Color mixture

• Prof. Rolf Kuehni, North Carolina State University

Color mixture is a colloquial term denoting mixture of direct and indirect color stimuli: lights or colorants (dyes and pigments) by physical combination, different stimuli appearing in rapid succession in the field of view, or stimuli so small that they cannot be individually resolved by the visual system. In addition, it refers to the implied mixture of percepts in the mind.

The best-known kind of color mixture and knowledge of its results, mixing of dyes and pigments, reaches back into antiquity in the work of painters and dyers. The results of mixing spectral lights were first investigated in some detail by Isaac Newton (1704) and later became the foundation of the colorimetric system. Mixture of stimuli by rapid succession in the field of view was first described ca. 170 CE in the Optics of Greek-Egyptian natural philosopher Claudius Ptolemaeus (ca.100 CE – ca. 170 CE; known as Ptolemy) (Smith, 1996). Mixture of spatially minute stimuli was probably known in antiquity from viewing mosaics or textile materials finely woven from differently colored yarn from a distance that did not allow the resolution of the colors of the individual tesserae or yarns. It became technologically important in the three-color image printing process by Jacob Christof Le Blon (ca. 1710) (Lilien, 1985) progressing to half-tone printing and display monitors.

Figure 1: Newton’s circular color diagram with spectral lights and a too-small section for non-spectral purple mixtures on the circumference. Color Y can be mixed from colors E and F and color z from color Y and colorless light stimulus O. (Newton, 1704)

All forms of color mixture rely ultimately on subjective judgments of identity or difference of color, i.e., on the operation of the color vision apparatus of color-normal observers. However, at this time there is no solid neurophysiological theory of human color experience. A form of purely subjective color mixture was proposed in the late 19th century by Ewald Hering and is based on six perceptual primaries, two achromatic: white and black, and four chromatic: yellow, red, blue, and green (Hering, 1964). All natural color percepts of the color-normal observer are considered to be the result of a single, or mixtures of two adjacent of these chromatic percepts, alone or together with one or both of the achromatic percepts.

Figure 2: CIE chromaticity diagram for the 10° standard observer. The wavelength of some spectral lights is indicated. E represents the equal energy light source.

Additive color mixture (mixture of light stimuli)

Each monochromatic light of the spectrum causes a slightly different stimulation of the color vision system but only approximately 120 different hues can be distinguished. In addition there are some further 30 hues not appearing in the spectrum, but generated by mixture in various ratios of the two lights from the ends of the spectrum. Together they form the complete hue circle.

Conventional mixture of light

In his Proposition IV of ca. 1670 Newton stated a key fact about the mixture of light stimuli: “Primitive colors can be exhibited by the composition of the neighboring colors on each side of them,” ‘primitive colors’ being those generated by monochromatic lights (Shapiro, 1984). Thus, the hue of a given monochromatic light can be matched by mixture of two nearby (in terms of wavelength) lights, one on each side of the test light: the appearance of light of a wavelength seen as having a pure green hue can be matched with lights appearing yellow-green and blue-green. The most surprising case is that an appropriate mixture of lights appearing slightly yellowish green and slightly yellowish red appears to be fully saturated yellow, indicating that in this case the pair of neighboring lights can be quite far apart on the wavelength scale. The green and the red hues involved in this mixture undergo what is known as hue cancellation.

In 1704 Newton, in his book Opticks, expressed these results in a semi-quantitative, center-of-gravity-based hue circle (Figure 1) in which the result of mixture of all hue stimuli is light appearing hueless, or white, located in the center. White is also the result of appropriate mixture of hue stimuli diametrically opposed in the diagram as well as of innumerable combinations of three and more properly selected monochromatic lights. Thus, the diagram also implicitly demonstrates the fact of color metamerism, a term for the concept that certain different spectral combinations of lights result in identical percepts. The wavelengths of diametrically opposed pairs of lights, called complementary, have been investigated in detail in the second half of the 19th century by Hermann von Helmholtz and others and were found to vary somewhat by observer. The rules, or laws, of additive color mixture were defined in 1853 by mathematician Hermann Günther Grassmann (mathematically formalized by D. H. Krantz in 1975)(Helmholtz, 1924; Krantz, 1975).

