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Seeing as there isn't a colourimetry stackexchange, I'm asking here where a number of useful colourimetry topics have already been posted.

A number of excellent resources exist with regards to the ubiquitous CIE 1931 chromaticity diagram. This is noted to be the consequence of two consecutive projections, the first onto a 3D plane and the second onto a 2D surface. Also noted is the fact that the Y tristimulus value, corresponding to the CIE 1931 photopic observer, represents lightness due to the choices of the XYZ tristimulus values.

Despite the fact that the chromaticity diagram rigidly defines which colours are "real" and which are only imaginary, little explanation seems to exist for which values of Y (corresponding to which chromaticities) are valid.

For instance, this link seems to suggest that certain colours that appear to be in gamut will in fact be outside gamut at certain brightnesses.

Examination of David Macadam's paper "Maximum Visual Efficiency of Colored Materials" seems to suggest that there are indeed rigorous limits (Macadam limits) which relate to the illuminant under which the chromaticities are viewed. How exactly does this work?

In addition, I found this interesting claim in Billmeyer and Saltzmann's "Principles of Color Technology;"

Only colors of very low luminance factor, such as spectrum colors, can lie as far away from the illuminant axis as the spectrum locus; all other colors have lower purity. The lim- its within which all nonfluorescent reflecting colors must lie have been calculated (Rösch 1929; MacAdam 1935) and are shown projected onto the plane of the chromaticity diagram inFigure 4.28. They serve to outline the volume within which all real nonfluorescent colors lie. Although Rösch predates MacAdam, these limits are known as the MacAdam limits

This claim seems to be reflected on Bruce Lindbloom's diagram and the diagram included in Macadam's paper, in which luminosity drops to zero towards the spectral locus. Pure (or almost pure) spectral colours can be generated via a laser (or similar), and appear bright to the average observer. As such, to what do Billmeyer and Saltzmann refer when they suggest that spectral colours must inherently have a very low luminance factor? If this is the case, why is this low luminance (apparently inherent to pure spectral colours, and almost pure colours) capable of appearing subjectively bright?

Wolfgang
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  • Also, any further resources to explore this area would be appreciated! I was surprised to find only two pages in the Billmeyer and Saltzmann textbook, and none in other textbooks I consulted. – Wolfgang Jan 26 '20 at 14:31
  • There are no such things as real colors in the way you seem to be using the term. All "colors" are a perception created by the eye/brain system of an observer (or an image sensor/processing algorithm designed to emulate biological eye/brain systems in order to be used by a color reproduction system that can induce the same perception in a biological eye/brain system.) There is nothing intrinsic in EMR with regard to color. What wavelength(s) one species perceives as a certain color, other species may see as a different color, or have no visual perception at all. – Michael C Jan 27 '20 at 01:47
  • Do Billmeyer and Saltzmann discuss Albert Munsell's work? Are you familiar with it? – Michael C Jan 27 '20 at 01:57
  • As this answer discusses in very simple "layman's terms", the limits of human perception are not a neat cylinder or sphere. – Michael C Jan 27 '20 at 02:06
  • Thank you for the replies. I understand that there's no such thing as a "real colour" and that colour is simply the perception of a certain spectrum of electromagnetic radiation, moderated by the sensitivity of different cones. I have looked at the Munsell system, and I'm aware that it is not a neat sphere due to the nature of the human cones... – Wolfgang Jan 27 '20 at 02:43
  • To rephrase my question in a more specific way; looking at the three dots on Lindbloom's animated 2D-->3D gamut, the upper dot is out of gamut while the lower dot is in gamut (despite the fact that all three dots appear to be in gamut on the 2D view. How would I know which lightness (Y) values would be in gamut for any specified (x,y) chromaticity? – Wolfgang Jan 27 '20 at 02:44
  • I've deleted my last two comments here and incorporated them into an answer. – Michael C Jan 27 '20 at 07:20
  • The ubiquitous CIE chromaticity diagram is not based on the XY coordinates but on xy coordinates where x=X/(X+Y+Z) and y=Y/(X+Y+Z). Thus XYZ triplets can be remapped to xyY where Z can be calculated from the above formulas using algebra. xyY shows the chromaticity (xy) but not the luminance (Y) – doug Jan 27 '20 at 23:28
  • I realise that. My question relates to when a colour volume is created (such as in the GIF diagram on Lindbloom's site that I linked) out of xyY dimensions. As Lindbloom's diagram shows, certain chromaticities are not in fact in gamut at certain Y values. What I want to know is what determines whether a given Y value is in gamut at any given chromaticity (i.e. the data that was used to compile that diagram) – Wolfgang Jan 28 '20 at 00:36

2 Answers2

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To rephrase my question in a more specific way; looking at the three dots on Lindbloom's animated 2D-->3D gamut, the upper dot is out of gamut while the lower dot is in gamut (despite the fact that all three dots appear to be in gamut on the 2D view. How would I know which lightness (Y) values would be in gamut for any specified (x,y) chromaticity?

In simplified layman's terms: Colors reproduced using trichromatic color reproduction systems reproduce colors other than the primary colors of that reproduction system by using ratios of the system's three primary colors. The combination of the primary colors in the correct ratio creates the same response in a viewer's eye/brain system as light of the target color would. This works for humans because we have a trichromatic vision system.

Each of the three primary colors has a maximum value. For colors which require one primary color to be brighter than the other two, only the brightest primary color may be at max value. The values of the other two primary colors are limited to values less than their maximum value. Limiting any of the primary colors to less than its max value to hold the correct ratio for a specific color also limits the total potential luminance of the three combined primary colors to less than the maximum potential luminance for the system. Maximum total luminance can only be achieved when all three primary colors are at full luminance (thus producing the perception of white light for the viewer).

