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The definition actually also looks to the A/D quantization, and it is a very precise description of what you want.
The step size at any point is defined as "The noise OR the quantization step, whichever is larger".
The exact point I was trying to make that once the signal above noise level, we can use more bits ADC to reduce quantization noise, so we have finer tonal step above deep black.
The question I have is do we really need each tonal step to be equal, we can let deep black have less step or the same small step (but no different black level)
This is the definition used by DXOmark.com, and it says exactly the same as the words Joakim uses here.
The tonal range can never be greater than the number of quantization steps, so if you use a shallow bit depth you do get a small Tonal Range, also according to the definition.
So looks like we are talking about same thing here that you agree have more bits ADC will have smaller tonal step.
Now I am not sure if you are talking about the very coarse quantization in a gamma corrected 8 bit image file, or in a raw file with 12-14 bits, or a theorethical case. If you are working in a very small bit space, you of course get problems with posterization, as when you try to edit 8 bit images, but nobody who is discussing Tonal Range here would even think about doing that?
Now, I think either I am not clear or you do not understand me correctly. Of course I am talking about raw file. That is all the talking I am try to do
It is also easy to think, since the SNR get better, that noise gets lower as you move up in luminosity. The opposite is the case. At sensor saturation, the noise is enormous compared to what it is in the deep shadows, because the photon shot noise is the square root of the number of photons. Normalized to the same scale: the more light, the more noise, and the larger the TR steps get.
Here, you lost me. Can I have some background information about noise source here: shot noise is from photons/sensor, so you mean more exposure will not only amplify signal, but also noise, so we are not change SN ratio here. Read noise is AA conversion, which is fixed, so more exposure/signal will have better SN ratio here.
Now go back to my original post that Now signal is there and signal level can be anywhere depend on DR of image. Having more bits ADC have two effect:
1. With low DR image, most bit might get wasted
2. but the low DR image also have more step which is useful signal can be processed in your 16bit, 32bit or whatever advanced engine, this is the benefit I was keeping to bring it out.
So, to summarize what I think about this whole thing, at deep black, sensor noise level define tonal step. Move up the grey scale, having more bit ADC potentially have more tonal step which could be even smaller than deep step/noise level. No matter what is the definition it is/was, this is the point I was trying to make here.