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Linearity

The fundamental process that occurs in CCD imaging is the conversion
of photonic input to electronic output. Photons incident on the
CCD will be converted to electron/hole pairs and the electrons
will be captured under the gate electrodes of the CCD. These electrons
are then transferred in a "bucket brigade" fashion to
the output amplifier where the charge is converted to a voltage
output signal. An analog processing chain further amplifies this
signal and finally it is digitized before being transferred to
a host computer for display, image processing and/or storage.
The transfer function between the incident photonic signal and
the final digitized output should vary linearly with the amount
of light incident on the CCD. Hence, non-linearity is a measure
of the deviation from the following relationship:

Digital Signal = Constant x Amount
of Incident Light
High-performance CCD (HCCD) imagers have extremely good linearity.
Deviations from linearity are often less than a few tenths of
a percent for over five orders of magnitude. This is far superior
to video CCDs and other solid-state imagers which can exhibit
non-linearity of several percent or more. For quantitative imaging,
linearity is a stringent requirement. CCDs must be linear in order
to perform image analysis such as arithmetic ratios, shading correction,
flat fielding, linear transforms, etc.

There is no standard method for measuring or reporting linearity
values. Typically the numbers are reported as percent deviations
from linearity (it may be specified as linearity or non-linearity,
however).

One method that can be used is to plot the mean signal value
versus the exposure time over the full linear range (linear full-well)
of the CCD. A linear least-squares regression can then be fit
to the data. The deviation of each point from the calculated line
gives a measure of the non-linearity of the system. The non-linearity
can be reported as the sum of the maximum and minimum deviation
divided by the maximum signal as a percentage: