Sophisticated software is needed
to exploit the matched images produced by the
PNS. We are developing the required procedures with the help
of simulated data. For the moment, we have tested the idea
with conventional software such as DAOPHOT, which gives
a *minimal* performance estimate.

An IRAF script
was used to estimate the *completeness* of the PNe
detection out to various distances in the fixed integration time
of 28,000s for a 4m telecope (but now for a bandwidth of 20Å):

D PN* SNR Detection Completeness Mpc counts PN* PN* +1.0 +1.5 +2.0 +2.5 25 3390 31 100% 70% 44% 13% 10% 15 9414 70 100% 100% 88% 56% 38% 10 21190 122 100% 100% 100% 100% 88%PN* are the brightest PNe and completeness was checked to 2.5 magnitudes below PN*.

The background level (B) was taken as 8772 counts, and SNR=S/sqrt(S+B) has been shown for PN*. Here `completeness' was estimated by running numerous trials with randomised noise.

**2. Receiver Operating Curves**

In the previous table,
no account was made of the number of accompanying
spurious detections, which is an important factor.
Roughly speaking, if each 2k x 2k image contains
100 false detections, then there is a 1/20 chance in
finding a corresponding peak in the second image for
each false detection (based on the fact that
PNe pairs must occur along the *same row*). Thus,
there will be 5 spurious final identifications.
The relationship between detection
efficiency and false detections been investigated by
TSA. In the
accompanying
figure, for three values of the SNR in the image,
a line is traced out from left to right corresponding
to the lowering of a detection threshold. As one does
this the number of detections increases but so
does the number of spurious detections (here, for
2000x2000 image cells). At a SNR of 5, if
the threshold is adjusted so that the
number of spurious detections is < 1,
the detection efficiency is around 85%.

For a fixed value of the final SNR, the second figure
shows the performance of a 2 arm (50:50) spectrograph
versus a 3 arm spectrograph. The distribution of
photons between the three arms is a variable which
has been optimised here. There is no improvement.

N.D. Aug 2000