Theoretical Constraints on the Participation of Rods and Cones in Color Matches

Abstract

The visual system is trichromatic for small, centrally fixated fields and high (photopic) light intensities. For such conditions, color matching requires three primary lights, because of the three kinds of cone photoreceptors involved. When light intensities are low (scotopic), color matching reduces to brightness matching, and vision becomes monochromatic. At scotopic light intensities, which are not enough to excite cones, vision is mediated by rods; on the other hand, photopic light intensities are high enough to saturate the rods so that only cones contribute to color matches. But what of light intensities (mesopic) that are above the cone threshold but below the rod-saturation intensity? If rods and cones participate together in mesopic vision, shouldn't mesopic color matches require four primary lights instead of three? To address this question, this paper first shows the possibility of a full tetrachromatic matching space by demonstrating that the rod spectral-sensitivity function is linearly independent of a set of color-matching functions for the cones. Secondly, the mathematical conditions for convergence of Trezona's [1] iterative tetrachromatic matching experiment are derived and shown to agree with the actual conditions of the experiment. This step is intended to show that some experimental results are consistent with the formal discussion. Finally, a simple diagram is introduced that represents confusion loci in a reduced "matching space" of rod versus cone stimulation. The topology of this diagram is used to show how mesopic trichromacy is possible.