Photoshop HDR Error: Not Enough Dynamic Range

[Colin Southern]

People keep saying this, but I'm still not sure I agree under certain circumstances

Hi Dave,

You're mad!

Just kidding - but - you are confusing Dynamic Range (number of stops of brightness) with Analog to Digital Converter resolution (the number of bits) - it relates well back to the "height of the staircase -v- the number of steps in the staircase" analogy.

Lets examine things in terms of highlight and shadows (since these are the "ends" we're trying to extend the dynamic rance to cover) ...

To "set the scene" (or "Define a scene that would require true high dynamic range"), consider a dolls house on a table with a large window directly behind it - and the objective is to capture the full tonal range of the dolls inside the dolls house -AND - the full tonal range of the trees, grass, and white fence visable through the window.

For a starting point you choose an exposure that correctly exposes the outside of the dolls house.

Remember the above sentence - as it sets the reference for everything that follows.

So - we've got a correctly exposed outer dolls house - through the window we've got grass and trees that are brighter than the outside of the dolls house - but still within the range of the sensor (thus captured) - but the white fence is a couple of stops brighter again and - unfortunately - exceeds the ability of the sensor to capture it. Read that last sentence again ... it exceeds the ability of the sensor to capture it - the photosites are fulls saturated, and in essence, it becomes a blown highlight. No amount of post-processing is going to be able to recover the white fence simply because the information the information describing it just isn't present in the capture.

Inside the dolls house things are very dark - and as a result there is only a tiny amount of light reflected off the dolls inside. The sensor records these few photons reflected off the dolls inside the dolls house, but the final exposure also contains low levels of noise ... and unfortunately the photons counted by the sensor are indistinguishable from the noise introduced from other sources - and again - no amount of post-processing is going to be able to seperate the shadow details from the dolls from the background noise; so again, for all intents and purposes, the shadow details just don't exist.

From here, lets consider two possible paths ...

Path 1 - is the true HDR path - 2 additional exposures are taken (one for outside the window, one for inside the dolls house) - these captures contain the required details and can be combined into an HDR image.

Path 2 - is a "psudo HDR" path where the original - single - capture is re-processed into 2 more additional files. Unfortunately, this approach fails: the file that deals with the bright end still cannot reveal the fence because details of the fence weren't contained in the source image (remember that it was too bright and fully saturated the sensor resulting in a blown highlight). And the file that deals with the shadow detail inside the dolls house fails also because the values relating to the figures inside the dolls house are indistinguishable from the noise floor - so any attempt to amplify them amplifies the random noise as well).

So ... by definition, you can't make an HDR image from a "normal" dynamic range capture - just like you can't get 2 litres of water from a 1 litre container without refilling it!

Hope this makes sense!

[Dave Humphries]

Hi Colin,

Thanks for taking the time, but I'm still not convinced, so I'm going to move the goalposts for you;

Ok, I am adding one more "certain circumstance" to my criteria; the illumination range of my scene equals the capture range of the sensor. No white fence and no dim dolls.

So now the sensor CAN hold the same 12 litres the scene contains, but the final image only can only be viewed throught the bottom of an 8 litre container!

The liquid analogy breaks down because it cannot deal with tone mapping, or altering the slope of the transfer characteristic, which effectively allows one to see elements of all 12 litres even in an 8 litre pot.

You were right the first time, I'm mad

I fully accept in your scene, wher dynamic range exceeds sensor range, loss is inevitable and you are 100% correct, it cannot be rectified from a single exposure.

Cheers,

[Colin Southern]

Ok, I am adding one more "certain circumstance" to my criteria; the illumination range of my scene equals the capture range of the sensor. No white fence and no dim dolls.

... in which case this is of course just a "normal dynamic range" capture for that sensor - HDR not required

So now the sensor CAN hold the same 12 litres the scene contains, but the final image only can only be viewed throught the bottom of an 8 litre container!

Essentially what we're talking about here is tonal range compression, which (unless you're the proud owner of one of those new fang-dangled 11-stops-of-DR monitors, is normal with any image (HDR or not) - the only difference is that with a HDR source things get far more critical when you're trying to fit it into a 4-stop range for printing and/or display, whilst still having it look normal.

