If one wants to express the values of the responses of the cones to a stimulus expressed in terms of its tristimulus values, one has the following expression:

where the coefficients k’cp , k’cd , k’ct are the inverses of the coefficients kcp , kcd , kct.

Once the coordinates of the points of confusion and the scaling factors have been chosen, the correspondence between the tristimulus values and the LMS values is established.

If the above equation is particularized to the case of an equal-energy spectrum, taking the

SL(λ), SM(λ), SS(λ) are the spectral sensitivities of the L, M, and S mechanisms, respectively. These values are the König-type fundamentals.

2. COMPARATIVE STUDY OF THE FUNDAMENTALS

Towards the end of the twentieth century, many authors derived their own cone fundamental response curves. In this section, we shall review the most important, trying to highlight the distinguishing particularities of each, and ending with a comparative study.

We shall begin chronologically in 1971, when Vos & Walraven [17] derived their fundamentals by equating the luminance Y to the sum of the output signals L, M, and S. I.e., the sum of the spectral sensitivities of the fundamentals is equal to the spectral sensitivity curve Vλ:

where X', Y', Z' are the tristimulus values obtained using the CMFs modified by Judd in 1951 [18].

Figure 1. Vos-Walraven fundamentals on a logarithmic scale.

In 1975, Smith & Pokorny [19] imposed the boundary condition Y = L + M on their fundamentals, i.e., Vλ = SL(λ) + SM(λ), leaving the S cone scaling condition open. The scaling condition related to the luminance implies that:

From this condition, the Smith-Pokorny fundamentals are given by the following general expression:

The S cone scaling condition may be taken to obey different criteria, so that which choice is made has led to different fundamentals. For instance, in 1982, Wyszecki & Stiles [14] derived their own fundamentals taking those of Smith-Pokorny and applying the scaling condition:

This scaling condition is not arbitrary. It is based on the invariant blue and yellow hues observed at 475.5 and 570 nm respectively by Walraven in 1961 [20]. Applying this condition yields the following fundamentals:

In 1990, Estevez, Vos & Walraven [22] derived their cone fundamentals from the colour matching functions of Stiles & Burch of 1955 [23], using the following expression:

These functions are given in normalized energy units according to the ratio L:M:S = 0.68:0.34:0.02.

Figure 3. The Estevez-Vos-Walraven fundamentals.

Similarly, in 1993 Stockman, MacLeod, & Johnson [24] developed their 2° cone fundamentals on the basis of the colour matching functions of Stiles & Burch of 1955 for fields of 2° [23]:

Figure 5. The Stockman-Sharpe fundamentals.

Figure 6. Comparison of rescaled L fundamental curves.

The diversity of fundamentals described above may give rise to doubt about which triad of fundamental curves is the most appropriate, and how to know which offers the greatest guarantee in a laboratory implementation. Doubt could also arise as to the population they are able to represent according to which population formed the subjects of the psychophysical experiments on which they were constructed. So as to allow a more reliable evaluation of the