X The trichromatic theory With Young and Fresnel, the beginning of the nineteenth century finally brought insight into the nature of light. The battle between the protagonists of corpuscular emission and of the wave theory was decided in favor of the latter. Spectral radiations could be defined by their wavelength, and puzzling phenomena like diffraction and the color of soap-bubbles could suddenly be integrated easily into one theory. Nevertheless the theory of color stagnated. That was understandable; how could the undefinable differences between the colors be explained by the unimpressive gradual differences in wavelength of the spectral radiations? Thomas Young was the only investigator who was brave enough to give an answer to this question in his 1801 Bakerian lecture: it is the retina that is responsible for the – presumably three – primary colors. It is not surprising that Young’s theory of color vision made so little impression. His ‘theory’ only consisted of a couple of paragraphs. He was quite vague about the number of primary colors, and chose red, green and violet, which was contrary to the general opinion that the primary colors were red, yellow and blue. But what chiefly prevented the acceptance of Young’s color theory was his hypothesis that color vision was a creation of the retina: that primary colors were in fact primary sensations. As he writes in one of his Lectures: It is certain that the perfect sensations of yellow and blue are produced respectively, by mixtures of red and green and of green and violet light, and there is reason to suspect that those sensations are always compounded of the separate sensations combined; at least this supposition simplifies the theory of colors: it may therefore be adopted with advantage, until it be found inconsistent with any of the phenomena; and we may consider white light as composed of a mixture of red, green and violet only, in the proportion of about two parts red, four green, and one violet, with respect to the quantity or intensity of the sensations produced [1]. Descartes would certainly have applauded Young’s hypothesis (page 56). He realized that it was absolutely unnecessary that there should be any resemblance between mechanical events in the outside world and what happens in the mind of human beings. Intensive recoding of the incoming signals takes

142 place when they pass through the special senses, are analysed in the brain, and give rise to either motor reactions or (via the conarium) representations in the mind. Of course Newton would have agreed with Young too. To convince oneself of this, one need only read what Newton wrote in his Opticks: For the Rays to speak properly are not coloured. There is nothing in the rays beyond their disposition to propagate this or that movement to the sensorium, and in the sensorium it is the sensation of these movements in the form of colors [2]. Young’s more precise statement (1801) of Newton’s idea, that each sensitive filament of the nerve can consist of three portions, one for each main color [3] that, in other words, the structure of the retina determined, or even dictated our color vision, was too far removed from naive thought to be directly comprehensible. The stagnation in color theory did not end until, in the middle of the nineteenth century, two intellectual giants, Helmholtz and Maxwell, almost simultaneously forced a breach in the situation and gave their support to Young’s theory. Helmholtz wrote about Young: When we speak of reducing the colors to three fundamental colors, this must be understood in a subjective sense and as being an attempt to trace the color sensations to three fundamental sensations. This is the way that Young regarded the problem [4]. Maxwell said the same in other words: We are capable of three different color sensations... In this statement there is one word on which we must fix our attention. That word is Sensation. It seems almost a truism that color is a sensation; and yet Young, by honestly recognizing this elementary Truth established the first consistent theory of color [5]. Helmholtz and Maxwell laid the foundations of the trichromatic theory. They received theoretical support from a scholar of equally exceptional caliber: Grassmann.

Helmholtz Helmholtz (p. 137) was one of the pioneers of the trichromatic theory. The first question he asked himself was: which three ‘primary’ spectral colors are most suitable for the composition of other colors? He discovered that he obtained the best results with two colors chosen from the ends of the spectrum

