14 development of the basic ideas of the duplicity theory
2.5 Conclusions
By his universal colour theory, his ideas of visual information processing and his model of colour mixture, Newton laid a solid foundation for the further development of our understanding of both cone and rod functions. All three contributions had profound influences on later theory construction within vision research.
Obviously, without his basic assumption that white sunlight consists of innumerable different rays, it would be impossible to develop any adequate theory about the light reception mechanisms in the retina.
Also, his theory about visual information processing (which he himself considered highly speculative) had profound influence. In fact, the suggestion that different colour-related processes behaved independently of each other remained dominant for more than two centuries, and the suggestion that sensory quality originated in the brain and that the processes in the peripheral visual pathways only differed quantitatively are still generally accepted.
The third major contribution (his ingenious model of colour mixture, where he applied his principle of gravitation to describe the colour-mixture data) paved the way for Maxwell’s discovery of the triplicity of colour vision. It also allowed the prediction that the primary colour-related processes would behave independently of each other in the light reception process. It is important to note, however, that the colour-mixture data obtained did not prove Newton’s assumption that different colour-related processes remained independent of each other during the whole journey from retina to brain as several vision research workers later mistakenly believed (see Wright, 1946, pp 146–152).
2.6 Young’s colour theory: three instead of seven primaries
Newton did not present any strong argument in support of his assumption of seven primary colours and it was challenged by the well-known fact that painters could produce any object colour by
the newton tradition 15
mixing only three pigment colours: red, yellow and blue, called the three primaries (green was in general assumed to represent a secondary colour, since it could be produced by mixing blue and yellow). There have been many attempts to explain this apparent triplicity of colour vision. Weale (1957) has given an interesting account of trichromatic ideas in the seventeenth and eighteenth centuries. He emphasizes the theories of Lomonosow and Palmer, proposed in 1756 and 1777, respectively. They both suggested that there were three different types of light and three different types of retinal molecule. Each type of retinal molecule was thought to be activated by its analogous type of ray, giving rise to red, yellow and blue sensations
Given the enormous authority of Newton and his convincing experiments, it appears surprising that both Lomonosow and Palmer opposed his basic assumption that white light from the sun is a mixture of innumerable kinds of different rays that are linked to different hue sensations (see Newton, 1671/1672, props. 1, 2 and 7). The acceptance of Newton’s assumption leads to a quite different explanation of the triplicity of colour vision. Thus, it would follow that the essential cause of the apparent triplicity should be sought for solely in the visual system. This lead was followed by Young (1802a), who was well acquainted with Newton’s ideas. He suggested that there existed three different kinds of particle or resonator in the retina which were maximally sensitive to different wavelengths. The activity of the different resonators was assumed to be independently conveyed to the sensorium and there give rise to three different kinds of colour sensations. At first, he assumed that the three primary activities gave rise to red, yellow and blue in the brain (Young, 1802a), but later he chose red, green and violet colours as primaries (Young, 1802b, 1807).
Yet, as pointed out by Helmholtz (1852), the finding by artists that all object colours may be reproduced by mixing red, yellow and blue pigments could not be a basis for colour theory construction, since the composition of the spectral lights reflected from pigments could not be adequately controlled. Thus, as already explained by
16development of the basic ideas of the duplicity theory
Newton (1730, pp.179–185, 245–288), a pigment may absorb, transmit and reflect the spectral lights that fall upon it and when two pigments are mixed, the new compound pigment reflects and transmits only those rays that are not absorbed by each of the two pigments. This complexity, of course, prevented an adequate control of the spectral composition of the light that entered the subject’s eye. Moreover, both Newton (1730, pp.132–134) and Helmholtz (1852) stressed that the experimenter could not control the composition of the spectral lights by the apparent colour of the pigment either, since the same colour sensation could be a composite of different spectral lights (the metamerism of colours).
On the other hand, when monochromatic prismatic lights were mixed and focused on the retina, the different rays that entered the eye were combined additively and could easily be controlled and varied by the experimenter. Thus, as was first clearly explained by Newton (1730) and later by Helmholtz (1852), mixing of pigments and mixing of spectral lights generated a subtractive and an additive result, respectively.
Another serious problem confronting the trichromatic colour theory of Young (1807) was the observation of Helmholtz (1852) that monochromatic spectral colours could not be reproduced by mixing three primary spectral lights. Thus, he found that prismatic yellow and blue colours could not be matched by mixing, respectively, red and green, and green and violet lights. The spectral colours were found to be more saturated than the mixtures. Adding another primary to the mixture would only enhance the saturation differences found. Helmholtz (1852) concluded that there had to be at least five so-called primary colours.
2.7 Maxwell: triplicity of colour vision proved
The results of Maxwell’s (1855, 1860) colour matching experiments, however, showed this conclusion to be wrong and the trichromatic colour theory of Young to be on the right lines. Maxwell’s treatment
the newton tradition 17
of his experimental results was based on Newton’s ideas of colour mixture. Thus, he presumed that the method of determining the position and strength of the resultant colour of mixed lights is mathematically identical to that of finding the centre of gravity of weights and placing a weight equal to the sum of the weights at the point so found. This presumption presupposes that colour mixing is additive. If, for example, the same light is added to or subtracted from both test and comparison fields, which have been matched with respect to all colour aspects, it is assumed that the match will still hold; or if two matched lights (A and B) are added to two other matched lights (C and D), the result is two lights that match, that is, (A + C) match (B + D). As Helmholtz (1855, p. 24) puts it, ‘Gleich aussehende Farben gemischt geben gleich aussehende Mischungen’ (mixing equally appearing colours gives equally appearing mixtures). Hence, Maxwell (taking account of Newton’s laws of gravitation) could express his colour-mixture results algebraically in the form of equations with the colour under test on one side of the equation and the mixture of three standard lights (red, green and blue) on the other.
Thus, Maxwell (1860) first made a colour match between a mixture of his standard red, green and blue lights and a constant reference white. He then replaced one of the standard primaries by the monochromatic spectral light to be studied, and a new match of the constant white was made. Now he had two equations for the match of the same standard white and could subtract one from the other to obtain the equation of the unknown spectral light investigated. By this procedure, Maxwell (1860) discovered that the colour effects of all monochromatic spectral lights could, in fact, be matched by using only three primaries. Hence, he had proved that the retinal colour response to spectral lights must involve a triplex mechanism. Since there was no histological evidence for such a triplex mechanism at the time, the triple subdivision had to occur on a sub-microscopic scale.
His mathematical treatment was as follows:
Given that the three standard lights are denoted R, G and B, white sensation W, the spectral light to be studied S and a, b, c,
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d and e are measurements of normalized light intensity, then the chromaticity of the unknown spectral light f(S) may be calculated. Thus when for instance:
a(R) + b(G) + c(B) = W = d(R) + e(G) + f(S), then a(R) + b(G) + c(B) = d(R) + e(G) + f(S) and
f(S) = (a – d)(R) + (b– e)(G) + c(B)
(It should be noted that the equals sign, ‘=‘, reads; ‘is matched by’.)
As will be seen, the application of Newton’s law of gravity made allowance for an algebraic treatment of the colour-mixture data and, hence, for the use of negative values of standard lights. The problem pointed out by Helmholtz (1852), that monochromatic spectral lights are too saturated to be matched by a mixture of primaries, could then be resolved on the assumption that each of the three receptors is activated by a large part of the spectrum. The mixture of two or three primaries may, therefore, activate the white component mechanism more than monochromatic spectral lights and, hence, be less saturated. In accord with this assumption, Maxwell (1860) showed that by adding one of the three standard lights to the spectral test light it could be desaturated (i.e. the white component of the spectral test light could be increased) to such an extent that it could be matched by the mixture of the two other standard lights.
The evidence provided by Maxwell (1855, 1860) was generally taken as conclusive evidence in favour of the basic assumption that the central fovea contains three different types of receptor. Thus, it was argued that if colours were determined by the relative activity of three independent receptor processes in the retina, then, by the use of three standard stimuli, one should be capable of stimulating the receptor systems in all possible combinations and, thereby, reproducing any of the spectral colours as demonstrated by Maxwell (1855, 1860).
Maxwell adduced further strong evidence in favour of the triplicity of the normal retina by demonstrating that a protanope (‘red’-colour-blind) could match every colour in the spectrum by using only two primaries. In fact, his results suggested that the protanope
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520
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540 |
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560 |
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0.5 |
580 |
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490 |
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480 |
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620 |
470 |
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r
Fig. 2.2 Chromaticity coordinates of monochromatic spectral lights measured at the central fovea in a dark-adapted state and expressed in the WDW (i.e. W. D. Wright) diagram. Thus, the data points are plotted in terms of the matching stimuli 650, 530 and 460 nm and the normalized units are based on matches of 582.5 and 494 nm. That is, the amount of the 650 nm and 530 nm stimuli required to match 582.5 nm were regarded as equal, as were the amounts of 530 nm and 460 nm stimuli required to match 494 nm.
had a reduced form of colour vision in that the red mechanism was lacking (Maxwell, 1855, 1860, 1872).
On the basis of his discovery that all spectral lights can be matched by using only three standard lights, and by using Grassmann’s (1853) vector diagram for representation of resultant colours, Maxwell (1860) could present his colour matching results graphically in a two-dimensional colour space by an equilateral triangle (the Maxwell colour triangle). (Fig. 2.2 gives an example of a modern representation of colours of monochromatic spectral lights in a two-dimensional colour space.)
The conclusions of Maxwell (1855, 1860) departed from the colour theory of Newton in two important respects: (1) He made use of only three primaries, and (2) he found the essential cause of