Skip to content

Emulating the Wright-Guild experiment

(To go right to the emulator, click here – sorry, only in Spanish so far).

At the end of the 20’s, british scientists David Wright and John Guild run independently from each other a series of experiments with the purpose of reach an objective way of measuring color. Both started off from the empiric result obtained by Hermann Grassmann about linear additive behavior of light mixing; Grassmann found out that it’s possible to recreate, within certain limits, an arbitrary chromatic sensation by means of a certain mix of three colored lights, as long as none of them can be obtained mixing the other two (linear independence). This way we may assign each chromatic sensation a set of three numbers: the intensities of the primary light sources chosen to match a given reference.

In a nutshell, experiment consists in placing an observer in front of an area that subtends a visual angle of 2º (corresponding to the angular size of human fovea) in such a way that he or she sees at the same time one half having a reference color, while the other half is illuminated by an adjustable mix of three convenient primary colored lights. Subject is asked to operate the intensity level controls of each light until he matches the reference. The three intensities found are taken as a measure of the reference color.

However, no matter the three primary lights chosen, there will always be colors that “resist” to be matched to any combination of them. It can be clearly seen when this process is analyzed with the help of CIE xy chromaticity diagram. This graph represents human vision gamut, i. e., the set of all colors a human being is able to see, and its shape is commonly referred to as “a horseshoe”. Inside it, each primary color (as any other) is represented by a point; Grassmann laws tell us that any mix of two of them will lay on the straight line connecting them. One can follow that, given three distinct primaries, colors obtained by additive mixing them will lay inside a triangle defined by them. But, given the human gamut shape, it’s impossible to enclose all possible colors inside a triangle whose vertex lay all inside that shape; it’s like to try to enclose all points of a circle by a triangle whose vertex must be all inside that circle.

Despite of this fact, color linear additivity allows a workaround: if a reference color lays outside the primaries’ triangle, we can reach a color match by adding one of those primaries (wisely chosen) to the reference and write that primary’s intensity as negative, because it’s not added to mix but to the reference.

how
Relation between full gamut, monitor gamut (sRGB) and reduced gamut tRGB.

It is not easy to accept a color may have to be represented by one or more negative quantities; in fact, when Wright y Guild propose to their american colleagues this system in 1931, they refused to accept it and it was necessary to “invent” some kind of “imaginary” primaries named X, Y and Z to reach an agreement and write down for the first time the standard that settled the science of colorimetry as we know it today.

In order to simulate this experiment on-screen, I developed a Virtual Color Lab where it is possible to do that to an extent. But to emulate a color match on a screen, which itself cannot render the full human color gamut, it was necessary to build an even smaller color space, so it relates to screen’s gamut as this one to full gamut.

So I sintetized a new color space inside sRGB (which represents typical monitors and tablets) which I named tRGB (kind of “twisted RGB“). This space is built upon colors orange (234, 117, 0), green (0, 234, 117) and purple (117, 0, 234) taken from sRGB. You can notice a reduction in the gamut achievable by additive mixing with these “less-saturated” primaries, to the point that certain colors within sRGB cannot be reached by positive quantities of tRGB primaries (added to the adjustable mix) but allowing negative quantities (added to the reference color) . This fact was taken into account by Wright and Guild in their experiments.

color-lab-full
Virtual Color Lab view.

In this lab, user is invited to find a match between a reference chosen by a selector on top, playing around with three virtual controls which adjust primeries’ intensities. Three digital displays at the bottom provide a readout.

color-labThere will be cases when a match cannot be reached; it will be necessary then to “invert” one of the primaries (adding it to the reference) by means of a switch to the right of that control.