The link between gamma, greyscale and gamut

Hello guys,

Personally, this one confuses me a very great deal. I thought perhaps it would be useful to make a thread on this subject as I hope it could become a useful reference for fellow calibration starters like myself.
So, here goes.

Grey scale
1) Calibrating Grey scale (setting the color of white) is all about obtaining a neutral shade of grey for each step of the grey scale for the gamut you are targeting. You need to do this for the darkest shade of gray up to full white. It needs to be correct for each level of stimulus up to 100% grey, which is in fact full white. Thus, you are adjusting the x,y coordinates for white to obtain the D65 color temperature for every step of the grey scale. The coordinates for Rec.709 white are x= 0.3127; y= 0.3290.

The ratio between red green and blue must be equal to obtain your goal. However, you still need to get Y (luminance) correct.

Gamma
2) This leads me to gamma. Gamma is about getting the brightness (luminance) correct for each step of the grey scale. Each step should get brighter by the same amount as the previous step. Adding green to green for instance, will increase the luminance of green. Gamma is then about the amount of red, green and blue.

It goes without saying that adjusting the amount of R, G or B will also adjust its ratio, and vice verse. In many Color Management Systems there is a separate control for Y. This is a control that will adjust the ratio and amount at the same time (if it works well). Otherwise, adjusting gamma (the amount) might yield an unequal ratio between R, G and B, thereby invalidating your grey scale.

Gamut
3) The part of the story that is still unclear to me, is how this all links to the Rec. 709 gamut. Primary and secondary colors also have x,y coordinates and also have a luminance that needs to be correct. Obviously, gamma will also affect the luminance of these colors and will therefore indirectly affect their hue and saturation. Thus when you use a CMS to get the x,y coordinates for the colors correct, and also set luminance correct, setting gamma might mess up the hue, saturation or luminance of the colors.

Only for 100% and 0% stimulus this is not an issue because 0% and 100% do not have "gamma". ALL other stimulus levels for a given primary or secondary color, regardless of the saturation, will have "gamma". I know that Lightspace CMS separates gamut profiling from gamut calibration but I would really enjoy understanding this last part of the puzzle.

edit: so my question is rather. Why do we adjust gamma as a last step AFTER we do the CMS work? It seems that, since gamma influences the color, it should be the other way around?

Thanks for reading:-)
Edited by Jeroen1000 - 12/5/12 at 7:38am

Truly an excellent reply Joel and well laid out. One small "remark"

Say we have 235,235,16 (yellow), two values are non zero and the same but is it not so that only the hue (and luminance) have changed here?

@HDTVChallenged I read that thread you are referring too. I'm a victim of that lingering confusion

Thanks everyone. It's all clear now. My RS232 to USB cable has arrived which will make calibration a lot easier with an Iscan DUO. It also seems that its standard window patterns (those accessible using the remote) are at a whooping 50% of screen area. Yes, I've used them to calibrate :rolleyes.