No-one is disputing that binning helps to achieve a higher S/N ratio, but it is of limited value ...You can see that we get between 1-2 stops more S/N ratio with 2x2 pixel binning.
Agreed; and 1/2 to 1 stop for a 2:1 downsampling or binning. Also, for normal photographic exposure times, substantially less than one second, dark current is rather irrelevant so S/N ratio scales about
- proportional to sqrt(M) for well lit parts of the scene, where shot noise dominates and the result is approximately sqrt(M P Q_e t).
and
- proportional to M in deep shadows, where read noise dominates and the result is approximately M P Q_e t/N_r.
But if instead of binning from 60MP to 30MP (or in general M to 1 down-ressing), one just uses a 30MP sensor to start with (or more generally, reduce the pixel count by factor M, and so increase pixel area by a factor M), the result is about the same: again about half to one gain in S/N ratio in exchange for halving the final pixel count!
- In well lit parts of the image, shot noise again dominates: S/N ratio approximately sqrt(P Q_e t).
Reducing photosite count by factor M and so increasing photosite area by a factor of M has the effect of increasing P by about that factor of M, so has the same effect on S/N ratio as above: a factor of sqrt(M).
- In dimly lit parts of the scene where read noise dominates the S/N ratio is about P Q_e t/((N_r)^2).
It is tricker to work out the effect of photosite increase because you have to know how the read noise N_r varies with photosite size. For this you should note that the major source of read noise is probably amplifier noise, and with larger photosite size and well capacity, the amplifier has to be larger, and it is likely that the read noise level in electrons increases. For example, CCD's for digicams with small photosites have read noise of around 2-4 electrons, whereas the best large photosite CCD's from Kodak are at around 12 electrons. Also, the history of Kodak CCD's show read noise in electrons increasing with pixel size. What is more, the Kodak data I have seen has read noise scaling roughly with the square root of pixel area! This makes some sense in terms of what little I know about amplifier shot noise.
If that pattern of read noise N_r increasing as the square root of photosite are holds, then increasing pixel size by a factor M increases P by a factor M and also increases N_r by sqrt(M), so S/N ratio improves by factor sqrt(M). That would be worse that for binning!
If instead, amplifier noise does not increase at all, the improvement is a factor of M, as for binning.
In all these rough reckonings, I see no clear advantage for fewer, bigger photosites over binning when the lower resolution is sufficient. So I am inclined to trust Kodak, Dalsa and other industry players over half-baked theory in internet forums, including my own.
Of course if one NEVER needs the higher resolution, a lower res. sensor probably has some marginal advantages. But unfortunately for MF makers, high end 35mm systems will probably take over that market.