(V.E.1)
Potential detections in any data stream were found by applying a narrow-bandpass, digital filter at each point in the data stream. This filter consisted of an eight-point, zero-sum, square-wave which subtracted the first and last two data points from the middle four (Eq. (V.C.1)). When the filter passed over a source it gave rise to a characteristic peak, and thus picked out structures whose width spanned approximately four sample points. If we denote the spatial sampling frequency of the level 0 data stream by S (i.e. S is the number of data samples per arc min in the data stream of level 0), then the approximate width of an object (in arcmin) detected by the square-wave filtering the kth level data stream is given by,
(V.E.2)
The spatial sampling frequency, S, was approximately 4 in
the 12 µm and 25 µm wavelength bands, 2 in the 60 µm
wavelength
band and 1 in the 100 µm wavelength band. Since it was not
intended to detect structures greater than 8' in extent, the 12
um and 25 µm detections were retained from levels 1, 2 and 3,
corresponding to characteristic square-widths of 2', 4', and 8'.
At 60 µm the level 1 and 2 data streams were searched for sources
4' and 8' in size while at 100 µm only level 1 detections were
kept for small extended sources.
A peak in the kth level data stream which was
picked out
by the square-wave filter was accepted as a potential detection
if its amplitude was greater than 3 times the local noise appropriate
for that data stream. The amplitude of a square-wave peak was
defined as
(V.E.3)
where E is the maximum value attained above zero in the square-wave
filtered data stream. The noise was estimated in the same way
as described for point sources.
Since a source typically produced detections in more than
just a single data stream for a given detector, each candidate
detection from a level k data stream was compared with all candidates
from the level (k + 1) data stream of the same detector that were
within a distance of five level k samples. In such a comparison
the detection with the largest square-wave peak was chosen as
the best representation of the source, and other detections were
rejected. To reject sources larger than 8', a comparison was also
made with the amplitude on a scale of 16'. If, as a result of
this comparison, the accepted detection had a characteristic size
of 16' (corresponding to a level 4 detection at 12 µm and
25 µm, a level 3 detection at 60 µm, and a level
2 detection at 100 µm),
then this source was rejected. Similarly, since point sources
were also to be excluded a comparison of each extended source
detection was made with any level 0 detections (point source)
in the neighborhood. If the level 1 detection was found to have
a square-wave
amplitude less than 0.75 times the level 0 amplitude, then no
extended source was identified. The value 0.75 proved to be optimal
for the discrimination between point-like and extended sources
and was evaluated after processing data from the Large Magellanic
Cloud, where many small extended sources could be clearly seen.
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