Will the real Q please stand up?. Issue 6 (26th July 2022) - Brill, Michael H.
Abstract: In my 1996 article on units of tristimulus values, I used as a definitional equation Jozef Cohen's Q = A ′N, where N is a radiometric function of k wavelengths and Q is a column vector comprising N 's associated tristimulus values. With Cohen, I took as Matrix A (having no units) a set of three column vectors comprising color‐matching functions. The relation Q = A ′N then forced Q to have dimensions of power, which was inconsistent with the dimensionlessness of matrix A . Besides this problem, calling A ′N the tristimulus values of N still left them in an unspecified basis, so you could get a wide variety of Q vectors from a single N vector by changing the basis of A . Simply specifying Q = A ′N did not supply enough information to specify tristimulus values uniquely. I now propose to define Q = (A ′ P ) −1 A ′ N, where k‐by‐3 matrix P contains the (unscaled) spectra of the primaries. Using this definition resolves both the above problems.