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Author Topic: Bit Depth and Highlight Gradation  (Read 2834 times)
bjanes
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« on: February 07, 2013, 11:53:10 AM »
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In early analyses of ETTR, it was theorized that the benefits were derived by pushing up the exposure towards sensor saturation where more levels would be available in the digital capture inasmuch as half the levels are in the brightest f/stop of the image at saturation. Later analysis (such as that of Emil Martinec) showed that the advantage was in a higher signal:noise rather then the number of levels. It makes no sense to quantize the data in finer steps than the noise at that level. At higher levels of exposure, noise in a digital capture is largely photon noise which follows a Poisson distribution where the noise is the square root of the number of photons collected. Camera data numbers (ADUs) are related to the number of photo electrons by the gain, which is the number of photons/ADU. For a sensor with a full well of 50,000 electrons, the gain (assuming that amplification is such that the full range of the ADC (analog to digital converter) is used at the full well of the sensor) would be 3.05 e-/ADU for 14 bit quantization and  12.21 e-/ADU for 12 bit.

For a highlight captured with this sensor with 40,000 electrons, the noise would be 200 e-. With this sensor one level would be 3 e- with 14 bit quantization and 12 e- for 12 bits, and it is apparent that the finer quantization is wasted. This is the basis for compressed NEF raw files used by Nikon, which records 2753 levels for 14 bits and 689 levels for 12 bit (according to Emil) with no visual loss, visually lossless in Nikon terminology. The number of levels that can be distinguished by human perception is described by the Weber-Fechner law (see Norman Koren for details). According to this law, visual perception is sensitive to relative differences of illumination of about 1%, so 1 f/stop would be about 70 levels (1.01 ^ 70 = 2.0). Accordingly, only 70 levels would be needed for the brightest f/stop, but more levels would be advisable to allow for subsequent editing. These considerations underlie the DXO measurement of tonal range, which is the effective number of gray levels the system can produce. For example, the tonal range of the Nikon D800 is far less than 14 bits (readers can look this up, the DXO site is not responding at the time of this writing).

The benefit of a higher bit level is in the shadows where a change in signal from 1 to 2 ADUs would represent  an increase of 100%, whereas a change from 14,000 to 14,001 ADUs is insignificant.

Discussion as to the practical effect of these theoretical considerations is welcome.

Bill

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sandymc
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« Reply #1 on: February 07, 2013, 12:15:30 PM »
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Bill,

I'm not what's left to discuss on this - as you point out, Emil wrote about the theory extensively, and I (as well as others, e.g., Ctein on TOP to name one) have written about the practical implications in various levels of detail. At this point, it's kind of been beaten to death, no?

Sandy
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bjanes
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« Reply #2 on: February 07, 2013, 12:44:29 PM »
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Bill,

I'm not what's left to discuss on this - as you point out, Emil wrote about the theory extensively, and I (as well as others, e.g., Ctein on TOP to name one) have written about the practical implications in various levels of detail. At this point, it's kind of been beaten to death, no?

Sandy

Apparently not. My post was an offshoot of another thread.

Regards,

Bill
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thierrylegros396
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« Reply #3 on: February 07, 2013, 12:45:08 PM »
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In early analyses of ETTR, it was theorized that the benefits were derived by pushing up the exposure towards sensor saturation where more levels would be available in the digital capture inasmuch as half the levels are in the brightest f/stop of the image at saturation. Later analysis (such as that of Emil Martinec) showed that the advantage was in a higher signal:noise rather then the number of levels. It makes no sense to quantize the data in finer steps than the noise at that level. At higher levels of exposure, noise in a digital capture is largely photon noise which follows a Poisson distribution where the noise is the square root of the number of photons collected. Camera data numbers (ADUs) are related to the number of photo electrons by the gain, which is the number of photons/ADU. For a sensor with a full well of 50,000 electrons, the gain (assuming that amplification is such that the full range of the ADC (analog to digital converter) is used at the full well of the sensor) would be 3.05 e-/ADU for 14 bit quantization and  12.21 e-/ADU for 12 bit.

