The normal observer, with three types of cones, can match any spectral light to a mixture of three fixed-colour primary lights (one of which may have to be added to the spectral light to complete the match). The match is determined at the cone level: the total quantal catch produced by the three primaries in each of the three cone types is the same as the quantal catch produced by the spectral test light. The three functions relating the matching intensities of the three primary lights to the wavelength of the spectral light are known as the colour matching functions or CMFs.
If we knew the sensitivity of each of the three cone types to the three primary lights, we could reconstruct the cone spectral sensitivities from the three CMFs by a simple linear transformation. Those nine sensitivities, however are unknown. They are traditionally estimated (Young, 1807; Helmholtz, 1866; König & Dieterici, 1886, 1893) by assuming that the three types of dichromatsprotanopes, deuteranopes and tritanopesall possess reduced forms of trichromatic vision, lacking one of the three normal cone types -- the L, M and S, respectively. The nine missing values, which can be reduced to five since we are typically uninterested in the absolute cone sensitivities and since the S-cone sensitivity to the red primary can be assumed to be zero, can be obtained by determining the locations of the confusion points of the three types of dichromats in the trichromatic chromaticity diagram (see Wyszecki & Stiles, 1982), but a better method is to measure the dichromat's cone spectral sensitivities directly. The cone fundamentals in this section represent estimates of those unknowns. The cone fundamentals can be thought of as CMFs of three imaginary matching lights, each of which exclusively and separately stimulates the one of the three cone types.
The three cone spectral sensitivities, [or L(λ)], [or M(λ)] and [or S(λ)] , are related to the three CMFs, , and , according to:
where , and are, respectively, the L-cone sensitivities to the R, G and B primary lights, and similarly , and are the M-cone sensitivities to the primary lights, and , and are the S-cone sensitivities. The absolute values of (or ), (or ), and (or ) remain unknown, but are typically chosen to scale three functions in some way: for example, so that , and peak at unity.
The determination of the five unknowns: , , , and is an important goal of colour vision research. Further information about the relationship between CMFs and cone fundamentals.
Helmholtz, H. (1866). Handbuch der Physiologischen Optik, 1st ed. Leipzig: Voss.
König, A. & Dieterici, C. (1886). Die Grundempfindungen und ihre Intensitäts-Vertheilung im Spektrum. Siz. Akad. Wiss. Berlin, 1886, 805-829.
König, A. & Dieterici, C. (1893). Die Grundempfindungen in normalen und anomalen Farbensystemen und ihre Intensitätsverteilung im Spektrum. Z. Psychol. Physiol. Sinnesorg. 4, 241-347.
Young, T. (1807). Lectures on Natural Philosophy. London: Johnson, Vol. II.