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A Few Words About Colorimetry

BPI has a new product called the BPI RGB Spectrometer™, which is in fact a colorimeter: a device which measures and characterizes color as it appears to an actual observer, according to a mathematical model of color vision.

The subject of colorimetry is dauntingly complex, but in a nutshell it can be described as follows:
  • You can do a pretty good job of describing all of the colors that people see by specifying a mixture of three colors that span the visible spectrum.
  • There is an enormous number of ways to choose the three colors, some of which do a better job than others.
  • No choice of colors is perfect.
Colorimetry usually starts by specifying a white light source, which illuminates everything that will be tested, and three colored filters, which will modify the light coming from the white source. The choice of the white light source strongly affects the way people see color: for example, navy blue clothes will appear almost black under incandescent lights, but they are clearly blue in sunlight. Incandescent lights are lacking in blue and violet wavelengths that the navy blue dye reflects; sunlight contains those wavelengths. A typical choice of colored filters includes a "red," which passes mostly light from the long-wavelength part of the spectrum; a "green," which passes light from the middle of the spectrum but not so much from the long and short wavelengths; and a "blue," which passes mostly light from the short-wavelength side of the spectrum. When we add light from the three filters, we shine a proportion of light from the red filter (from 0% to 100%) into the eyes of a test subject at the same time as proportions of light from the green and blue filters. Notice that this "additive" process is different from the more familiar "subtractive" process that we all remember from mixing two or more colors of paint together in the same container.

The white light and every possible combination of the three primary colors form a color space. There are as many color spaces as there are people willing to choose filters and measure the results. A good color space would include every color people can see (none of them do that), with no duplicates (no combinations that result in the same color as some other combination; most spaces are good about that), and no "imaginary" colors (numerical combinations that make sense mathematically but don't actually correspond to a visible color; some color spaces have imaginary regions). When someone talks about the RGB value of a color, he or she is specifying the percentage of red, green and blue from a particular set of filters
that matches the color in question, starting with an understood light source.

BPI RGB Spectrometer™ has a light source, which we have chosen because it covers most of the visible spectrum, and a set of filtered sensors, which give the red, green and blue readings. The light and filters are chosen so that the sensors don't respond to invisible wavelengths (infrared and ultraviolet).


So far, that's what all of this sounds like. The color space of your TV set doesn't match your printer. Your CRT monitor has a different space from the LCD monitor. Color film covers a different space from digital cameras, but that's OK because the digital camera doesn't use the same space as the monitor or printer that you view its pictures on. And on top of that, BPI has its own quirky color space for its colorimeter. There are thousands of color spaces, or anyway a dozen or so that people actually use. 

Fortunately, the color response of the eye is more or less linear: if you shine two lights with certain RGB values into someone's eyes, you get the same response as if you used one light with an RGB that is the sum of the original RGB's. That means that the RGB measurements of one color space can be translated into another space, within limits.

Even more fortunately, starting in the 1920's, the CIE (Commission Internationale de l'Eclairage -- the International Commission on Illumination) began the work of standardizing color measurements based not on color filters but on matching eye responses to monochromatic light with mixtures of monochromatic primaries. This led to the 1931 CIE XYZ standard measurements, in which X represents a proportion of the red side of the spectrum, Z is the blue side of the spectrum, and Y is the proportion of a color that matches the photopic efficiency function of the standard observer. When RGB measurements from different color spaces are translated into XYZ space, everyone is comparing oranges to oranges.

But How Do I Draw It?

The three-dimensional representation of color is nice, but people like to visualize things in two dimensions, so they can be printed in a book. Since Y in the XYZ system represents the overall color-weighted sensitivity of the standard observer's eyes (we're all pretty standard, aren't we?), there is a clever transformation which can be used to describe color in two dimensions separately from "brightness." That way, a dark green can be the same color as a bright green: it differs only in how much of the color reaches your eyes. This system is known as xyY space (keep your eye on the capital letters), and the coordinates x and y together define chromaticity, while Y defines luminosity. Specifically, we define x=X/(X+Y+Z) and y=Y/(X+Y+Z). In the two-dimensional xy space, the x-axis describes colors varying between blue and red as x varies from 0 to 1, and the y-axis describes colors going from blue to green as y varies from 0 to 1.The xy-space horseshoe

In xy space, the gamut of all possible visible colors forms a "horseshoe" shape, with the perfectly monochromatic colors along the outer edge and the less saturated colors in the interior. The horseshoe is usually drawn with the wavelengths of monochromatic light marked on the edge and some (inferior) approximation to the color of each point on the inside based on the ability of your printer or monitor to display colors. There is also usually a special curve drawn into the horseshoe, called the "black-body curve," which is the color of a glowing incandescent object as it is heated to ever higher temperatures. Notice that the black-body curve is extended to temperatures that no real object could ever achieve without vaporizing.

One Last Complication

If you study the xy horseshoe, you will notice that it has an awful lot of green, whereas the reds and blues seem to be squeezed into the corners. The sensation of color difference is not constant: if you pick pairs of points the same distance apart in different parts of the diagram, the perceived color difference won't be the same. For some purposes, it would be nice to be able to simply measure the distance between two color points and use that distance to describe the feeling of color difference. That's why there is yet another set of color coordinates known as the CIELAB space. In this space, the number L* varies from 0 to about 100 and represents a sensation of "lightness". The number a* varies from about -100 to +100 and represents the change from green to red. The number b* varies from about -100 to +100 and represents the change from blue to yellow. For example, if (a*,b*) is: 

  • (30, 30), then you have an orange color. The positive a* tells that it has red, and the positive b* tells you it has yellow.
  • (-50, 0), that is a strong green.
  • (-20, 20), a light yellowish-green. Avocado?
  • (0, 0), white or gray, depending on L*.
  • (-40, -30), pretty strong bluish green, maybe aqua.
If you'd like more specific information about this subject, Wikipedia is a good place to start. They have some detailed articles and plenty of references to reliable sources. Try looking up color space, the CIE 1931 color space , the Lab color space, and other articles that you can surf to from there. Another good website with very extensive detail is the Bruce Lindbloom site.