Topic 45. Hue, Saturation and Intensity

As we saw in the previous topic, when a beam of light containing many wavelengths strikes the eye, its response is not given by the sum of the responses that would be produced by each one of the component wavelengths acting alone. Although there are many different distributions of wavelengths that can be observed, our characterization of the appearances of these distributions can be expressed using a relatively small number of parameters. That is, there are many different combinations of wavelengths which appear to produce the same visual color.

Although a number of different methods can be used to characterize a combination of wavelengths, it turns out that all of them use either 3 or 4 parameters. This is not an accident, since this small number of parameters is related to the way the eye perceives color. The simplest triplet of parameters are called hue, saturation and intensity.

If we break up a beam of light into each of its component wavelengths and if we plot the intensity of each component as a function of wavelength, then, loosely speaking, the hue is the peak of this plot – the wavelength (or relatively small band of wavelengths) which has the greatest intensity. The hue is generally the single word that we would use to describe a composite color. Hue values range from about 440 nm for violet, 450 nm for blue, up to about 700 nm for red light. The names associated with different hues follow the spectral decomposition of a rainbow: red, orange, yellow, green, blue, and violet. These descriptive colors are associated with ranges of wavelengths rather than with unique values, and some people can see colors outside of this conventional range of wavelengths (ultra-violet with a wavelength shorter than violet or infra-red with a wavelength longer than red).

The saturation of a beam of light is related to the width of the plot of intensity vs. wavelength described above. A completely saturated beam would have only one wavelength and would be called monochromatic, which a completely unsaturated beam would contain all wavelengths in equal proportion and would appear white. A completely saturated beam therefore has a very narrow intensity distribution function (possibly consisting of only one non-zero value in the limit), which a completely unsaturated beam has a very wide distribution function, possibly consisting of a constant value over most or all of the visible spectrum.

The intensity is related to the strength of the light beam. Intensity is very tricky to specify because the apparent brightness and the actual brightness can differ significantly. Loosely speaking, intensity is related to the total power in the light beam as measured by some objective instrument (such as a photographic light meter), but the perceived brightness of a light (or lightness of a surface) is strongly influenced by lots of other factors and cannot always be specified objectively.

These parameters are often not independent of each other. For example, the intensity and hue of a standard light bulb are related through the black-body relationships – decreasing the output intensity of a black body also shifts the hue towards longer wavelengths.

The hue, saturation and brightness of a light beam are often specified using a three-dimensional color tree, as shown below. The vertical axis of the tree specifies the intensity of the beam, from nothing at the bottom (that is, black) through gray to some maximum value at the top corresponding to the brightest possible white. At each level of the tree (which corresponds to a given lightness or brightness), we draw a circle whose circumference shows the various pure, fully saturated, monochromatic colors of the rainbow in wavelength order from red to violet. The points on a radius line from the center of the tree to some point on the circumference represent different unsaturated colors formed by mixing some amount of white from the center of the tree with some amount of the color at the end point of the line.