The Smith & Pokorny cone fundamentals were obtained from the following transformations:
where , and are the Judd, Vos modified CIE, XYZ 2-deg color matching functions.
See Smith & Pokorny (1975), and p. 615 of Wyszecki and Stiles (1982).
Note that L(λ)+M(λ) = V(λ).
The logarithmic M- and L-cone fundamentals calculated here using the above equations from Smith & Pokorny (1975) differ slightly from other published tables of their fundamentals in the 3rd or 4th decimal place < 680 nm (e.g., Wyszecki and Stiles (1982), Table 2(8.2.5)). The S-cone function, however, differs by up to ~0.3 log unit from the calculated tables > 600 nm. The authors provided us with this note about the origin of their S-cone function, for which we thank them:
Here is the history: “Some time ago we had the Wyszecki & Stiles 1 nm tabulation of the 1931 CIE CMFs and coordinates scanned into one of our computers. When we needed 1-nm Vos/Judd data, we used the Vos equations and the scanned coordinates to derive the coordinates. These yield close but not identical chromaticity coordinates as the Vos tabulation. The discrepancies are small. We typed in the Vos and computed the CMFs.”
DeMarco, P., Pokorny, J. & Smith, V. C. (1992). Full spectrum cone sensitivity functions for X-chromosome linked anomalous trichromats. Journal of the Optical Society of America A, 9, 1465-1476.
Smith, V. C. & Pokorny, J. (1975). Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision Research, 15, 161-171.
Wyszecki, G., & Stiles, W. S. (1982). Color Science: concepts and methods, quantitative data and formulae. (2nd ed.). New York: Wiley.