Why is there no blue peak in the photopic luminosity function?

Question

A luminosity function "describes the average spectral sensitivity of human visual perception of brightness". My understanding is that basically, for the same power, we perceive green light as brightest. Red and blue are less bright, infrared and ultraviolet are invisible. The SI unit candela is defined in terms of the luminosity of green light at a wavelength of 555nm.

Anyway, how come the photopic luminosity function (in black): only has a single peak at about 555nm? Photopic vision uses cones, and is the kind of vision that is active in bright light. Cones, as opposed to rods, are sensitive to different wavelengths and give us colour vision. Here's a graph of the spectral sensitivity of cones in human eyes:

So how come the curve for photopic luminosity doesn't look like the integral of the spectral sensitivity curve? Or is it an integral, but the blue cones are actually so much less sensitive that the blue curve gets scaled down to almost nothing?

[Both images from wikipedia with CC0 and CC BY-SA 3.0 licenses]

Answer 1

Actually, S cones are thought to not contribute to the photopic luminosity^1,3 nor to mesopic one². This is true for dim background, with which the CIE 1931 standard observer was defined. With intense background adaptation this is not generally true⁴.

To see it in real world color appearance models based on the CIE 1931 color space, consider the transformation matrix from XYZ to LMS color space from the Hunt and RLAB models for equal-energy illuminants (taken from this paragraph of the above link):

$$M_{\text{HPE}}=\begin{pmatrix} \hphantom{+}0.38971 & 0.68898 & - 0.07868 \\ - 0.22981 & 1.18340 & \hphantom{+}0.04641 \\ \hphantom{+}0.00000 & 0.00000 & \hphantom{+}1.00000 \end{pmatrix},$$

so that

$$C_{\text{LMS}}=M_{\text{HPE}}\cdot C_{\text{XYZ}}.$$

Its inverse, transforming from LMS to XYZ color space, will look like

$$M_{\text{HPE}}^{-1}=\begin{pmatrix} 1.910\hphantom{0} & - 1.112 & \hphantom{+}0.2019 \\ 0.3710 & \hphantom{+}0.629 & - 8.06\times 10^{-6} \\ 0.000\hphantom{0} & \hphantom{+}0.000 & \hphantom{+}1.000\hphantom{0} \end{pmatrix}.$$

Notice that the entry in the second row corresponding to contribution of the S cones is 5 orders of magnitude smaller than that for L cones. This is negligible compared to uncertainty of other matrix elements of $M_{\text{HPE}}^{-1}$. This confirms that, in (at least some) color appearance models dealing with cone responses, luminosity function has negligible contribution from S cones response.

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^{1 Alvin Eisner and Donald I. A. MacLeod, "Blue-sensitive cones do not contribute to luminance," J. Opt. Soc. Am. 70, 121-123 (1980)
2 Wayne Verdon and Anthony J. Adams, "Short-wavelength-sensitive cones do not contribute to mesopic luminosity," J. Opt. Soc. Am. A 4, 91-95 (1987)
3 (open access) L Schnapf, J & Kraft, Timothy & Baylor, Denis. (1987). Spectral sensitivity of human cone photoreceptors. Nature. 325. 439-41. 10.1038/325439a0.
4 (open access) Caterina Ripamonti; Wen Ling Woo; Elizabeth Crowther; Andrew Stockman. The S-cone contribution to luminance depends on the M- and L-cone adaptation levels: Silent surrounds? Journal of Vision March 2009, Vol.9, 10. doi:10.1167/9.3.10}