143 and one from the middle, thus green. His primary colors were therefore the same as Thomas Young’s (and Wünsch’s). He then asked himself a second question: was Young right in thinking that our color vision is built up from three primary sensations? He could not solve that problem at first. He reasoned as follows: If all colors can be composed from three primary colors, it must be possible to reproduce all spectral colors in my apparatus by mixing three well-chosen primary spectral colors. But that was not the case: the mixed colors were all less saturated than the spectral colors themselves. Therefore Helmholtz concluded that Young was wrong and that at least five fundamental sensations were necessary. And why not? Young himself had left this possibility open and had only stated that the number of fundamental sensations ‘is limited, e.g. to the three main colours’. Fortunately two men helped Helmholtz in this awkward predicament. Grassmann thought that Helmholtz had dealt too lightheartedly with Newton’s theory and gave him theoretical coaching, and Maxwell convinced him that Young had been right with his three-color theory. Grassmann Hermann Günther Grassmann (1809–1877) was a remarkably all-round scholar, of a sort which does not exist any more (7]. After a theological study he became teacher of mathematics at the Gymnasium in Stettin. He was famous in his lifetime for his linguistic studies; among other things he wrote a Sanskrit dictionary. At the age of thirty-five he wrote his Ausdehnungslehre, a book about geometrical quantities which was so difficult that it hardly received any response from the scientific world. Posthumously Grassmann is mainly remembered as the initiator of vector analysis. Directly after Helmholtz article on color mixing, Grassmann writes an article, Zur Theorie der Farbenmischung (1853) in the same journal. It is not more than 15 pages long but contains ‘Grassmann’s laws’, which form the theoretical basis of the trichromatic color theory. With all respect for Helmholtz’ experiments, Grassmann states that Helmholtz should have found more pairs of complementary colors than blue and yellow alone, and that he had mistakenly neglected the intrinsic three-dimensionality of Newton’s system. Grassmann sets himself the task of explicitly formulating the laws which are hidden in Newton’s system. He tackles the dimensionality of our color collection from the linguistic standpoint. There are only three attributes (Fig. 10.1) which can be given to color: the hue (e.g. blue, orange or violet); the intensity or brightness (which is greater for the sun than for the moon); and the saturation (which

144

Figure 10.1. Grassmann’s ‘monochromatic system’. Every color can be defined by its hue, saturation and intensity.

Figure 10.2. According to Grassmann, colors – in this illustration C and C1 – can be added like vectors. The resultant color is the long axis of the parallelogram (1853).

determines the difference between a full, blazing color and a pale, drab color). After centuries of bickering over three primary colors this was a completely new viewpoint. In fact, Grassmann was the first to emphatically propound the three-dimensionality of the color collection, although men like Lambert and Runge had prepared his path for him with their color pyramid and color globe. Grassmann was more of a physicist and thought more abstractly than the above. They had only been interested in the surface colors, so that their range of brightness ran from black to white, and maximum saturation was

145

Figure 10.3. Complementary colors according to Helmholtz. Green has no spectral complementary color (1855).

determined by the nature of the pigments. For Grassmann black was ‘the zero of light’ and brightness could increase unimpeded up to the moment of blinding [8]. He considered the spectral colors to be maximally saturated. The system in which Grassmann classified the colors is called the ‘monochromatic system’. Other than systems based on three primary colors, Grassmann’s system has only one colored variable: the wavelength of the spectral color. (Grassmann’s three variables are thus, in modern terms: dominant wavelenght, luminance and saturation). After Grassmann has arrived on linguistic grounds at his color space with three coordinates, he starts, as a mathematician, to work on the formulation of laws of color mixing. Figure 10.2 demonstrates that colors (with hue and brightness as co-ordinates) can be added like vectors. This implies that, in Newton’s color circle (with hue and saturation as co-ordinates) the barycentric rule (Fig. 5.7) applies. From the fact that calculations with colors can be made in the same way as with vectors, Grassmann deduced all sorts of rules, for example: if similar colors are added to similar colors, the resulting colors must also be similar. This is not pure mathematics, of course, and experiment must always prove

146

Figure 10.4. Helmholtz’s reconstruction of Newton’s color circle. White is not at the center; there is a long ‘purple line’ between red and violet (1866).

whether the outcome is true. Does it really signify that calculations can be made with colors? Can sums be done with secondary qualities, with sensations? Certainly not! Grassmann’s laws do not refer to color sensations but to additive mixing of physical color stimuli (see the paragraph on psychophysics at the end of this chapter). Grassmann also formulated a law on the continuity of colors. His argument was as follows: if (according to Helmholtz) yellow and indigo together produce white, a slightly warmer yellow and a slightly greener blue must also be complementary, and the whole way round Newton’s color circle complementary pairs must be encountered. Grassmann was not quite right here because there is a discontinuity in Newton’s circle, at the junction between red and violet. Newton knew that purple did not occur in the spectrum, but this fact was ignored by Grassmann, so that in 1853 he could say: The following statement can be deduced with mathematical evidence: for every [spectral] color there exists another homogeneous color which, mixed with the first, produces colorless light [9], Helmholtz made haste to investigate whether Grassmann was right (1855). He had to admit that Grassmann was right in saying that there were more spectral colors which were complementary to each other than he had first thought. These are shown in Figure 10.3. Part of the spectrum between blue-green and violet has a complementary color in the area between red and yellowishgreen. But a wide band in the spectrum, between yellowish-green and bluegreen, is complementary to purple, which does not occur in the spectrum. Helmholtz also made another discovery during this study: white was usually not formed by mixing equal proportions (equal slit-widths) of complementary wavelengths. Especially in the case of violet, little was needed to produce white when mixed with yellow. Violet appeared to have great color power. All these facts compelled Helmholtz to reorganize Newton’s color circle (Fig.