If green must be at half the value of red for a specific color, then the total potential luminance for that color will be less than for a color that allows both green and red to be at max value.

Think of it this way. When one is calibrating/profiling a monitor the first step is often to measure the monitor's output when a neutral white signal is sent to it. The monitor's red, green and blue channels are adjusted individually until the measuring device says all three primary colors are equal in brightness. Adjusting one of the colors also affects the relative strength of the other two. If I increase green, for example, the relative portion of the total signal that is red and blue go down. But what happens if I've already got green pushed to 100% and my colorimeter is telling me green is still weaker than red and blue? I can't increase green by any more. It's already turned up as high as it will go! I must turn down both red and blue until they are balanced with green and the output is neutrally white. At that point, that's the brightest the monitor can be and output white light. For any color other than white light, the monitor must be dimmer as at least one of the three primary colors is reduced in strength.

How would I know which lightness (Y) values would be in gamut for any specified (x,y) chromaticity?

The only way you could know is to use a 3D map. It is beyond the capability of a 2D map based strictly on chroma that can be produced by a system at lower brightness levels to show how the gamut for that system decreases as desired luminance increases.

Pure (or almost pure) spectral colours can be generated via a laser (or similar), and appear bright to the average observer. As such, to what do Billmeyer and Saltzmann refer when they suggest that spectral colours must inherently have a very low luminance factor? If this is the case, why is this low luminance (apparently inherent to pure spectral colours, and almost pure colours) capable of appearing subjectively bright?

Billmeyer and Saltzmann are speaking about the ability of trichromatic color reproduction systems capable of producing white light, not single wavelength lasers. Given enough power, it is possible for a trichromatic color reproduction system to produce green light as bright as your green laser. But such a system will necessarily be able to produce even brighter white light when all three primary colors are outputting at maximum brightness. "Low" and "high" are always relative to one another.

Michael C
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  • Thank you for this excellent answer. Can you provide any further details or links to resources on how such a 3D map (adding a luminance dimension, to form a solid showing the valid luminance values for each set of chrominance coordinates) would be produced? I've seen volumes like this one - https://www.colour-science.org:8020/ - in a number of places, but none of the resources I've seen provide detail on how those values are obtained. – Wolfgang Jan 27 '20 at 14:06
  • To clarify - I'm not interested in how one might go about graphing such a thing, I'm sure that could be done in any software. I'm more interested in understanding what constraints are operating on the Y value for any given chromaticity (i.e. the data used to produce the 3D color volume) – Wolfgang Jan 27 '20 at 14:07
  • Additionally, how do those limits change when we restrict our colour space to something like sRGB? Looking at the 3D gamut on the website I just mentioned, there are a number of odd cutoffs and partial peaks on that diagram. – Wolfgang Jan 27 '20 at 14:32
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Also noted is the fact that the Y tristimulus value, corresponding to the CIE 1931 photopic observer, represents lightness due to the choices of the XYZ tristimulus values.

Y in the CIE 1931 2 Degree Standard Observer is the CIE 1924 Photopic Standard Observer: there is no such a thing as the CIE 1931 photopic observer.

Note that the CIE 1924 Photopic Standard Observer models the wavelength-dependent sensitivity of the Human Visual System (HVS) to electro-magnetic radiation, i.e. Luminance and not Lightness which is perceived brightness and has a non-linear relationship with the actual physical intensity of the stimulus.

Luminance and Lightness are purposely ignored in the various chromaticity diagrams, only flavours of chroma and hue are represented.

The CIE 1931 Chromaticity Diagram is built on-top of the CIE xyY colourspace which is a linear transformation of the CIE XYZ colourspace and thus of the CIE 1931 2 Degree Standard Observer:

CIE 1931 Chromaticity Diagram

The CIE 1976 UCS Chromaticity Diagram, however, is built on-top of the CIE L*u*v* colourspace which is a perceptually uniform colourspace resulting from a non-linear transformation of the CIE XYZ colourspace:

CIE 1976 UCS Chromaticity Diagram

CIE L*u*v* and CIE L*a*b* both adopts CIE L which characterizes the perceptual response to relative luminance. CIE L*u*v* being more perceptually uniform, MacAdam ellipses exhibit less distortion:

MacAdam Ellipses

The diagrams are rendered with Colour.

Kel Solaar
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  • Thank you for the response. My mistake in referring to the '24 observer as the '31 observer. I recognise that the 1931 and 1976 diagrams are built on different colour spaces, with one intended to have greater perceptual accuracy, and I realise that luminance is not typically displayed as part of a chromaticity diagram (hence the name). I'm simply wondering what rules govern luminance and the chromaticity diagram, seeing as diagrams like that present at Lindbloom's site and in Macadam's paper make it very clear that only certain luminance values are valid for any given chromaticity. – Wolfgang Jan 27 '20 at 00:14
  • Typically you represent the values with the most Luminance/Lightness. The CIE 1931 Chromaticity Diagram is a CIE xyY perspective projection along the Y axis from the top, so what you see are the colours with the most Luminance, note that the colours in the above diagrams are normalised and there are no defined rules for how to normalise them. If you go at that url: https://www.colour-science.org:8020/ and look down the Y green axis you should see the CIE 1931 Chromaticity Diagram forming. – Kel Solaar Jan 27 '20 at 04:46