Beam Shapes and Observing Techniques

  
Figure 1: Theoretical beam sensitivity pattern for the Parkes multibeam instrument at 1370 MHz. The individual beam patterns (Trevor Bird, private communication) have a pixel size of 1.5' and have been added in quadrature to give this image. Intensity is inversely proportional to rms noise. Coma distortion (radial elongation of the beam patterns) is evident in the outer ring of six beams, although the beam efficiency is down by only 10%. The RA-DEC grid is appropriate for an observation on the northern meridian with the multibeam array at the nominal pa. The principal electric field is in the vertical (DEC) direction.

The theoretical beam patterns for each of the 13 beams have been added in quadrature as follows:

to give the beam sensitivity pattern shown in Figure 1. The feeds are spaced on a hexagonal grid of side 262.5 mm which translates to an average beam separation on the sky of 28.6', or approximately 2.0 FWHP beamwidths. Because of the beam illumination pattern, the separation of adjacent beams on the sky can vary by % from this nominal value, depending on which pair of beams is considered.

The overlap between the beams in Figure 1 is very small, and so a survey of a contiguous region of sky requires some method to `fill in' the gaps.

Point-and-shoot

The first method of interleaving the beams is perhaps most familiar to spectral-line radio astronomers, especially those used to the `on-off' or position-switching observing technique. The `point-and-shoot' method (also known as the `hop-and-dwell' or `step-and-stare' method) involves moving the telescope to the desired celestial position, integrating for a given time then moving to a new position to fill in the sensitivity gaps. We consider three methods to fill in these gaps, each with an increasing number of interleave positions.

 
 

Figure 2: Three possible point-and-shoot sampling functions for the multibeam array on the left-hand side, with the corresponding sensitivity functions on the right-hand side. i=3 (see Table 2) fills in the largest gaps in the beam pattern, using three interleaved observations per field; i=4 corresponds to a diamond-shaped interleave pattern giving a beam separation of 14'; i=16 corresponds to a nested diamond interleave with a 7' beam separation. Dark regions in the sensitivity functions have higher than average sensitivity.

  
Table 2: Uniformity of sensitivity and beam response for different spatial sampling functions. The observing method is point-and-shoot (Pointed); i is the number of interleaved pointings per field (i.e. i=1 gives the beam response of Figure 1); is the final beam separation on the sky; is the ratio of the maximum and minimum beam response when all beams are linearly summed; is the sensitivity variation, or the ratio of the maximum rms noise to the minimum rms expected in a survey of an extended region.

The simplest method is to fill in the largest gaps in the beam pattern, which requires a total of three interleaved observations for each field. The optimum sky sampling function required to achieve this is shown in Figure 2 (i=3), and the final sensitivity function, produced by convolving the sampling function with the beam sensitivity pattern:

is also shown in Figure 2. The beams are unfortunately too far apart for this to be a useful mode of observing. The theoretical peak-to-peak sensitivity variation across the sky is a factor of 2.71 (Table 2).

A second, more useful, sampling function is the diamond-shaped interleave shown in Figure 2 (i=4), which puts extra beams at the midway position of the line joining each adjacent pair of beams. This gives a average beam separation of 14.0', which is slightly less than the theoretical FWHP beamwidth of 14.4'. The resultant sensitivity variation for a survey of a large region of sky is 1.82 (Table 2).

The final discrete sampling function we consider is the nested diamond-in-diamond interleave pattern of Figure 2 (i=16). This achieves a somewhat better sensitivity variation of 1.28 (Table 2). More importantly, this sampling function provides a 7.0' beam separation which is comfortably close to the Nyquist separation for a hexagonal grid which is for m (1370 MHz).

Scanning

Scanning the telescope across the sky whilst observing is commonly used for continuum surveys in order to reduce the effect of gain instabilities. An example is the Parkes-MIT-NRAO survey at 5 GHz (Griffith et al. 1994). With the Parkes multibeam array, scanning is also possible without substantial beam smearing.

 
 

Figure 3: (a) Sampling function; and (b) Sensitivity pattern for a scanned multibeam observation. A rotation angle of and a track separation of 93' is used. In (b), dark regions have higher than average sensitivity.

  
Figure: Contours of equal peak-to-peak sensitivity variation for images made by scanning the multibeam receiver at various position angles, and with various translations. The contour values are shown, and reach a minimum value of about 1.13 at pa , translation = 93'. The translation direction is taken to be along the vertical axis in Figure 3.

Scans along horizontal or vertical tracks in Figure 1 will produce a `striped' sensitivity function. However, scans at intermediate rotation angles can produce very uniform sensitivity distributions and Nyquist sampling. Based on the theoretical beam pattern, the fastest sampling function (in the sense of covering the most sky for the least number of scans) that gives uniform coverage and Nyquist sampling appears to be one based on an array rotation of and an array translation of 93' as shown in Figure 3a. The sensitivity variation of such a scanning scheme (Figure 3b) is a very low 1.13. This is very acceptable, especially given that the efficiency ratio of the inner and outer beams is . The effect on sensitivity variation of nearby values of array rotation and translation is shown in Figure 4. Uniformity falls off very rapidly for rotations and translations much different from the values at the minimum. However, many other solutions exist which give extremely uniform sky coverage. These exist mainly at translations less than 35' and position angles in the range to , where there is much redundancy in sky coverage.

© Copyright Astronomical Society of Australia 1997