The significance of unity is an illusion.
[a href=\"index.php?act=findpost&pid=86298\"][{POST_SNAPBACK}][/a]
I agree that unity is an illusion, or at least an extreme that is not a natural practical choice. At most, it limits the worst case quantization error to 1e, and no matter how much more one amplifies, the error will in fact not get any less, because the original error sources all come in quanta of one or more electrons, even if subsequent amplification and charge-to-voltage conversion renders these discrete errors into variations in a continuous voltage signal.
But I think, contrary to you, that counting accurate to one electron is more than enough precision, rather than not enough, by considering the minimum magnitude of the errors already present in the signal reaching the A/D convertor.
The real-world problem is readout noise, which varies RAW values by much more than one electron.[a href=\"index.php?act=findpost&pid=86298\"][{POST_SNAPBACK}][/a]
I agree that the noise levels arriving at the A/D converter are already "much more than one electron", and that is precisely why I believe that an A/D convertor that measures accurate to a single photo-electron ("unity conversion") is already _more_ precision than has any practical value.
The real world problem is the total of read-out noise plus other noise present in the signal reaching the A/D convertor, including photon shot noise. You might be right that in practice, read-out noise dominates, but I use photon shot noise only because fundamental physics sets a known, absolute lower limit on noise levels in the signal reaching the AD convertor. That is, photon noise gives an upper limit on the "precision" of the signal that arrives at the A/D convertor.
No matter how low other noise sources get, the minimum possible noise level (in RMS variation in the count of photo-electrons in the electron well) will be the square root of the number of photo-electrons of signal, the contribution of photon shot noise. This can somewhat arbitrarily be divided into two cases:
Case 1: photo-electron signal less than about 16e [higher, like 25e, might be a more reasonable cut-off?]
Case 2: photo-electron signal of about 16e or more [or 25e?]
Case 1: Under 16e is 12 or more stops below the maximum possible signal in larger current DSLR photosites, so 8 or 9 stops below mid-tone levels at ISO 100 and 4 or 5 stops below mid-tones at ISO 1600. Total black on a print comes about four stops below mid-tones, so these levels are well into total black on a straight print even from an ISO 1600 image. Moreover, the S/N ratio can be at most the square root of the electron count, so at most 4:1 with this few photo-electrons, and this is so miserably low that I cannot imagine any interest in rendering such extremely dark and noisy pixels as anything except pure black.
That is, the black point would almost surely be set above the 16e level, so that the signal from a pixel receiving such a low illumination level would be transformed to level zero, eliminating any visible print noise in any part of the image receiving such low illumination.
[25e would move minimum S/N ratio up to 5:1, still I suspect uselessly low for artistic photography, and so destined to be zeroed out by the black point. Kodak has suggested 10:1 as the minimum S/N ratio needed for "acceptable" image quality, along with 40:1 for "excellent".]
Case 2: Signal of 16e or more has photon shot noise of at least 4e RMS, and thus thus the total "analog domain noise" (photon noise , dark current noise , read-out noise, pre-amplifier noise, and any others I have missed) in the signal entering the A/D convertor already has this much "error". An experimentalist would probably tell you that there is no point in measuring a quantity down to less than 1/4 of the error already present: your already get more than enough precision, "two bits" to spare, if the A/D convertor counts accurate to the level of one photo-electron, as with "unity conversion".
To quantify this, adding 1e RMS of quantization noise to 16e RMS of "analog stage" noise give a total of sqrt(17)=4.12e RMS, an increase of 0.12e, or 3% in total noise. I doubt that this change, in the deep shadows, would be even slightly visible.
And as the signal increases, the effect of an additional 1e RMS quantization error becomes less. For example, setting the black point a bit higher by requiring at least 5:1 S/N ratio at "non-black pixels" increases the minimum electron count to 25e, minimum "analog phase noise" to 25e RMS, and then adding 1e RMS to 25e RMS only increases the total noise by 0.1e, less than 2%.
If any posterization in extremely dark parts of the image still arises at the transition from black level to lowest non-zero level (which I doubt), it can be eliminated by interpolation of additional finer levels of near black, a kind of "dithering". There is no need to use the illusory precision of even more "accurate" A/D conversion to produce such levels: that would simply be using random noise in the signal as a form of random dithering.
The weakest point in this argument is the somewhat arbitrary choice of S/N ratio thresholds like 4:1, so I am open to evidence and arguments that very dark pixels with S/N ratios less than 4:1 are worth printing as anything other than pure black. But for now I am skeptical, given expert opinions like the guideline of a 10:1 minimum S/N ratio stated in a Kodak technical paper.
