Mysterium-X...

[Stephen Pruitt]

Okay, resident experts. Is Mr. Caesare correct or incorrect? I like the logic of his explanation. I'd like to know if I like it because I can understand it, or because it is correct, or both.

Thanks.

Stephen

 

[David Rasberry]

The big increases in dynamic range for digital sensors of all kinds, not just camera sensors, have been the result of dramatic decreases in circuit noise, on the order of 10dB or so, from new chip fab processes and materials developed over the last several years.

 

[Daniel Browning]

I'm not sure I understand where you are going with this. If the clipping point is a fixed property of the chip then why isn't there one analog gain setting that is ideal for all shooting situations?

Because in low light, a small improvement in shadow noise is often more valuable than a large improvement in highlight headroom.

Let's say you have a certain camera in low light in tungsten. The f-number, shutter, and light level are already as bright as you can make them. Your only choice is to use analog gain or not.

First you try the shot with 4 stops of analog gain (e.g. ISO 1600 instead of ISO 100). That gives you 2.5 stops of highlight headroom over middle gray (on that camera). All the highlights above 2.5 stops are clipped. The shadows are clean enough that you can use 3.5 stops below mid gray, for a total dynamic range of 6 stops.

Next you try the shot with no additional analog gain (ISO 100 instead of 1600). Now you have 6.5 stops of highlight headroom over middle gray! Wow! The downside is that shadows are so much noisier that you lost an entire stop of usable "footroom". Now instead of 3.5 stops below mid gray, you can only use 2.5 stops. That's a total of 9 stops of dynamic range. It's much higher than the 6 stops above, but there is an important difference: in low light, that 1 stop of cleaner shadows is often far more important than 3 stops of clipped highlights.

In ample light, there is one optimal analog gain setting. That's because adding more light is always superior to increasing analog gain. The tradeoff only comes when light cannot be increased.

Is Mr. Caesare correct or incorrect?

I think he is correct. When shadow noise (read noise) is improved, it doesn't affect highlight headroom unless you use more ND to take advantage of it.

 

[Steve G]

(Warning: long post ahead)

It seems that some source of confusion here is based on the idea (fear?) that if the sensor ISO increases significantly, that everybody will either have to stop lenses down significantly (and thus lose DoF), or stack an insane amount of ND filters in front of the lens.-sc

If you stop the lens down, you gain depth of field.

 

[Steven Caesare]

If you stop the lens down, you gain depth of field.

Indeed you do.

I was loosely using the term as it is often used (technically incorrectly) here and elsewhere by people to indicate that they like the "greater" DoF that 35mm exhibits as compared to other formats. In reality, they prefer the shallow DoF...

To be technically correct I should have said "lose DoF characteristics", but mt point was to discuss the issue of the sensor sensitivty and it's impact.

-sc

 

[I Bloom]

Daniel,

This doesn't really answer the question. The position of middle gray is determined in post. Noise is a constant across the entire image, it only comes out in the blacks because of the curve we apply to the image.

There is no question that in bright low contrast situations we can expose to the right. But in all other situations (high contrast sunlight, low contrast low light) we want as much shadow detail as we can get.

So the question is why wouldn't I always want the image with the least noise?

IBloom

 

[Daniel Browning]

The position of middle gray is determined in post.

Yes, but for any comparison to make sense, whatever choice you make about middle gray during post processing must apply equally to both shots. To do anything else would be to compare completely different styles. For example, if you take one R3D file and develop it three different ways: overbright, normal, and DFN, you'll end up with three totally mid-grays and noise levels. The DFN will have the least noise because any given tone in original scene is pushed down to the darks in the post processed image. The overbright shot will appear much noisier because tones that were 8 stops under clipping in the original scene are now at the midtone level. So my statements are meant to assume that both post-processed images will have mid gray on the same tone.

So the question is why wouldn't I always want the image with the least noise?

