In order to optimally find sources that are the size of the telescope beam, and suppress this residual large-scale
noise, the Picard recipe
SCUBA2_MATCHED_FILTER may be used. If there were no large-scale noise in the map, the
filtered signal map would be calculated as follows:
where and are the signal and RMS noise maps respectively produced by Smurf, and is a map of the PSF. Here denotes the 2-dimensional cross-correlation operator. Similarly, the variance map would be calculated as
This operation is equivalent to calculating the maximum-likelihood fit of the PSF centered over every pixel in the map, taking into account the noise. Presently is simply modelled as an ideal Gaussian with a FWHM set to the diffraction limit of the telescope.
However, since there is large-scale (and therefore correlated from pixel to pixel) noise, the recipe also has an additional step. It first smooths the map by cross-correlating with a larger Gaussian kernel to estimate the background, and then subtracts it from the image. The same operation is also applied to the PSF to estimate the effective shape of a point-source in this background-subtracted map.
Before running Picard, a simple parameters file called
smooth.ini may be created.
SMOOTH_FWHM = 15 indicates that the background should be estimated by first smoothing the map and
PSF with a 15 arcsec FWHM Gaussian. The recipe is then executed as follows:
The output of this operation is a smoothed image called
map_mf.sdf. By default, the recipe
automatically normalizes the output such that the peak flux densities of point sources are conserved.
Note that the accuracy of this normalization depends on how closely the real PSF matches the
7.5 arcsec and 14 arcsec full-width at half-maximum (FWHM) Gaussian shapes assumed at
respectively (an explicit PSF can also be supplied using the
PSF_MATCHFILTER recipe parameter).