While looking at resolution so far we have only considered ideal scenarios. In practice, images are never without noise. Noise can come from a variety of factors, including:

• Shot noise caused by the quantum nature of light
• Electronic noise from the imaging sensor we use to measure light, including read noise and dark current
• Out-of-focus light appearing at the plane we're imaging from points either further up or down the imaging axis
• Crosstalk or bleedthrough from different fluorophores from the on we are trying to measure

All of these, and their relative prominence relative to the signal we are trying to image, make up the signal-to-noise ratio. Let's look at how two of these work to better understand how they might affect our ability to separate objects.

When we measure the light coming from the sample, we usually have a system whereby a photon of light hits our sensor, and there is a given probability that this photon will excite an electron. Then, after a given period of time, we measure the voltage from the accumulated charge and we store this as a proxy for the intensity of the light emission intensity.

The probability that a photon will excite an electron is called the quantum efficiency. The excited electrons we measure are called photo-electrons. Shot noise comes from the fact that we may be measuring relatively few photons. If we have 10 photons of light hitting our sensor, with a quantum efficiency of 50%, it would not be uncommon to collect either 0 or 10 photo-electrons due to the probability that none of the photons manage to excite an electron or all the photons do. We could think of it as flipping a coin. From multiple series of 10 throws of the coin, we would expect the average to be 50/50 heads and tails, but it would not be that rare to end up with 10 heads in a row. However, if we take 1000 flips of the coin, the probability that none or all of them are heads diminishes towards 0. Likewise, as the number of photons we collect increases, the individual probability of error in the photo-electron count of individual pixels diminishes. Because of this, generally, the longer the exposure time, or the brighter the signal, the less noisy it will be.

At the same time, when we try to measure the accumulated charge from the excited photo-electrons, there is a certain degree of error in that measurement. We call this the read noise. When looking at specification sheets for cameras, the read noise is normally expressed as a number of electrons. If the read noise is 10 electrons, then we need to collect at least 10 more electrons in one pixel compared to its neighbor to reliably know that it collected more light. When we add the error in the measurement to the shot noise we get much closer to what you might actually expect from your imaging system.

In the end, the main concern is whether the signal-to-noise ratio allows us to reliably see the connections or gaps between objects. In our example above, we can see the connection between the axon and the spines in the high-exposure image, but the noise in the 100ms image is too much to reliably know that they are connected. We could, with our knowledge of the sample and expected behavior tweak a segmentation pipeline to make it more likely to make that connection, but that would introduce a bias in our analysis that should be clearly stated when communicating these results.