Because you have to sacrifice 4 stops of clipped highlights to get it. There is no way around that: analog gain *always* clips highlights and reduces the total dynamic range. The only question is whether the improvement in shadow noise (if any) is worth the loss of highlights.

Here's an illustration. The following two images have the exact same exposure, but different analog gain settings. The ISO 1600 shot has far less noise than the ISO 100 shot:

But this improved noise comes at a great cost: blown highlights. Look:

In this example, the reduction in noise is clearly not worth the loss of highlights. But if the light was lower, then the highligh clipping would have been acceptable, and ISO 1600 would have been the best choice.

Let me walk through a different scenario. 5D2, f/5.6, 1/60. You're in ample light, and with the ISO set to 100 you have just the right amount of headroom. If you changed to ISO 1600 (but kept exposure the same at f/5.6 1/60), then you would get 1.3 stops of cleaner shadows. But you clip 4 whole stops of highlight headroom. Clearly a very bad trade.

Now consider low light. f/1.4 1/60 is the best you can do without making the DOF too thin or having too much motion blur. If you left the ISO at 100 like above, the result is very noisy. If you increase analog gain to 1600, that improves the shadows by 1.3 stops or so, greatly improving the result. It still clips 4 stops of highlights, just as above, but now that is much less important.

Of course, the ideal situation would be to have the best-in-class low noise of ISO 1600 combined with the highlight headroom of ISO 100. Maybe that will happen to DSLRs some day in the future, but it hasn't yet.

Say you have a RED ONE and a fixed amount of light. First you try a shot at f/1.4 and find it has too much clipped highlights. So you cut exposure by 1 stop to f/2. Now the highlights are much better, but the shadows are noisier. Now you cut exposure by another stop to f/2.8. Noise is much worse, and there is more highlight headroom. But this time, you didn't really need more highlights. So you go back to f/2 because the shadows were more important.

But what if you can't go to f/2? What if you need f/4 for DOF? Your only option is to expose two stops lower than what you really want. You can change the ISO from 320 to 1250 just to indicate to post production that your intention is for the image to be boosted. The noise will be bad, but you will have two stops more highlight headroom as a bonus.

Now compare that to the Canon 7D. In order to simulate the metadata of the RED ONE, you leave the ISO setting on 320 and write a little sticky note on the flash card "push to ISO 1250". Just like the RED ONE, the noise will be bad and the headroom will be more than you need. But there is a different option available on the 7D: analog gain. It so happens that the analog gain has less read noise (shadow noise). So instead of putting a sticky note on the flash card, you set analog gain to 1250. This causes a slight reduction in shadow noise, but causes two stops of highlights to be clipped. In this case, you're willing to make the trade.

I hope that makes it clearer.

 

[I Bloom]

I hope that makes it clearer.

Well,

Essentially what you are saying is that the resulting noise created by analog gain has less amplitude than the resulting noise of it's metadata (i.e. post production) equivalent because metadata gain is applied after the third and final noise adding step, the analog to digital converter.

There is a "sweet spot" where the right amount of analog gain boosts the signal above the noise from the ADC and results in the least overall noise. I'm asking why can't we keep it at the sweet spot and you're saying we can't always use that sweet spot because it causes additional clipping... well maybe.

I think that there is tremendous variability in the design of CMOS sensors. So your direct comparison of Red to Canon cameras and your conclusion that Red should consider analog gain because Canon has it, is based on assumptions about the Mysterium technology that maybe can't be tested.

So I guess the issue will remain a.. cough.. mysterium.

IBloom

 

[David Rasberry]

The ISO 1600 shot has far less noise than the ISO 100 shot:

At least as far as processing .r3d files in Redcine is concerned, the opposite is true. For a given file and raw exposure, increasing ISO brightens the image and increases visible noise. This is distinct from any applied gamma curve or other corrective measures.

