The Significance of S/N as distinct from Dynamic Range

[Dave Ellis]

Hello, I have a question for all you noise gurus out there 

DXOMark publishes sensor measurement figures for S/N (at 18% grey level) and Dynamic Range. I understand the significance of Dynamic Range in relation to shadow noise (which is mainly read noise) but am wondering what the significance of S/N is in relation to image appearance. Typically S/N (at 18% grey level) for ISO 100 is of the order of 40db (and I believe that for 18% grey, photon noise, which is proportional to the square root of the signal level, is the dominant contributor). As ISO is increased, the S/N reduces by about 3 db per ISO stop.

So what sort of degradation is caused by the S/N value, or in other words, where might it manifest itself. eg in a clear blue sky ? I'm having trouble visualising what degradation might occur so I would appreciate any comments please. Instinctively I can't help but feel that noise 30 or 40 db below the main signal would not be noticeable by the human eye but I don't really know.

Dave

[EricV]

You are correct that for this brightness level, S/N is dominated by photon statistics.  S/N of 40db means S/N = 100, which in turn means the sensor collected 100000 photons (per pixel).  You can get an idea of what this level of noise means by taking your image of a blue sky and sprinkling in a fair number of pixels with values a few percent different from the average.  This may well be visible in a very uniform area like clear sky, but probably not in an area with any detail or local contrast variation.  If you reduce the illumination by several stops, for example looking at dark shadows rather than bright sky, the relative effect of noise becomes greater, and will become quite visible, long before electronics noise becomes significant.

The following link has more discussion and some images illustrating noise levels:
http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/

[Jack Hogan]

... am wondering what the significance of S/N is in relation to image appearance.

Yes, I've also wondered why they chose 18% of full scale, where at base ISO noise is typically due to shot noise and prnu, hence related to sensor size (the shot noise part) and patents (the prnu part).  Of course as ISO increases read noise becomes more relevant and eventually predominant there also.

18% could have been chosen because it represents L*50, supposedly mid-gray - that is a tone perceived to be half way between brightest diffused white and pitch black.  However, no current camera I know meters mid-gray to 18% of clipping in the raw data, many meter it a stop or two lower than that.  So I guess that would put it somewhere in the higher mid-tones once rendered.

Jack

[Dave Ellis]

You are correct that for this brightness level, S/N is dominated by photon statistics.  S/N of 40db means S/N = 100, which in turn means the sensor collected 100000 photons (per pixel).  You can get an idea of what this level of noise means by taking your image of a blue sky and sprinkling in a fair number of pixels with values a few percent different from the average.  This may well be visible in a very uniform area like clear sky, but probably not in an area with any detail or local contrast variation.  If you reduce the illumination by several stops, for example looking at dark shadows rather than bright sky, the relative effect of noise becomes greater, and will become quite visible, long before electronics noise becomes significant.

The following link has more discussion and some images illustrating noise levels:
http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/

Thanks for your comments Eric. I am familiar with that article and have found it very useful. I must re-read it because it's more than likely that I have missed some salient points ! I think I will go out and do some test shots of blue sky myself, with different exposure levels and different ISO settings.

Dave

[Dave Ellis]

Yes, I've also wondered why they chose 18% of full scale, where at base ISO noise is typically due to shot noise and prnu, hence related to sensor size (the shot noise part) and patents (the prnu part).  Of course as ISO increases read noise becomes more relevant and eventually predominant there also.

18% could have been chosen because it represents L*50, supposedly mid-gray - that is a tone perceived to be half way between brightest diffused white and pitch black.  However, no current camera I know meters mid-gray to 18% of clipping in the raw data, many meter it a stop or two lower than that.  So I guess that would put it somewhere in the higher mid-tones once rendered.

Jack

Thanks for your comments Jack. At this signal level, when comparing different sensors, I guess the S/N comparison is fairly predictable as photon noise is directly related to pixel size and the prnu noise is relatively small ?

I am starting to think that I am looking at the effect of noise on real images a bit too simplistically and should be looking not just at read noise visible in areas close to black but also considering how the read noise and photon noise contribute at somewhat higher luminance levels.

In your last sentence are you referring to the use of gamma encoding ?

Dave

[Bart_van_der_Wolf]

I am starting to think that I am looking at the effect of noise on real images a bit too simplistically and should be looking not just at read noise visible in areas close to black but also considering how the read noise and photon noise contribute at somewhat higher luminance levels.

Hi Dave,

I would agree. Looking at S/N ratio in the deepest shadows is important if the image has lots of shadow regions that may need to be boosted. But there are lots of other brightness levels (especially after gamma adjustment!) that may be more noticeable to human vision. Those higher brightness levels will usually be dominated by photon shot noise at capture time. That will then be processed by a Raw conversion which will turn it into more or less 'colored blobs' (because the noise at the R/G/B filtered positions is not correlated but random, and demosaiced into color differences), and apply a Gamma pre-compensation. The gamma compensation tends to amplify low exposure noise, but compress high exposure level noise.

