About 8% of men and 0.4% of women have deficient colour vision, called colour blindness. Some people have fewer than three types of cones; some people have cones with altered spectral sensitivities.

Spectral properties can be measured in electron volts (eV); the visible spectrum encompasses the range from 3.1 eV to 1.6 eV. Sometimes wave number, the reciprocal of wavelength is used, ordinarily expressed in cm-1.

Bill Schreiber points out that the words saturation and purity are often used interchangeably, to the dismay of purists.

Fundamentals of vision

As I explained in Retina, on page 247, human vision involves three types of colour photoreceptor cone cells, which respond to incident radiation having wavelengths (λ) from about 380 nm to 750 nm. The three cell types have different spectral responses; colour is the perceptual result of their absorption of light. Normal vision involves three types of cone cells, so three numerical values are necessary and sufficient to describe a colour: Normal human colour vision is inherently trichromatic.

Power distributions exist in the physical world; however, colour exists only in the eye and the brain. Isaac Newton put it this way, in 1675:

“Indeed rays, properly expressed, are not coloured.”

Definitions

On page 27, I outlined brightness, intensity, luminance, value, lightness, and tristimulus value. In Appendix B,

Introduction to radiometry and photometry, on page 573, I give more rigorous definitions. In colour

science, it is important to use these terms carefully. It is especially important to differentiate physical quantities (such as intensity and luminance), from perceptual quantities (such as lightness and value).

Hue is the attribute of a visual sensation according to which an area appears to be similar to one of the perceived colours, red, yellow, green, and blue, or

a combination of two of them. Roughly speaking, if the dominant wavelength of a spectral power distribution shifts, the hue of the associated colour will shift.

Saturation is the colourfulness of an area, judged in proportion to its brightness. Saturation is a perceptual quantity; like brightness, it cannot be measured.

Purity is the ratio of the amount of a monochromatic stimulus to the amount of a specified achromatic stimulus which, when mixed additively, matches the colour in question. Purity is the objective correlate of saturation.

Figure 25.2 Spectral and tristimulus colour reproduction. A colour can be represented as a spectral power distribution (SPD), perhaps in 31 components representing power in 10 nm bands over the range 400 nm to 700 nm. However, owing to the trichromatic nature of human vision, if appropriate spectral weighting functions are used, three components suffice to represent colour. The SPD shown here is the CIE D65 daylight illuminant.

31 Spectral reproduction (31 components)

The more an SPD is concentrated near one wavelength, the more saturated the associated colour will be. A colour can be desaturated by adding light with power distributed across the visible spectrum.

Strictly speaking, colorimetry refers to the measurement of colour. In video, colorimetry is taken to encompass the transfer functions used to code linear RGB to R’G’B’, and the matrix that produces luma and colour difference signals. Colorimetry is spelled without u, even in England and Canada.

Spectral power distribution (SPD) and tristimulus

The physical wavelength composition of light is expressed in a spectral power distribution (SPD), also known as spectral radiance. An SPD gives radiance [W·sr-1·m-2] or relative radiance as a function of wavelength, symbolized λ [nm]. An SPD representative of daylight is graphed at the upper left of Figure 25.2.

One way to reproduce a colour is to directly reproduce its spectral power distribution. This approach, termed spectral reproduction, is suitable for reproducing a single colour or a few colours. For example, the visible range of wavelengths from 400 nm to 700 nm could be divided into 31 bands, each 10 nm wide. However, using 31 components for each pixel is an impractical way to code an image. Owing to the trichromatic nature of vision, if suitable spectral weighting functions are used, any colour on its way to the eye can be described by just three components. This is called tristimulus reproduction.

The science of colorimetry concerns the relationship between SPDs and colour. In 1931, the Commission Internationale de L’Éclairage (CIE) standardized weighting curves for a hypothetical Standard Observer. These curves – graphed in Figure 25.5, on page 271 – specify how an SPD can be transformed into three tristimulus values that specify a colour.

Pronounced meh-ta-MAIR-ik and meh-TAM-er-ism.

For a textbook lowpass filter – but in the signal domain – see Figure 20.23 on page 212.

To specify a colour, it is not necessary to specify its spectrum – it suffices to specify its tristimulus values. To reproduce a colour, its spectrum need not be reproduced – it suffices to reproduce its tristimulus values. This is known as a metameric match. Metamerism occurs when a pair of spectrally distinct stimuli have the same tristimulus values.

