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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.