The
photon noise, or more commonly called shot
noise, is a
basic physical
characteristic of each light source that cannot be influenced, i.e.
diminished, by any technical device. As described in section performance regimes light
consists of single particles, photons. The
lower the light level the smaller the number of photons which reach our
detecor per unit of time. As a consequence there will not be a
continuos illumination but a "hail like" bombardement by single photons
and the image will appear granulous. The signal intensity, i.e. the
number of arriving photons per unit of time, is stochastic and can be
described by an average value and the appropriate fluctuations.
If I is the intensity of the light signal the Poisson
distribution
gives the signals fluctuations by the standard
deviation
The average intensity value divided by the standard
deviation of the
fluctuations is called signal to noise ratio or SNR
The graphic below illustrates the consequence of
this physical
situation. Lets consider a 16 bit A/D conversion in the ICCD or EMCCD
camera. This results in a 2-byte data word which is forwarded to the
computer by camera. The left hand ordinate gives the
actual signal intensity I, ranging from 20-1 to 216-1.
The abscissa
gives
the numbers of the 16 bits of the data word, which is always divided
into three basic
categories:
- bits which contain the time resolved signal fluctuations, i.e. the
shot noise,
- bits which contain the underlying non-fluctuant part of the signal,
i.e. mainly the average intensity value and
- leading bits which only contain "0".
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What we see is that the number of the bits which
contain the signals
fluctuations due to the shot noise always equals the number of bits
which
denominate the non-fluctuant part of the signal. This is simply due to
equation (2) which may also be written as
This consideration tells that a 16 bit A/D
conversion has no benefit in
itself. If we would use e.g. a 12 bit A/D conversion, the quantization
steps would be larger by the factor 2^(16-12) = 16. The resolution
would be decreased by this factor 16 which means that at the
less-significant-bit end of the data word resolution would be lost. But
the lsb end of the data word only contains the signals fluctuations,
the shot noise. So, reducing the data word from 16 bit to 12 bit would
result in a decreased resolution of the shot noise. The resolution
of the significant non-fluctuant part of the signal would be preserved.
May be its hard to believe but in fact more bits in the A/D conversion
can actually not increase the resolution of the data. There is only one
chance
to increase the resolution: go for higher intensity levels,
i.e. longer time integration of the signal to reach higher signal to
noise ratios. Of course there is a second chance, i.e. to use STANFORD
COMPUTER OPTICS Dynamic Range
Expansion system which strongly
enhances real resolution after
the A/D
conversion and which is
described in
the following section.
To conclude: the usage of a high-bit A/D converter cannot increase the
resolution of the aquired intensity data due to the physical shot noise
restriction. High-bit A/D conversion is a valuable advertising point,
not less, but also not more.
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