wrote:

ISO is constant*standard_effect/necessary_exposure, and this is
directly tied to the signal-to-noise ratio.

Funny; my 10D has lower RAW values with the same subject, lens,
aperture, and shutter speed than my 20D, and has a bell-curve of noise
3x as wide at "ISO 800", giving a S/N ratio about 4x as high for the 20D
at the same ISO. ISO 100 has a slightly narrower bell-curve of noise on
the 10D.

Indicated ISO is not necessarily "the" ISO. Measurements on my 1DMkII
show that if we accept that the indicated ISO 100 is really "100", then
indicated ISO 50 is actually ISO 75, and indicated 200,400,800 and 3200
are about 0.9*indicated, and indicated 1600 is 1.0*indicated.

There is also further structure inside the 'constant'; breaking it out
a bit mo

ISO = C(K)*Q*F*(P/SNR)^2

K is the 'standard effect' -- the relative brightness, as that is all
we can observe with our cameras; Q is the quantum efficiency of the
combined filter/sensor, F is the fill-factor of the sensor, P is the
dimension of the pixel, and SNR is the signal-to-noise ratio measured
at 'K'. C(K) is a further constant that depends on the value of K, the
geometry of the pixel and the final scaling to the standard ISO metric.
This formula holds only for values of K that are large enough that the
noise is dominated by photon shot noise: it is the embodiment of the
resolution vs. SNR tradeoff (ie, big pixels == low noise, but sucky
resolution).

If you collect a series of images at all indicated ISO's, for a wide
range of brightnesses (from sensor saturation to bias current), and
make log-SNR plots, you will observe the above equation in effect:
each ISO factor of 2 maps to a 3dB SNR step.

Cross-comparing: the 1D2 is about 3dB better at all indicated ISO's
than a Canon 10D (ie, indicated ISO 400 on a 10D has approximately the
same properties as indicated ISO 800 on a 1D2). This can be explained
with the above equation as as a combination of quantum efficiency, fill
factor, and pixel size improvements. If the DIGIC II has
noise-reduction crud beyond the usual anti-FPN, then from the
standpoint of the above, this just increases the size of 'P' beyond the
physical dimensions of the pixel.