• Symmetry law: If color A matches color B, color B matches color A.
• Transitivity law: If color A matches color B and B matches C then A matches C.
• Proportionality law: If color A matches color B then xA matches xB, where x is any positive factor increasing or decreasing the radiant power to describing the physics. The reader is not prepared for this jump.</review> of the light, without spectral change.
• Additivity law: In the case of any four color stimuli A, B, C, D where A matches B and C matches D and (A+C) matches (B+D) then also (A+D) will match (B+C). These laws apply under normalized conditions of viewing for a given observer.

Figure 3: Representation of additive color mixture showing the results of partially overlapping beams of “red,” “green,” and “blue” lights.

The basis of additive light stimulus mixture is the spectral sensitivity of the three cone types responsible for human color vision (see Figure 2 in article ‘Color vision’). In the CIE colorimetric system they have been replaced with experimentally determined color matching functions that are linearly related to cone functions. In this system Newton’s color diagram is replaced by the fully quantitative chromaticity diagram (Figure 2). The horseshoe-shaped outline in the diagram is the locus of spectral stimuli. The straight line connecting the ends is the locus of the extra-spectral purple colors. The theoretical “white” light of equal power per unit wavelength interval across the spectrum (E) is located at x = 0.333, y = 0.333. Real daylight has slightly different coordinates. The chromaticity of all possible color stimuli falls on the outline or within it. Complementary stimuli lie on straight lines passing through the white point. Hues form a circle around the white point. It is evident that while it is possible to generate all hues with three stimuli where each cannot be generated by mixture of the other two, it is not possible to generate all at full spectral saturation. Lights that provide the largest gamut of stimuli are located at the two ends and near the middle of the spectrum, in terms of hues violet, green, and red. Most points in the diagram can be matched with multiple stimuli; exceptions are spectral lights in curved sections of the spectral locus. The diagram is quantitative in nature and its additive basis allows relatively simple calculation of stimuli required to match a given target stimulus. The diagram does not consider the brightness of light which requires the third dimension.

Figure 4: Enlargement of a portion of a color reproduction by halftone printing. Separate as well as overlapping dots of cyan, magenta, and yellow printing inks are visible.

The standard, simplistic, demonstration of additive color mixture is shown in Figure 3. It represents, for example, an experimental situation where white light is projected through three colored transparent filters, arranged so that on a screen the three beams partially overlap. In this case the individual lights are not of a single wavelength but mixtures that depend on the transmittance function of the filters. If the light source and the filters are appropriately selected the sum of the three beams is colorless, as shown in the center. As can be seen, mixtures of two of the lights are brighter than the single light, and even more so if all three beams are mixed. As can be seen, in this example ‘green’ and ‘red’ light mix, in the appropriate ratio, into light seen as pure yellow, blue and green mix to turquoise blue, and red and blue to magenta, all three lighter than any of its components. In all cases the stimuli of the components simply add up. In the center all hues are lost as a result of hue cancellation.

Figure 5: Enlarged image of two different kinds of LCD electronic displays, with always a red, green, and blue light forming a pixel. The light output of each source can be adjusted at 256 levels. Copyright: Peter Halazs.

Additive mixture due to rapid succession of stimuli

Colorants achieve their perceived color by reflecting light of selected regions of the spectrum and absorbing light in other regions. One way to mix the light reflected from differently painted surfaces is to place the surfaces on a disk that is made to rotate rapidly. Investigations in the 18th century (D’Arcy, 1765) showed that a disk has to rotate at least 8 times per second for the fields displayed on it to visually fuse (no longer separately visible). Disk mixture was used extensively by J. C. Maxwell in the 19th century to establish facts of color vision and mixture (Maxwell, 1860). Even though in disk mixture lights reflected from the differently painted disk surface are mixed additively, the results are somewhat different from mixtures of spectral lights because considerable portions of the light are absorbed by the paints, with the total reflected light less than the incoming light. Thus, disk mixture of sectors painted to approximate the three primaries of Figure 3 would appear to be gray, the lightness of the gray depending on the colorants used and the surround of the spinning disk.

Figure 6: Reflectance functions of a red dye applied in six different concentrations on a textile material with the reflectance function shown on top.

Additive mixture due to small size of stimuli (partitive mixture)

The best known practical examples of this effect are in image reproduction in books and newspapers (halftone printing) and on electronic display systems. But this process is also active when fabrics finely woven from differently colored yarns are viewed from a distance. This kind of color mixture was the impetus behind pointillist painting in post-impressionism (the best-known artist being Georges Seurat, 1859-1891), however with somewhat disappointing results because the viewer rarely has sufficient distance from the painting for the colored dots to fuse and if they fuse the image is often grayish because of hue cancellation. Halftone printing is not purely additive because the halftone dots on the paper are not always independent but often overlap more or less, resulting in a form of subtractive mixture in the areas of overlap. Figure 4 shows the enlargement of a portion of a halftone image, showing separate as well as overlapping dots of the three chromatic halftone primaries cyan, magenta, yellow, and black (CMYK). Complex algorithms are required to calculate the result of such combination of additive and subtractive mixture (Field, 2004).

