The concept of ISO invariance is in vogue at the moment although it is probably relevant to just a few photographers, for example astro-photographers. The concept addresses the relationship between ISO and image noise and, more specifically, asks what is the effect on noise of increasing the ISO setting on a camera.
This article follows on from the one about digital sensors noise. If you haven't read that article, please do so before reading on here.
ISO and noise
It is often said that increasing the ISO setting on a digital camera results in an increase in noise. However, this article will argue that the opposite is the case.
In the article on digital sensors we looked at the electronic process which takes place in the camera to capture an image and record it onto a file, JPEG or RAW. See the diagram below. During the exposure of a scene, an electronic signal is gathered at each element of the sensor. This signal is processed, amplified and then processed further including conversion to a digital format for writing to the memory card.
When we set a value for ISO on the camera, it adjusts the gain of the amplifier in this process and also adjusts the light meter. If the baseline sensitivity of the sensor is equivalent to ISO 100, a setting of ISO 800 will tell the camera to underexpose the sensor by 3 stops and then increase the gain of the amplifier to compensate.
We saw in the article on noise that underexposing a picture reduces the strength of the signal coming from each element but does not reduce the noise and so we get a reduction in signal to noise ratio (SNR) and therefore a reduction in image quality. In our example above of setting ISO 800, it is important to be clear that the corresponding increase in noise and reduction in quality arises from underexposing the sensor, not from increasing the gain of the amplifier.
We tend to think of ISO as one of the 3 factors in exposure: shutter speed, f/number and ISO. In the old days of film, the ISO described the sensitivity of the film emulsion and was fixed, so to achieve a "correct" exposure we only had shutter speed and f/number to adjust. Now with digital cameras we tend to think that we can get a correct exposure by adjusting ISO as well. But this is not the case; we only get a correct exposure of the sensor when we set the baseline ISO of the sensor (typically 100). Whenever we set a higher ISO, we are deliberately underexposing the sensor and therefore degrading the image.
Signal to noise ratio
Refering back to the diagram at the top of the page, we can say that the shot noise and a certain amount of read noise is introduced within the sensor and its elecronics before amplification; this is known as "upstream noise". More noise will be introduced by the electronics after amplification, known as "downstream noise". Clearly, things are much more complicated in a real camera but bear with me.
If we have an underexposed image and increase the ISO to compensate, we will amplify the signal and the upstream noise but not the downstream noise. There should therefore be an improvement in overall SNR. This is a critical point; if we start with an underexposed picture, increasing the ISO setting will tend to improve image quality. However, if we keep increasing ISO, at some stage the amplified upstream noise will likely become much geater than the unamplified downstream noise. As the amplifier increases both the signal and upstream noise equally, the overall SNR will tend to level off.
The diagram above shows this effect for a hyperthetical camera; SNR is shown against ISO on the horizontal axis, with 1 representing ISO 100. Initially an increase in ISO improves SNR as the signal is amplified above any downstream noise. At higher ISO, the (amplified) upstream noise becomes dominant and the curve levels off. This area where ISO has little effect on SNR is the ISO-invariant region.
What this means in practice is that there is little point increasing ISO once in the the ISO-invariant region. We could just download the underexposed image and adjust the exposure in Lightroom or another image processing program.
Different camera designs show different characteristics with respect to ISO and noise, with some being partially ISO invariant and others not. Experimentation with my Canon cameras shows that for all normal use, when underexposing a photo, increasing the ISO always improves image quality when compared to making the same correction in post-processing. Your mileage may differ.
In summary, increasing the ISO on our camera does not degrade image quality by introducing noise. However, increasing ISO is usually associated with underexposure of the sensor, which does introduce noise. In situations where we underexpose the sensor, an increase in ISO setting will generally improve image quality until we reach the ISO-invariant region, beyond which no further impovement will be gained. Whether or not a camera has ISO-invariant characteristics depends on the manufacturer and model.