Mesopic color matching: some theoretical issues

In this paper I address some theoretical issues concerning the additivity laws of Grassmann as they might apply to color matches in mesopic vision (in which light intensities are such that both rods and cones are active). It is first shown that rods and cones have linearly independent spectral responses, and hence rod and cone spectral responses span a four-dimensional matching space. Next, the iterative tetrachromatic-matching experiment of Trezona [Vision Res. 13, 9 (1973)] is examined for consistency with a four-dimensional Grassmann structure; convergence conditions for the technique are derived and shown to be consistent with the actual conditions of the experiment. Finally, a discussion is presented of the conditions under which mesopic color matching would require only three primaries, even when color matching obeys four-dimensional (but not three-dimensional) Grassmann laws. A two-dimensional rod-cone diagram gives significant but not complete insight into the conditions for trichromacy in a four-dimensional color-matching space.