In electronic reproduction images are separated into image elements or pixels, each one containing individually controlled mini devices in which the output of “red”, “green” and “blue” (RGB) light is controlled in 256 steps (32 bit processor). Thus, each pixel can have nearly 16 million different states of activation (not all of which are distinguishable). Pixel components are displayed against a black background either as dots or dashes too small to be individually discerned and thus they fuse additively within a pixel but also between neighboring pixels (Figure 5).

Figure 7: Presumably the first published illustrations of results of subtractive color mixture, by Moses Harris (ca. 1770). Left: mixture of yellow, red, and blue pigments (considered primaries); right: mixture of the three resulting intermediates orange, green, and purple. (Harris, ca. 1770)

Subtractive color mixture

The generally best known kind of color mixture is colorant mixture, the mixture of dyes and pigments. As mentioned, pigments are natural or artificial chemical compounds with selective reflectance or transmittance and absorption properties of light in the visible spectrum. Dyes impart specific light transmittance and absorption properties to liquids they are dissolved in or reflectance and absorption properties to substrates to which they are applied. The transmittance or reflectance properties are a non-linear function of colorant concentration. Figure 6 shows an example of the reflectance curves of a dye applied in different concentrations to a textile material. For solutions of dyes, the relationship between dye concentration, thickness of the transmitting layer, and light transmittance is approximately logarithmic, as determined by P. Bouguer (1698-1758) and A. Beer (1825-1863), known as the Beer-Bouguer law. For various reasons actual dye solutions frequently deviate somewhat from the law. The situation is more complex in case of reflecting materials. The corresponding laws have been developed by physicists P. Kubelka and F. Munk (1931) known as the Kubelka-Munk laws, and since then expanded by several authors. In case of dyes the material to which they are applied in addition to transmitting light also scatters light. Pigments themselves not only transmit but also scatter light to different degrees. As a result, the relationship between colorant, its concentration, and the reflectance function of a single colorant or its mixture with other colorants is complex and nonlinear. Both the Beer-Bouguer and the Kubelka-Munk laws are used extensively in technology for purposes of quality control and colorant formulation.

Figure 8: Illustration of a key demonstration of the difference between additive and subtractive color mixture by H. von Helmholtz (Shapiro, 1984).

The optical effect of subtractive mixture

The colorimetric results of subtractive color mixture can also be expressed in the CIE chromaticity diagram. However, due to their non-linear nature the locus of single colorants at different concentrations or of mixtures is rarely, if ever, a straight line but usually curved. The conventional representation of the result of subtractive mixture is shown in Figure 7 in the earliest published example. (Harris, ca. 1770) The left figure shows the result of appropriate mixture of yellow, red, and blue paints, the long-presumed primaries of subtractive mixture. The intermediate mixtures of pairs of these result in orange, purple, and green paints. In both cases, with appropriate mixture, the result is black-appearing paint, indicating that black can be mixed from an infinite number of combinations. A comparable result is obtained when partially overlaying three appropriately colored filters and projecting a hueless beam of light through them. The largest gamut of possible color stimuli is generated not by mixture of yellow, red, and blue subtractive primaries but by cyan (blue-green), magenta (reddish purple), and yellow, the chromatic primaries used, as mentioned, in halftone printing. However, usually black ink is also required as the three chromatic primaries tend not to form a solid black in subtractive mixture (complicated by the fact that the subtractive ‘mixture’ is obtained by sequentially printing the three inks one on top of others).

Figure 9: Idealized reflectance curves of a red and a blue dye and the reflectance curve resulting from making a mixed dyeing (Purple) containing both dyes.

