[nanok]

let's try it in the "i don't have a degree in math" version: the data (well, analogue signal of some sort, not yet data) sent by the amp to the adc can be in a range (of arbitrarly 1-100, let's say), basically, the adc will see nothing of any use outside that range (won't tackle snr yet), when you multiply digitally, you are actually not getting anything more within the range, you are just playing with what you have. unless you have an adc able to handle input the size of china (well, 22bits is pretty close to that, i guess ), you don't have much room for playing, for instance a 14bit adc (recording 12b data on the output pipe) will definetly need a very capable amp behind it to help along. in other words, the amp's job is to bring the input valuesof the slice of "data" the sensor has detected that _you_ are interested in in the rnage where your adc can read it confortably, the closer the match, the more valuable data you get to the adc, in the event where you would have an adc capable to take an input range equal or greater to what the sensor can put out, _and_ an amp capable of amplifying that sensor output across the entire range without any issues (distorsions, bad snr, and so on), there would be no need to vary the gain of the amp (and you would reach a dinamic range limited only by the quantum characteristics of the sensor, btw). when you take into account that cmos sensors have one amp for each photosite, if i am not mistaking, it probably makes sense to just put a volume button on each instead (but i am on very thin ice here, somebody with a clue might want to step in).

keep in mind that the amp will be there, in any case, as with current technology the adc is not able to handle the signal from the sensor without prior amplification, so noise added by the amp will always be there, but the first concern is to have as much meaningful data as possible on the input of the adc to begin with, otherwise you are effectively throwing away data wich is readily available from the sensor, if only you would ask for it.

nanok, on "translation duty" tonight

[Quension]

I was a bit loose in my explanations, so let's see if this helps...

Amplifying the signal in analog form results in the A/D converter having a different range to quantize, resulting in a different and more precise set of values on output.

I still dont' see where "more precise" comes from.

Let's say the analog signal has a nominal range of 0 to 4V (AFAIK the real values are ridiculously small, but those details are beyond my knowledge), and the ADC's output is 12 bits (4096 values). Each output unit of the ADC therefore represents about 1mV.

We'll say the sensor is 2 stops underexposed, so the signal peaks at 1V. Only the bottom 10 bits of the ADC's output contain data, giving a range of 1024 values. Digitally amplifying this will still only leave us with 10 significant bits of image data.

Using an analog linear amplifier to boost the input to the ADC to peak at 4V will result in each ADC output value representing 250uV of the original signal, and the entire range of 4096 possible values will be restored. This is four times more precise than the same data digitally amplified.

I guess if we assume that the A/D converter was actually capable of generating more bits of precision than is being stored in the RAW file - as is supposedly the case with the K10D - then I might believe that amplifying the signal could result in more precision - or at least a better guarantee that the least significant bit of the RAW data actually had any real significance.

I don't follow your reasoning here. What I meant with the 22bit ADC is that in theory that would be the perfect digital amplifier: the input signal is converted at maximum precision in one shot, so you can slice the 12 bits of output from any appropriate section of it without losing anything -- just chop off the bits you don't need.

(I don't know why the K10D had a 22bit ADC. Pentax was proud of it at the time, but I believe the later cameras are all using 14bit ADCs. Some web searching just now suggests the extra bits are oversampling primarily used to reduce noise from the sensor digitizing hardware itself, but I can't find an authoritative reference for that. The company that supposedly made the chips has mysteriously lost its web presence, and I don't have the engineering background to fill in the blanks myself.)

But this would still require still trusting that this analog amplification is perfect, would it not?

At least close enough to perfect that it can faithfully scale the weaker parts of the input signal to a range the ADC can handle, yes.

OK, I can also see that the very least significant bit in the original (unamplified) data would have been the result of rounding, and digital amplification now "promotes" this a place or two. Assuming it was rounded *correctly* in the first place, though, we're still rounded correctly in the bit-shifted resulting, meaning we're off by at most only half the amount represented (eg, is we're now talking about 100b = 4, we're off by no more than 10b = 2. So I'd still need to see some assurance that the analog amplifier was capable of doubling the signal accurately enough to guarantee better accuracy than this.

Right. In practice I gather this is mostly true for the lower ISO levels in many cameras, but higher ISOs are apparently dominated by both amplifier and sensor noise.

Also keep in mind that due to the logarithmic nature of the exposure, "half" is a significant amount for the darker tones (for how we perceive them), which are often important when push processing. The brighter tones aren't affected nearly as much because they have such a huge gradation range to work with from the start that we normally don't change them enough to notice any loss of precision.

(This is the point that's most relevant to ETTR.)

the specifics of which method works better would seem likely to depend on all sorts of factors like the specific sensor, a/d converter, the amount of amplification, and the nature of the data being amplified.

This is where the analyses by GordonBGood and Oleg_V come in. Sadly the details are still over my head.

If the actual noise level was below that point but caused the rounding, the analog amplifier just gained you an extra bit (or more) of real signal to work with.

Like I said, for some reason I didn't quite follow your example, but it seems possible you are here saying the same thing I just did? That an analog amplifier *could* improve on digital, but the results actually depend on the specifics?

Yes. Using my new example above, let's say the median noise level from the sensor is about 250uV, and the amplifier is perfect. The least significant bit may then be rounded at ISO 100 and 200, but we can resolve the noise itself at ISO 400. Beyond that it wouldn't matter whether it was amplified in analog or digital form, because the brighter tones are already as gradated as we can resolve, and the darkest tones are buried in noise, so the bottom bits are useless anyway.

