5 GHz (6cm) here, and tabulate some indicative values for the radial distance from the phase-centre for which time smearing is limited to a 10% reduction in the response to a point source, for a sampling of correlation integration times and for typical "short" (2500 km) and "long" (10000km) EVN baselines.

integration time | B = 2500 km | B = 10000 km |
---|---|---|

2 s | 22.2" | 5.55" |

0.25 s | 178" | 44.4" |

Again, the FoV Guide contains a more detailed table covering other standard EVN observing bands, along with the formulae by which the FoV values were computed.

## Smallest/Largest Detectable Angular Structure

The angular size of the smallest strcture that can usefully be discriminated is of course closely related to the synthesized VLBI beam. For a truly thermal-noise limited image, the minimum size would scale as ~beam/SNR (but of course, this ideal condition is often not met...)

The angular size of the largest structure detectable (mappable) by the EVN depends on the length of the shortest (projected) baseline (typically Ef-Wb, 266 km). A conservative estimate of the largest detectable angular size is therefore about 0.1 arcsec at 18cm. (Note however that for the time being, Wb is limited to a single 25m antenna, which is currently reflected in the EVN status table and EVN calculator.)

If the source of interest has radio structure on a larger angular scale-size, then joint EVN + e-MERLIN observations can be proposed. In joint EVN + e-MERLIN observing, a number of e-MERLIN out-stations participate in the array and are correlated as individual antennas along with all the other EVN stations, providing a number of baselines in the range of 11-217 km. Currently, all five out-stations can be incorporated at 512 Mbps each (other EVN stations can be observing at higher bit-rates in joint EVN + e-MERLIN observing). VLBI baselines to the Jb, Wb, and Eb telescopes. The inclusion of these shorter baselines allows larger-scale structure on the scales of several arcseconds to be recovered.

Further, it is possible to propose for (near-)contemporaneous separate EVN and e-MERLIN observations, for which e-MERLIN can observe alone at higher bit-rate than it can in a joint observation within a single EVN array. The downside of this would be that there is no baseline in common between the two arrays to help with the mutual calibration of the distinct inner/outer regions of the uv-plane.

EVN webmaster (jive{at}jive.eu)