Certain similarities and obvious differences have resulted in historically extended confusion about color mixture. Newton mixed powdered yellow, red, and blue pigments together and pronounced the result “whitish gray”, yet if they are appropriately mixed as paints the result, as any painter knows, is black or a shaded version of it. The common experience is that a mixture of yellow and blue paints results in a green paint. Yet if appropriate yellow and blue painted sections of a disk are optically mixed the result is a neutral gray. It was H. von Helmholtz who in the second half of the 19th century was the first to clearly explain the difference. In Part II of Physiological Optics he described an experiment in which disk mixture of sectors painted with cobalt blue and chrome yellow is directly compared to paint mixed from the two colorants (Figure 8, Helmholtz, 1924). Equal-sized outer areas a and b are painted with a yellow and a blue pigment, respectively, whereas the interior area c is painted with a mixture of the two paints. On spinning, the outer section of the disk appears pale gray, whereas the color of the inner section is, before and during spinning, a dark green. As Helmholtz stated: “Evidently, therefore, the result of mixing pigments cannot be used to deduce conclusions as to the effect of combining different kinds of light. The statement that yellow and blue make green is perfectly correct in speaking of the mixture of pigments; but it is not true at all as applied to the mixture of these lights.” (Helmholtz, 1924, Vol. 2, p. 125) The key differences between additive and subtractive color mixture are: In additive mixture the result has always a brighter appearance than any of its components because the mixture consists of more light than any component. The saturation of a given hue obtained by mixture of lights spectrally falling on both sides of the light with the hue to be mixed is either not reduced or reduced only to a small degree compared to that from the test light.

In a subtractive mixture the result nearly always has a darker appearance than any of the components. This is because each colorant absorbs a certain portion of light and the mixture reflects less light. (In exceptional cases light scattering by pigments or substrates can invalidate this claim.) The chroma of the mixture may be reduced relatively little (orange mixed from yellow and red) or substantial (purple mixed from blue and red) because in the latter case each pigment absorbs light in the area where the other pigment reflects light, as shown in Figure 9. In this figure dyes, applied at 1% each on the weight of the textile material, result in the (idealized) reflectance functions named Blue and Red. When they are applied together at 1.25% of Red and 0.75% of Blue they result in the reflectance function named Purple. It is obvious that, compared to the individual components, reflectance of light is drastically reduced and absorption has increased. As a result, the mixture is darker by about three grades of Munsell value and less saturated by about 10 grades of chroma compared to the components. It appears as a purplish dark gray. This applies comparably to the mixture of pigments. Thus, artists desiring to work with high chroma colors have found for centuries that individual pigments of a specific hue (specific reflectance properties) can have significantly higher chroma and value than mixtures of “primary” pigments.

References

• Newton, I. (1704) Opticks, London: Smith and Walford
• Smith, A. M. (1996) Ptolemy’s theory of visual perception, Philadelphia: American Philosophical Society.
• Lilien, O. M. (1985) Jacob Christoph Le Blon, Stuttgart: Hiersemann.
• Hering, E. (1964) Outlines of a theory of the light sense, translation, Cambridge, MA: Harvard University Press.
• Shapiro, A. E. (1984) The optical papers of Isaac Newton, Vol. I, Cambridge: Cambridge University Press, Proposition 4, pp. 507-508.
• Helmholtz, H. von (1924) Helmholtz’s treatise on physiological optics, 2 vols., translated, Washington, DC: Optical Society of America.
• Krantz, D. H. (1975) Color measurement and color theory II: Opponent-colors theory, J. Mathematical Psychology 12, 304-327.
• D’Arcy, P. (1765) Mémoire sur la durée de la sensation de la vue, Mémoires de l’Académie des Sciences de Paris, 439-451.
• Maxwell, J. C. (1860) On the theory of compound colours, and the relation of the colours of the spectrum, Proc. Royal Society of London 10:57-84.
• Field, G. G. (2004) Color and its reproduction, 3d ed. Pittsburgh: GATF Press.
• Kubelka, P. and F. Munk (1931) Ein Beitrag zur Optik der Farbanstriche, Zeitschrift für technische Physik 12:593-601.
• Harris, M. (ca. 1770) The natural system of colours, Licester-Fields: Laidler.

Further reading

• Berns, R. S. (2000) Billmeyer and Saltzman’s Principles of color technology, New York: Wiley. Chapter 6: Producing colors.
• Shevell, S. K. (2003) Color appearance, Chapter 4 in S. K. Shevell (ed.) The science of color, New York: Elsevier.
• Kuehni, R, G. (2005) Color, 2nd ed. Hoboken, NJ: Wiley. Chapter 8: Colorants and their mixture, Chapter 9: Color reproduction.

Sponsored by: Robert P. O'Shea, Southern Cross University, Australia

Reviewed by: Anonymous

Accepted on: 2011-01-12 17:31:52 GMT