For a highlight captured with this sensor with 40,000 electrons, the noise would be 200 e-. With this sensor one level would be 3 e- with 14 bit quantization and 12 e- for 12 bits, and it is apparent that the finer quantization is wasted. This is the basis for compressed NEF raw files used by Nikon, which records 2753 levels for 14 bits and 689 levels for 12 bit (according to Emil) with no visual loss, visually lossless in Nikon terminology. The number of levels that can be distinguished by human perception is described by the Weber-Fechner law (see Norman Koren for details). According to this law, visual perception is sensitive to relative differences of illumination of about 1%, so 1 f/stop would be about 70 levels (1.01 ^ 70 = 2.0). Accordingly, only 70 levels would be needed for the brightest f/stop, but more levels would be advisable to allow for subsequent editing. These considerations underlie the DXO measurement of tonal range, which is the effective number of gray levels the system can produce. For example, the tonal range of the Nikon D800 is far less than 14 bits (readers can look this up, the DXO site is not responding at the time of this writing).

The benefit of a higher bit level is in the shadows where a change in signal from 1 to 2 ADUs would represent  an increase of 100%, whereas a change from 14,000 to 14,001 ADUs is insignificant.

Discussion as to the practical effect of these theoretical considerations is welcome.

Bill

Interresting, but in practice I've made a lot of comparison between RX100 (14 bits) and G15 (12 bits) and  the biggest diference (improvement) is clearly in the shadows.
More, the G15 seems to clip more "cleanly" but I don't know why Huh
And last, Highlight recovery is far better with LR4 than with DXO8, better gradation and less color drift.
Of course it's only a comparison between 2 particular cameras.

Have a Nice Day.

Thierry
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Mark D Segal
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« Reply #4 on: February 07, 2013, 12:56:03 PM »
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Bill,

Do you think there's a risk that with the large number of different factors that could influence image quality from capture to post-capture processing these days that the kind of differentials you find in these calculations may be overwhelmed by other factors?
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Mark D Segal (formerly MarkDS)
Author: "Scanning Workflows with SilverFast 8....." http://www.luminous-landscape.com/reviews/film/scanning_workflows_with_silverfast_8.shtml
sandymc
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« Reply #5 on: February 07, 2013, 12:59:36 PM »
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Apparently not. My post was an offshoot of another thread.

Regards,

Bill

Bill,

Ahhh, well, not everybody accepts the theory/some people have alternate theories. Not much to be done about that.

Regards,

Sandy
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ErikKaffehr
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« Reply #6 on: February 07, 2013, 01:52:26 PM »
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Hi,

This issue showed up on another thread, Bill just started a new thread. My view is that bit depth is most significant in shadow details, if it matters at all. My guess is that DR is more limited by lens flare than by bit depth, anyway.

Best regards
Erik
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Mark D Segal
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« Reply #7 on: February 07, 2013, 02:16:15 PM »
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Isn't the noise floor one of the key determinants?
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Mark D Segal (formerly MarkDS)
Author: "Scanning Workflows with SilverFast 8....." http://www.luminous-landscape.com/reviews/film/scanning_workflows_with_silverfast_8.shtml
Ray
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« Reply #8 on: February 07, 2013, 06:12:49 PM »
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My guess is that DR is more limited by lens flare than by bit depth, anyway.

That's not my experience, Erik. This can be tested by shooting a high-contrast scene, which includes blue sky, white clouds and forest undergrowth, for example, or even the scene out of one's living room window, exposing correctly for the sky whilst including much of the living room in the shot, using both Canon and Nikon cameras.

The Nikon, if it's a recent model, will produce significantly more detail and less noise in the shadowy undergrowth, or the less well-lit areas of one's living room.

However, you've raised an interesting issue in relation to my Dynamic Range Test Chart (or Jonathan Wienke's to be precise). This method of assessing the DR of a camera by progressively underexposing a target with constant lighting, should largely bypass the issue of lens flare.

In other words, an extremely underexposed shot (11, 12 or 13 stops underexposure) of a well-lit scene should have little or no lens flare compared with a normal exposure of a well-lit scene which happens to contain certain areas which are darker by 11, 12 or 13 EV.

Now that I've sent you the Test Target, you should have no trouble in comparing these two methods to assess the significance of lens flare on dynamic range.. You might find that two cameras that differ in DR by two full stops, using the DR Test Target, differ by only 1.33 stops in the so-called real-world shots.

I look forward to your results.  Grin

Cheers!
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