The colours produced in reflective systems – such as photography, printing, or paint – depend not only upon the colourants and the substrate (media), but also on the SPD of the illumination. To guarantee that two coloured materials will match under illuminants having different SPDs, you may have to achieve a spectral match.

Spectral constraints

The relationship between spectral distributions and the three components of a colour value is usually explained starting from the famous colour-matching experiment. I will instead explain the relationship by illustrating the practical concerns of engineering the spectral filters required by a colour scanner or camera, using

Figure 25.3 opposite.

The top row shows the spectral sensitivity of three wideband optical filters having uniform response across each of the longwave, mediumwave, and shortwave regions of the spectrum. Most filters, whether for electrical signals or for optical power, are designed to have responses as uniform as possible across the passband, to have transition zones as narrow as possible, and to have maximum possible attenuation in the stopbands. At the top right of Figure 25.3, I show two monochromatic sources, which appear saturated orange and red, analyzed by “textbook” bandpass filters. These two different wavelength distributions, which are seen as

different colours, report the identical RGB triple

[1, 0, 0]. The two SPDs are perceived as having different colours; however, this filter set reports identical RGB values. The wideband filter set senses colour incorrectly. At first glance it may seem that the problem with the wideband filters is insufficient wavelength discrimination. The middle row of the example attempts to solve

that problem by using three narrowband filters. The narrowband set solves one problem, but creates

3. CIE-based LMS filter set

What I call the Maxwell-Ives criterion is sometimes called Luther-Ives, or just Luther. In my view, James Clerk Maxwell and Herbert E. Ives mainly deserve the credit.

CIE 15 (2004), Colorimetry, 3rd Edition (Vienna, Austria: Commis-

x, y, and z are pronounced

ECKS-bar, WYE-bar, ZEE-bar.

Some authors refer to CMFs

as colour mixture curves, or CMCs. That usage is best avoided, because CMC denotes a particular colour difference formula defined in British Standard BS:6923.

them. A camera that meets this requirement is said to conform to the Maxwell-Ives criterion.

The famous “colour-matching experiment” was devised during the 1920s to characterize the relationship between physical spectra and perceived colour. Today, we might seek the best approximation to the spectral sensitivities of the cone photoreceptor cells. Those functions are illustrated at the bottom of Figure 25.3, and they are graphed at larger scale in Figure 25.5. Different researchers prefer slightly different versions of these functions; the ones shown here are the Hunt-Pointer-

Estévez (HPE) cone fundamentals.

The CIE did not attempt to directly determine the responses of the cone cells. Instead, theirs was an indirect experiment.that measured mixtures of different spectral distributions that are required for human observers to match colours. In 1931 the CIE took data from these experiments, transformed the data according to certain mathematical principles, and standardized

The CIE curves are called the x(λ), y(λ), and z(λ) colour-matching functions (CMFs) for the CIE Standard Observer, and are graphed in Figure 25.5. They are defined numerically; they are everywhere nonnegative.

The term sharpening is used in the colour science community to describe certain 3× 3 transforms of cone fundamentals; the “sharpening” is in the spectral domain. I consider the term to be unfortunate, because in image science, sharpening more sensibly refers to spatial phenomena.

The CIE 1931 functions are appropriate to estimate the visual response to stimuli subtending angles of about 2° at the eye. In 1964, the CIE standardized a set of CMFs suitable for stimuli subtending about 10°; this set is generally not appropriate for image reproduction.

The functions of the CIE Standard Observer were standardized based upon experiments with visual colour matching. Research since then revealed the spectral sensitivities of the three types of cone cells – the cone fundamentals. We would expect the CIE CMFs to be intimately related to the properties of the retinal photoreceptors; many experimenters have related the cone fundamentals to CIE tristimulus values through 3× 3 linear matrix transforms. None of the proposed mappings is very accurate, apparently owing to the intervention of high-level visual processing. For engi-

neering purposes, the CIE functions suffice.

_ _

The y(λ) and z(λ) CMFs each have one peak – each is

_

“unimodal.” However, the x(λ) CMF is bimodal, having a secondary peak between 400 nm and 500 nm. This “bump” does not directly reflect any physiological