I think that what gives "credibility" to the (psudo) HDR approach is that it's easier to deal to shadow and highlight areas as seperate entities especially when it's easy to boost shadow detail (when you can ignore the highlight areas) and then deal to highlight detail (whilst ignoring what's happening with the shadow end of the image), in a seperate interpretation of the image.

In reality the actual dynamic range of the scene isn't changing - you're just getting to the final result via different paths (a psudo HDR approach -v- an approach that only uses a single image, but will most likely require extreme adjustments to essentially tone map the extremes of shadow and highlight). So the psuso HDR approach may well be easier, but it still can't reproduce something that wasn't there in the first place.

What we REALLY need is a sensor with a non-linear response!

[Davey]

I don't yet know the best way to do it since I'm new to HDR photography but if it helps what I do is I work out if a single capture is feasible. If it isn't then I go the HDR route (which I'm still refining somewhat). If has range than can be adequately captured in one shot then I choose how, my usual choice is always to capture just under the threshhold (ie just before it blows any detail), although the resultant file is "too bright" sometimes I started doing this because a: no scene info is lost b: snr is better due to more separation between shadows and noise floor.

I find if you work on a 16bit image it shouldn't be necessary to tonemap multiple developed images. You could just do to the single image using masks/selection etc what you would in developing 3 separate images. Obviously it's a little more work than tone map route but you won't get the drawbacks. Tonemapping is a necessary evil to display true HDR images. I can see why you find merge and tonemapping useful and would say it's far from mad, I've just found there are better tools for doing it. Unsure what options PSE has but I reckon you should have enough. I know PSE definately has selection mask tools and using those with exposure adjustment tools and the like you could do to selected regions of a single 16bit image what you would do globally to an 8 bit image (which is then merged). The merge/tonemap step is the problem since it introduces issues you cannot work around, but merge is not needed in this case since the source is the same no combo is needed.

edit: Merge is problem because essentially you are merging values from 3 sources when the values are accounted for in the single source. This merge than means it needs to be tonemapped which introduces issues of it's own (contrast problems for instance).

On another some exposure software might be handy, I've been playing with tufuse and found that can do some interesting things that isn't limited to just merging different images. Still it's something you could do better manually in ps (or pse I imagine) but it might save time and doesn't suffer from the tonemapping issues.

[Dave Humphries]

~ is normal with any image (HDR or not) - the only difference is that with a HDR source things get far more critical when you're trying to fit it into a 4-stop range for printing and/or display, whilst still having it look normal.

So, showing my ignorance (I'll call it forgetfullness at this late hour).
What does the tonal compression do when I view the image?
The gamma of the display device, and the printer driver?

[hannibf]

I have followed the HDR discussion in this thread for a while now, and I have a few comments to the true vs. pseudo HDR technique which may clarify a few things.

A RAW image contains 12 or 14 bits per pixel. Thus, when converting from RAW to an 8-bit JPEG, some image information is bound to be lost - whether or not this is done in camera or "manually" (i.e. through ACR or the like). Either highlights/shadows must be sacrificed (clipping), or contrast must be reduced for some tonal ranges.

The HDR technique, while still not resulting in a true HDR, can be used as a tool in the conversion from RAW to JPEG. Note, however, that the resulting JPEG can just as well be obtained via manual work, e.g. through ACR fiddling and layering/masking and adjustment layers in PS!

If one does choose to make one RAW image into e.g. three differently "exposed" shots, the HDR technique can be thought of simply as a tool for converting/adjusting the 12-/14-bit tonal range of the original RAW into the 8-bit range of a JPEG. But, once again: From the one original RAW shot, the same pseudo HDR result could be obtained through manual PS work!

Most importantly, as mentioned by others, the dynamic range of the camera sensor is the same whether RAW or JPEG is used, and so the HDR approach described above will do nothing else than can theoretically be done in PS using manual techniques when converting from RAW to JPEG. True HDR (i.e. a dynamic range beyond that of the camera sensor!) can _only_ be obtained using several shots with different exposures.

Hopefully, this came out the way I meant it. Let me know if anything is unclear - or plain wrong!

[Dave Humphries]

Hi Hannibf,

I think it has (come out the way you meant); you've managed to acknowledge what I was getting at and I can cheerfully accept the validity of the last paragraph too. Which is what Colin's been trying to drum into me for weeks

Welcome to the forums by the way, it would be great if you could tell us a little more about yourself in the
Introduce Yourself & Welcome Other Members (2) thread.

