Will Michael revisit ETTR?

[bjanes]

In the classic example shown on this site and originally by Bruce Fraser, the last stop of shadow detail had 16 levels (as opposed to the first at 2048).

The fallacy of this reasoning is that the brightest f/stop of a 12 bit capture from a real camera contains far fewer than the claimed 2048 levels. See my previous post. Even the P65+ using a 16 bit ADC yields only 117 levels in the brightest f/stop.

Regards,

Bill

[kwalsh]

Really! Do you mean it's possible to have an unprocessed ettr RAW file with the resultant benefit of a better SNR but without the concomitant increase in the number of levels that one expects from an ETTR? I never realised that.

Yes.  This is in fact exactly what happens when using ETTR with a Nikon camera that uses "lossy" compressed NEF format.  ETTR doesn't get you any more levels because of the compressed NEF format and yet you still get all the benefits of ETTR since the SNR has improved.  ETTR has never had a dang thing to do with "levels".  It has always been about SNR and photon counting statistics despite what well meaning and capable photographers might write on their web sites.

Ken

[Hans Kruse]

Thanks for pointing this out. Honestly I never combined the DxO tonal measurements with ETTR and probably should have

So even with a lot of underexposure like 5 stops on a 14 bit camera there is still bits enough to record the levels in the highlights og that this camera can capture at base ISO.
So thanks to those who pointed this out.

So ETTR is

1) Maximizing S/N ratio
2) Maximizing DR (some cameras more than others)
3) Levels which seems to almost drop off the list based on this discussion.

[kwalsh]

Its a good point that no matter the exposure, its still 16 levels, how do we define the relationship and effect of these fewer levels, noise and S/N?

How about working on a sentence that takes all of the above into account and explains the relationship and effect of these fewer levels, noise and S/N.

The sentence is pretty easy actually:  

The number "levels" in the RAW file have no measurable effect on the noise at all from shadows to highlights, read noise and photon shot noise always are larger.

As an example, lets take the lowest read noise sensor in existence (for photography).  

The D7000 sensor has a read noise of 1.4 times the least significant bit at base ISO.  That means even ignoring photon shot noise at every exposure level read noise is randomly toggling more than one "level".  Adding more levels anywhere on the scale from shadows to highlights will not improve noise.

Looked at another way, each "level" of the D7000 14-bit RAW file is equivalent to to just 2.6 photons hitting the pixel.  Forget even the "16 levels" shadows.  Lets look at just the bottom two bits "four levels" shadows.  As stated the read noise is already greater than a single "level" but lets pretend it was made zero.  At this "fourth level", two stops below the example you cite, we are accumulating about 10 photons.  The shot noise from the counting statistics will be about 3.2 photons.  Again, larger than a single "level".

At the risk of getting overly emphatic - levels don't matter - never have, never will.  Photon counting statistics and read noise matter - always have, always will.  If some idiot of an engineer were to ever design a camera with an ADC that caused the IQ to be limited by the number of levels they would be summarily fired.

Ken

[bjanes]

Really! Do you mean it's possible to have an unprocessed ettr RAW file with the resultant benefit of a better SNR but without the concomitant increase in the number of levels that one expects from an ETTR? I never realised that.

I always had some vague notion that an ETTR exposure, as compared to an underexposure, would allow a greater number of levels to be recorded.

As the DXO data and Emil's analysis show, each stop of additional exposure increases the SNR by a factor of sqrt(2) and the number of distinguishable levels by the same factor. The number of levels is not doubled as the usual ETTR analysis would indicate.

Of course, I understand whether or not such increased levels can be seen is another issue. In the midtones and shadows, they no doubt can be seen. In the upper tones, many of the levels may to be too similar for the eye to distinguish.

Is this a myth then?

The question here is whether your image is constrained by SNR or the number of levels. The effect of SNR is obvious. An insufficient number of levels will result in posterization. As Emil has pointed out, the raw file is never posterized, but posterization can result from overzealous editing of the raw file. However, posterization is mitigated by dithering of the image by noise. In my work, I rarely see posterization with underexposed raw files. What about you?

