A major factor in deciding which focal station and CCD to use is how to get the required signal-to-noise ratio in the minimum observing time.
As is discussed in some detail in Section 6.4, the noise level in any CCD image consists of three components, the Poisson noise in the signal, the Poisson noise in the sky background, and the read-out noise. By adding these components in quadrature, the signal to noise ratio (SNR) for stellar objects can be derived:
= Total signal from object being observed * = Signal per pixel from sky background * R = Number of pixels in seeing disk * = RMS readout noise in electrons per pixel * E = Responsive quantum efficiency of the CCD * k = number of photons s A cm at the bottom of the atmosphere from * a star of magnitude . At 548 nm k 1000 photons s A cm * = apparent magnitude of the object being observed * = sky brightness in magnitudes per arcsec (see section 1.3.2) * = pixel area in arcsec * = effective filter bandwidth in Å * = effective aperture of telescope, or geometrical collecting area efficiency * t = exposure time in seconds
These equations can be adapted straightforwardly to spatially extended objects, by putting R equal to the number of pixels in a spatial resolution element, and equal to the apparent brightness of the object in magnitudes per spatial resolution element.
The number of counts obtained in each pixel of a CCD image is actually expressed in ADU (Analogue to Digital converter Units). However, the calculation of the signal-to-noise ratio must be done in terms of detected electrons. The conversion factor between these two numbers (electrons/count) is known as the ``gain'' and is different for each CCD.
The signal-to-noise ratio which can be obtained with a CCD depends only on the following four chip parameters: quantum efficiency at the required wavelength, readout noise, pixel size and saturation level. One further factor may limit exposure time -- cosmic ray detection rate. For broad-band imaging the readout noise is really only important for the currently little used RCA CCD, so for most of the dynamic range of the CCD the signal-to-noise ratio depends upon the square root of the exposure time. Deep exposures should be split into a number of shorter exposures, the length of the short exposures should be sufficient that readout noise is unimportant; should be short enough that objects of interest are not saturated, and ideally should be short enough that there are a number of separate exposures which can be used to filter out the cosmic ray events.