Many thanks for taking the time to explain this.

Regards,

[Colin Southern]

Hopefully, this came out the way I meant it. Let me know if anything is unclear - or plain wrong!

All looks OK to me

Just one comment though ... I agree that for a single capture there's nothing to be gained by "re-developing" - IN THEORY. IN PRACTICE however, sometimes it's just easier, as it usually does away with the need for masking and extreme curves etc. Small caveat to that ...

... nothing says that having redeveloped, say, 3 shots that they then need to be processed as part of an automated process into a (psudo) HDR image; often it sufficient to simply layer them all up and paint a diffuse transition mask between the layers (surprisingly easy).

[_GUI_]

If the source image is a properly exposed 12 bit RAW, that has 12 bits of dynamic range, which I make to be 4 stops more than can be displayed in an 8 bit jpg.

In know this post by Dave is quite old now, but can't stay without saying two amazing things:

First is that a 12-bit RAW doesn't have 12 stops of DR but much less (over 8-9) because of noise in the shadows, and that up to 256 stops (yes, 256) can be displayed in an 8 bit JPEG.

The second amazing thing is that the first amazing thing is totally true

BR

[Colin Southern]

First is that a 12-bit RAW doesn't have 12 stops of DR but much less (over 8-9) because of noise in the shadows,

Err doesn't really work that way I'm afraid. Dynamic Range doesn't really bare any corelation to the resolution of the A/D Converter. What you're referring to here is the "number of steps on the staircase" (A/D resolution) not "The height of the staircase" (Dynamic Range). Dynamic range is primarily a function of sensor design. Case in point, a Canon 20D with a 12 bit A/D converter probably has a very similar Dynamic Range to a Canon 1Ds3 with a 14 bit A/D converter ... the 14 bit A/D converter just slices the range into smaller pieces. The dynamic range of a typical high-end SLR is around 11 at 100 ISO, dropping to around 8 at the highest ISOs. (www.dxomark.com).

and that up to 256 stops (yes, 256) can be displayed in an 8 bit JPEG.

Ummmm ... technically yes, but I think that a lot of people are going to get mislead into equating stops of light with binary maths. In reality (amongst other things) a JPEG chops off the parts of the range of the image that we can't see and then chops the remainer into 256 levels. It's generally accepted that the human eye can't differentiate more than 200 levels in the context of a typical print or typical monitor, so an 8 bit JPEG is absolutely fine as an output format -- it just fails miserably when people try to dig out detail thats not normally visable - that's when RAW wins out of course. Horses for courses; JPEG is designed to give small file sizes relative to the likes of RAW and TIFF files - and it achieves that by chucking out bits we can't see, normalising sections we can't differentiate, and then compressing the whole shabang! In talking about "stops" people need to remember that we're talking about the doubling or halving of light entering the lens, not the doubling or halving of the data that the cameras is processing.

[Dave Humphries]

Hi Guillermo,

Funnily enough I was thinking about this again today and realised there's a flaw in my logic.
I haven't figured it out yet (and won't tonight).

However, if

a 12-bit RAW doesn't have 12 stops of DR but much less (over 8-9) because of noise in the shadows

and this is true, because of the second point

The second amazing thing is that the first amazing thing is totally true

Does that mean that

and that up to 256 stops (yes, 256) can be displayed in an 8 bit JPEG

ISN'T true?

I hope so, because I really can't get that bit straight in my head

My background is video engineering and for simplicity's sake we'll say a 1 volt signal is max amplitude possible and it codes to 255 (all 8 bits are 1), so half a volt (one stop less) is going to (linearly) code to 127, so if you keep dividing by two until you run out of bits, that's 8 stops isn't it? So if there are 12 bits, why doesn't it hold true?

I think where I maybe going wrong is linear coding means a straight line on a graph of input vs output, but it doesn't necessarily mean the slope of that line is 45 degrees.

My brain hurts, I'm going to go and lie down now....

[Colin Southern]

I thought of a couple of ways to clarify things ...

