The human eye has 3 types of color cones: red, green and blue. Their spectral sensitivity peaks in short (S, 420–440 nm), middle (M, 530–540 nm), and long (L, 560–580 nm) wavelengths. See diagram below.

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Then we have the CIE standard observer. Wikipedia says it can be thought as the spectral sensitivity curves of three linear light detectors yielding the CIE tristimulus values X, Y and Z.

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I don't get why the red line in the CIE standard observer color matching function also peaks at 440 nm. To be more specific: What causes the x-line in a CIE standard observer color matching function to peak at around 440nm?

Can someone explain me that?


1 Answer 1


Probably you've noticed that primarities are $\mathbf{X}$, $\mathbf{Y}$, $\mathbf{Z}$, not $\mathbf{R}$, $\mathbf{G}$, $\mathbf{B}$ (which are corresponding to the color values $R$,$G$,$B$). This is the aftermath of original work conducted by Wright and Guild yielded the Color Matching functions: $r(\lambda)$, $g(\lambda)$, and $b(\lambda)$ having a negative value of the red primarity around $522 \;\texttt{nm}$ (figure below). Everyone will agree that it is non-intuitive and somewhat confusing.

Why values of $r(\lambda)$ are negative? Well after tristimulus color matching experiments, it turned out that not every color can be created with the preset primarities ($700\; \mathtt{nm}$, $564.1\; \mathtt{nm}$, and $435.8\; \mathtt{nm}$). So for example, if you wanted to create the blue-green color of wavelength $\lambda = 490 \; \mathtt{nm}$ it cannot be done only by adding blue and green primarity alone. You also need to subtract the red one. Mathematically speaking, the color equation:

$$\mathbf{C}=r\mathbf{R} + g\mathbf{G} + b\mathbf{B} $$

Must by modified by adding the outer mixture $-r_{out}\mathbf{R}$ to both side of the above equation:

$$\mathbf{C} + r_{out}\mathbf{R} = g\mathbf{G} + b\mathbf{B} $$

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That is why CIE introduced new set of so-called virtual primarities: $\mathbf{X}$, $\mathbf{Y}$, $\mathbf{Z}$. In order to obtain only positive or null values of the Color Matching Functions. That's how $2^{\circ}$ observer Standard Color Matching Functions (also called CIE 1931) were created. By doing so they ensured that (amongst other assumptions):

  • New SCMF's $x(\lambda)$, $y(\lambda)$, $z(\lambda)$ have values $\ge 0$ (not like $r(\lambda)$).
  • Are related to previous CMF's ($x$,$y$,$z$) by a appropriate transform.
  • $\mathbf{X}$, $\mathbf{Y}$, $\mathbf{Z}$ must be independent (kind of orthogonal).
  • Only color value $Y$ is proportional the the lightness of a colour.

Newly obtained color quantities $X$,$Y$,$Z$ are called Standard Color Values. The relation between CMF's and SCMF's is given by a following linear transform: $$ \left( \begin{array}{c} x(\lambda) \\ y(\lambda) \\ z(\lambda) \\ \end{array} \right) = \left( \begin{array}{ccc} 2.7689 & 1.7517 & 1.1302 \\ 1 & 4.5907 & 0.0601 \\ 0 & 0.0565 & 5.5943 \end{array} \right) \cdot \left( \begin{array}{c} r(\lambda) \\ g(\lambda) \\ b(\lambda) \\ \end{array} \right) $$

After over a three decades people from CIE had realised that $2^{\circ}$ observation angle might not be enough for adequate color assessment. That's why in 1946 they introduced the $10^{\circ}$ observer, also known as CIE 1964 observer. Latter is recommended for visual angles above $4^{\circ}$, whereas CIE 1931 should be used for any angle below that. Of course there is no sudden change in perception of colour at $4^{\circ}$, this number is just arbitrary. Comparison of these two standards is depicted of a following plot, on which you can see the 'bump' mentioned by you for the $x(\lambda)$ standard color value:

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  • $\begingroup$ 10° observer is from 1964, not 1946. $\endgroup$
    – Ruslan
    Commented Sep 29, 2018 at 12:27
  • $\begingroup$ Thanks for that, Czech mistake. Luckily CIE standard has a correct date, later in that sentence. $\endgroup$
    – jojeck
    Commented Sep 29, 2018 at 12:50

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