The Signal-to-Noise Ratio quantifies the performance of a sensor in response to a particular exposure. It quantifies the ratio of the sensor’s output signal versus the noise present in the output signal, and can be expressed as :
SNR = 20·log(Sout/?out)
With :
- SNR : signal-to-noise ratio [dB],
- Sout : output signal of the sensor [DN, V, e–],
- ?out : noise present in the output signal [DN,V, e–].
Notice that :
- the output signal and the noise level need to be expressed in the same way : in digital numbers (DN), in Volts (V) or in number of electrons (e–),
- the specification of the SNR only makes sense if also the input signal is clearly specified. Without input signal, there is not output signal,
- the noise is the total temporal noise of all parts, included in the pixel itself as well as the readout chain of the pixel. For some applications the photon shot noise is included in ?out as well, for others it is not (see further).
A few important remarks w.r.t. signal-to-noise ratio :
- the signal-to-noise ratio specified for an imager is a single number that is valid for all pixels. Because the pixels are analog in nature, they all differ (a little bit) from each other. About 50 % of the pixels will have a lower signal-to-noise ratio than the specified value and about 50 % of the pixels will have a higher signal-to-noise ratio than the specified value,
- that single number does not have any information about the dominant noise source, neither about the column noise, row noise and/or pixel noise,
- the fixed-pattern noise is not included in the definition of SNR. The argumentation very often heard is that fixed-pattern noise can be easily corrected, but any correction or cancellation of fixed-pattern noise may increase the level of the temporal noise and will reduce the signal-to-noise ratio,
- in the case the sensor is used for video applications, very often the photon shot noise is omitted in the total noise ?out, and actually the SNR listed in the data sheets is much higher than what the reality will bring. If the sensor is used for still applications, mostly the photon shot noise is included in the total noise ?out,
- in a photon-shot noise limited operation of the sensor, the noise ?out is by definition equal to the photon shot noise, and the maximum SNR that can be delivered by the sensor will be :
SNRmax = 20·log(Ssat/?Ssat) = 20·log(?Ssat) = 10·log(Ssat)
With :
- SNRmax : maximum signal-to-noise ratio [dB],
- Ssat : saturation output signal of the sensor [e–],
- the various noise sources present in a sensor do (strongly) depend on temperature, so will the SNR. There is not a single noise source that is becoming better (= lower noise) at higher temperatures. But in most data sheets the SNR is specified at room temperature. Be aware that sensors that are not cooled or temperature stabilized, will run at a higher temperature than room temperature due to the self-heating of the sensor in the camera. This effect will automatically reduce the SNR below the specified numbers in the data sheet.
In conclusion : the SNR specified and its value found in data sheets can never be reached in real imaging situations by all pixels because it is an average number, the fixed-pattern noise is not taken into account, the self-heating of the sensor lowers the SNR, and moreover, in many video applications the photon shot noise is omitted.
Albert, 16-12-2016.