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digitaldog
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If we could have a dynamic range consisting of steps of equal height we could increase DR dramatically. Those steps at the top are too steep to climb   .
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The point is, the stair case has a fixed height. That the steps (bits) are ˝ inch apart or a foot apart doesn't change the height of the stair case.
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Andrew Rodney
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Bernd B.
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But given that 14 bits doesn't change the actual DR, wouldn't those extra 2 bits go a long way to smooth the transitions at the point between blown and some detail?
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I`m a photographer. I prefer to talk about aesthetics, not about bits. My older Leaf back is quite good. My 5D isn`t that good for my personal expectations. If others have different expectations, I don`t care. I wouldn`t like to take a picture of a celebrity with a 5D and have a look at that image in five years.
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EricV
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Bit depth and dynamic range really are the same thing, provided that
1) System noise is low enough that bits are not wasted digitizing noise
2) The ADC is linear, so each bit represents twice as much signal as the previous bit.

The "steps on a ladder" analogy is flawed, because the ADCs we are talking about are linear.  With a linear ADC, extra bits necessarily extend the length of the ladder, as well as providing smaller steps.

Here is a thought experiment to illustrate the connection between bit depth and dynamic range.  Suppose we photograph a perfect gray scale, with discrete steps of exactly one f/stop in brightness, using linear ADCs with 8 bits or 12 bits, in a camera with no noise.

The 8-bit ADC will record 8 steps of the gray scale, with output values from maximum white (8-bits = 255) to minimum not-quite-black (1-bit = 1), for a total dynamic range of 8 f/stops.  The 12-bit ADC will record 12 steps of the gray scale, with output values from maximum white (12-bits = 4095) to minimum not-quite-black (1-bit = 1), for a total dynamic range of 12 f/stops.  Extra bits increase the dynamic range which the ADC can record.

Depending on the relative exposure, the extra steps of the gray scale recorded by the 12-bit ADC can be darker or brighter than the steps recorded by the 8-bit ADC.  Let's assume we expose optimally in each case, so that the brightest step of the gray scale which we are interested in recording barely saturates the sensor, turning on all bits in the ADC output.  Then the 12-bit ADC will record four steps of the gray scale which are too dark to be recorded by the 8-bit ADC.

With this exposure, each section of the gray scale will be represented with much finer gradation by the 12-bit ADC than by the 8-bit ADC.  This is easy to see mathematically -- just divide the output of the 12-bit ADC by 16.  Now every discrete step of the gray scale will be numerically the same for both ADCs, but the step size of the 12-bit ADC will be 16 times finer than the step size of the 8-bit ADC.

Another way to think about this is to replace the discrete gray scale steps by a continuous brightness ramp.  The 12-bit ADC will record any small section of the continuous scale with 16 times as many discrete output values as the 8-bit ADC.  Extra bits provide more resolution across the entire dynamic range.
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BJL
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John, do you have data on the 1DMIII or is this merely conjecture? From Roger Clark's analysis of the noise characteristics of the 1DMII, there is reason to believe that a 14 bit ADC would improve the DR of that camera at low ISO.
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Clark's "sensor DR" figure of 14 tops for the 1D Mark II is dubious when you notice that the nice low read noise of 4 electrons is only at ISO 3200, where high DR work is usually not done. At lower ISO speeds read noise gets higher, reaching 16.61e at ISO 100. I think this means that most read noise is introduced after the pre-amplification done at each photosite on Canon CMOS sensors.

Clark computes a more trustworthy "camera DR": at each ISO, based on the maximum signal and read noise at that ISO setting. The result for the 1D MkII is a S/N ratio of 3190, or 11.5 stops, within the gamut of a 12-bit A/D convertor. (Ref: Figure 5 of [a href=\"http://www.clarkvision.com/imagedetail/digital.sensor.performance.summary/and]http://www.clarkvision.com/imagedetail/dig...nce.summary/and[/url] Table 1b of http://www.clarkvision.com/imagedetail/eva...1d2/index.html)

To obtain Clark's higher "sensor dynamic range" of about 14 stops would require increasing the "headroom" in the pre-amplifier and A/D conversion. Getting that 14 stops would require using ISO 3200 (i.e. massively amplifying at each photosite, which reduces read noise in electrons) even though the image contains bright highlights, at a level more suited to low ISO speed, and having pre-amplifiers that could apply this high amplification to those large electron counts. Normally, this high pre-amplification is only applied to the dimmer on-sensor images (lower electron counts) given by high exposure indices like ISO 3200.

