Mr. Poynton's false FAQ

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On this page the errors and misconceptions in Chapter 15 of Mr. Poynton's false Gamma FAQ are explained in detail with the aid of accurate visual demonstrations created with Excel in double-precicion math, the Excel chart is available for download, link is at the bottom of this page.

The Chapter 15 in Mr. Poynton's so called Gamma FAQ is not just some chapter 15, it is the foundation stone on which all the rest of Mr. Poynton's misinformation stands, or as it happens, falls apart.

Mr. Poynton's text from the Chapter 15 is printed using red below.

Errors and Misconceptions in Chapter 15 of Mr. Poynton's "Gamma FAQ"

15. How many bits do I need to smoothly shade from black to white?

At a particular level of adaptation, human vision responds to about a hundred-to-one contrast ratio of luminance from white to black.

That is correct but something is hidden, about 100:1 contrast ratio can be detected over or around a contrast edge. But we can not limit the digital coding in digital imaging to this very small range, for example:

the above calibration chart has and shows a range of 77.33 /0.28 = 276:1 (both the above image as well as the real print do so) and we do perceive it rather well from the Dmax to Dmin. Almost 3 times the 100:1 of Mr. Poynton's. We happen to perceive this 276:1 range "at a particular level of adaptation" to cite Mr. Poynton himself.

That the vision is only able to detect about 100:1 (or 1%) contrast range (contrast edge) is demonstrated below:

Call these luminance values 100 and 1. Within this range, vision can detect that two luminance values are different if the ratio between them exceeds about 1.01, corresponding to a contrast sensitivity of one percent.

This 1.01 ratio is derived from the Weber's Law and is way incorrectly used in this context: "at a particular level of adaptation". Weber's law requires that adaptation is free to do it's job. When we view photographic images the luminous adaptation is strongly restricted.

In order to examine closer this foundation stone of Mr. Poynton's we need to do some math.

Firstly the maximum luminance of a typical CRT conveniently happens to be about 100cd/m^2, it outputs this luminance at level 255. However the actual amount of the max luminance of the CRT however has no bearing on Mr. Poynton's claim nor to the below clear-up since the question is about ratio, could as well be e.g. 137cd/m^2 and 1.37cd/m^2 etc as long as the ratio is 100:1.

As the CRT monitors have gamma 2.5 transfer function they outputs the luminance of 1/100 (or 1 cd/m^2 for themonitor that has 100cd/m^2) at level 40, as:

(40/255)^2,5*100cd/m^2 = 0,975cd/m^2

Here we must notice that Mr. Poynton seem not to bother himself with the levels range from level 0 to level 39 at all.

We find firstly that Mr. Poynton's 1.01 ratio is too small to be demonstrated on the CRT due to the 8-bit gamma 2.5 coding !!! Please see the Excel workbook on this.

Fortunately, since it is a ratio, we can expand the stepping just by multiplication, what ever ratio is chosen it should give similar perceptual significance in the light end of the range as in the dark end of the range.

For the below example we use the ratio 1.063676743:1 that is the ratio between the luminances that level 41 and level 40 produces on the typical gamma 2.5 CRT monitor. In the light end of the range the monitor has this ratio between the luminances of level 255 and 249. Let us see how it appears for the vision:

Demonstrating luminance ratio 1.063676743:1

Above we do not detect any visual difference in the dark end, even if Mr. Poynton claims that we should discern far smaller ratio of 1.01. The 1.063676743:1 step contains as many as 6 of Mr. Poyntons 1.01 steps !!! We do detect a rather clear difference in the light end.

So we must evaluate using a ratio that gives some visual significance in the dark end also, the luminance ratio of levels 50 and 40 was chosen for the next example, this give luminance ratio of 1.746928107:1, in the light ends of the range levels 255 and 204 produce luminances whose ratio is the same.

Note that the 1.746928107:1 step contains 56 Poynton's 1.01. steps. Yes 56 of them since 1,01^56=1.745809819.

Demonstrating luminance ratio 1.746928107:1

Now evaluate if the visual significance of the difference in the dark end is similar like it is in the light end. Evaluate at normal reading distance, the patches are already 400 times too big.

Clearly the difference is huge in the light end and very very small in the dark end so we can conclude that Mr. Poynton's claim is completely false. To add to this do not forget that Mr. Poynton has already discarded all the levels from level 0 to level 39.

