Cone spectral sensitivities
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 tritanopes
all
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.
References
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.