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Subtractions of bias and dark-count frames are unlikely to make any
noticeable improvement, but together they represent a zero level which
must be removed before multiplicative operations can be performed. The
bias is a DC level, preset electronically, to ensure that only positive
numbers result in the digitizing process. The bias frame may be modelled
as (A + F(x, y
)); F, the pixel-to-pixel structure of the frame, is
time-invariant, but experience has shown that A, the overall level, may
vary on time scales less than one hour. Determing F is simply a matter of
reading out the CCD many times without opening the shutter, i.e.
recording many exposures of zero seconds. Adding these together and
normalizing defines F(x
, y
) with minimal uncertainties due to readout
noise. A, the level of the bias frame for each exposure, is best
determined by the commonly-used overscan procedure, clocking out a number
of pixels on the chip from which the charge signal has already been
extracted and measured. The result is an oversize array with a strip of
signal-free pixels from which A can be measured for the particular
exposure.
Strictly speaking, a dark-count frames should also be subtracted from each raw frame at the start of the reduction process. In practice, this is rarely necessary. If the dark count is significant (e.g. long exposures, very narrow-band filters, very few photons from the sky background), then the chip dark-count response must be measured. This requires long ``exposures with the shutter closed. Addition of many such exposures (bias removed as above) yields a master dark-count frame, relatively free from readout noise. This frame can then be scaled according to exposure time and subtracted from the data frame. Dark-count frames show significant structure, usually having a ``warm" corner near the readout point.