ISO noise quantified

Warning: geek content!

In my previous post, I looked at noise in bokeh areas on my D300. You can clearly see some noise at ISO200 in darker out-of-focus areas on that camera. At the end I showed that the noise is quantified in the jpeg filesize. Being the science geek that I am, I did a quick analysis on it. Here is the filesize plotted vs the ISO rating:



The red curve shows a fit to a simple square-root dependence on ISO. This is not just some arbitrary choice. If the noise is coming from simply photon-counting statistics, you expect approximately a square root dependence of the signal-to-noise ratio on exposure time. In this case, this means that the absolute noise should also scale with the square root of the ISO rating. Indeed, you can see, barring an offset of 129 KB owing to the fileheaders and the actual scene information, there is a square-root dependence of the filesize on the ISO speed. Interestingly, since the jpeg encode is a visual compression scheme, this should correlate with how visible the noise is as you could clearly see in my previous post. Also, at ISO 100, the amount of noise is indeed almost negligible as you can see from the negligible difference in size between the ISO 100 jpeg (144 KB) and the limit at (the impossible) ISO 0 of 129 KB.

Now there are some issues here that I have not addressed. 1. Lightroom might be doing more noise reduction at higher ISOs than it is at low ISOs, and 2: Jpeg filesize does not linearly correspond to the amount of noise. This is a toughie!
So you should just take this for what it is, despite appearances, rather unscientific! I do find it intriguing however, that the metric clearly seems to scale with visible noise and that the metric seems to indicate simple statistical noise, meaning that the amplifiers in the camera do not seem to introduce much noise at this light level.