 

[Deanan]

There is a "sweet spot" where the right amount of analog gain boosts the signal above the noise from the ADC and results in the least overall noise. I'm asking why can't we keep it at the sweet spot and you're saying we can't always use that sweet spot because it causes additional clipping... well maybe.

Noise is a multi-dimensional problem and while analog gain can help reduce noise at one stage, it may not improve other types of noise. However what it will do is reduce quantization noise and increasing gain above unity will definitely clip. Reducing gain below unity just becomes less efficient use of code values (ie. increasing quant noise).

 

[Daniel Browning]

Well,
Essentially what you are saying is that the resulting noise created by analog gain has less amplitude than the resulting noise of it's metadata (i.e. post production) equivalent because metadata gain is applied after the third and final noise adding step, the analog to digital converter.

Yes.

There is a "sweet spot" where the right amount of analog gain boosts the signal above the noise from the ADC and results in the least overall noise. I'm asking why can't we keep it at the sweet spot and you're saying we can't always use that sweet spot because it causes additional clipping... well maybe.

On RED cameras, there is no improvement in read noise from analog gain, so they don't even offer the choice.

On the 5D2, there is sometimes a huge improvement in read noise from analog gain, so it makes sense to at least offer it as a choice. (Unfortunately, Canon forces it on us whether we want it or not, because they don't offer metadata ISO as a choice. It was not always that way. There must have been someone who knew what they were doing back when Canon made the 10D, because the ISO 1600 mode had no decrease in read noise, so it was implemented as metadata. Unfortunately they must have fired that one clueful fellow because ever since then they have willingly destroyed highlight data for no reason.)

I think that there is tremendous variability in the design of CMOS sensors. So your direct comparison of Red to Canon cameras and your conclusion that Red should consider analog gain because Canon has it, is based on assumptions about the Mysterium technology that maybe can't be tested.

I don't know where you got that impression. I do not want RED to add analog gain. I want them to have the electronic noise that stays the same no matter what analog gain is used. Then I would not have to ever use analog gain at all, or make the choice to sacrifice 4 stops of highlights to get 1 stop of shadows (a difficult choice I have to make all the time with my 5D2). However, if RED cannot figure out a way to do that, and they are forced to start offering analog gain as a workaround to achieve lower noise levels, I will accept the compromise, just as I must accept it with Canon.

The reason I entered the thread was to try and help explain to Shawn why having DSLR-style ISO settings would not be an improvement for the problem he was talking about (needing too much ND). While I was at it, I wanted to describe the circumstances where analog gain is needed (any time that noise added by post-gain electronics is significant enough to contribute to the read noise).

At least as far as processing .r3d files in Redcine is concerned, the opposite is true. For a given file and raw exposure, increasing ISO brightens the image and increases visible noise. This is distinct from any applied gamma curve or other corrective measures.

It's the same as Canon. ISO 640+HTP on the 5D2 results in the exact same raw file as ISO 320, just like ISO 640 on RED ONE results in the exact same raw file as 320. They're both metadata ISO settings. The only difference, as you pointed out, is that one "recommends" brighter post processing than the other, which increases the "visibility" of noise, even though the measured SNR is the same in both. That's what Ian and I were talking about above with regards to middle gray.

As you know, raw photographers are far more concerned about the data than whatever the default post processing will reveal. For example, we know that on the RED ONE, f/2.8 and ISO 1250 will have far more visible noise than f/5.6 and ISO 160. But that's only because the brightness is cranked way up, and the f/5.6 brightness is way down (the images can't really even be compared because one is bright and the other is dark). Once you correct both to the same brightness, it is very obvious that f/2.8 has far less noise than the f/5.6 shot.

The same thing applies to analog gain. f/2.8 ISO 1600 on the 5D2 is five times brighter than f/2.8 ISO 100. The noise will look much much worse. But once you correct them both to the *same* brightness (by pulling down the 1600 or pushing the 100), it becomes clear that the ISO 1600 has far less read noise.