The number of levels that the human visual system can distinguish is described by the Weber-Fechner law. Humans can distinguish a 1% difference in luminance, which corresponds to about 70 levels (see Norman Koren). Fewer levels can be distinguished in the shadows. Excess numbers of levels in the brightest portions of the image can be discarded without affecting image quality.

Some subjective degradation in tonal quality may occur before overt posterizatioin, but this would be difficult to quantify.

Regards,

Bill

[ejmartin]

Indeed and a good point to reinforce. But if we look at the distribution of levels in a linear encoded file, we see half of all that data in the first stop of highlight and on the other end, the smallest number of levels. The question is, how do we describe in a sentence or two the relationship of those fewer levels in the last stop, the noise that results there with a higher or lower S/N ratio? In the classic example shown on this site and originally by Bruce Fraser, the last stop of shadow detail had 16 levels (as opposed to the first at 2048). Its a good point that no matter the exposure, its still 16 levels, how do we define the relationship and effect of these fewer levels, noise and S/N?

Maximizing the number of levels, and increasing S/N, often point in the same direction -- both go up as the exposure increases.  But the details differ, and those differences can be important in some situations.  Here is the base ISO number of distinguishable tones per channel, based on S/N, for the P65+ (continuing Bill's example), together with the number of raw levels (the calculated values include the effects of read noise as well as photon count fluctuations, aka "photon noise"):

top stop = 166 distinguishable tones, 32768 levels
2nd stop= 117 distinguishable tones, 16384 levels
3rd stop= 82 distinguishable tones, 16536 levels
4th stop= 57 distinguishable tones, 8192 levels
5th stop= 39 distinguishable tones, 4096 levels
6th stop= 26 distinguishable tones, 2048 levels
7th stop= 17 distinguishable tones, 1024 levels
8th stop= 10 distinguishable tones, 512 levels
9th stop= 6 distinguishable tones, 256 levels
10th stop= 3 distinguishable tones, 128 levels
11th stop= 2 distinguishable tones, 64 levels
12th stop= 0.9 distinguishable tones, 32 levels

So yes, they both trend upward as one increases the exposure; both imply ETTR for fixed ISO.  But if one really subscribed to the "it's the number of levels that's important" mantra, one would be led to incorrect conclusions.  For instance, suppose your base ISO exposure doesn't reach the top stop; does one do better by increasing the exposure a stop (eg by doubling the exposure time), or by doubling the ISO?  If you double the ISO, you don't change the S/N because S/N on this camera is entirely determined by exposure.  You do however double the number of levels, because the histogram is pushed to the right where the levels are denser.  On the other hand, if you double the exposure, you again double the number of levels taken by a given patch of the image; you also increase the number of distinguishable tones by a factor ~1.4 according to the above.  So the "#levels mantra" leads you to think you do just as well by raising the ISO at fixed exposure, whereas you actually only do better by increasing the exposure.  

As a side note, on a camera such as the P65+, raising the ISO never increases the number of distinguishable levels; as far as quality of the raw data goes, raising the ISO accomplishes nothing but reduces the available highlight headroom (and therefore the room for increasing exposure, should you be able to do so without compromising DoF or motion blur requirements).  (Caveat: raw data is no better, but your raw converter may treat it differently, since profiles often read the ISO and change the conversion accordingly, eg by applying more noise reduction at higher ISO.)

It is really quite remarkable how few distinguishable tones there really are in an image file (note that the above is per channel; modulo subtleties having to do with white balance, color filter response and output color gamut, the number of distinguishable colors is roughly the cube of the above numbers).  The vast majority of all those wonderful raw values in the upper zones are wasted in quantizing noise, and not adding anything to image quality.