There is a serious question as to whether this high amplification could be applied to the strong signals from nearly full electron wells without amplifier clipping or other problems, especially since the amplifiers are tiny ones at each photosite.

In other words, the S/N ratio of the tiny pre-amplifiers at each photosite is one DR limit not assessed by Clark.
 « Last Edit: October 02, 2007, 02:44:16 PM by BJL » Logged
bjanes
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The point is, the stair case has a fixed height. That the steps (bits) are ˝ inch apart or a foot apart doesn't change the height of the stair case.
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As EricV explained in a previous post, the height of the stair case is not fixed. With a linear ramp and integer encodeing, the height (dynamic range) depends on the number of bits used for encoding. Under these conditions, 12 bits linear can encode a maximum of 12 f/stops and the darkest f/stop would contain only one level, which would be unsuitable for photographic continuous tone reproduction. If you require 8 levels in the darkest f/stop, the DR is reduced to 9 stops as [a href=\"http://www.normankoren.com/digital_tonality.html]Norman Koren[/url] demonstrates in a table on his web site.

Moreover, with linear encoding (rather than gamma), the steps are of unequal size, as shown in the graphic on Greg Ward's web site. The steps in the shadows are much larger than those at the top of the range. Look at the table below the stair step graphic, which shows the dynamic range with various encodings. The scRGB being proposed by Microsoft is linear with a bit depth of 16. According to Ward's criteria (5% error), it can encode only 3.6 orders of magnitude (engineers use log base 10, while photographers prefer f/stops, or log base 2). This corresponds to 12 f/stops.

If you use log or floating point encoding, then some of these limitations are removed, and for a given bit depth one can record a much higher dynamic range.

Bill
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Tim Gray
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I`m a photographer. I prefer to talk about aesthetics, not about bits. My older Leaf back is quite good. My 5D isn`t that good for my personal expectations. If others have different expectations, I don`t care. I wouldn`t like to take a picture of a celebrity with a 5D and have a look at that image in five years.
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The 5d is only 12 not 14.  My point is that the new technology might render images more to you standards. (might....)
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digitaldog
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As EricV explained in a previous post, the height of the stair case is not fixed.

Once my head clears from a taxing image editing project, I'll certainly check this all out.

It sounds like this is different for digital linear capture than gamma corrected scanners of the past.
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Andrew Rodney
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eronald
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I think we should remove quantization errors in non linear encodings from this discussion before we go crazy. Let's assume for the benefit of the discussion that sensor readouts are counting photons plus or minus noise.

Edmund
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Bernd B.
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The 5d is only 12 not 14.  My point is that the new technology might render images more to you standards. (might....)
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If it does, I´m open. It would be nice. If not, then maybe the next generation.

Why is it so difficult to produce a system with a DR of 12 stops ? What makes the difference? The sensor? The AD conversion? Can it ever be achieved by a 35mm DSLR ?
 « Last Edit: October 11, 2007, 04:19:32 PM by Bernd B. » Logged
bjanes
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Clark's "sensor DR" figure of 14 tops for the 1D Mark II is dubious when you notice that the nice low read noise of 4 electrons is only at ISO 3200, where high DR work is usually not done. At lower ISO speeds read noise gets higher, reaching 16.61e at ISO 100. I think this means that most read noise is introduced after the pre-amplification done at each photosite on Canon CMOS sensors.
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A DR of 14 stops is quite dubious, since a bit depth of 12 can only encode 12 stops with linear integer encoding as we have been discussing. As I read Roger's essay, the higher dark frame noise at ISO 100 is due mainly to ADC noise and could be reduced by an ADC with a better SN, i.e. higher bit depth if other factors remain the same.  The gain with the 1D MII is 13 electrons/12 bit data number, and it would be only a fourth that with a 14 bit ADC. An error in the least significant bit would have less effect.

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There is a serious question as to whether this high amplification could be applied to the strong signals from nearly full electron wells without amplifier clipping or other problems, especially since the amplifiers are tiny ones at each photosite.
In other words, the S/N ratio of the tiny pre-amplifiers at each photosite is one DR limit not assessed by Clark.
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It will be interesting to see what he reports for the 1D MIII. Already, he has noted that the 14 bit 40D falls short because of in inferior ADC.

Bill
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brumbaer
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DR is about the range of brightness covered and bit depth about smoothness.