[pingflood]

This is a really interesting discussion, but let me pitch this in: if it was better to amplify the signal in software/digitally, why would the companies go through the trouble of putting in circuitry to change the gain on the a/d conversion?

It would be interesting to see the effect of something like the 22 bit a/d converter and software amplification compared to 12 bit a/d with analog gain though...

[Marc Sabatella]

OK, I do see the points being raised. Although it still seems there are lots of questions left unanswered. So for now, I'll just add a couple of additional observations:

- Say a RAW file is 12 bits. We do a bit shift two places to push two stops. We are now wondering about the "noise" in those last two or maybe three bits. Well, by the time we display it on a standard 8-bit RGB monitor, we're only looking at the most significant 8 bits anyhow (I realize this is an oversimplification, but hopefully it doesn't completely invalidate this). Yet there is a *lot* of noise visible at this level. This suggests to me the actual noise levels we are dealing with in practice is *way* more than anything represented by these least significant few bits we are quibbling about.

- As for why camera companies include analog amplifiers: many if not most only do that up to around ISO 800 or so, and do simple bit shifting (or perhaps some slightly more clever non-linear but still digital amplification). This has been shown to be true of several Pentax models - at high ISO, you *do* have essentially nothing but zero in the least significant bits (or at least, what Gordon refers to as "missing codes"). So I take that as a tacit admission that analog amplification is only viable up to a point.

Bottom line for me is that I can see this is all complex enough that is going to be beyond my ability to ever convince myself I *completely* understand the issues well enough to be confident my reasoning would lead to the correct answer. So to the extent I care about the difference, the only way I'm likely to feel sure about any conclusion is by actually seeing empirical tests.

[jeffkrol]

Again the problem is EVERYTHING varies by camera make/model with only a few commonalities.....
I did find some confirmation re: Canon and what they do in various models..
"Higher end Canon models implement ISO gain via a two-stage amplification system; one amplifier for the "main" ISO's 100-200-400-800-1600 etc, and a second-stage amplification to implement the "intermediate" ISO's 125-250-500-1000 etc. and 160-320-640-1250 etc.....Lower end Canon models do not perform analog amplification for the intermediate ISO's, rather the intermediate ISO's are implemented by a multiplication of the raw data in software after quantization, and there is only a single stage amplification in hardware; strictly speaking, they do not have intermediate ISO amplification.".........................The read noise vs. ISO graphs show that, at some point around ISO 1600 to 3200, it ceases to make much difference whether the ISO gain is implemented as a hardware amplification or as a software multiplication of the highest hardware ISO. For instance, on the 1D3 the read noise 26.2 ADU at ISO 3200 is just about double the value 13.4 ADU at ISO 1600. This is why the so-called extended high ISO settings on Canon and Nikon (ISO 6400 on the 1D3, ISO 3200 on the 1Ds3 and 5D; all ISO's above 6400 on the D3) are implemented in software after digitization rather than as hardware amplifications -- the read noise will be the same, and its magnitude is so much higher than the quantization step that the "missing" levels after multiplying the raw values by 2, 4, 8, etc to make the extended ISO's have no effect whatsoever (they are once again dithered away by the noise). Photon noise, being a property of the light itself, couldn't care less what ISO is set in the camera; only the read noise enters into the question of whether the data amplification is as well done in software post-capture as it is by hardware during image capture.

On the other hand, if shooting raw, it makes little sense to use the extended ISO's since they are simply mathematical manipulations of the raw data post-capture, and their main effect is to throw away one or more stops of highlight headroom as the doubling, quadrupling etc of the raw values pushes more and more of them beyond the maximum recordable value of 4095 for 12-bit, or 16383 for 14-bit data. Setting the highest analog ISO amplification keeps the headroom, and one can always do as much additional software amplification as is needed afterward during raw conversion.
Noise, Dynamic Range and Bit Depth in Digital SLRs -- page 2
You could really only test your camera and your processing software to come to a one of conclusion.. the rest is all.... err ..... academic.
Guess this only slightly relates to ETTR

[mithrandir]

Jeff that is right on the money. The purpose of ETTR is to get the best exposure with the lowest cost in noise. You have clearly explained on factor that should be included in lowering the noise present in the RAW file. Thanks for the research.

[pingflood]

- As for why camera companies include analog amplifiers: many if not most only do that up to around ISO 800 or so, and do simple bit shifting (or perhaps some slightly more clever non-linear but still digital amplification). This has been shown to be true of several Pentax models - at high ISO, you *do* have essentially nothing but zero in the least significant bits (or at least, what Gordon refers to as "missing codes"). So I take that as a tacit admission that analog amplification is only viable up to a point.

Viable, and also preferable, I believe. It looks like up to a certain point the signal/noise ratio is better than digital amplification (2x) and past that they just say screw it and go with digital. On my 1Ds2 1600 is the last "real" ISO and 3200 is digitally enhanced. As for image quality comparing shooting 1600 at -1 or 3200, well, I don't see much difference so sometimes I go 3200 (aka "H") just because I'm lazy.

[Ash]

This has been a very informative and comprehensive thread.

The theory of ETTR comes together quite nicely with the science of sensors and ISO.
Jeff, Marc, pingflood and Quension - great input.