In the original ETTR article here, Ian Lyons is quoted as saying: The ideal exposure ensures that you have maximum number of levels describing your image without loosing important detail in the highlights. The closer you get to this ideal then the more of those levels are being used to describe your shadows. How about working on a sentence that takes all of the above into account and explains the relationship and effect of these fewer levels, noise and S/N.

Replace "levels" by "distinguishable tones" and you have a correct statement.  Roughly, two tones S1 and S2 are distinguishable if |S2-S1|>N where the noise is N.  If S1 and S2 differ by less than the noise, you don't know whether they are different tones, or the same tone pushed to different values by noise fluctuations.

[digitaldog]

Replace "levels" by "distinguishable tones" and you have a correct statement.  Roughly, two tones S1 and S2 are distinguishable if |S2-S1|>N where the noise is N.  If S1 and S2 differ by less than the noise, you don't know whether they are different tones, or the same tone pushed to different values by noise fluctuations.

Good, excellent. Assuming everyone is in agreement <g>

[fdisilvestro]

Good, excellent. Assuming everyone is in agreement <g>

Agreed, excellent and elegant explanation (As any other explanation from Emil, I would say).

[ejmartin]

What is the appropriate mantra?  I would prefer "Maximize Exposure"; maximize subject to three constraints:

(1) maintaining needed DoF, which limits how much you can open up the aperture;
(2) freezing motion, which limits the exposure time;
(3) retaining highlight detail, by not clipping wanted highlight areas in any channel.  

Note that ISO is not part of exposure.  Exposure has only to do with aperture and shutter speed.  Maximizing exposure guarantees that one captures as many photons as possible subject to photographic constraints, and therefore optimizes S/N.

How does ISO enter?  It enters as a subsidiary aspect of optimizing S/N.  On many cameras (those with CCD sensors, and the newer Sony Exmor sensors), there is little or no advantage to raising the ISO, which aids point (3) -- leaving the ISO at a low value may leave the histogram "to the left" for your chosen exposure, it will give more highlight headroom but will not degrade S/N; such cameras can safely be operated at close to their lowest ISO (the precise optimal ISO depends on the details of a given camera design).  On the other hand, for many other CMOS sensor'd cameras, such as Canon's offerings, and Nikons with Nikon-designed CMOS sensors (D3/D700/D3s, for example), noise relative to exposure is improved by increasing the ISO; after you have maximized the exposure (ie by satisfying criteria (1) and (2)), you have a tradeoff to make for (3) -- raising the ISO lowers shadow noise (up to a camera-specific point of diminishing returns, usually about ISO 1600), therefore improving S/N, but reduces highlight headroom for your chosen exposure, so one has to decide how high the ISO can go and still keep wanted highlights unclipped.  

Anyway, the prescription is to set the exposure (shutter speed and aperture only) according to (1) and (2); back off the exposure if at base ISO and you are compromising (3).  If you are compromising (3) with your chosen exposure and you are not at base ISO, then you should have started with a lower ISO.  Afterward, depending on the specifics of the camera's noise profile, further optimization results from raising the ISO, up to the limit specified by (3), or the camera's ISO point of diminishing returns, whichever is arrived at first.

So, it's (almost) all about ME.    

[jrsforums]

So, Emil...

If I correctly read your post....CCD and Exmor sensors, ETTR provides no benefit, is that correct?

On Canon and Nikon-designed CMOS sensors, is ETTR a benefit...up to the camera specific ISO limit?

John

[ejmartin]

So, Emil...

If I correctly read your post....CCD and Exmor sensors, ETTR provides no benefit, is that correct?

On Canon and Nikon-designed CMOS sensors, is ETTR a benefit...up to the camera specific ISO limit?

John

Rather, CCD and Exmor sensors provide little or no benefit to raising the ISO; Canon and Nikon-designed CMOS do provide benefit, up to a camera-specific ISO.  You always get a benefit from increasing the exposure, if that does not conflict with your DoF and motion blur requirements.