To shade smoothly over this range, so as to produce no perceptible steps, at the black end of the scale it is necessary to have coding that represents different luminance levels 1.00, 1.01, 1.02, and so on. If linear light coding is used, the "delta" of 0.01 must be maintained all the way up the scale to white. This requires about 9,900 codes, or about fourteen bits per component. If you use nonlinear coding, then the 1.01 "delta" required at the black end of the scale applies as a ratio, not an absolute increment, and progresses like compound interest up to white. This results in about 460 codes, or about nine bits per component.

It is correct that Mr. Poynton's 1.01 ratio requires 464 codes to represent a mere 100:1 range. Above we have already shown the Q-60 scan that has 276:1 range.

With the 256 levels of the 8-bit space code range the Mr. Poynton's 1.01 ratio can store only a tine 12.6:1 range. Please see the Excel sheet for more about this.

On the right we demonstrate how smoothly a 51 step (52 patches) gray wedge appears using Mr. Poynton's "perceptual" coding over his 100:1 luminance range that, once again, discards the levels range from level 0 to level 39. The wedge spans over levels range 40 ...255 and has 1.094499799:1 luminance ratio between the steps. Note that each step in this wedge holds as many as nine Mr. Poynton's 1.01:1 steps, as 1.01^9=1.093685273. Evaluate at normal reading distance, the patches are already 160 times too big. As can be seen about 1/5 or more of the range in the dark end in Mr. Poynton's coding appear very dark with very little or absolutely no perceptual significance between the steps and in the light end the steps become progressively more visible. Eight bits, nonlinearly coded according to Rec. 709, is sufficient for broadcast-quality digital television at a contrast ratio of about 50:1. If poor viewing conditions or poor display quality restrict the contrast ratio of the display, then fewer bits can be employed. If a linear light system is quantized to a small number of bits, with black at code zero, then the ability of human vision to discern a 1.01 ratio between adjacent luminance levels takes effect below code 100. If a linear light system has only eight bits, then the top end of the scale is only 255, and contouring in dark areas will be perceptible even in very poor viewing conditions. Next we will evaluate this claim, again we need to do some math since the Rec. 709 specifies a very strong slope in the dark end and in digital photographic imaging we do not have such a code space. Please see the provided Excel workbook where the matching gamma space for the Rec. 709 is evaluated.
The Rec. 709 coding matches a gamma 1.92 space so we now compare the coding provided by that gamma space against Mr. Poynton's ratio coding using his tiny 100:1 range. What do we perceive: Even if these code-spaces are incredibly different from each other Mr. Poynton negligently draws the equal sign between them.    The Rec. 709 (as far as it can be approximated by Photoshop using a working-space gamma) is the most coarse in the midtones, in both the dark end as well as in the light end the visual significance between the steps is minimal or nonexistent. It is clearly demonstrated that Mr. Poynton's foundation stone is false, totally false. In his quest for perceptually uniform coding he blithely equates totally different functions that, in the first place, are no where close to perceptual uniformity to start with. vision can detect that two luminance values are different if the ratio between them exceeds about 1.01, corresponding to a contrast sensitivity of one percent. On the right, the left wedge has ratio of 1.094499799:1 all steps should be clearly visible since according Mr. Poynton we should be able to detect a luminance ratio as small as 1.01 that is about 9 time smaller than the steps this wedge. The Excel workbook containing the calculations related to this debugging. Please read also the Main Goal of Mr. Poynton's ColorFAQ and GammaFAQ.
Even if Mr. Poynton's documents have been proved to be false many times before this, Mr. Poynton continues to post his misinformation to several Usenet newsgroups monthly and refuse to make any corrections to his writings. Everything in his writings rely on this totally incorrect Chapter 15.
Ask yourself, why is it that we do not ever see these kind of demonstrations and evaluations from the CMCs (Color Management Clowns), just the cleverly formulated text with references to what ever research that appears to back up one claim here and with another reference that appears to back up another claim there. It is very easy for a gamma and color faquir to just take Laws from the established research and science when not considering at all the actual situation where those Laws are valid and then just write the misconceptions with title like Color or Gamma FAQ. It comes a little bit more difficult when one has to really prove that the FAQ actually is the fact.