First up, think of two identical cars with an identical top speed. Since both are capable of being stopped, and both are capable of doing the same top speed, it can be said that they're both capable of the same RANGE of speeds. Think of "stopped" as "Black" and "Top Speed" as "White", so that the dynamic range of a sensor equates to the range of speeds that the cars are capable of. Now - if the speedo in one car is in miles-per-hour, and the speedo in the other is in kilometers-per-hour, then it doesn't make any difference to their top speeds - only the numbers used to describe those speeds change, just as defining a brightness level somewhere on a scale of 0 to 4096 (12 bit) or 0 to 16383 (14 bit) doesn't change the range of brightnesses that a sensor can capture - it just changes the precision of the number (the bigger the range of numbers, the greater the accuracy you can define areas with subtle changes with).

Whew.

With regards to "8 Bit JPEGs etc" ...

All that we're achieving with 8 bits is the ability to define 256 different levels of "something" they could define 256 levels within 1 stop - they could define stops - they could define increments of 10 or 100 stops - but - Dynamic Range is a ratio (of biggest to smallest) - so by definition, the potential dynamic range of an image capable of 256 levels is ALWAYS going to be 256:1, but I can't stress enough how this bares no co-relation what so ever to the dynamic range of the sensor. If you could create an image that could resolve everything between the level of light inside a cave at night and the surface of the sun shot from a mile away, you could still resolve this range using 8 bits / 256 levels - heck, you could do it with 4 levels - but - the fewer the levels, the bigger the "jumps" between levels. Conversely, the more levels we have, the smaller the interval between the levels. So when talking about dynamic range I really really really think it's most helpful if people think of this simply as the ratio of the brightest thing a sensor can capture divided by the darkest thing that's still decernable above the noise floor; 8 / 12 / 14 bit etc doesn't come into it.


Double Whew!

[_GUI_]

Dynamic Range doesn't really bare any corelation to the resolution of the A/D Converter.

Correct, but I didn't say anything about that correlation. The resolution of the ADC is a physical limit to DR on a linear sensor: a N-bit linear sensor will NEVER be able to capture more than N stops of DR. Does this mean a N-bit linear sensor can capture N stops of DR? NO, it will be able to capture less than N stops and this is because of noise appearing in lowest f-stops, which is the true limiting factor for DR.

DR in a digital camera is just the number of EV's between sensor saturation, and that low f-stop in which noise becomes too visible to consider valid information. 'Too visible' is subject to a criteria, normally SNR in dB.

DYNAMIC RANGE = NOISE IN THE SHADOWS

There is no more to it.

BR

[_GUI_]

My background is video engineering and for simplicity's sake we'll say a 1 volt signal is max amplitude possible and it codes to 255 (all 8 bits are 1), so half a volt (one stop less) is going to ([COLOR="Red"]linearly) code to 127, so if you keep dividing by two until you run out of bits, that's 8 stops isn't it? So if there are 12 bits, why doesn't it hold true?

And who said we were [COLOR="Red"]linearly encoding the JPEG data? who misty god prevents us from encoding 1 stop of DR of a hypothetical super huge DR scene to each of the 256 available levels in a JPEG file? In that situation we would be able to encode up to 256 stops of DR.

I just wanted to point that the DR contained in a JPEG file, that supports up to 256 different levels for being a 8-bit file, can be any as long as we are not specifying anything about the processing applied to the original signal to map it onto the final information container (the JPEG file).

BR

[Colin Southern]

Correct, but I didn't say anything about that correlation.

I know what you mean - and I know you know what you mean, but I was just a bit concerned that your precise meaning may get a bit "lost in translation" in favour of the usual misassociation that people often seem to get ...

First is that a 12-bit RAW doesn't have 12 stops of DR but much less (over 8-9) because of noise in the shadows

When you said this I felt that in essence it had the appearance of agreeing with the "12 bits of resolution equating to 12 stops of (sensor) DR, with the exception of what's below the noise floor". Technically of course it's quite true, but it's also totally "academic" - I think it's important to draw the readers attention to the fact that Dynamic Range is now referring to the ratio of potential values available from the A/D converter rather than from the sensor. Or put another way, sensor dynamic range is important - and I'm sure we'd all love to have a lot more; Dynamic range of A/D outputs is of relatively little consequence - at 14 bits, I think we're at the "law of diminishing returns" stage (for todays sensors anyway).