I'd like to decouple the discussion from the histogram, which is where 'To The Right' refers to in ETTR.  The most important consideration is always collecting the most photons during the exposure; you do that by maximizing the exposure (widest possible aperture consistent with DoF requirements, longest shutter time consistent with motion blur restrictions).  Keeping a fixed (maximum subject to the constraints) exposure, where the histogram lies varies with ISO.  You want the histogram as far to the left as possible to capture the most highlights, which you accomplish by lowering the ISO; you want to move it as far to the right as possible if in so doing you lower the camera's ISO-dependent noise contribution (the so-called read noise), which you can sometimes but not always be accomplished by raising the ISO.  If your exposure choice leads to clipped highlights at base ISO, you need to back off the exposure.

So the choice of ISO for a given exposure is a tradeoff.  Let's look at a few cameras (horizontal axis is ISO in stops; first data point is ISO 100 in each case):

For the Canon 5D2 and the Nikon-designed CMOS D3, the camera read noise drops until about ISO 1600 or 3200; for these cameras, you get a S/N benefit from raising the ISO, subject to the constraint of not clipping wanted highlights, up to this point; there is no benefit to raising the ISO beyond this point.  For the remaining bottom three examples (D7000, Sony Exmor CMOS sensor; Nikon D2x, CCD sensor; Phase One P65+, CCD sensor), the read noise is relatively flat with ISO, and there is little to be gained in the quality of the raw data from raising the ISO much above the base value.

[dmerger]

Perhaps a better title for this thread would have been “Stalking the Reichmann Hypothesis”?   

[bjanes]

I'd like to decouple the discussion from the histogram, which is where 'To The Right' refers to in ETTR.  The most important consideration is always collecting the most photons during the exposure

Perhaps a better title for this thread would have been “Stalking the Reichmann Hypothesis”?   

Michael's main point that one should maximize exposure is correct, but use of the histogram and the term ETTR can be misleading, as Emil points out above and in his reply to the DitigalDog. By now, everyone seems to agree that the number of levels has little significance.

Regards,

Bill

[Ray]

As people have been saying (repeatedly) the issue is S/N ratio, not the number of levels.  At a given illumination level (number of photons = S), the noise goes as sqrt(S), so the S/N = sqrt(S).  You improve S/N by capturing more photons -- raising the exposure.  Regardless how many levels there are, two tones are distinguishable (on average) if they are spaced more than the noise.  So there are roughly sqrt(S2)-sqrt(S1) distinguishable tones in the exposure range between S1 and S2.  If you increase the exposure by a stop, you increase this number of distinguishable tones by a factor sqrt(2)~1.4, even though the number of levels in the raw data has doubled.  Similarly, if you took the same picture with a D700 in 12-bit mode and 14-bit mode, the 14-bit capture would have 4x more levels in the raw data, but the same number of distinguishable tones, because at the same exposure the same number of photons is captured.  It's the S/N, not the number of levels.

There are corrections to the above analysis due to read noise, that are only important at low exposure (deep, deep in the shadows at low ISO, creeping upward into higher zones as the ISO is raised).

Emil,
Believe it or not I do understand the principle that the signal comprising the image we capture consists of photons, and that increasing the number of photons during an exposure, by increasing exposure time, increases the strength of the signal and consequently improves the ratio of signal to noise.

I'm not arguing that this is not the case. It's just that I fail to see the logic in the statement that it is not the number of levels also. It seems to me that SNR and the 'potential' number of levels that the camera can record as a result of increasing exposure, go hand in hand.

Now, you have given us an example whereby simply increasing the camera's capacity to record a greater number of levels, by switching from 12 bit mode to 14 bit, may have no visible impact on the image. Fair enough! However the key phrase here is visible impact.

The increased number of levels in a 14 bit capture may be in regions of the tonal range where there may already be more levels in the 12 bit capture than the human eye can distinguish.

If we are to look for such increase in the number of levels, in the 14 bit capture, we stand a better chance of seeing them in the shadows where there are relatively few distinguishable levels in the first instance. Any increase at all may be appreciated.