Let's paint a picture. For simplicity sake a black and white picture.

Let's say on a 8 fstop System you are allowed to use 0% white as black and 100% white as eh... white.
If you have only 4 fstops you would be restricted to use something like 0% to 6% or 22% to 28%.

The fstop limits the difference between min and max brightnesses you can use to paint.

The bit depth defines how smooth you can make a transition between minimum and maximum brightness.

If you have 5 Bits in the first case every step in your transition would be 3% white in the second case it would be 0,2% white.

The second would be much smoother because the distinguishable values are much closer together.

To have a comparable "smoothness" the 8 fstop image needs 9 bits. So for comparable smoothness higher DR needs more bit depth.

DR and bit depth work just exactly like that. The DR defines the spread of the min and max values. And the bit depth defines how smooth the transition between min and max is.
Of course larger spread of min max needs more bit depth to get the same smoothness.

And of course bit depth is only "usable" bit depth. If 4 of the 12 bits are just noise, they do not count.

Depending on the subject, a shot might look better with high DR and lower bit depth, or lower DR with higher bit depth.

Regardless of subject insanely high DR combined with horrendous high bit depth (can depth be high ?) will give the best images.

Regards
SH
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EricV
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DR is about the range of brightness covered and bit depth about smoothness....[a href=\"index.php?act=findpost&pid=143460\"][{POST_SNAPBACK}][/a]
It sounds like you are trying to separate dynamic range and bit depth.  This is possible conceptually, but as I discussed in a previous post, it is not possible in practice, at least with current linear sensors.  Increased bit depth gives both increased smoothness and increased dynamic range.

Taking your own example, covering the range 0-100% with 5 linear bits gives a step size of roughly 4%, while covering the same range with 8 linear bits gives a step size of roughly 1/2%.  The three extra bits provide steps which are eight times finer.  But the dynamic range is also 8 times greater.  DR is not calculated as 0-100%, which would be infinite when you divide by zero.  Rather, DR is calculated as the maximum brightness divided by minimum non-zero brightness.  Since the 8-bit system can faithfully record brightness as low as 1/2%, it has 8 times the DR of the 5-bit system, which cannot faithfully record anything darker than 4%.  The system with higher bit depth necessarily has higher dynamic range.
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bjanes
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I think we should remove quantization errors in non linear encodings from this discussion before we go crazy. Let's assume for the benefit of the discussion that sensor readouts are counting photons plus or minus noise.

Edmund
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The quantization errors we have been talking about occur in the linear part of the work flow before gamma is applied. You can't really ignore them, since at low ISO they contribute significantly to total apparent read noise and thus dynamic range. According to Roger's analysis, the main source of read noise at low ISO is ADC induced noise.

Bill
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TechTalk
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It sheds some light on why dynamic range is a moving target for any device.
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Ray
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Or is it both at top and bottom that is critical? Whereas with lower bit depth top and bottom would render as white and black without distinguishable details, the larger bit depth allows detail to be rendered in these regions due to the more steps of the ladder there.

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As I understand it in my technically limited way, the brightests f/stop (or brightest 2 or 3 stops) of dynamic range use an unnecessarilly large proportion of the available bits to describe the signal. The steps are too small, the gradations unnecessarily fine; too fine for the eye to discern.

Such a system is wasteful. There needs to be a redistribution of bits. If we simply increase the number of bits available to describe the signal, by moving from 12 bit depth to 14 or 16 bit depth, most of the additional bits will be used to quantise the brighter stops of dynamic range, serving absolutely no purpose whatsoever because we already have more than enough bits for those brighter stops.

At the lower end where the signal tends to be obscured by noise, it's not clear to me how additional bits can improve matters much because the additional bits would surely also be used to describe the noise with even greater clarity. Both signal and noise are equally enhanced. Unless there is a way of separating the noise from the signal, any improvement in the quality of the signal cannot be realised simply by providing greater bit depth.

The ideal system for great dynamic range would be one where the individual photoreceptors were able to reduce their quantum efficiency in proportion to the amount of light they received, in real time. As the wells fill, the quantum efficiency gradually decreases, in a non-linear way that more closely matches human vision, so that each brighter stop of DR requires increasingly more than double the amount of light.

