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, nonlinearity is a measure of the
deviation from the following relationship:
Digital Signal =
Constant x Amount of Incident Light
Highperformance CCD cameras 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
solidstate imagers, which can exhibit nonlinearity
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 nonlinearity, 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 leastsquares
regression can then be fit to the data.
The deviation of each point from the calculated
line gives a measure of the nonlinearity
of the system. The nonlinearity can be reported
as the sum of the maximum and minimum deviation
divided by the maximum signal as a percentage:
