Luminous Landscape Forum

Equipment & Techniques => Digital Cameras & Shooting Techniques => Topic started by: Guillermo Luijk on December 02, 2015, 07:31:24 pm

Title: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 02, 2015, 07:31:24 pm
PHOTOGRAPHIC DYNAMIC RANGE

Looking at the SNR curves provided at DxOMark, a very powerful but not so popular information since it is only available for each particular camera out of the comparison tool ("Full SNR" option):

(http://www.guillermoluijk.com/misc/titanes_snr_dxomark.png)

I have (re)calculated the Dynamic range for the Canon 5DS R, Nikon D810 and Sony A7R II, adding the A7 II and the A7S with a more photographic criteria than the one used in DxOMark:

The following image represents at a pixel level how noisy SNR=0dB and SNR=12dB are:

(http://www.guillermoluijk.com/article/digitalp02/ruido_0db_12db.jpg)

Taking the SNR values from the DxOMark curves and normalizing them to an 8Mpx output (the same resolution as used in the "Print" plots of DxOMark) from each camera pixel count we get the following SNR curves at base ISO (the D810 has some advantage here for being the only camera with a ISO64 base ISO, lower than the ISO100 found on the other four cameras):

(http://www.guillermoluijk.com/misc/titanes_snr.png)

To calculate the Dynamic range we just need to count how many stops we can find between sensor saturation (0EV) and the 12dB crossing point. Zooming the former plot to be more accurate:

(http://www.guillermoluijk.com/misc/titanes_snr_zoom.png)

We have the following Photographic Dynamic Range table:

(http://www.guillermoluijk.com/misc/titanes_rd.png)

Differences of up to 0,5 stops can be considered negligible; from that point a real advantage arises. As usual the Canon gets the worst results, although it is not so far from the Sony's as the usual "2 stops", specially compared to the A7S (a high ISO device). The Nikon D810 is the clear winner with more than 2 stops over the Canon.

These figures perfectly match those offered by DxOMark ("Print" mode for 8Mpx normalization), just need to substract 2 stops to DxOMark's Dynamic range figures. The reason is that in the areas where Dynamic range is calculated read noise is dominant, and read noise remains constant with exposure for a given ISO. This means going from SNR=0dB (DxOMark) to SNR=12dB (suggested photographic criteria) is equivalent to increasing exposure by 2 stops:

(http://www.guillermoluijk.com/misc/titanes_rd_vs_dxomark.png)


IQ IN HDR

With the calculated curves we can answer the following question: how important is the Dynamic range of a sensor to produce high quality HDR images? (in this case I'm assuming HDR=blending a bracketed series of exposures).

The answer is that the sensor's Dynamic range is irrelevant to HDR since in creating the HDR composite we are never going to use the deep shadow areas, where Dynamic range is defined. Instead we are just using the last stops before saturation (let's assume the last 3 stops of those curves in an optimum 2-stop intervals bracketing).

To find out the camera that will produce the cleanest HDR outputs we must look at the curves near saturation. In this way the best of the 5 cameras would be the Sony A7R II, but the advantage will be none in practice for two reasons: the gap is not so big (about half a stop or less), and all cameras will produce a very high SNR in those areas anyway. A cheap compact camera has enough Dynamic range to produce high quality HDR output images in terms of noise.

Regards.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Jack Hogan on December 04, 2015, 09:29:54 am
Hi Guillermo,

Bill Claff takes a somewhat similar approach with his excellent Photographic Dynamic Range (http://www.photonstophotos.net/GeneralTopics/Sensors_&_Raw/Sensor_Analysis_Primer/Engineering_and_Photographic_Dynamic_Range.htm): it's well worthwhile understanding how it is arrived at.  He has quite an extensive camera database at his  site (http://www.photonstophotos.net/), with data he measures himself.  Imho it's better quality information than what can be found in DxO's Full SNR curves (hence sensorgen.info).

Also, once one starts thinking in terms of multiple exposures, stacking enters the picture and random read noise becomes less relevant compared to other parameters we typically ignore, such as PRNU, DSNU and FPN.

Jack
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: BernardLanguillier on December 04, 2015, 09:38:53 am
Thank you Guillermo.

Cheers,
Bernard
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 07, 2015, 03:52:06 pm
It is not clear to me how the raw data are collected -- before the post proessig to draw these curves.
FOr example, are the/ data collected according to single shot or multiple shot?
 
If it is multip-shot, there are a lot of meothods to reduce noise in the shade and to recover the burned out highlight, but none of these are very useful for real life, ..., the exception is steady object, such as product close ups. In fact, some of HDR post processig is along this line.   
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 07, 2015, 04:04:59 pm
There is really no need to go this suspiciously complicated manipulation. For realy life dynalic range just do this:

-Pick up three ISOs, a low Iso (200?), a mid ISO (800?), and a high ISO (6400?).
-For each ISO, if  it is higher, the ISO is udder rated, otherwise it is over rated.
-Find the distance between the zone 5 and the two ends, that is the effective, meaningful dynalmic range.
- Any data other than this method is just manipulation and is suspiciously trying scare normal people.
----- stop the nonsense.
 
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: bjanes on December 07, 2015, 05:12:05 pm
There is really no need to go this suspiciously complicated manipulation. For realy[sic] life dynalic[sic] range just do this:

-Pick up three ISOs, a low Iso (200?), a mid ISO (800?), and a high ISO (6400?).
-For each ISO, if  it is higher, the ISO is udder rated, otherwise it is over rated.
-Find the distance between the zone 5 and the two ends, that is the effective, meaningful dynalmic [sic] range.
- Any data other than this method is just manipulation and is suspiciously trying scare normal people.
----- stop the nonsense.
 

I'm sorry, but your post is unintelligible to me. Could you walk through your method for the A7R ii. What is your noise floor and what is the DR.

Bill

PS turn on your spell checker.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 08, 2015, 02:56:10 pm
Which point do you not understand?
--  Can you shoot a grey scale?
--  Can you judge for yourself the acceptable darkest grade?
--  Can you judege for yourself the acceptable brightest grade?

May be you have problem to choose the dark grade, not sure whether to choose the noise or the darkness? It is your call, but I would choose darkness first, YMMV.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: SZRitter on December 08, 2015, 04:38:41 pm
It is not clear to me how the raw data are collected -- before the post proessig to draw these curves.
FOr example, are the/ data collected according to single shot or multiple shot?
 
If it is multip-shot, there are a lot of meothods to reduce noise in the shade and to recover the burned out highlight, but none of these are very useful for real life, ..., the exception is steady object, such as product close ups. In fact, some of HDR post processig is along this line.   

It's all single shot, as Mr Luijk notes that multishot (i.e. HDR) makes dynamic range virtually unlimited. His process isn't really much different than what you were talking about, he just assigned a 12db noise level as his floor for "useable" darks. He starts at that bottom and counts up to the max.

Personally, I would error towards even less noise than his 12db, but that is just me. I also would love to see this test done with an older camera (say a D2x or older 1D) just to see how far we have come.

I also find the full sensor saturation seems to lead to color shifts. Possibly due to demosaicing, or maybe I am actually clipping, or maybe there is just a bit of unreliable data at full saturation, so I would tend to lop off that last bit the sensor can actually handle. So, instead of shooting only gray scale, I'm thinking at some point I am going to start shooting a color checker at different level of over exposure until I see color shifts on exposure corrected photos. See if there is a separate color ceiling from the sensor's ceiling.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 10, 2015, 02:50:14 pm
Can you judge for yourself the acceptable darkest grade?

This is always the problem when measuring Dynamic range: judgement. Judgement is like asses, everyone has its own. DxOMark defines an objective criteria to measure DR in numbers that are comparable among cameras. I just added a change in that criteria (from 0dB to 12dB) to obtain a much more "photographic" (i.e. useful for the photographer) dynamic range figure.

BTW I wrote a longer article about all this story, hope the online translator works fine enough:
TITAN'S DUEL: 5DS R, D810 AND A7R II. ABOUT PHOTOGRAPHIC DYNAMIC RANGE, HDR AND ML DUAL ISO (http://www.guillermoluijk.com/article/titansduel/index.htm)

This weird image is an interesting exercise:
(http://www.guillermoluijk.com/article/titansduel/hdrcomposite_origen.jpg)

It shows a 3 shots HDR composite at 2EV intervals, with the original captured exposure on each of the 3 shots (i.e. exposure has not been matched) to demonstrate how good HDR practices mean not using at all low values in RAW data. This means sensor's dynamic range is, or can be, irrelevant to HDR.

Regards
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 13, 2015, 02:55:26 am
A method based on skeptics of human judgement implies it is measuring unjudgeable parameters. More likely it is measuring unpractical or unrealizable difference. One bothering problem to me with some high pixel count sensor is the color shift. This is also mentioned in one of the post in this thread. 

Th problem is the image could show weirded saturation of white balance when sliding the exposure value or fill-n the shade.

Maybe you can give a demonstration with your method to show, channel by channel, the consistency of dynanamic range.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 13, 2015, 08:09:46 pm
All three RGB channels behave similarly and have the same dynamic range, that is why it is nonsense to analyse them separately. Once they receive the same amount of photons (and this depends on the scene and on the CFA filter allocated over the photosites), they produce the same RAW levels with the same SNR (visible noise). The B channel being noisier is a myth, what is true is that the B channel most of the times receives less photons than the other two, and this ends in lower RAW levels and worse SNR.

Regards
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 14, 2015, 12:44:56 am
The color shift can happen due to the  in camera processing with cross channel interaction.

The in camera noise processing can be either channel independent or channel correlated. Neither us ideal.. It could be more profound in find pitch sensors.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: dwswager on December 14, 2015, 01:38:51 pm
I am enjoying this thread immensely.  I work with both Military systems acquisitions (build things) and pre-systems acquisitions (technology development) folks and when you put them in the room together it is like they are from different planets.

While I tend to lean toward EinstStein in that I want MY JUDGEMENT applied and to MY TEST CONDITIONS as opposed to some objective standard that might be irrelevant to me.

W/ respect to HDR IQ, I will almost always shoot a sequence using Exposure Compensation even in a situation where I know the D810 will capture the entire scene.  I just find it easier to work with, especially if using and HDR specific software that might not allow for significant movements.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: SZRitter on December 15, 2015, 11:00:31 am
W/ respect to HDR IQ, I will almost always shoot a sequence using Exposure Compensation even in a situation where I know the D810 will capture the entire scene.  I just find it easier to work with, especially if using and HDR specific software that might not allow for significant movements.

While not HDR, I've been shooting scenes lately with a bracket from 0 to +3EV and then using lightroom to exposure match back to the "correct exposure". Load them all as layers in PS and align them, then use a mask to get the ones with the best noise and color characteristics. Basically, I think it is a manual way of doing exposure fusion, but I can do it almost as fast as I used to do HDR in Photomatix while being a bit more accurate to the look I want.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 15, 2015, 12:57:34 pm
That IS HDR. The problem of the manual blending is you cannot optimize as much as software can do in order to achieve the cleanest (noiseless) possible resulting image. In addition to this you'll probably need to introduce a considerable amount of progressiveness in making the fusion to obtain a seamless composite; this adds the possibility of losing sharpness when shots are not milimetrically aligned.

Regards

Enviado desde mi GT-I9195 mediante Tapatalk
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Jack Hogan on December 15, 2015, 04:38:29 pm
Just curious, as I am usually not pleased with how software puts together into a single image several captures of the same subject at different exposures (say three captures 4 stops apart: -2,0,2).  Has anyone compared that to what can be obtained from four identical back-to-back 14-bit captures of a 'properly' exposed image, added together to form a true 16-bit raw image?  8 captures and floating point? Very quick: just set the camera up and hit the shutter as many times as you think you need to bring the SNR of the shadows out, then add them up.  My guess would be that given the current state of HDR software the latter would result in a more pleasing final image.  But I haven't tried it yet.

Jack
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 16, 2015, 06:37:10 am
Jack, by averaging four shots you just double SNR, that is not rival to increasing exposure. Just one extra shot overexposed by 4 stops increases SNR by 16 times, and you don't have the issue of losing sharpness because of minimal misalignment as when averaging.

- Averaging on 4 standard shots -> SNR is multiplied by 2
- Pixel selection on 2 shots 4 stops apart -> SNR is multiplied by 16

Regards

Enviado desde mi GT-I9195 mediante Tapatalk
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EinstStein on December 16, 2015, 07:08:40 am
Are you going to pubish your tests for channel consistency?
It is easy judgeable and important for us common users, far more than the hardly judgeable DxO invented extended dynamic range.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Bart_van_der_Wolf on December 16, 2015, 07:50:04 am
Just curious, as I am usually not pleased with how software puts together into a single image several captures of the same subject at different exposures (say three captures 4 stops apart: -2,0,2).  Has anyone compared that to what can be obtained from four identical back-to-back 14-bit captures of a 'properly' exposed image, added together to form a true 16-bit raw image?  8 captures and floating point?

Hi Jack,

The problem is probably in the tonemapping software. The only one that gives results that I find very realistic, is SNS-HDR (https://translate.google.com/translate?sl=pl&tl=en&js=y&prev=_t&hl=en&ie=UTF-8&u=www.sns-hdr.com%2F&edit-text=). It is currently in its Version 2 Alpha 3 (http://www.sns-hdr.com/forum/viewtopic.php?f=7&t=5255) stage but, like Version 1, it still produces a very natural looking result. Version 2 will be a free upgrade for current owners of the current stable version 1. Version 2 will add lots of useful controls and further quality improvements (and maybe a version for the Mac OS), but not all features are implemented yet in this Alpha stage of development.

As for the differences in noise that Guillermo mentioned, that's basically what it is, but for the issue of tonemapping to achieve a realistic looking tonality of HDRIs, additional solutions are required.

Cheers,
Bart
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 16, 2015, 09:55:52 am
Are you going to pubish your tests for channel consistency?
It is easy judgeable and important for us common users, far more than the hardly judgeable DxO invented extended dynamic range.
Not sure about what you are asking for. If you mean a demonstration that all three RAW channels behave similarly, when I calculated the SNR curves I found there was no differentiation so I just plotted (EV, SNR) pairs to draw the curves, indistinctly from what RAW RGB channel they came from:

(http://www.guillermoluijk.com/tutorial/noisedr/curvassnr.gif)

http://www.guillermoluijk.com/tutorial/noisedr/ruidoyrangodinamico.xls

Regards.

Enviado desde mi GT-I9195 mediante Tapatalk
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Jack Hogan on December 16, 2015, 10:04:58 am
I understand Guillermo, I was trying to go perceptual on you :)  What's better looking: X identical images stacked or 3 HDR (-2:0:2 stops)?  I am thinking that the HDR process may be less than ideal, introducing distortions/noise which may be more/less objectionable than a little extra noise in the stacked set?

And thanks Bart, I will try SNS-HDR when I get the chance.
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 16, 2015, 02:34:41 pm
I understand Guillermo, I was trying to go perceptual on you :)  What's better looking: X identical images stacked or 3 HDR (-2:0:2 stops)?  I am thinking that the HDR process may be less than ideal, introducing distortions/noise which may be more/less objectionable than a little extra noise in the stacked set?

There has to be no difference at all, just an improved SNR in the HDR composite over the stacked version. What you refer to as "better looking" doesn't depend on the source of the information (HDR bracketing vs average stacking), but on the tone mapping applied afterwards as Bart pointed. If the HDR process is performed linearly, there will be no colour or contrast difference between the HDR blend and any of the single shots. So the resulting image will look the same no matter how you started; it will just be less noisy in the HDR.

Real world example: left the least exposed shot preserving the windows, right the HDR composite when information from +2 and +4 shots is added:
(http://www.guillermoluijk.com/misc/linearhdr.jpg)

HDR fusion map:
(http://www.guillermoluijk.com/misc/linearhdr.png)

100% crops (right is 16 times less noisy):
(http://www.guillermoluijk.com/misc/linearhdr_crop.jpg)


Just curious: to achieve the same noise reduction (16x) with standard averaging, you would need to average as many as 256 standard shots.

Regards



Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: bjanes on December 16, 2015, 03:23:25 pm
A method based on skeptics of human judgement implies it is measuring unjudgeable parameters. More likely it is measuring unpractical or unrealizable difference. One bothering problem to me with some high pixel count sensor is the color shift. This is also mentioned in one of the post in this thread. 

Th problem is the image could show weirded saturation of white balance when sliding the exposure value or fill-n the shade.

Maybe you can give a demonstration with your method to show, channel by channel, the consistency of dynanamic range.

EinstStein,

I see nothing wrong with Guillermo's DR analysis. After all, it closely follows the method outlined by Emil Martinic in this LuLa post (http://forum.luminous-landscape.com/index.php?topic=42158.0) and more fully explained in his outstanding and widely cited  article (http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/index.html) on the University of Chicago web site. Emil has a PhD in physics, is a full professor at this prestigious institution, and has published more than a hundred articles in peer reviewed scientific journals. I don't know your qualifications, but imagine that they are less than those of your namesake.

A channel by channel analysis would not be easy to perform, as indicated in the DXO web site here (http://www.dxomark.com/About/In-depth-measurements/Measurements/Color-sensitivity) and quoted below.

Full-color sensitivity
The noise on the sensor is processed by a RAW converter to lead to the final image. In particular, RAW converters apply a color rendering which maps the RAW values to RGB values in the final image (for instance, sRGB values). Color rendering includes at least white balancing and a color matrix, as described above. These steps yield an amplification of noise. For each triple RGB in the final image, noise can be predicted from the RAW noise characteristics, the white balance scales, and the color matrix coefficients. The noise on the three color channels is described by a three-dimensional covariance matrix, which is not easy to represent. In the full-color sensitivity tab, we chose to illustrate the noise in the (a,b) plane of the CIE Lab color space. For different values of luminance and different ISO sensitivities, the noise at given colors is represented by an ellipse which shows the colors that are likely to be generated in the image instead of the real color (displayed at the ellipse center). The orientation and the size of the ellipses show the coloration of noise and its amplitude.


Bill
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Jack Hogan on December 17, 2015, 03:12:47 pm
Real world example: left the least exposed shot preserving the windows, right the HDR composite when information from +2 and +4 shots is added:

All right Guillermo, sold.  HDR trumps stacking in that situation.

Jack
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: IliasG on December 17, 2015, 05:30:51 pm

100% crops (right is 16 times less noisy):
(http://www.guillermoluijk.com/misc/linearhdr_crop.jpg)


Just curious: to achieve the same noise reduction (16x) with standard averaging, you would need to average as many as 256 standard shots.

Regards

Why is the right 16X times less noisy ?. Shooting with 16X more exposure (+4EV) gives sqrt(16) = 4X better SNR .. so I would expect to be equal with 16 standard shots averaged ;)
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: Guillermo Luijk on December 17, 2015, 07:09:58 pm
Why is the right 16X times less noisy ?. Shooting with 16X more exposure (+4EV) gives sqrt(16) = 4X better SNR .. so I would expect to be equal with 16 standard shots averaged ;)

It is not that simple but luckily it can be estimated more accurately from the SNR curves:
- In the sensor "highlights" where photon noise prevails, SNR increases by 3dB/EV (i.e. SNR is multiplied by sqrt(2) with each extra stop of exposure as you mention) but...
- In the sensor "deep shadows" where read noise prevails, SNR increases by 6dB/EV (i.e. SNR is multiplied by 2 with each extra stop of exposure).

For the case of HDR we are closer to the second situation since we are reallocating the deep shadows of the scene from the sensor's "deep shadows" (many stops below sensor saturation in the least exposed shot that preserves the highlights) to areas 4 stops closer to sensor saturation. That is why I made the 16x times less noise approximation.

But the real resulting SNR improvement will depend on the region we fall into. In my example this is the EV distribution of the +4EV crop:

(RAW histogram in EV)
(http://www.guillermoluijk.com/misc/canon350d.jpg)


On average we can assume that the information from the crop is located around 5 stops below sensor saturation, this means in the 0EV shot the same information is on average located 9 stops below sensor saturation. Let's find out the exact SNR improvement from -9 to -5 following the SNR curves of the camera used (DxOMark info):

(http://www.guillermoluijk.com/misc/canon350d.png)


SNR improvement is around 19,5dB (less than 24dB but more than 12dB), i.e. noise was reduced by 9,44x (less than 16x but more than 4x).

To achieve the same improvement with averaging we would need: 9,44^2=89 standard shots (less than 256 but more than 16).

Since a real world scene is a continuous luminance distribution (my crop spreaded over around 6 stops of DR), the deepest shadows of the scene will always enjoy a larger SNR improvement than the not so deep shadows. This is good news since it means more benefit is obtained where more help is initially needed to produce a well balanced output image in terms of SNR.

Regards
Title: Re: Photographic dynamic range, IQ in HDR and the 3 beasts: 5DS R, D810, A7R II
Post by: EricV on December 18, 2015, 12:27:43 pm
In the really dark shadows, where sensor read noise is comparable to or higher than photon shot noise, it is better to take one long exposure than many short exposures, in order to incur fewer read noise penalties.  In the less dark shadows, where photon statistics dominate, it should not matter how the photons are collected, as long as the total exposure is the same.

For this same reason, when evaluating sensor noise performance at SNR=1, sensor full-well capacity and read noise are equally important, but when evaluating sensor noise performance at much higher SNR, full-well capacity is almost all that matters.

By definition, dynamic range at SNR=1 is (full-well capacity) / (read noise).  A good approximation to dynamic range at much higher SNR would be (full-well capacity) / (target noise level), where the target noise level is the specified SNR squared.  For example, SNR=16 occurs when the shadows have 256 electrons, so dynamic range at SNR=16 is just (full-well capacity) / 256.