Optical Brightening
Past the optimum, more brightener makes fabric less white and greener. The complaint "we doubled it and it looks worse" is this curve.
— W
Whiteness achieved at the dose applied
Both the saturation constant and the greening penalty are fitted to a specific brightener on a specific substrate and must be recovered by running a dose ladder and measuring CIE whiteness and tint on your own goods — they are not transferable between brightener classes or between cotton and polyester. The single whiteness number also hides the tint deviation, which is what an observer actually objects to; a fabric can hold its whiteness index and still look visibly green, so judge a ladder on tint as well. Whiteness measurement is itself illuminant-dependent, since the fluorescence needs UV in the source, and a result read under one instrument condition will not reproduce under another.
Fluorescent Brightener Whiteness Index Saturation Limit — free, with the formula and a worked example, at Textile School.