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The CIE 1931 colour-matching functions

The three functions that turn a spectrum into three numbers. They are all positive, which is why XYZ exists — the RGB functions they were derived from are not. ȳ is by construction the luminous efficiency function, which is why luminance comes out of Y.
The CIE 1931 colour-matching functionsThe three functions that turn a spectrum into three numbers. They are all positive, which is why XYZ exists — the RGB functions they were derived from are not. ȳ is by construction the luminous efficiency function, which is why luminance comes out of Y.400450500550600650700wavelength / nmȳȳ is the luminous efficiency functionCIE 1931 2° observer

Drawn at its defaults, in spectra and illuminants. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 5 essays

the blast radius of changing it

Where the model breaks

Seventeen observers in 1931

The standard observer that governs every colour specification in industrial use is an average over seventeen young British men, measured with equipment from the 1920s. It is known to be wrong in the blue, the correction has existed since 1951, and it has never been adopted.

What the eye does

Why colour is exactly three-dimensional

Matching every wavelength with three primaries requires, for some wavelengths, a negative amount of one of them. That physical awkwardness is why the colour-matching functions were transformed into XYZ, and why the horseshoe is curved.

Where the model breaks

Two degrees or ten

This site names the observer on every figure it draws, which was supposed to be the point. Measuring what it had actually done found two hundred and four figures naming the same observer, three naming the other, and sixty-two of sixty-four generators printing a string that had never once varied.

What the eye does

The eye stops at the lens

Neither standard observer is tabulated below 360 nanometres, and the reason is not that the photopigments stop absorbing there. It is that the light never arrives — the cornea and the crystalline lens take it — so the short-wave limit of human colour vision is a piece of optics, it moves by a factor of twenty across a lifetime, and it can be surgically removed.

Matching and measuring

The observers differ by a unit's worth

The gap between the 1931 and 1964 standard observers is the one quantity in this collection's audit with no published number under it — nothing here reports it as a single figure over a stated set. It also has the second-largest dependence on which colour-difference formula is used, running from 1.60 to 3.55 across the menu.

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