[Dave Humphries]

Hi Guillermo, Colin,

Let's forget 8 bit jpgs and how they might code to enormous (impossible) DR, it's not relevant here, it's a PP issue, not relevant to DR at camera sensor. I was actually meaning the sensor data conversion, but picking 8 bits as a demo just confused the issue, sorry, my fault

However, I still think I was right about the dynamic range of a sensor, in fact we're probably all agreeing, let me put it like this:

A digitised maximum amplitude luminance signal from a 12 bit pixel occurs when all bits are 1, represented by 4096 in decimal.

I also still maintain the camera sensor is, to all intents and purposes, linearly coding** this.

Thus half the light will be half the analogue amplitude, and code to half that starting digital number; i.e. 4096/2 = 2048, so that's our first stop of dynamic range.
Halve again 1024 (2nd stop)
Halve again 512 (3rd stop)
Halve again 256 (4th stop)
Halve again 128 (5th stop)
Halve again 64 (6th stop)
Halve again 32 (7th stop)
Halve again 16 (8th stop)
Halve again 8 (9th stop)
Halve again 4 (10th stop)
Halve again 2(11th stop)
Halve again 1 (12th stop)
We cannot halve again because we've run out of bits to express the number!

So basically the number of A-D bits do equal the maximum THEORETICALLY possible dynamic range of the camera (not necessarily the sensor though).

Acknowledging that sensor + circuit noise is going to wipe out 2 or 3 bits, equivalent upto 8 levels or so (at say 100 ISO, even more at higher ISO - just as seen in real life), that gives the 9/10 stops dynamic range that I think you both accept.

Having a sensor with 14 bits MAY increase the DR the camera can record, but only IF the noise floor is reduced accordingly AND/OR the photosites are bigger to accomodate more photons. As Colin says, the two could well be unrelated, but there's no (commercial) point designing for 14 bit processing if the sensor can't deliver that much DR.

I accept that if a given analogue signal amplitude is split into 12 or 14 bits (4096 or 16383 decimal values) this is not directly related to sensor DR (like the speedo example), but if the sensor does have say, 14 stops of DR, a 12 bit A-D makes it impossible to exploit it, given a linear coding. The halving example above would seem to prove this. I think the speedo analogy fails here unless you look at it as trying to be VERY accurate quoting the speed, arguably the (12 bit) mph version is not calibrated in small enough units, but the (14 bit) kph version is.


** At the top end of DR, as the number of photons overflow the pixel 'pot', the input/output slope will flatten off. At the bottom end of DR, the random sensor noise will ensure that the dimmest light trails off into the speckly noise signal. Between those points, I maintain that unless there's non-linear gain, or excessive charge leakage, the coding will be linear. Unless of course, the sensor/A-D incorporates any DR extending mechanism - it might do this by flattening the slope (gamma < 1) or bending the ends more (knees and lifts).

Given all of the above, I find it difficult to reconcile some camera manufacturers claims for an EV range being in the region of 18 to 20 if they only have 12 or 14 bit RAW capture, they MUST be doing it by non-linear coding - or they're wrong!

Please bear in mind that all of the above are the ramblings of an inexperienced amatuer, so take it as no more than that and afford it no great seriousness. I'm sure you both know more about this than I do at the practical level.

[Colin Southern]

Hi Dave,

I think that multiple definitions of the term "dynamic range" will confuse things. In my opinion, Dynamic Range should only refer to the ratio of brightnesses that the sensor can handle; when one starts talking about "the dynamic range" of A/D converters etc you're really just talking about the resolution of the A/D converter (although I suppose that that will inturn get confused with sensor resolution -- so probably can't win here).

So basically the number of A-D bits do equal the maximum THEORETICALLY possible dynamic range of the camera (not necessarily the sensor though).

No. All you're doing is "proving" that the "dynamic range" of any numbering system is equal to 1:(n^2). As you say, this ratio (which is irrelivant in these terms by the way) would increase if the noise floor dropped accordingly for, say, 14 bit -v- 12 bit, but it doesn't, although a reduced noise floor may well be "part and parcel" of other camera design characteristics that may also include 14 bit processing.

14 Bit (a-la Canon 1Ds3 et al) wasn't introduced to have any effect on Dynamic Range - it was introduced to get better resolution of shadow detail. As you work through your previous example you'll notice that as light levels drop further and further the number of bits available to describe them get less and less. Unfortunately, the human eye is the least sensitive to the areas that have the most bits available, and the most sensitive to the areas that have the least bits available ... so by going from 12 to 14 bits they quadruple the available levels for describing any given range of levels - including (most importantly) shadow detail. (remember also that we're still in linear gamma at this stage - converting to gamma 2.2 demands even more from shadow detail.)