In essence, the "default brightness" of the image has no importance in raw shooting. All that matters is what you can *do* with the raw file. (Of course, it would be nice if the default settings were configured close to the ideal, but that's secondary importance.) The value of the raw data is the clipping point and the SNR over the entire range below the clipping point. Analog gain in DSLRs makes the clipping much worse, but it slightly improves the SNR of some tones (any tone that is not dominated by photon shot noise).

 

[David Rasberry]

Once you correct both to the same brightness, it is very obvious that f/2.8 has far less noise than the f/5.6 shot.

No real substitute for properly exposing the sensor in the first place is there? Same as film in this regard no matter what you do with it after the fact.

 

[david farland]

opps

 

[David Rasberry]

I makes sense to filter analog gain to minimize external noise, EMI, RFI impinging on the system as well as known self noise of the sensor and associated circuitry.

 

[Lauri Kettunen]

All that matters is what you can *do* with the raw file.

Daniel, thank you for your interesting and intellectual posts in this thread. It has been a pleasure to read them. I feel very much the same way as you and would like to have a full manual mode in DSLRs meaning I could set the analog gain and select ISO just as metadata. Moreover, would like to see the histograms for the raw image.

I've been wondering whether the problem is that companies like Canon try to make the GUI of modern cameras as if they were old fashion film cameras. In the same spirit can't quite understand why people still talk of mid grays etc as the whole point of raw mode is about linearity. That is, the sensor reacts linearly to the amount of photons/light where as that's not how our visual perception works. Thus, there is a need for what is called the gamma curve. The gamma curve maps the light the sensor has detected into a "format" that match with our visual perception.

But now, our visual perception is not the same in all situations. So, different situations call for different gamma curves. Consequently, it's a great idea to leave the choice of the gamme curve to as late point as possible instead of "baking it" to the stored file.

Linearity in this context means addition and multiplication by real numbers (or more precisely multiplication by a field of scalars) can be done before or after the sensor without changing the result. This means, when shooting say a gray card one can open the iris and double the amount of light and then scale down in post by factor 1/2 and linearity guarantees the result is in principle the same.

Now, obviously, to minimize noise it makes sense to shoot-to-the-right as the band width and available data storage in cameras is limited and there's a better bit depth in post. So, if one shoots something that's about mid grays and opens the iris by one stop and scale down only in post, as a result one gets a better sampling than exposuring in the old fashion way according to the mid grays. All this works as long as the asumptions of linearity are not broken. For instance, clipping or applying a gamma curve ruins immediately the whole idea.

Analog gain is in my understanding somewhat different story. Although the sensor read photons, it's not possible to count them one by one. Instead, the output of the sensor is about voltages/currents/charge (not sure which one precisely, but this does not matter) and this is about analog data. Consequently, one needs an analog-to-digital conversion and in this context analog gain before the AD-conversion may result in less noise in the digial data. Deanan seems to say, the reduction of noise depends on the situation and that there is no simple recipe for all situations. Consequently I feel the choice of gain should be left to the user instead of binding it with the ISO setting as Canon does. For, the sensitivity of the sensor cannot be changed in reality, so the ISO setting affects only the monitor.

Summing up, in the past one was able to change the sensitivity of the "sensor" by changing the film whereas the properties of the optical VF were fixed. Nowadays it's the other way around. It's not possible to change the properties how the sensor detects light, but it is easy to change the properties of an electric VF. This is why there is a need for metadata; Metadata settings affects the final image on a monitor, but they should not affect the exposure. For, thanks to linearity, that should be independent of whether it is made before or after the sensor.

 

[Carsten Kurz]

Hmm. I still don't get it. Go to http://reduser.net/forum/showthread.php?t=36368

You shoot the Stouffer at ISO800. You have say 12.5stops DR. You 'develop' at 400 - you loose one stop at the top end. You develop at 1600 - you loose one stop at the bottom?

