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Color Basics

Most often, the purpose of color imaging in industrial and scientific applications is to measure, as accurately as possible, the color coordinates of each sampled point in the area being viewed.  To specify the hue (red/orange/yellow/etc.) and the brightness requires three numbers so collecting enough data to specify a color requires at least three measurements.  As it turns out, the accuracy of these measurements can be improved if more measurements are taken (most point colorimeter probes now use 6 or 7) but for most area imaging applications, three is generally sufficient.  The three numbers used to identify colors are based on the concept of color matching. 

Color Imaging Requirements

The fundamental requirement for production of color images, that is, images that can be presented in such a way that the eye perceives them as having color characteristics reasonably approximating the colors in the original, is that at least three spectrally-separated samples of the original must be taken.  A couple of examples will show the need for this requirement. 

color-examples.gif

Here is a basically sample task, sorting oranges. If a detector is set up that measures the amount of red light reflected from the object, then it can distinguish from unripe oranges - which reflect only green – and ripe oranges, which reflect both red and green. The red signal can be represented as a gray scale, which can be used to automatically select ripe oranges. Unfortunately, this single color method cannot distinguish ripe oranges from dead ones, which are yellow. To distinguish orange from yellow requires measurement of green reflected light so this simple task already requires two detectors. Similarly for the task in the illustration on the right, two detectors are required.

In another example, if we want to measure the brightness of blue emission from an LED, we need one detector sensitive in the blue range. However, this detector tells us nothing about the emission out of the blue range so another detector, which measures everything except blue, is also needed. With these two detectors, we can assure that the ratio of blue to not-blue is suitable.  

blue-example.gif

 

Note that we do not know anything about the actual wavelength of the blue light.  Everything in the "Blue" band is detected without discrimination.

Now, let us assume that we want one system to perform both tasks. For the oranges, we need red and green detectors, and for the LEDs, we need blue and not-blue detectors. This seems like four detectors, however, with a little experimentation, we might notice that the sum of the red and green detector signals tracks well the signal from the not-blue detector and that the blue detector signal doesn’t change much as we look at the three classes of oranges oranges. This could lead us to believe that three detectors are both necessary and sufficient to define colors. We would turn out to be right but with a few important constraints. After all, what about purple?

Color matching

Early on, it was decided that the useful thing to know about color would be some rigorous description of color as seen by human eyes that could be used to produce any color at any time with some assurance that the various color samples produced would all look the same. In the 1920s several experiments were set up as shown in figure 32 to determine a color matching function. An observer was positioned in a dark room so that a color sample subtending a 2-degree circle, while illuminated by a 5000-degree Kelvin incandescent source, could be viewed on the left side of a screen.

human-color.gif

The viewer was given control of a projector pointed at the right of the screen containing three monochromatic sources at 435.8, 546.1 and 700 nm that illuminated a 2-degree circle with amounts of light from the sources set by three knobs. Various color discs were inserted on the left and the viewer was asked to set the knobs so that the projected color matched the color sample.

Almost immediately, it was discovered that some of the matches were impossible. In order to match some of the color samples, a second projector had to be added to the left side so that the viewer could project monochromatic light from one or more of the sources on the sample while those same sources were set to zero on the right. By simple algebra, this meant that to avoid using projectors on the left, projectors that would subtract light from the right were needed. It had turned out that the color matching function had negative parts.

spectral-match.gif

That finding confirmed that it is not possible to duplicate the appearance of all spectral colors with three monochromatic sources.   Since negative light is inconvenient, some other solution for matching needed to be found.

Tristimulus values

The solution came again from algebra. It was decided that if three spectral primaries would not work, perhaps a different set of primaries might. To make new color matching curves that can be combined linearly to form the measured curves, it is only necessary to combine the experimental curves algebraically to produce a set of three that are all positive. Since this process has more degrees of freedom than are necessary, one of the curves was preassigned the shape of another key curve, that which plots the luminous efficacy of the eye. This is the plot of the apparent brightness of equal-energy spectral colors. This was designated the curve and the other two computed curves were designated x-bar(lambda) and y-bar(Lambda).

x-bar-match.gif

Note that the negative parts are gone. With this set of curves, however, the primaries are imaginary, that is, they are physically unrealizable. What they form is a color space that is larger than that required to produce all physical colors, thus defining a space that provides positive numbers describing every possible color.  

It is essential when using these curves to understand that they have two separate but equally valid meanings. Assume that it is desired to produce the perception of 500 nm spectral illumination. To do this, the color matching curves require that 3 units each of the “blue” primary and the “green” primary are required. Conversely, if we had detectors with spectral response curves shaped like these color matching curves, then applying a 500 nm spectral illumination to them would produce equal signals in the “blue” and “green” channels and no signal in the “red” channel. To extend this principle, if we have a source that is a mixture of spectral colors (which, of course, is what any color is), then the signal it produces will just be the sum of the amount of each of the spectral colors multiplied by the value of the curves at each color. This leads to the generalization in which we take the integrals over all wavelengths of the products of the applied spectral distribution and the three color matching curves.   The results of these integrals are designated X, Y and Z and called the tristimulus values.

Chromaticity values

One further simplification was implemented. Since brightening or darkening a color in the XYZ space simply means that all three values are made proportionally larger or smaller, it is possible to remove the brightness variable simply by normalizing the curves. To do this, each of the three curves is divided by the sum of X, Y and Z to produce a new set of curves designated x, y, z. The sum of x, y, and z is always 1 in this calculation so only two numbers are needed to specify a color (independent of brightness). These are the chromaticity values and can be plotted in a plane to generate the chromaticity diagram.

chromaticity.gif

This plane shows only the color or chromaticity. The brightness is indicated by the Y value, which is the integral of the product of the luminous efficacy curve and the spectral power distribution of the color being measured. This combination is called the CIE xyY color space. 

Chromaticity chart

Several important points about the chromaticity chart need to be understood.

  • Imaginary primaries – The chromaticity chart shows all visible colors within the central horseshoe shape. The black space around the horseshoe indicates the rest of the space created by the imaginary primaries at x = 1 and y = 1.
  • Spectral locus – The curved portion of the boundary of the horseshoe is the spectral locus. It represents all of the spectrally pure visible colors. The numbers on this line indicate the spectral wavelengths. Part of this locus falls along the line connecting the primaries because these colors have no z content. This can be seen from the tristimulus curves.
  • Magenta line – The straight line connecting red and blue shows the non-spectral mixtures of these two real colors.
  • White point – Since the three curves have been normalized to sum to 1, the equal energy point, called the white point is at x = y = z = 0.3333.
  • Blackbody locus – The black line with the numbers indicates the visual color of a blackbody radiator at the temperature indicated by the number.
  • Color differentiation – moving from any point on the chart to any other point requires changing two of the coordinates; if only x or y are changed, then z will also change. This means that if a color change is to be visible, the change must result is the change of two chromaticity values. At the red end of the horseshoe the chart indicates 650 nm but the eye is sensitive out to about 780 nm. However, beyond 650 nm, the x and y curves are nearly proportional. This is equivalent to having a change in only one value so the change in wavelength from 650 to 780 nm will result only in a decrease in brightness, not a change in color.

The actual visible colors cover a much wider range than can be displayed or printed so the chart must be taken only as a rough representation. Violet at 400 nm, for instance, is missing completely because it cannot be displayed or printed using standard phosphors, dyes or inks.