Grassmann’s laws and individual color-matching functions for non-spectral primaries evaluated by maximum saturation technique in foveal vision

Over time, much work has been carried out to ascertain the validity of Grassmann's laws, Abney's law, CIE standard color-matching functions and, up to now, no definitive answer has been given. Some of the phenomena subject of this debate are considered. An apparatus for color matching in 1.8° visual field has been realized with two sets of primary lights with broad spectral bands. This kind of primaries is the great difference with respect to other laboratories because it allows an indirect check of the Grassmann additivity law on the basis of the spectra and individual color-matching functions by evaluating: (1) the tristimulus values of the primary lights; (2) the transformation matrices between the two reference frames defined by the two primary sets; and (3) the tristimulus values associated to all the pairs of matching lights in the bipartite field produced in the evaluation of the two sets of color-matching function. The discrepancies of the data resulting in the check (1) and (2) are all compatible with the range defined by the uncertainty propagation of the individual color-matching functions. In the check (3) fifteen tristimulus values over 18 have a discrepancy lower than one standard uncertainty. Grassmann's proportionality law is checked directly by reducing the matching lights with a neutral filter and holds true.