Now you do that with film rated 50, 100, 400 whatever. Of course, their DR will not be equally high, but if you have more light and use ISO100 you still do not sacrifice as much DR, you have less light and do not sacrifice as much at 400?

Now a different cam, be it Canon DSLR, with 'useful analog gain stage'. Wouldn't you still have a much wider working range by adjusting 'useful analog gain'? Just by leveling the signal output perfectly into the A/D range alone?

To me it still seems the Canon can utilize a much wider 'input range' that way compared to a 'fixed sensivity' R1?

Sorry...

- Carsten

 

[Daniel Browning]

Great post, Lauri. Only one minor nit to pick:

Now, obviously, to minimize noise it makes sense to shoot-to-the-right as the band width and available data storage in cameras is limited and there's a better bit depth in post.

Actually, that's a common misconception. The reason why ETTR is so beneficial is that it increases the amount of light. More light means less noise (both photon shot noise and further distance from read noise). Less noise means more color depth (tonal gradations), dynamic range, and many other things (flexibility in sharpening, etc.). The utilization of bit depth has nothing to do with it.

If bit depth was all it took to increase tonal resolution, camera manufacturers would all be using 24- or 32-bit files. In fact, some MFDB do store 16-bit files even though, by their own admission, they need less than 13 bits. Here is a Phase One 16-bit where one half has been quantized to 12 bits and the other left at 16:



So there is no benefit to additional bit depth except to avoid quantization error.

Let's say there is a Skin Tone "A" that is exposed to be 3 stops below clipping at ISO 100, and it is completely dominated by photon shot noise. Skin Tone "B" is 2 stops below clipping, so there is one stop between the two tones. If it was a computer generated 12-bit file, there would be 512 different values possible between the two tones (the entire theoretical maximum is utilized). But in a camera-generated 12-bit file, there enough photon shot noise that the effective number of levels is much lower, we'll say 128 (I'm too lazy to calculate the real number). That means the theoretical maximum is not achieved.

Now, say we increase analog gain two stops (100 -> 400). That reduces read noise, which affects shadows, not midtones like this one. So there is no effect on the SNR. But it does increase the brightness, so now Skin Tone B is right as the very maximum value (4095) and Skin Tone A is one stop behind it: 2047. The theoretically possible number of tones is 2048, up from a theoretical 512 before. But the SNR has not changed, so the noise std dev still reduces the effective number of levels to the same amount it was before: 128.

Now say we took the same camera and scene, and upgraded it from a 12-bit ADC to an amazing (think Star Trek) 32-bit ADC that actually had 32 bits of precision. Now Skin Tone B goes from 4095 to over 4 billion and Skin Tone B goes from 2047 to 2 billion. The file can now store over 2 billion possible tonal gradations between the two skin tones. And if the file is computer-generated, it can actually have that many gradations. But the camera-generated file is still limited by photon shot noise. And still restricted to just 128 distinct gradations.

Now, let's change the 12-bit example so that instead of increasing the gain, we do the exposure. ISO is left at 100 and exposure (f-number, shutter, flash, ND, etc.) is increased two stops. (f/8 -> f/4). Just as before, Skin Tone B goes from 1023 -> 4095 and Skin Tone A goes from 511 -> 2047. The theoretically possible number of tones is still 2048. But now, the SNR has increased due to photon shot noise. Instead of 128 possible gradations, there are many more (we'll say 512, as long as I'm pulling numbers from thin air).

For a real-life example, consider the following 14-bit image (Canon 40D) quantized to a variety of different bit depths. The noise is so high that there is no loss at 9 bits.



