In light of a recent discussion I had with a photographer about the grain inherent in high ISO speeds, I thought I would take minute and write about Signal to Noise Ratios and how they affect image processing in both video and photography. I will try my best to explain this subject as I understand it. I am no electrical engineer however, and this subject can quickly delve into the physics of electronics deeper than I fully comprehend so if you have more observation or clarity on the subject please let me know in the comments below. Ok here we go. So what is a signal to noise ratio?
Wikipedia gives us a good concise base definition: “Signal-to-noise ratio is an engineering term for the power ratio between a signal (meaningful information) and the background noise:”
Basically for an electrical device there is an inherent noise floor in the signal, in a video camera this would be the CCD (or CMOS in some newer camcorders), and in Digital SLR cameras it would be the CMOS chip. The higher the ratio, the more the signal can be “boosted” electronically without increasing noise. However, as we already stated there is always a threshold where noise exist by default simply because of the fact that we are dealing with electronics. For example, a S/N ratio of 60db would give you a cleaner signal than say a 50db ratio.
In video whenever you bump up the gain in the camera you add noise to the image. Why is this the case? By bumping gain, you are essentially adding power to the CCD to AMP or boost the signal, just like audio. However if the signal, or light, is too low, then it’s very close to the noise floor of the CCD or CMOS sensor. So while your signal (the image brightness) is increased, you are also increasing the noise in the chips by electrically boosting the sensitivity of the chip. In a digital still camera the same principal applies. Just the terms change…now we are dealing with ISO, but for the most part its the same process. Higher ISO speed are boosting the sensitivity of the CMOS chip at low light levels to brighten the image, thus also boosting the noise.
Lets examine this in terms of audio. If we record a signal to low and then have to amplify that signal, we hear noise. As we are boosting the overall signal, we are boosting the noise. Because the audio levels are so low as to be close to the levels of the noise, we wind up boosting both of them (and the result is a “noisy” soundtrack). The noise is always there, it’s just that at the right recording levels the difference between the input and the noise floor is so great it will never be heard.
The same principal applies to image processing, whether video or still. Which begs the question…is it possible to use gain or ISO and not see grain? Sometimes it is. Basically the noise increases as the signal decreases, and in imaging that signal corresponds to light. Maybe this waveform will help.
Bright Light
This waveform graphically represents the brightness of an image with 0 (7.5 for ntsc video) being black and 100 being pure white. The noise floor typically resides right around black and just above it. In the first waveform shown above, the signal is plenty strong. There is ample light in the room so the noise isn’t noticed as it resides so low in the signal.
Dark Light
This second waveform represents an image in much lower light. You can see here how much closer the entire signal is to that lower black threshold where all that noise resides. Now to brighten the image we would have to increase the gain, which would amplify the entire signal. What used to reside in the black area of the image (around 0 or 7.5 for ntsc) suddenly gets moved up to say 20, and the noise is now a very visible part of the signal. This is why in the Digital arena its typically advised that you expose to the right of a histogram, preserving as much highlight detail without clipping, and this keeps the majority of the exposed image in the middle and upper end of the vector scope and out of that nasty noise floor in the lower tonal range. Then when you grade the image, pushing it down where you actually want the exposure to be, the noise gets pushed down even darker in the shadows and is even less visible.
Now, all cameras are not created equal and some have a higher sensitivity to light than others. Traditionally in the video world this has been assigned by a lux rating, in the digital photography world this has been designated by a native ISO rating. In addition to the actual sensitivity of a camera to light, and how much light the camera can actually see at a given exposure, the S/N ratio tells us how clean that image can be at that exposure. This measurement in the digital video world is measured in dB or decibels. The higher the number in any given camera system, the higher the ratio of the signal to the noise floor. For example, a camera with a S/N ratio of 61dB (with all other factors being equal) will yield a cleaner image than a camera with a S/N ratio of 51dB. This Chart provided by CCTV clearly illustrates this and gives the ratios in both dB and numeric ratios. 
Obviously signal to noise is just one aspect of a given camera system; there is a daunting list of factors that all work together to contribute to overall image quality. A quality lens, the camera’s digital signal processor, codec and compression, dynamic range, resolution, and many other factors all contribute. However a proper understanding of signal to noise helps us in understanding camera systems and their weaknesses. As a good Director of Photography we of course realize that we make the camera gear work for us and not the other way around, right? So knowing our system and how to compensate for areas of weakness allows us to tweak every ounce of performance out of a camera system. Since signal to noise plays an important role in image quality, both understanding and working with it is helpful information.