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The minimum detectable count
rate for the WFC depends mainly on the background count rate, and the effective
size of an unresolved source. The minimum detectable count rate, ,
can be estimated from the following formula (e.g., de Korte et al., 1981,
*Space Science Reviews*, 30, p. 495-511):

where is the required significance threshold (i.e., signal-to-noise),
is the background count rate in the ``detection cell'', *f* is the fraction of
the total source count included in the ``detection cell'', is
the minimum number of photons required to
constitute a detection and *t* is the integration time.

The ``detection cell'' is the region of the image used to detect the source. For
the WFC, assuming an on-axis source, an appropriate cell area
depends on the filter used, since the point response function is
energy-dependent. For the *S1, S2* and *P1* filters the appropriate
radius enclosing 70% of the total count (i.e., ) is
, whilst for *P2*, . The corresponding cell areas, , are thus arcmin and
arcmin respectively.
The count rates in the background cell are then calculated
as , where arcmin is the
area of the
whole field of view and it the total background count rate of the
whole field.

The minimum detectable count rate as a function of *t* is shown
graphically in Figure 12.1
for , *f*=0.7, .
Three curves are shown, the two labelled `LOW' and `HIGH' are to be used
for the
*S1,S2, P1* filters and are plotted for and
counts s , i.e. for the typical range of
background rates
expected. The low background rates are only achieved for restricted
time intervals, guest investigators should therefore assume the `HIGH' curve
when proposing.
The curve labelled *P2* is to be used for observations with
the *P2* filter
and assumes counts s , i.e. the night-time
background rate expected in this filter (see § 7.8.4 ).

Tue Jun 11 16:18:41 EDT 1996