This is usually pretty well controllable in the resulting image file with a good noise reduction process, which addresses the artificial color noise, and leaves the luminance noise mostly alone. I rarely use noise reduction, because I usually shoot at low ISOs, but if necessary a plugin like Topaz Denoise can do wonders by just slightly reducing the noise, not remove it totally, for which I tend to turn down the amounts of reduction considerably.

Cheers,
Bart

[Jack Hogan]

In your last sentence are you referring to the use of gamma encoding ?

I was avoiding gamma* and thinking more of how people typically apply some sort of a curve to squeeze 11+ stops of captured DR into the 8- stops displayed by the output medium.  Where (in terms of L*) does the information in the raw data originally recorded at 18% of clipping end up then?  Closer to the highlights?

Jack

*In a well behaved imaging capture-display system gamma cancels out before we get to see the image.  Its main claim to fame is in encoding efficiency.  Since LCD monitors can be effectively linear, once we move to floating point arithmetic gamma will imho disappear in a puff of smoke.  Good riddance.

[Bart_van_der_Wolf]

I was avoiding gamma* and thinking more of how people typically apply some sort of a curve to squeeze 11+ stops of captured DR into the 8- stops displayed by the output medium.  Where (in terms of L*) does the information in the raw data originally recorded at 18% of clipping end up then?  Closer to the highlights?

Hi Jack,

To answer your (rethorical) question, it typically ends up almost half way between White and Black, 255 * (0.18^(1/2.2)) = 117, where it's quite noticeable, and is encoded in integer numbers (hopefully 16-b/ch, better in floating point numbers) which will often get manipulated further.

*In a well behaved imaging capture-display system gamma cancels out before we get to see the image.  Its main claim to fame is in encoding efficiency.  Since LCD monitors can be effectively linear, once we move to floating point arithmetic gamma will imho disappear in a puff of smoke.  Good riddance.

I agree, but don't forget that the "lightness" sensitivity of human vision is not necessarily linear (the lightness sensation of vision is roughly the 0.4-power function of Luminance, see page 258 of this book), that also changes with average illumination levels and varies by color and wavelength.

The bigger issue is the non-linear tonemapping, which will often mostly just lift the lower end of the scale, and compress the high end, a lot (instead of more advanced local contrast adjustments like with Topaz Clarity and Adjust). So an 18% point (some 2.5 stops below clipping white) seems like a decent average point of departure for S/N ratio analysis. It's not too dark, and not too light, and it is where human vision seems to attach a lot of weight to. In that sense, it's a kind of an average.

Cheers,
Bart

[Jack Hogan]

To answer your (rethorical) question, it typically ends up almost half way between White and Black, 255 * (0.18^(1/2.2)) = 117, where it's quite noticeable, and is encoded in integer numbers (hopefully 16-b/ch, better in floating point numbers) which will often get manipulated further.

Hey Bart,

This discussion piqued my interest, so I found the first capture I could get my hands on in this machine and checked it out.  It wasn't hard as I always shoot RAW+Jpeg (small, basic) just to be ready for such occasions  Here is the original SOOC jpeg, with the full exif.  Guess what tones in the image below correspond to 18% of clipping in the raw file (green channel)?



The far sunlit grass behind the trees to the right, the yellow sunlit tree at the far bend of the river and the reflection of the sky, 15% up from the bottom of the frame.  The sky is partly blown and its reflection in the water starts off at around 55% of clipping in the raw file.  The red sunlit trees are at less than 10%.  Looks like I shot it in manual mode and ADL was on.

Jack

[Bart_van_der_Wolf]

Hey Bart,

This discussion piqued my interest, so I found the first capture I could get my hands on in this machine and checked it out.  It wasn't hard as I always shoot RAW+Jpeg (small, basic) just to be ready for such occasions  Here is the original SOOC jpeg, with the full exif.  Guess what tones in the image below correspond to 18% of clipping in the raw file (green channel)?
...
The far sunlit grass behind the trees to the right, the yellow sunlit tree at the far bend of the river and the reflection of the sky, 15% up from the bottom of the frame.  The sky is partly blown and its reflection in the water starts off at around 55% of clipping in the raw file.  The red sunlit trees are at less than 10%.  Looks like I shot it in manual mode and ADL was on.

Hi Jack,

That seems indeed to be correct. It is apparently very hard to predict where, after demosaicing, white-balancing, gamma adjustment, tonemapping, color correction, the different Raw color channel data will wind up to be. In the attached JPEG I marked in Magenta the RAW G1 channel data at 18% of clipping +/- 50 ADUs. They correspond to RGB levels, in sRGB space, of something like 205 green, quite a bit brighter than average grey. I didn't try the other channels, but I guess they'll be all over the place, probably on the brighter side of average.

Cheers,
Bart

[Jack Hogan]

That seems indeed to be correct. It is apparently very hard to predict where, after demosaicing, white-balancing, gamma adjustment, tonemapping, color correction, the different Raw color channel data will wind up to be. In the attached JPEG I marked in Magenta the RAW G1 channel data at 18% of clipping +/- 50 ADUs. They correspond to RGB levels, in sRGB space, of something like 205 green, quite a bit brighter than average grey. I didn't try the other channels, but I guess they'll be all over the place, probably on the brighter side of average.

