How to get the best raw exposure, part 2

In a CMOS sensor the saturation is determined by the SF output swing, that in turn is determined by the supply voltage of the output circuitry. The CG is determined by floating diffusion capacitance, and will be chosen to give the design voltage swing at the highest design exposure ('base ISO') - which in the end makes it all linked - the saturation voltage in the pixel itself will be inversely proportional to the CG. Still, Don was talking about small-signal performance, as I understood it - and small pixel/high conversion gain has an 'advantage' in the voltage domain so far as that goes. I think it's the kind of 'advantage' that is purely theoretical.

Rejected. Colour me unsurprised. These purveyors of nonsense rarely enjoy having their pearls of wisdom questionsed.

What gets me is that there is a very obvious logical fallacy right there at the beginning - yet they wrote it and people seem to read it uncritically.
This bit seems particularly relevant to this thread: - at the end

Edit: Just added another comment - posting it here so I don't lose it when he rejects it.

So yes, small signal performance. But what you said is not quite right on several levels, but let's take as a given that accuracy of the measurement determines accuracy of the colour. In that case what would be important is accuracy of measurement of the charge, not the voltage - the voltage is just an intermediary - its absolute value is unimportant. Plus, accuracy of its measurement does not depend on its magnitude. And smaller pixels can provide a more accurate measurement.
Suppose we have a pixel with a saturation capacity S and read noise r. The DR (i.e. how many separate values of that pixel output can be measured) is S/r. Now we make another sensor with pixels half the linear dimension, 1/4 the area. We're going to make these new pixels simply by taking the reticles for the old pixel and scaling to 1/2 the linear dimension (This never happens in practice, where a completely new design would likely be adopted for that large a scale - but for the purposes of thinking about what are the intrinsics it's possibly a sensible simplification). The scaling means that the capacitance of the pixel is reduced by a factor of four, which in turn means 1/4 of the saturation level and four times the conversion gain, which controls the input referred read noise. Now the saturation level is S/4 and the read noise is r/4. If we combine the signal from these four pixels the saturation is correlated. so adds - the read noise is uncorrelated so adds in quadrature. So the combined saturation is 4S/4 = S, whilst the combined read noise is √(4(r/4)²) = 2*(r/4) = r/2. The DR at the resolution of the original sensor is S/(r/2) = 2S/r. So by halving the linear size of the pixel we've doubled the DR. Of course, as said, that's not in practice how sensors are designed, so we don't see the full advantage of reducing pixel size - but nonetheless the trend is there. If your thesis was correct, the highest DR cameras would tend be the low pixel count ones of a given sensor size, but results tend to show the opposite. For instance ranking DxOMark's tests by DR we find:

Of course DR is affected by quite a few things as well as pure pixel performance, such as - but we certainly are not seeing a clustering of large pixel cameras at the top.

Bob,

Are you sure that is correct? Or have you simplified it? Something doesn't feel right to me.

Alan

It's a bit simplified, in that I have bundled a load of noises into 'read noise' - but it's essentially correct. DR is generally 'maximum signal/noise floor', and in this case 'noise floor' is dominated by read noise. Or maybe you're not sure about DR being how many separate values can be measured - that's essentially what DR tells you. The size of the noise floor tells you how big a range a 'distinct' value takes and the maximum divided by that tells you how many distinct values there are. It's a bit more complex in photography due to shot noise, which means that most of the 'distinct values' that would be available in a classic DR become indistinct.

Humm.

I always imagined that DR was (maximum signal-noise floor) - (minimum signal-noise floor). So you end up with a voltage range for what the sensor (pixel?) has measured. Divide that into discrete units (DB?) and you have the DR.

I assume I am wrong since you guys have been doing this for a lot longer than me.

[edit - oh. is it because it's log scale?]

Alan

At it's basics it's just maximum signal/noise floor - other definitions of the lower bound do exist but that's the default. The minimum signal is defined by the noise floor. Take it in binary terms. If you measure something that's within the noise floor, you don't have any information about what it's intended to be because it's noise. If you measure something above the noise floor you know it isn't within the noise floor, so now you have two states - within the noise floor and higher than the noise floor. That's one bit of information. Now measuring above the noise floor if it's above the noise floor and more than twice the noise floor you have three states. If more than twice the noise floor but less than three times the noise floor you have four states, that's two bits of information, and so on.
The log scale doesn't have much to do with it, you can measure it in plain numbers, dB or stops, all the same measurement just expressed differently.