Is there an analytical method for calculating relative powers needed to achieve a specific white balance for monochromatic sources (eg: lasers) of known wavelengths?
First, this answer assumes you are using three monochromatic sources, such as lasers. I will use the wavelengths of the three lasers are red = 671 nm, G = 532 and blue = 473. Further, we need to select a target whitepoint, for which I will use D65. Basically, the solution is to use the CIE color matching functions to find out how much relative power of each of the three wavelengths you need to achieve a desired ratio of X:Y:Z. In your case the desired result is the tristimulus values of CIE Illuminant D65, X = 95.05, Y=100.0, and Z=108.88. The color matching functions define a 3×3 matrix transformation from RGB power levels (on a relative scale) to the XYZ values. What you need to do is invert that matrix in order to compute the required RGB values to produce your given set of CIE tristimulus values. Using your three laser wavelengths the forward equations are: X = x-bar(671)*R + x-bar(532)*G + x-bar(473)*B Y = y-bar(671)*R + y-bar(532)*G + y-bar(473)*B Z = z-bar(671)*R + z-bar(532)*G
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