# DxOMark Tonal Range Specification

gollywop wrote:

Detail Man wrote:

Tonal range is the effective number of gray levels the system can produce. This measure has to take noise into account (indeed, a very thin gray-level quantization is irrelevant if the quantization step is much smaller than noise). The standard deviation of noise can be viewed as the smallest difference between two distinguishable gray levels. The expression of the tonal range is:

Source: http://www.dxomark.com/index.php/About/In-depth-measurements/Measurements/Noise

Found an interesting explanation regarding the nature of Tonal Range (by ejmartin) here:

DxO's Tonal Range is a measure of how many tones can be distinguished within the set of raw levels available. Two tones cannot be distinguished if their difference is less than the noise std dev.

If the noise were constant, the number of distinguishable tonal levels would be the range of available raw levels divided by the noise std dev; but since the noise varies with tonality due to photon noise (it grows with the illumination level, as the square root) one has to add up (integrate, in math terms) over the range of raw levels the fractional amount of a distinguishable tonal level that each raw level constitutes.

The total is what DxO calls Tonal Range; a higher value means more tones are distinguishable. They present the result in "bits", ie two to the power of the number of bits distinguishable levels. Similar to the dynamic range, but accounting for the light-gathering capacity as well as the noise.

ejmartin, April 02, 2010, 07:21:19 AM

http://www.luminous-landscape.com/forum/index.php?topic=42756

Yikes. No wonder I never have quite figured this out. DxO Labs does not tell the entire story. Have found this information from DSPographer.

"X" is in units of electron-charge (e-). It scales with sensor-size as well as quantum-efficiency.

The denominator of the integrated quantity is the Maximum (max) function, which returns only the greater of the two values within it's argument. The first value in the argument is the standard-deviation of the measured total noise as a function of "X". The second value in the argument (identified simply as "1" in the identity displayed above) is equal to:

( X ) / ( ( 2 ) ( SQRT ( S + R^2 ) - R ) )

where:

X is electron-charge resulting from the sensor illumination multiplied by the quantum efficiency;

S is the full-well-count in electron-charges that exists at sensor-saturation for a given Sat. ISO;

R is the (root-mean-square) read-noise (as measured on the level of the entire image-sensor).

The limits of the integration (Xmin to Xmax) are (I think) between "Xmin" (corresponding to the electron-charge associated with the minimum quantized value) and "Xmax" (corresponding to the electron-charge associated with the maximum quantized value).

The (dimensionless) result is then converted to a log base 2 value (corresponding to "bits").

Sources (posts by DSPographer):

http://forums.dpreview.com/forums/post/39514181

http://forums.dpreview.com/forums/post/39514317

bobn2 wrote:

People tend to ignore the tonal range measurement because they don't know what it means, but I suspect that its closer to the generic 'IQ' indicator that people are looking for.

http://forums.dpreview.com/forums/post/40255712

Note: I am not sure that I quite have all this (about the derivation of Tonal Range) exactly right, and am not sure how well DxOMark's Tonal Range speciification may (or may not) possibly be more indicative of "overall performance" than DxOMark's Dynamic Range specification based on a reference level of SNR = 0dB. Perhaps others may possibly take some interest in the above information, also read DSPographer's referenced posts, and make some relevant and informative comments.

I'm confused, DM. As I read DSPographer's posts, he seems to be providing the formula you give above as a means for calculating a TR-like figure, the number of discernible tones, as determined from full well-count and read noise -- and not as the meaning of the second argument in the denominator of the TR expression.

You are right. I was calculating the number of levels needed based on read noise and shot noise: without considering the effect of the input A-D quantization noise.

By my reading of the DxO definition of TR, I would interpret the second argument of the denominator simply as unity, the number one. They appear to be factoring in the noise only if it exceeds the increment size 1*dx, and hence if σ(x) < 1, it no longer deflates the total. If, just for illustrative purposes, we assume σ(x) < 1 ∀ x, TR simply becomes xmax - xmin, which makes sense.

I think that in most enthusiast and professional camera raw files, it is very common for σ(x) < 1 A-D count ∀ x

So this is a reasonable assumtion.

By the way, if anyone is having trouble getting to DSPographer's posts from the embedded links (when I click them I get a message indicating the page is no longer available), simply copy them into a new browser page.

-- hide signature --gollywop

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