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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 ).