Calculating CCD Signal to Noise Ratio
A related measurement to sensitivity and noise is the signal to noise ratio. Let's consider the theoretical prediction of signal to noise for a typical camera. If we assume we have a number of photons P falling on a camera pixel with a Quantum Efficiency DQE this will generate a signal of Ne electrons as below.
The incoming photons have an inherent noise ?signal known as photon Shot noise and as the photons follow Poisson statistics this is the given below:
The other noise sources are: ?readout is the readout noise, ?dark is the noise resulting from thermally generated electrons (so called dark signal) and ?signal is the noise generated by the photon signal. Putting these terms together we can then generate an expression for the signal to noise ratio for a typical camera:
Substituting for the expressions for Noise we can see the equation for signal to noise is as follows:
The thermal noise component Ndark is a function of temperature and exposure time and in the limit where the exposure time is very short and the CCD is cooled to a low temperature this term is negligible.We have also neglected other factors that affect the signal to noise especially of EMCCD cameras and ICCD cameras these will be covered in more detail in a later section.The plot for the signal to noise ratio for a typical back illuminated CCD camera versus for an ideal detector is shown in figure 1. In this plot we have taken the example when the readout noise of the CCD is 10e and the QE is 93%.It can be seen by manipulation of the equation that the signal-to-noise ratio approaches that of an ideal detector in the situation when:
which can be rearranged as thus:
To achieve good signal to noise performance for a camera with a readout noise of 10e- the photons per pixel P must therefore be greater than the read noise squared or ~100electrons.