Right, interesting.  Not that it matters much in practice, as most sensors today have excellent prnu performance.

Jack

[BJL]

Firstly, as has maybe already ben explained, the "18%" is measuring visible noise in the main mid-tone parts of the image, as opposed to the "lets push shadows that would normally be rendered totally back up about five stops and stare at that" as measured by overall system dynamic range.

As already noted, this will be dominated by the basic quantum mechanics of photon shot noise when at low to moderate exposure index (ISO setting), so it is mainly relevant as a measure of how high the exposure index can go before
(a) read noise become significant, and/or
(b) photon shot noise become significant even in the mid-tones, in turn predictable from "photo-site area times quantum efficiency".

This does seem useful for one very common case of noise problems: images in low-light and/or high shutter speed situations that require a high exposure index, and so are at risk of visible noise degrading even the main subject, not just when peeping into the shadows.  Also, any prominent background region of very little spatial variation, so that noise is more noticeable: "digital confetti in the blue sky".

[Dave Ellis]

Thank you Bart, Jack and BJL for your very helpful comments. All is starting to become clear.

As a matter of interest, here is a 100% crop from a raw image I took yesterday with my D610 of clear blue sky. ISO for this shot was 3200. I took several exposures hoping to get one with the sky at around 18% but was off in my approach and the highest exposure only yielded about 12% in the blue channel (according to RawDigger). Interestingly this translated to about 75% in ACR with no adjustments other than the default tone curve.

The noise is certainly visible and this just confirms what others have been saying above. Based on DXOMark results, S/N for this shot would have been a bit under 30 db.

Dave

[dwswager]

Thank you Bart, Jack and BJL for your very helpful comments. All is starting to become clear.

As a matter of interest, here is a 100% crop from a raw image I took yesterday with my D610 of clear blue sky. ISO for this shot was 3200. I took several exposures hoping to get one with the sky at around 18% but was off in my approach and the highest exposure only yielded about 12% in the blue channel (according to RawDigger). Interestingly this translated to about 75% in ACR with no adjustments other than the default tone curve.

The noise is certainly visible and this just confirms what others have been saying above. Based on DXOMark results, S/N for this shot would have been a bit under 30 db.

Dave

Bottom line for me is High ISO noise on my D810 is visible across the entire spectrum of tones and for the most part seems to be photon noise.

It is more visible in lower tones because the SNR will be variable across the tonal range and it is easier to see because of the contrast between the shadow tone and the noise.  Also it is obviously more visible in flat areas of similar color that lack local contrast variations.  Hence, black skies tend to be the area where noise is most visible.

[Dave Ellis]

Bottom line for me is High ISO noise on my D810 is visible across the entire spectrum of tones and for the most part seems to be photon noise.

It is more visible in lower tones because the SNR will be variable across the tonal range and it is easier to see because of the contrast between the shadow tone and the noise.  Also it is obviously more visible in flat areas of similar color that lack local contrast variations.  Hence, black skies tend to be the area where noise is most visible.

Yes that sounds like a reasonable summary. The following extract from Emil Martinec's article referenced by Eric in post 2 gives a good indication of how dominant noise transitions from read noise to photon noise as signal is increased.

Dave

[BJL]

The following extract from Emil Martinec's article referenced by Eric in post 2 gives a good indication of how dominant noise transitions from read noise to photon noise as signal is increased.

The only thing wrong with Emil Martin's article is the line at the top: "last update: August 6, 2008". The theory is unchanged, but it would be interesting to see some of the example graphs updated from the Canon 1D3 to one or two of the current leading professional models; maybe one with a Sony sensor and one Canon.

But I fully understand that Emil has more important things to do in his day job!

[Jack Hogan]

The only thing wrong with Emil Martin's article is the line at the top: "last update: August 6, 2008". The theory is unchanged, but it would be interesting to see some of the example graphs updated from the Canon 1D3 to one or two of the current leading professional models; maybe one with a Sony sensor and one Canon.

For Sony and Nikon you can keep an eye on Jim Kasson's site.  And here's the D810 at base ISO.  Don't know anyone who does Canon other than DxO (look for their 'Full SNR curves').

Jack

[AlterEgo]

Don't know anyone who does Canon other than DxO (look for their 'Full SNR curves').

the author of http://home.comcast.net/~nikond70/ shall probably be petitioned to add something like this

[Dave Ellis]

The only thing wrong with Emil Martin's article is the line at the top: "last update: August 6, 2008". The theory is unchanged, but it would be interesting to see some of the example graphs updated from the Canon 1D3 to one or two of the current leading professional models; maybe one with a Sony sensor and one Canon.

But I fully understand that Emil has more important things to do in his day job!

Yes I suppose so ! 

[Dave Ellis]

For Sony and Nikon you can keep an eye on Jim Kasson's site.  And here's the D810 at base ISO.  Don't know anyone who does Canon other than DxO (look for their 'Full SNR curves').

Jack

Thanks a lot Jack. You've given me some great material to go through there with your stuff and Jim's. Also, I didn't realise DXOMark published the full SNR curves as I usually refer to the sensor comparison section rather than the single sensor data section.

Dave