Greg, I appreciate your summary of the entire process.
Following up on your comments that the 6-axis CMS gives us separate control over the RGB transformation matrix in each part of the CIE triangle, I thought I would do some further experimentation with this. I think if you bear with the long description, you will see that the results support what Bill and you wrote. The context for my comments is still a very limited situation, where the CMS allows us to get close to but not identical to the Rec709 color points in the x-y domain, and after achieving the best possible match to the primary colors in the x-y domain, two procedures had been suggested for a calibrating the set: calibrate the primary Y values and the secondary colors to the Rec709 coefficients, calibrate the primary Y values and the secondary colors to match the simple XYZ<-->RGB conversion matrix constucted by Lindbloom's formulas using the primary x-y points.
A couple of points on which there should be agreement:
(a) Were there only three CMS color controls and no white balance, we would have to use the Y coefficents predicted by Lindbloom's formulas in order for red-green-blue to add together to the intended D65 white point.
(b) Given that we have six color controls plus white balance, an idealized CMS would act as if there are six different RGB->XYZ conversion matrices, one for each sextant of the triangle.
(c) Using the Rec709 Y values for the colors intuitively should give a better fit at the primary/secondary 100% saturation points. In other words, if we had some magic Rec709 color flash cards tuned to match the set's max white luminance, were we to compare these flash cards to the colors for the two alternative calibrations, one would expect to see a closer match when the calibration used the Rec709 Y values, because the Y values would match even though our x-y coordinates did not.
So my experiment was to simulate this idealized CMS in Excel, to see how it would work given the two alternative calibrations. My assumption was that I started with my best achievable calibration, taking my actual x-y cooordinates of the primary colors and their exact complements as the secondaries. The two alternatives were, to use the Rec709 Y coefficients for the six colors, or to use the calculated Y cooefficients implied by taking the primary color x-y values as defining the color gamut.
(1) Not surprisingly, if one takes the close-but-not-exact primaries with the Rec709 Y values, reversing Lindbloom's calculation of the RGB<-->XYZ conversion matrix M, these imply a different white point. With my data this worked out to have (x,y) coordinates of (.314,.337), and HCFR gives this a color temperature of about 6380.
(2) It is indeed fairly straight forward to calculate the RGB->XYZ matrix separately for each of the six pieces of the CIE gamut. When the Y values were set using the actual primaries to define the target gamut, these six matrices are all identical. When the Y values are calibrated using the Rec709 Y cooefficients, the matrices are distinct.
(3) To compare the two calibrations, for convenience I used the RGB values associated with the saturation patterns on the AVSHD disk. This gives 30 points of comparison, six colors times 5 saturations, although six of the points are all white with varying intensities. Here is where things get interesting. Looking at all 30 points, comparing each point against where it should be in a perfect calibration to Rec709 using CIELUV76, the calibration using the target gamut Y values faired slightly better, with an average delta E of 2.02 compared to 2.60 using the Rec709 Y values. For some of the 100% saturation points, using the Rec709 Y value gave a worse error than using the actual gamut, but this seems to be an anomaly of the interaction of lightness with the other coordinates in CIELUV76. Looking at all 30 points, again compared to a perfect Rec709 calibration but using CIE94, the average delta E values were nearly identical, 0.59 and 0.60 using target gamut Y values and Rec709 Y values respectively. And with CIE94, all the 100% saturation points have a lower delta E when calibrated using the Rec709 Y coefficients.
Comparing the two calibrations, one to the other, over the 30 points, the average delta E using CIELUV76 is 1.0 and using CIE94 0.36, so comparing the two side-by-side, you would on average not see a difference, although the differences would be perceptible around 100% red, blue and magenta. I have attached the spreadsheet I used for this simulation experiment, if anyone would like to look through the detail. I hope it is not too cryptic; most of the labels match the relevant formulas on Lindbloom's site.
The experiment tends to say that calibrating to the Rec709 Y values gives a better calibration for the 100% saturation points, matching one's intuition, but that calibrating using the actual primaries to define a new gamut may give an equally good calibration when looking at intermediate points in the CIE triangle. But this experiment was not conclusive, one way or the other. This might be an accident of the actual primary color x-y coordinates. It might also be an accident of the 30 data points chosen, all on the edges of the six triangles. I did not expand this to try all 10 million combinations of studio RGB. Nor did I look for any research weighting errors in one part of the CIE gamut, e.g., skin tones, as more annoying than errors in another part. And I did not yet look at whether one calibration did a better job than the other at preserving perceptual distances between points; the comparisons were between the expected points in each calibration and the corresponding intended color in an ideal Rec709 calibration.
Even were the result conclusive, the domain where it was true might be limited, e.g., only in this particular situation of an actual color gamut strictly contained in the Rec709 gamut. Perhaps only in the case where the primary x-y coordinates were calibrated to minimize hue error, as I did using CIE94, so they are essentially in line between white and the Rec709 points.
When dealing with a real set, e.g., mine, I can see that the saturation points for each color are not in a straight line, so we know that the actual Samsung CMS varies from the idealized one of six linear matrices. This may be from the CMS itself, or the fact that one cannot get perfect grayscale or gamma linearity either. So, in practice on a particular set, one or the other calibration approach might yield a better result. The only way to distinguish would be to compare the delta E values on all the color and saturation measures. There does not seem to be any magic in using the actual primaries to define a new gamut and keeping straight lines in the CIE chart that would lead to a demonstrably better calibration; when it does, it may be a complete accident.
CMSSimulation.zip 74.51171875k . file