Now a more technical example. Say we have a 12-bit raw file of a white card from any semi-modern DSLR at ISO 100, exposed so that its average value is one stop below clipping. We'll say the number of detected photons is 43008, which makes the conversion gain 21 photoelectron per ADU. We'll set aside the effect of PRNU (which is very minor anyway). The mean raw level will be 2048 (out of 4096). The ADU will fluctuate wildly due to photon shot noise: one pixel will be 2038 and its next door neighbor 2058, because the std dev is 10 ADU (sqrt(43008)/21). Since read noise, thermal noise, and all other noises sources are insignificant at this luminance, the total S/N is 2048/10 = 202:1 = 7.66 stops.

What is the effect of going to 16-bits? Now the conversion gain is 1.3125 e-/16-bit ADU (20/2^(16-12)). With the same exposure (1 stop below clipping), the mean ADU is 32768 (2^(16-1)), and the number of photons is still the same (43008). But the the std dev is now 162 (sqrt(43008)/1.3125). Instead of jumping around by an average distance of 10 raw levels from the mean, they're now jumping around by 162. So you have 32606 right next to 32930. The S/N is 32768/162 = 202:1 = 7.66 stops, same as with 12 bits.

Technically speaking, it could be said that precision has increased, but there is no change in actual information content, accuracy, or S/N.

So the location inside the raw file doesn't really matter: the SNR is what's important, becuase the SNR itself is what limits the tonal resolution. The raw file should have a the theoretical maximum number of gradations that is larger than the actual gradations. Fortunately, that is always the case, because most cameras are correctly engineered. If they weren't, there would be quantization error (cases of that are pretty rare and minor).

So, if one shoots something that's about mid grays and opens the iris by one stop and scale down only in post, as a result one gets a better sampling than exposuring in the old fashion way according to the mid grays. All this works as long as the asumptions of linearity are not broken. For instance, clipping or applying a gamma curve ruins immediately the whole idea.

Agreed.

Hmm. I still don't get it. Go to http://reduser.net/forum/showthread.php?t=36368

You shoot the Stouffer at ISO800. You have say 12.5stops DR. You 'develop' at 400 - you loose one stop at the top end. You develop at 1600 - you loose one stop at the bottom?

I think what you're saying is that metadata ISO never changes the DR, and that's correct. The data changes with exposure only, not the setting. Once the file gets in post, the range is what it is. You can of course clip the top or crush the blacks according to the needs of the shot, but the raw data is still available. Metadata ISO 400 is no better or worse than metadata ISO 50.

Now you do that with film rated 50, 100, 400 whatever. Of course, their DR will not be equally high, but if you have more light and use ISO100 you still do not sacrifice as much DR, you have less light and do not sacrifice as much at 400?

Correct. ISO 400 film does indeed result in a better picture than ISO 50 film push-processed 3 stops.

Now a different cam, be it Canon DSLR, with 'useful analog gain stage'. Wouldn't you still have a much wider working range by adjusting 'useful analog gain'? Just by leveling the signal output perfectly into the A/D range alone?

Canons have a problem where the electronics (probably ADC and amplifier) have so much noise that small signals get drown in noise. If you use a Canon camera to simulate metadata ISO 400 by shooting ISO 100 and pushing 2 stops in post, you will get a ton of really nasty noise (particularly pattern noise). It's necessary to use analog gain to drown out that noise, but the unfortunate side effect is that 2 stops of highlights are lost compared to metadata ISO.

Metadata ISO is clearly the ideal, but the only way that DSLR manufacturers have been able to get the noise down is with high analog gain. I would much rather they do it with low analog gain, but they probably could not overcome the difficult technical problems of doing so.

To me it still seems the Canon can utilize a much wider 'input range' that way compared to a 'fixed sensivity' R1?

That's only true if they get lower noise with high gain. If RED can achieve low noise with no analog gain, then they get the best of both worlds: improved shadows *and* highlights. Analog gain forces you to make a cruelly difficult choice: is losing 3-4 stops of highlights worth it to reduce shadow noise by such-and-such amount? For most low light shots the answer is yes, and that's why so many high ISO Canon shots have very nasty highlight clipping.

