Signal-to-noise ratio (SNR) describes the quality
of a measurement. In CCD imaging, SNR refers to
the relative magnitude of the signal compared to
the uncertainty in that signal on a per-pixel basis.
Specifically, it is the ratio of the measured signal
to the overall measured noise (frame-to-frame) at
that pixel. High SNR is particularly important in
applications requiring precise light measurement.
Photons incident on the CCD convert to photoelectrons
within the silicon layer. These photoelectrons comprise
the signal but also carry a statistical variation
of fluctuations in the photon arrival rate at a
given point. This phenomenon is known as photon
noise and follows Poisson statistics. Additionally,
inherent CCD noise sources create electrons that
are indistinguishable from the photoelectrons. When
calculating overall SNR, all noise sources need
to be taken into consideration:
Photon noise refers to the
inherent natural variation of the incident photon
flux. Photoelectrons collected by a CCD exhibit
a Poisson distribution and have a square root
relationship between signal and noise.
Read noise refers to the
uncertainty introduced during the process of
quantifying the electronic signal on the CCD.
The major component of readout noise arises
from the on-chip preamplifier.
Dark noise arises from the
statistical variation of thermally generated
electrons within the silicon layers comprising
the CCD. Dark current
describes the rate of generation of thermal
electrons at a given CCD temperature. Dark noise,
which also follows a Poisson relationship, is
the square root of the number of thermal electrons
generated within a given exposure. Cooling the
CCD from room temperature to -25°C will reduce
dark current by more than 100 times. In addition,
many scientific-grade CCD's employ MPP
technology to even further reduce dark current.
Taken together, the SNR for a CCD camera
can be calculated from the following equation:
I = Photon flux (photons/pixel/second)
= Quantum efficiency
t = Integration time
Nd = Dark current (electrons/pixel/sec)
= Read noise (electrons)
Under low-light-level conditions, read noise
exceeds photon noise and the image data is said
to be read-noise limited. The integration time can
be increased until photon noise exceeds both read
noise and dark noise. At this point, the image data
is said to be photon limited.
An alternative means of raising the SNR is to
use a technique known as binning.
Binning is the process of combining charge from
adjacent pixels in a CCD during readout into a single
superpixel. Binning neighboring pixels on the CCD
array may allow you to reach a photon-limited signal
more quickly, albeit at the expense of spatial resolution.
Once you have determined acceptable values for
SNR, integration time, and the degree to which you
are prepared to bin pixels, the above equation can
be solved for the minimum photon flux required.
This is, therefore, the lowest light level that
can be measured for given experimental conditions
and camera specifications.
Visual impact of increasing
SNR of a typical test pattern.