Now, I understand there are claims that 14 bit in-camera processing in DSLRs is over-kill and that it's sometimes difficult to see any IQ benefit at all because maybe 12 bit is already sufficient. But, surely this is a different issue.

Supposing we were able to compare 6 or 8 bit captures with 12 or 14 bit captures in a modern DSLR, using identical exposures. Now I know that no manufacturer would waste their time providing the consumer with a 6 or 8 bit option in a modern DSLR, but my point is, if they were to, I think you would actually be able to discern more levels in the 12 bit capture using the same exposure.

Finally, if you wish to claim that the number of levels is not the issue with ETTR, perhaps you can provide an example of a comparison demonstrating that an increase in exposure, resulting in a better SNR, has not also resulted in an increase in the number of levels. That could be a convincing demonstration that the number of levels is not the issue.

But, before you attempt this, there should be a few ground rules. It is understood that the levels to be distinguished must exist in the scene being captured, across the whole tonal range, and must be greater in number than the eye can distinguish, across that entire tonal range, otherwise the demonstration would be flawed. There would be no point in photographing a large grey card consisting of one level, say 128, 128, 128.

Do I get the prize for obfuscation or for clarity? 

[Ray]

To add even greater clarity to the issue, perhaps the following could be considered true.

Increasing exposure towards an ETTR, just short of highlight clipping, will always result in a better SNR whatever the nature of the scene. However, the increased number of visually distinguishable levels in the resultant image may not be greater, if such differences in levels do not exist in the first instance, in the scene being photographed.

The primary effect of increasing exposure is therefore a better SNR. A secondary consequence is a potential increase in the number of levels recorded, and the number of levels visually distinguishable.

[degrub]

Are the words "levels" and "tones" being used interchangeably  ?

Frank

[Ray]

Are the words "levels" and "tones" being used interchangeably  ?

Frank

I believe so. 128, 128,127 is one level, or tone, and 127,128,127 is another. However, I doubt very much that these would be visually distinguishable, side by side.

[degrub]

i think Emil may have a slightly different definition if i understand what he is saying correctly from the quotation above -

" If you increase the exposure by a stop, you increase this number of distinguishable tones by a factor sqrt(2)~1.4, even though the number of levels in the raw data has doubled."

Frank

[ejmartin]

Finally, if you wish to claim that the number of levels is not the issue with ETTR, perhaps you can provide an example of a comparison demonstrating that an increase in exposure, resulting in a better SNR, has not also resulted in an increase in the number of levels. That could be a convincing demonstration that the number of levels is not the issue.

I don't have the equipment, the time, or the interest to go off chasing this particular wild goose, but it is certainly possible to make such a demonstration with currently available gear.  For instance, take a D7000; take several images of the same scene:

1) ISO 4X, with exposure Y (in EV), with no clipped highlights.
2) ISO X, with exposure Y (thus 'ETTL' by two stops, using lower ISO).
3) ISO 4X, with exposure Y-2EV (thus 'ETTL' by two stops using two stops less exposure).

(2) and (3) will have the same number of levels for any given patch of the image, but I guarantee (2) will have higher quality because it has higher S/N due to higher exposure.  I also guarantee that (1) and (2) will be indistinguishable, even though (2) has 4x fewer levels on any patch of the scene (I might ask that X=200 or higher to avoid issues in the 12th or 13th stop below clipping ).  If you want higher exposure with fewer levels, try comparing eg example (1) with ISO X/2, exposure Y+2EV.  The latter will have twice the S/N but half the levels in any image patch, compared to (1).  Conversions need a level playing field -- the raw converter can't monkey with conversion parameters based on ISO in metadata.  RawTherapee 4.0 is acceptable for this purpose.

[ejmartin]

I believe so. 128, 128,127 is one level, or tone, and 127,128,127 is another. However, I doubt very much that these would be visually distinguishable, side by side.

Do the number of 'levels' and 'distinguishable tones' in reply 85 look the same to you?