 

[Lauri Kettunen]

Great post, Lauri. Only one minor nit to pick:
Actually, that's a common misconception. The reason why ETTR is so beneficial is that it increases the amount of light.

Daniel, interesting ... I assumed this increase of light is so obvious that it's not even worth of mentioning. But also, if it was ONLY about increase of light, when one scales downwards one would not gain that much.

Say, if the data is stored with n-bits and the post system was also about n-bits, in principle, when scaling down, the difference between ETTR and the old exposure style would not be that big. Still, the increased amount of light implies more light is obtained from shadows and thus less noise. But now, if in post one has higher bit depth, when one decreases the exposure of a ETTR raw image, one ends up with ALSO higher sampling of the shadows, and that was my point.

 

[Carsten Kurz]

Thanks Daniel! Your effort is highly appreciated on this topic!

(This is important techspeak and may be referenced to multiple times, so

'and the number of photons is still the same (40960).'

probably should be corrected to '(4096)'

- Carsten

 

[Daniel Browning]

Hi Lauri. I appreciate the discussion and I'm glad we agree for the most part. However, there is still this one important area:

...if it was ONLY about increase of light, when one scales downwards one would not gain that much.

That's incorrect, and is disproven by the 14-bit image I posted above. In the top highlight tone, going from 14 bits to 7 bits made absolutely no difference. That's because photon shot noise itself limited the accuracy, not the number of raw levels. Shadows are a different story. They are still noisy enough (due to photon shot noise and read noise combined) that at 9 bits there is still sufficient dithering to prevent quantization error. But at 8-bits there is a subtle increase in quantization noise (AKA error) and at 7-bits it all goes to pot.

Again, in a linear raw camera, noise is *always* the limitation in color depth. The only time that noise is not the limitation is when you have quantization error. No self-respecting camera designer would allow that to be the case. In fact, the far majority of cameras are criminally wasteful with bit depth. If there were more photographers who knew the truth about bit depth, they would demand raw-level-thinning that follows the SNR of the camera, like Nikon's NEF "compression", which isn't actually compression at all, but the simple act of using the correct amount of levels necessary to extract all the information from the sensor.

In the presence of photon shot noise, when you increase exposure by one stop, you *double* the possible number of raw levels. But SNR only improves by 41% (sqrt(2)). So it's never possible to realize the benefit of more levels because the noise doesn't improve fast enough.

There are some cases of quantization error, like the Pentax K10D and perhaps some of the Sony models, but even then the quantization error is only in the very deepest shadows (11th or higher stop of dynamic range). But otherwise, since noise is the only limitation, the only way to increase the number of levels is to reduce noise. Where the tone falls in the linear raw file is irrelevant.

CGI is different, of course, because they don't have photon shot noise or read noise. Increasing brightness by 1 stop *does* have a practical effect there, and 12-bit CGI linear file can indeed store all 4096 different values.

Say, if the data is stored with n-bits and the post system was also about n-bits,

The only time that ETTR can help suppress quantization error is when the post system is highly flawed. For example, some raw converters used to be so braindamaged that they processed 12-bit linear raws and quantized back to 12 bits with no dithering. 14-bit raw files helped forced those raw converters to into using 14 bits in which the last two bits were always noise, so the dithered and quantized value had no error. To me, that is not a benefit of 14 bit raw files, it is a flaw in the raw converter. The converter must have sufficient bit depth (e.g. 16-bit int or 32-bit float) or dithering to suppress quantization error. Even 10-bit log systems do just fine thanks to the careful choice of a curve that has enough noise at every level and/or additional dithering.

'and the number of photons is still the same (40960).'

probably should be corrected to '(4096)'

Thanks for letting me know, I do make lots of typos. In this case it so happens that the number is actually correct. But I think it would be much clearer if it were a different number, so I edited the post to change the conversion gain from 20 e-/ADU to 21 e-/ADU; now the number of photons is 43008, and will be more clearly separated from the number of maximum values (4096).