With such a system, we would be able to substantiallyincrease exposure without blowing highlights and at the same time provide more light for better exposure of the darker parts of the image. This would be a more sophisticated version of Fuji's SR system which employs 2 photoreceptors of different sensitivity under the one microlens.
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EricV
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If we simply increase the number of bits available to describe the signal, by moving from 12 bit depth to 14 or 16 bit depth, most of the additional bits will be used to quantise the brighter stops of dynamic range, serving absolutely no purpose whatsoever because we already have more than enough bits for those brighter stops.[{POST_SNAPBACK}][/a]
The extra bits provide finer resolution throughout the range.  You are correct that the extra resolution is wasted at the high end, but it is potentially useful at the low end (depending on noise).  If the system has as many bits as needed at the low end (bit resolution comparable to noise) and therefore too many bits at the high end, then a compression scheme like gamma encoding can be used to redistribute the bits, lowering the total bit count but preserving the useful resolution.  This is how Photoshop manages to work with 8-bit images derived from 12-bit sensors without much loss.

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At the lower end where the signal tends to be obscured by noise, it's not clear to me how additional bits can improve matters much because the additional bits would surely also be used to describe the noise with even greater clarity. Both signal and noise are equally enhanced. Unless there is a way of separating the noise from the signal, any improvement in the quality of the signal cannot be realised simply by providing greater bit depth.[a href=\"index.php?act=findpost&pid=143518\"][{POST_SNAPBACK}][/a]
If the system is limited by noise rather than bit resolution, then by definition the bit depth is already sufficient to capture all the available information.  In this case you are right, more bits (also redistributed bits) are not needed and do not help.

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The ideal system for great dynamic range would be one where the individual photoreceptors were able to reduce their quantum efficiency in proportion to the amount of light they received, in real time. As the wells fill, the quantum efficiency gradually decreases, in a non-linear way that more closely matches human vision, so that each brighter stop of DR requires increasingly more than double the amount of light.[a href=\"index.php?act=findpost&pid=143518\"][{POST_SNAPBACK}][/a]
Sensors like this have been designed and built, but they have not found widespread use in photography.  The most common architecture is a CMOS sensor with logarithmic voltage conversion.  See for example [a href=\"http://www.photonfocus.com/html/eng/cmos/linlog.php]http://www.photonfocus.com/html/eng/cmos/linlog.php[/url].
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Ray
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The extra bits provide finer resolution throughout the range.  You are correct that the extra resolution is wasted at the high end, but it is potentially useful at the low end (depending on noise).  If the system has as many bits as needed at the low end (bit resolution comparable to noise) and therefore too many bits at the high end, then a compression scheme like gamma encoding can be used to redistribute the bits, lowering the total bit count but preserving the useful resolution.  This is how Photoshop manages to work with 8-bit images derived from 12-bit sensors without much loss.

EricV,
That seems reasonable but isn't gamma encoding done at the output stage, either in ACR conversion of RAW or in-camera conversion for viewable jpeg purposes? Does redistribution of bits after the initial A/D conversion serve much purpose regarding fundamental image quality?

From what I've read, the 14 bit A/D conversion does seem to provide some benefits in the 40D, but one can't be sure to what extent such improvements are due to the greater bit depth.

John Sheehy claims there is about 1/2 a stop improvement in the shadows, for example. Bob Atkins claims the noise reduction feature of the 40D (which can be on or off) does not reduce resolution in any discernible way and results in a slightly cleaner image than the 20D can produce in the same circumstances. However, with noise reduction off, the 40D image is actually slightly noisier than the 20D.

It would be fun to buy a 40D (or hire one if possible) to check out such factors to see what is really going on and what practical significance there might be in any pixel-peeping improvement one might discover.
 « Last Edit: October 04, 2007, 12:00:35 AM by Ray » Logged
John Sheehy
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John Sheehy claims there is about 1/2 a stop improvement in the shadows, for example.[a href=\"index.php?act=findpost&pid=143742\"][{POST_SNAPBACK}][/a]

Well, I mean in the shadow end of the DR at ISO 100; if the camera exposes the RAW data more conservatively, however, there could be less improvement in the shadows and more in the highlights.  Metering is somewhat arbitrary.
 « Last Edit: October 04, 2007, 07:59:33 AM by John Sheehy » Logged
jeremydillon
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I wonder if its time to do some real world tests.

We can argue 'till the cows come home about wether it's the bit depth that makes the difference (my opinion is that it isn't).

Back at school when we did film tests we would shoot a grey card at different exposures and plot the desities on a graph.  Can't we do the same with our digital cameras and compare our results?

I'll test mine and post my results ... will you post yours?
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BJL
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