16.3.1 UV_SINGLE

Incorporating short spacings from the 30-m into Plateau de Bure data is a 3 step process for the user.

• Creation of a table of spectra
  First, one should resample (in frequency) all spectra to same frequency grid than interferometer data, using command RESAMPLE in CLASS). Then a table of spectra is produced using command GRID (with no options) in CLASS.
• Image creation
  The next step is the creation of ``well behaved'' map from the table of spectra. It starts with resampling (in space) on a regular grid by a convolution kernel (interpolation techniques such as the GREG command RANDOM_MAP are inappropriate). Weights are also resampled. Then, we follow by extrapolation to zero outside the convex hull of the mapped region, using a kernel twice broader than the single-dish beam, to avoid introducing spurious structure.

  Because of noise, the map still contains spurious high spatial frequencies. These are removed during the uv table creation. The algorithm steps are

  • Fourier transform of map and weight images
  • Division by Fourier Transform of the single-dish beam
  • Gridding correction (division by Fourier Transform of the gridding function)
  • Truncation to some maximum uv distance (< dish diameter)
  • Inverse Fourier Transform back to image plane
  • Multiplication by primary beam of the interferometer
  • Fourier Transform to uv plane
  • Normalization of the weights so that the sum of weights is the weight of the total flux (derived from integration time, bandwidth and system temperature).
  • Optional application of an amplitude scaling factor.
  • Optional application of a weight scaling factor.
  This produces a uv table with optimal weights in terms of signal to noise ratio for the total flux, and with effective tapering following the single-dish illumination pattern, except for the truncation at some uv distance.

• Merging with interferometer data
  The final step is to merge the resulting uv table with the interferometer uvtable. Re-weighting and re-scaling is again possible at this stage. Note that the choice of weighting function is arbitrary. It may result in poorly behaved synthesized beams when combined with the interferometer uv data. Weights can be lowered by any arbitrary factor (increasing the weights is only allowed if signal to noise is not an issue). A good choice is to adjust the weights so that there is almost no negative sidelobe.