= 500 nm carries an energy of E = h
= hc/
= 3.97 x 10-19 Joules. Modern CCD cameras are sensitive
enough to be able to count individual photons. (Camera sensitivity will be
discussed in Section 7.2.) The noise problem arises from the fundamentally
statistical nature of photon production. We cannot assume that, in a given
pixel for two consecutive but independent observation intervals of length
T, the same number of photons will be counted. Photon production is
governed by the laws of quantum physics which restrict us to talking about an
average number of photons within a given observation window. The probability
distribution for p photons in an observation window of length T
seconds is known to be Poisson:
where 
is the rate or intensity parameter measured in
photons per second. It is critical to understand that even if there were no
other noise sources in the imaging chain, the statistical fluctuations
associated with photon counting over a finite time interval T would
still lead to a finite signal-to-noise ratio (SNR). If we use the
appropriate formula for the SNR (eq. ), then due to the fact that the
average value and the standard deviation are given by:
we have for the SNR:
The three traditional assumptions about the relationship between signal and noise do not hold for photon noise:
* photon noise is not independent of the signal;
* photon noise is not Gaussian, and;
* photon noise is not additive.
For very bright signals, where T exceeds
105, the noise fluctuations due to photon statistics can be ignored
if the sensor has a sufficiently high saturation level. This will be discussed
further in Section 7.3 and, in particular, eq. .