Acknowledging that sensor + circuit noise is going to wipe out 2 or 3 bits, equivalent upto 8 levels or so (at say 100 ISO, even more at higher ISO - just as seen in real life), that gives the 9/10 stops dynamic range that I think you both accept.

I think that the theory is getting confusing - how about we look at some actual figures: The Canon 40D has a dynamic range of 11.3 (DxO Mark) - the Canon 1Ds3 has a dynamic range of 12.0.

I accept that if a given analogue signal amplitude is split into 12 or 14 bits (4096 or 16383 decimal values) this is not directly related to sensor DR (like the speedo example), but if the sensor does have say, 14 stops of DR, a 12 bit A-D makes it impossible to exploit it

No - it simply means that the steps between levels in a 12 bit system are bigger than in a 14 bit system. You could fully exploit it in a 2 bit system, but the steps would be very large and visibly obvious; it's all about how things look visually, the DR of the sensor being greater than the "DR" of the AD converter isn't an issue.

[quote]** At the top end of DR, as the number of photons overflow the pixel 'pot', the input/output slope will flatten off. At the bottom end of DR, the random sensor noise will ensure that the dimmest light trails off into the speckly noise signal. Between those points, I maintain that unless there's non-linear gain, or excessive charge leakage, the coding will be linear. Unless of course, the sensor/A-D incorporates any DR extending mechanism - it might do this by flattening the slope (gamma < 1) or bending the ends more (knees and lifts).
[quote]

In practice the response curve is "S" shaped -- but with a long and relatively straight "back".

Given all of the above, I find it difficult to reconcile some camera manufacturers claims for an EV range being in the region of 18 to 20 if they only have 12 or 14 bit RAW capture, they MUST be doing it by non-linear coding - or they're wrong!

No - again, the number of stops the sensor is capable of capturing doesn't relate to the number of stops the A/D converter is capable of resolving. Consider a 2 bit system; if it were applied to a model train with a top speed of 4 mph then each bit would represent 1 mph - does it mean that it can't be used to descrive the speed of a train that goes faster than 4 mph? No - if the train went a max of 12 mph then each bit woud be 3 mph. In a 12 bit system you have 4096 levels and the dynamic range (WHATEVER IT IS) is split evenly across these 4096 levels. Does this mean that in some circumstances a stop is greater than a level? ... could well be more, could well be less ... doesn't matter as it doesn't enter into the equasion either way :)

Hope this helps!

[_GUI_]

Given all of the above, I find it difficult to reconcile some camera manufacturers claims for an EV range being in the region of 18 to 20 if they only have 12 or 14 bit RAW capture, they MUST be doing it by non-linear coding - or they're wrong!

It all depends on the criteria used to measure DR. If the criteria is let's say SNR=12 dB (i.e. Signal = 4*Noise), it may happen paradoxically that a N-bit sensor yields more DR than N stops. But that's just a math illusion since as you say a N-bit ADC cannot represent more than N linear f-stops.

Imagine that you replace the 12-bit ADC in my Canon 350D (a camera with about 8 stops of real usable DR in the 12 dB criteria) by a 4-bit ADC.
You would claim, and you would be right, that only 4 f-stops can be properly encoded in the RAW file now (with 8,4,2,1 available levels). The sensor DR is higher, but due to the ADC rounding, signal can now only reach 16 possible levels spreaded along 4 f-stops.

But, what happens if now we want to measure this new sensor's DR? we set the criteria SNR=12 dB (meaning Signal = 4*Noise). We shoot over a stepped wedge and start to measure SNR in the different patches of the card (S=average encoded level, N=std deviation from average).

Both S and N are floating point numbers, not integer, and we will need to go to a patch about 8 f-stops below saturation in luminosity to find a SNR as low as 12 dB because this is the way our sensor (not ADC) behaves, so we will still insist that this sensor has 8 stops of DR in measurement.

It's simply that due to the 4-bit ADC that figure is just an illusion, and the user will never enjoy such a high DR in his shots.

That is why in some DR comparisions, N-bit cameras can sometimes yield more than N f-stops of DR. It's just a SNR criteria, and it's just about mathematics.

Hope you understood.

BR