Mosaicking
Keywords: astro-noema-sensitivity-estimator

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Mosaicking

Mosaicking is a particular case of wide-field imaging: The user wishes to observe a given field of view larger than the primary beam size with a sensitivity as uniform as possible.

The targeted field (which area is , define by the user) can be divided in a number of independent resolution elements or independent (primary) beams . We have:

| (25)

where is the area of the primary beam. It is linked to the telescope full width at half maximum ( ) by

| (26)

The 0.8 factor represents the truncation of the beam at 20% of its maximum, which is performed during the imaging process.

Note that is not the number of pointed positions that are observed for the mosaic ( , see below).

For the sensitivity estimation we assume a standard sampling of targeted field and the on-source time is equally divided between the independent primary beams in the targeted field of view. To first order, we thus yield:

| (27)

| (28)

There are several subtleties in this computation.

- must be larger than 2 times (below this we advise to use the track sharing mode with two independent fields).
- The processing (imaging and deconvolution) of a mosaic implies a division by the primary beam of the interferometer. As the primary beam is to first order a Gaussian decreasing to zero, this implies that the noise of the mosaic will vary over the field of view. In particular it increases sharply at the edges of the field of view. In other words, Eq. 27 does not apply to the mosaic edges!
- The cycling of the pointings of the mosaic should ensure Nyquist sampling of the observed field of view. This implies that there is an important redundancy between the pointings, contrary to track sharing where the sources are supposed to be fully independent on the sky. For instance, when mosaicking with a hexagonal compact pattern, each line of sight will be observed by 7 contiguous pointings, except at the mosaic edges. It can thus been shown that the number of mosaic pointings, , is related to the number of independent elements through

  | (29)

  for a correctly sampled mosaic. Equation 27 is only valid inside a correctly sampled mosaic.
- The pointings of a mosaic must be observed in short time cycles to ensure that all pointings are observed with similar weather conditions and that they share similar coverage. This minimizes the shift-variant part of the interferometer wide-field imaging response. This calls for the shortest possible integration time per pointing. However, the interferometer takes time to slew from one pointing to the next one without integrating. As a result, the observing efficiency is degraded in the cases of mosaics and we have another relationship between the elapsed telescope time and the on-source time as:

  | (30)

  where is the integration time per pointing and is the time to slew between two consecutive pointings. Having a large integration time per pointing compared to will decrease the mosaicking overhead. This requirement is in sharp contrast with the previous one, namely the need to homogenize the interferometer wide-field response. The best compromise comes from two different considerations.
  1. The smallest integration time is set by the acquisition system (for instance, the maximum achievable data rate). In pratice, we enforce that

     | (31)

  2. The distance covered by a visibility in the -plane during an integration should always smaller than the distance associated to tolerable aliasing (see Pety and Rodríguez-Fernández 2010 for more details). This can be written as the following condition (Eq. C.3 in this article)

     | (32)

     where is the map angular size, and the angular resolution. For a given angular resolution, the interferometer minimum integration time corresponds to

     | (33)

     where is a ad-hoc integer set to 5 to ensure the condition defined in Eq. 32.
  As the typical slew time between two pointings is sec, we yield that

  | (34)

- If the time to cycle all the pointings, , is set to 45 minutes, we yield that the maximum number of pointing per track is

  | (35)

- Finally, if the PI wishes to observe an area that will require more that 130 pointings per independent track, the estimator will ask to either increase the requested elapsed telescope time or to decrease the requested field-of-view area. The computation is done as follows.
  1. The number of tracks is then computed as described in section 4.1.
  2. The number of point per track is then This value must be lower than .

In summary, the sensitivity of a Nyquist sampled mosaic is

| (36)

| (37)

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