G Description of despiking method used by despike

Figure 13: A schematic of the different display modes for despike. The start of each scan is represented by the letter S and the end by the letter E.

The despike routine works in the following way:

• Create an output grid with a cell of size one quarter of the beamwidth ($\lambda /4D$).
• Calculate the position of every data point in the output coordinate frame and place it in the corresponding cell of the output grid.
• For each cell/bin calculate statistics (mean, median and standard deviation).
• If neither smoothing nor a plot are required simply remove spikes from each cell. Spikes are found if a point in a given cell is further than NSIGMA from the mean of the data in the cell. Spikes are marked bad.
• Write the despiked data to disk (one output file for each input file).

Displaying the data in 3 dimensions (x, y grid and n data points for each bin) would be far too cluttered so the 2-dimensional grid is transformed to a 1-dimensional strip before plotting. The plot shows data value against bin number for all the bins. The transformation from 1- to 2-dimensions can be achieved in many ways but only 5 methods have been implemented in despike. The supported methods, presented graphically in figure 13 and with reference to the bin numbers used in the figure, are:

• SPIRAL: A Spiral outwards from the reference bin (the pointing centre of the map). Using the example presented in the figure the bin order used by the plotting task becomes 28, 20, 21, 29, 37, 36, 35, 27 etc. This means that data from the centre of the array is displayed before the (sparse) data at the edges of the array.
• XLINEAR: unfold each X strip in turn for each Y. In this case the bin order becomes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc. A source in the centre of the array will be displayed in the middle of the default range provided.
• YLINEAR: unfold each Y strip in turn for each X. In this case the bin order becomes 1, 9, 17, 25, 33, 41, 49, 2, 10 etc.
• DIAG1: diagonal strips starting at position (1,1). The bin order in the example becomes 1, 2, 9, 3, 10, 17, 4, 11, 18, 25, 5 etc.
• DIAG2: diagonal strips starting at positions (nx,1). The bin order in the example becomes 8, 7, 16, 6, 15, 24, 5, etc.

In general this means that in the case where the source lies in the centre of the array, the spiral display mode will show the source in the first few bins whereas the other modes will display the source in the middle of the range.

Sometimes spikes skew the statistics of an individual bin to such an extent that a spike lies within the NSIGMA cutoff region (i.e. the spike makes the standard deviation so large that it lies within NSIGMA of the mean). In an effort to overcome this problem a smoothing option is provided. This option smooths the clipping envelope (the region that determines whether a point is a spike or not) across adjacent bins so that fluctuations in the statistics of adjacent bins are reduced. This smooth works in one dimension only and the definition of adjacent depends on the method used for transforming the data to 1-D (parameter DMODE).

Figure 14: Example despiking of a point source. The two outside lines on each diagram indicate the region outside which a spike would be found (the clipping envelope). The middle line indicates the median of the data in each cell. The top two diagrams show the data displayed using Spiral (left) and Xlinear (right) modes. The x-axis indicates that the source is visible for small bin number in spiral mode and for a much larger bin number in xlinear mode. The lower two diagrams show the same thing except that hanning smoothing has been applied to the clipping envelope in each case.

Figure 14 shows an example of the different modes with and without smoothing. Points lying outside the high and low lines are treated as spikes. In this example the smoothing has resulted in the detection of two spikes (probably too faint on this figure but the spikes are in bins 120 (spiral) and 2370 (x)).