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>the white balance slider is the same (blue => yellow) as the "b" channel in LAB and that the tint slider (green => magenta) is the same as the "a" channel.
Actually no...it's NOT the same. Lab does not use the Kelvin scale to describe the ab channels. Kelvin is based upon a blackbody radiation and is actually blue/amber and the magenta/green is perpendicular to that axis, which is NOT the same as the ab channels in Lab.
Camera Raw uses the Pro Photo RGB chromaticities in linear gamma for its internal color space and while a large set of functions are luminance only, it does that and the HSL corrections based on HSL which also is not the same as Lab.
Jeff, thank you for your reply. So, the bottom line is that the apparent correlation is coincidence only, right?
>the apparent correlation is coincidence only
Well, there is no direct correlation between Lab and Kelvin scale and Camera Raw uses HSL type controls, not Lab. There's a BIG difference between Hue, Saturation and Luminance and Lab. So, Camera Raw has NOTHING to do with Lab, correct.