A Little Math
What is the signal-to-noise ratio in a measurement?
The signal-to-noise ratio is a comparison between the strength of a measured signal to the background variation naturally present in the experiment. There are different ways of reporting the signal-to-noise ratio, but one commonly used measure is to compare the mean value of a measurement to the standard deviation of the background region.
For example, we might want to measure the intensity of a laser beam using a detector. The signal would be the measured intensity when we shine the laser beam on the detector. The noise would be measured as the standard deviation of the intensity measured due to the ambient light when the laser was not shined onto the detector.
Such a definition is commonly used when looking at weak signals in imaging or microscopy. Choosing an appropriate way of reporting the signal-to-noise ratio can depend on details of the situation in question, such as whether the data can take on both positive and negative values, or whether the data can only have positive values.