Color Perception

The properties of color which are inherently distinguishable by the human eye are hue, saturation, and brightness. While we know that the spectral colors can be one-to-one correlated with light wavelength, the perception of light with multiple wavelengths is more complicated. It is found that many different combinations of light wavelengths can produce the same perception of color. This can be put in perspective with the CIE chromaticity diagram.

The white or achromatic point E can also be achieved with many different mixtures of light, e.g. with complementary colors. If you have two illuminating sources which appear to be equally white, they could be obtained by adding two distinctly different combinations of colors. This implies that if you used them to illuminate a colored object which selectively absorbs certain colors, that object might look very different when viewed with the two different "white" lights.

The rainbow spectrum of pure spectral colors fall along t he outside curve of the chromaticity diagram. They can be described as fully saturated colors. The "line of purples" across the bottom represents colors that cannot be produced by any single wavelength of light. A point along the line of purples could be considered to represent a fully saturated color, but it requires more than one wavelength of light to produce it.

Tristimulus Values

Any color which can be produced by the primary colors blue, green, and red can be written:

where B,G,R can be considered to be "unit values" for blue, green, and red and B,G,R are the magnitudes or relative intensities of those primaries and are called "tristimulus values". Note that the "unit values" associated with B, G, and R are of different size in physical power units (watts) because the sensitivity of the eye will be different for the different primary colors. White would be

after the unit luminances are appropriately chosen. Note that if a different set of primary colors is chosen, the unit values necessary to produce white in mixture would have to be re-established. In modern color measurement the CIE tristimulus values are probably the most important.

C.I.E. Tristimulus Values

Any color on the CIE chromaticity diagram can be considered to be a mixture of the three CIE primaries, X,Y,Z. That mixture may be specified by three numbers X,Y,Z called tristimulus values. The CIE primaries are not real colors, but convenient mathematical constructs. Nevertheless, the tristimulus values X,Y,Z uniquely represent a perceivable hue, and different combinations of light wavelengths which gives the same set of tristimulus values will be indistinquishable in chromaticity to the human eye.

The derived CIE primaries and the associated color matching functions are used to calculate the tristimulus values, representing a color by

The light from a colored object is measured to obtain its Spectral Power Density (SPD) and the value for the SPD at each wavelength is multiplied times the three color matching functions and summed to obtain X, Y, and Z. These values are then used to calculate the CIE chromaticity coordinates.

The C.I.E. Chromaticity Coordinates

The CIE procedure converts the spectral power distribution (SPD) of light from an object into a brightness parameter Y and two chromaticity coordinates x,y. The chromaticity coordinates map the color with respect to hue and saturation on the two-dimensional CIE chromaticity diagram.

The procedure for obtaining the chromaticity coordinates for a given colored object involves the following:

1. Measuring its spectral power distribution (SPD) at each wavelength
2. Multiply by each of the three color matching functions.
3. Sum to get the three tristimulus values X,Y,Z (Y gives brightness).
4. Normalize the tristimulus values

The x and y are the chromaticity coordinates. Since z=1-x-y, it offers no additional information.

C.I.E. Brightness Parameter

The CIE procedure converts the spectral power distribution (SPD) of light from an object into a brightness parameter Y and two chromaticity coordinates x,y. The brightness parameter Y is a measure of luminance, which is light intensity factored by the sensitivity of the normal human eye.