Low light conditions: signal to noise ratio

The signal to noise ratio SNR is defined by the ratio of the incoming signals average value to its standard deviation. The diagram below shows the signal to noise ratio for image intensified CCD cameras and electron multiplying CCD cameras at very low light conditions.

signal to noise ratio: electron multiplying CCD camera compared to image intensified CCD camera

The EMCCD cameras strong difference between frame adding and long frame again results from the fact, that the EMCCD sensors readout noise is amplified and accumulated with each added frame. So, for the EMCCD camera type long frame operation should be preferred.

Whereas there is no cooling necessary for the ICCD camera, there is a indispensable need for  strong cooling of the EMCCD camera type. This is due to the fact, that the EMCCD sensor also amplifies its own darc current noise to the same amount as the wanted signal. However, the ICCD camera first amplifies the wanted signal to a high level by the image intensifier and then adds the comparativly marginal darc current noise. So, it does not make visible difference if the CCD sensor itself is cooled or not, as long as its temperature does not exceed about 30° C.

An ideal camera signal to noise ratio is just the ratio of the light signals average value to its shot noise, without any additional camera noise effects taken into account. The shot noise of the signal in turn is derived as the square root from the signals average value. Thus, the signal to noise ratio of every incoming light signal simply equals the square root of its average value:

shot noise limited signal to noise ratio for ideal EMCCD and ICCD camera

This ideal signal to noise ratio is shown as black line in both diagrams and the hatched area is therefore not accessible.

signal to noise ratio: EMCCD camera compared to ICCD camera

The second diagram gives the necessary total observation time to yield a unity signal to noise ratio. The total observation time may either result from a long exposure time, long frame, or from a corresponding accumulation of a series of shorter exposure times, frame adding.

For the ICCD camera type the readout noise is not amplified and no significant difference is visible between both operation modi. This predestines the ICCD camera type for frame adding operation which is the precondition for the significant resolution enhancement attainable from our Dynamic Range Expansion System.

The work from which the diagrams have been taken can be found here.