Michael,
The real issue I have with your article that you imply that noise would depend on the number of tonal steps in the dark areas, this is however not generally the case. Noise is coming from different factors, the obvious ones being shot noise (the natural variation of photons) and readout noise. Shot noise is as pointed out in your article proportional to the square root of the captured photons, while readout noise is fixed.
In general we talk about signal, which is essentially the light we detect, and noise which is the unwanted variation in sensor signal. We normally want to maximize signal/noise. If we look at shot noise we know that noise is the square root of the signal, so SNR (Signal Noise Ratio) is also the square root of the signal.
Let's assume that a sensor cell detects 10000 photons. The square root of 10000 is 100 so our SNR would be 100. Would we expose two stops less, the number of photons would be 2500 and SNR would be 50 (which is still very good).
If we assume that darks are three stops below midtones, and that midtones are at 10000 photons when correctly exposed to the right, SNR would be like sqrt(10000/8). With two stops less exposure we would have sqrt(2500/8) = 17.6.
When we reduce exposure further we need also to take readout noise into account which can be something like 10 electrons. This would add up with the shot noise. This addition would be in quadrature so for two step underexposed (relative to ETTR) and three stops under midtones we would have:
Shot noise = 17.6
Readout noise = 10
Noise = sqrt(17.6^2 + 10^2) -> 20.3
Now, a 12 bit converter would see 4096 different values, if we assume that saturation is about 50000 photons the lowest bit would correspond to about 12 photons, while the variation on the number of photons would be around 20. This pretty much also illustrates that there is little practical value in 16 bit converters. Let's assume that we have a new device from Phase Zero, totally devoid of readout noise and having pixels holding maximum 50000 electrons. If we assume 14 bit conversion we would have 16384 steps. Each step would correspond to 3 electrons. With no readout noise SNR would be 1.7, except that Poisson statistics would not be valid for three electrons. There would be little difference in doing 16 bit conversion or 14 bit conversion, and multiplying the signal by four and adding 2 random bits!
Best regards
Erik
Eric,
Saying "maximize signal" isn't terribly useful unless you also explain why. Not everyone (in fact not that many) has the technical understanding needed for that simple phrase to make sense.
Which is why I wrote the article.
Michael
