Signal-to-Noise ratio is a fundamental concept in engineering. It sounds intimidating — and it can be, if you really dig into it — but at a high level, the idea is simple: noise is an inescapable fact of life no matter what type of signal we’re talking about, and one way to gauge the quality of a signal is to compare the signal level with the noise level. This is called Signal-to-Noise ratio or SNR. An SNR of 1 indicates that the signal and noise are comparable which is (obviously) not desirable. Ideally, we want SNR to be much greater than 1 so that the signal is far greater than the noise and therefore easy to isolate.
SNR is typically measured as a logarithmic ratio in decibels (dB) where an SNR of 1 translates to 0 dB. For the sake of simplicity, in this article it will be discussed as a simple ratio.
Since photography involves a signal (light) as well as noise, a basic understanding of SNR is beneficial for most advanced photographers — including those without a strong technical/engineering background. To that end, I will present the information by way of an analogy that will explain the underlying concepts without delving into complex technical details.
Consider a signaling system where you are camping near the bank of a large lake. Your friend is on the opposite bank and communicates with you via Morse code by making waves at fixed time intervals that travel toward you. Metal cans, strung together and floating near the edge of the water, make a rattling sound when a wave is detected — a ‘dash’ — whereas silence indicates a ‘dot’. You record the incoming information and translate it to the final message. In this scenario, the wave is equivalent of the light signal and you are analogous to the image sensor receiving it. The fully decoded final message represents the image.
Now, even without any stimulus, the surface of the lake will have ripples, small waves and general random motion. That is equivalent to what we call ‘noise’ in photography.
There are multiple sources of noise in photography. For the sake of simplification, only the always-there, random component called ‘photon noise’ is discussed here.
The result will be a constant, low-grade rattling of the cans. Now if the waves being generated by our friend on the other side are roughly the same size as the random motion of the lake, it will be very difficult to distinguish the sound of an incoming wave from the noise (SNR ~ 1). You will hear a faint continuous rattle punctuated occasionally by a louder noise that could or could not be an incoming signal. The final decoded message will be full of errors. This is the equivalent of capturing very little light, resulting in a low SNR and a noisy image.
If the person on the other side is able to generate waves that are much larger than the random motion of the lake, resulting in a loud rattle that clearly indicates the presence of a wave, then our recorded message will be far more accurate. The larger the incoming waves, the fewer the errors. This is the equivalent of dialing up the SNR. The noise is still there, unchanged, but the incoming signal has overwhelmed it to the point where it has virtually no effect on the integrity of the incoming message. This is the same as letting in more light either by opening the aperture or slowing the shutter to increase the SNR so that the final image is effectively noise-free.
What if it is not possible to open the aperture or slow down the shutter? In other words, what if the person on the other side cannot generate waves larger than the random motion of the lake. To get around this, you’ve created a clever contraption (amplifier) that detects an incoming wave at the input and produces a large wave at the output. Now you’re able to clearly hear the rattle of the cans even when the incoming waves are very small. There’s one problem though. The contraption often confuses the lake ‘noise’ with an incoming wave and amplifies it as well. In this case, the final decoded message will contain fewer errors than before, but will not be error-free. This is because we’ve improved the signal but amplified some of the noise as well. The SNR is higher than it would be without amplification but not high enough since the noise component has increased with the signal. This is how ISO works — the incoming signal gets amplified, amplifying the noise with it — and that is why high ISO images tend to be noisy.
Finally, consider the very first scenario where the incoming waves are very small (SNR~1) but now you don’t have your clever ‘amplifier’ contraption. To get around this problem, you make an audio recording of the sounds being detected and then play them back at a high volume. In other words, you are digitally emulating the behavior of the wave amplifier. Now there are two possibilities. If the recording device is of low-quality and adds noise on top of the recording, then the net effect would be to decrease the SNR (Noise has increased while Signal has stayed the same). By turning up the volume and amplifying the signal, you will be able to better hear the incoming waves but in addition, you will not just hear the noise that was always there but also the noise added by the recorder. The final decoded message will be worse than when you had employed the contraption. On the other hand, if the recording device does not add any noise on top of what was already there, then the digital amplification will be no different from analog amplification and the final decoded message will be identical. Viola! This is what we call ‘ISO Invariance’.
Now, let’s step away from the analogy and recap what we have learnt purely from the perspective of photography:
Noise is always present and there is no way to get around it. Our goal is to increase SNR as much as possible by capturing enough light such that it overwhelms the noise and renders it invisible. If there is no way to capture more light, we can try to amplify whatever light is being received. But this will amplify the noise as well resulting a higher than desirable SNR. Cameras with ISO invariant sensors don’t affect SNR and so brightening the image in-camera with ISO amplification is equivalent to brightening the image in post-processing.
Minimizing noise is key to capturing the highest quality images possible. Since light and noise are inextricably linked, we need a tool that quantifies one relative to the other. SNR is that tool.