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Signal-to-noise

For stellar objects:

with

where readout = rms readout noise per pixel in electrons. is quantum efficiency N is number of photons/sec//cm at the bottom of the atmosphere from a star of 0 magnitude is the magnitude of the star is the effective filter bandwidth in is the effective aperture of telescope, geometrical collecting area efficiency is the pixel area in arcsec is the sky brightness in magnitudes/arcsec is the seeing FWHM in arcsec is the exposure time

CCDs are commonly used to image very faint objects. Most faint objects beyond 20 mag are galaxies, but their extent may be similar to or smaller than the seeing disc, so that the stellar-object s/n calculation above still applies. Alternatively, if the extent of the object is known to be , the s/n can be calculated from (1) by 'modifying' the seeing FWHM from to .

For very extended objects the s/n as a function of time is given by:

where is object surface brightness in magnitudes/arcsec.

The geometric aperture of the INT is 44110 .

Data to carry out these calculations are given in tables 1.1 and 1.2. The starred quantities are typical, intended as guidelines. The current operational values can be found in a performance folder for each chip in the INT control room. Copies may be requested in advance of an observing run from the Support Astronomer. Be aware that electrical pickup, which depends on cabling, ground loops etc. can turn up erratically and increase the readout noise; it is especially noticeable with the GEC chips.

• To try to fix a noisy chip, ask the NA or Duty Tech. to check cables, cards, connectors at the prime focus.

Some sample sums for stellar objects are shown in Fig. 1.8. These curves may well provide adequate information to estimate exposure times for most INT CCD observations. The dramatic effect of seeing is only crudely modelled by the approximation used in (1), which is that the usable signal is spread into an area occupied by the half-power area of the seeing disc. (Clever analysis might recover more signal at the higher values of s/n, but is unlikely to do so at low s/n.) Observations cannot be continued to infinitely faint limits. For short exposure times, s/n signal/readout, i.e. s/n t, the noise-limited case. But for faint objects and long exposure times, s/n , i.e. s/n , the sky-limited case. The point at which the observation becomes sky-limited, the `knees' in Fig. 1.8 marks the point of diminishing returns.