147 10.4). The complementary colors were positioned so that the lines connecting them passed through white. Violet was placed much further away from white than yellow. A long ‘purple line’ came between red and violet. This figure of Helmholtz was undoubtedly better than Newton’s color circle, but was only hypothetical, i.e., it was not supported by quantitative measurements. The quantitative measurements were to be performed by Maxwell. Limitations of Grassmann’s system Anyone who tries to apply Grassmann’s system in practice, discovers that there are countless colors – possibly most of the colors that one encounters in daily life – for which there is no room. Where should beige, brown and olive green be situated? Where should grey go? If grey is dingy white, why is the moon not grey? There is clearly a problem here (which Voigt recognized earlier, see p. 137). Grassmann’s system creates order in the colors as long as they are not influenced by their surroundings. A white object becomes grey in surroundings with a level of brightness above that of the ‘white’ object. In the same circumstances orange becomes brown and yellow becomes olive green. If a brown paper is placed on black velvet in a dark room and illuminated with a bright lamp, the paper appears to be orange instead of brown. Our color collection is thus larger than is suggested by Grassmann’s figure, which only describes the colors in the ‘aperture mode, as seen, for instance, in spectral apparatus. Grassmann thus thinks only in terms of isolated colored lights. There is a place for all of them in his three-dimensional color space, independent of the spectral composition of the color stimulus. In this chapter it is not necessary to pay attention to the surroundings (whether achromatic or chromatic). The influence of the surroundings will be considered later in our history of color (p. 240).

Maxwell James Clerk Maxwell (1831–1879) is regarded as the greatest theorist of 19th century physics [10]. As scion of a distinguished Scottish family he went to school in Edinburgh, at that time a center of intellectual activity, known as the ‘Athens of the North’. At the age of fifteen he made a mathematical discovery; he was considered too young to address a scientific meeting himself and the task was performed by his teacher and later friend Forbes. Soon the young man got permission to help Forbes in his investigations of color vision. As gentleman and amateur scientist, he divided his time, after completing his study at Cambridge, between the university (Edinburgh, London and

148

Figure 10.5. Maxwell’s electromagnetic theory of light. An alternating current i induces a magnetic field that, in its turn, induces an electric field. The electromagnetic wave is propagated with the speed of light (after van Heel & Velzel, 1967).

Cambridge) and his Scottish estate. His particular talent lay in the mathematical analysis of physical problems. From his experiments in the field of color it appears that he also had great experimental talent. Maxwell thanks his fame to the electro-magnetic theory of light. Maxwell could base his ideas on the then-known facts about electricity, which indicated a close relationship between magnetism and electricity. Faraday had just discovered that an electric current could be generated by changing the strength of a magnetic field. Maxwell framed the hypothesis that the reverse was also possible: that magnetism could be produced by changes in the strength of the electric field. On the basis of this hypothesis he obtained formulae which were so strikingly symmetrical that magnetism and electricity could not be other than closely connected. He stated that an alternating current in an aerial (Fig. 10.5) could generate an electro-magnetic wave in space with the periodicity of the current and the speed of light. The idea then followed naturally that light was an electro-magnetic vibration, with the speed which had been estimated

149

Figure 10.6. Maxwell’s color disc (from Sherman, 1981).

by Rømer (but was later much more accurately measured) and the wavelength ascribed to it by Young. This theory found little support at first. One of its few supporters was Hermann von Helmholtz, who encouraged his pupil Heinrich Herz to test the accuracy of Maxwell’s hypothesis. Herz succeeded in this after years of experimenting, and our radio is a product of the brains of Maxwell and Herz. Helmholtz was a great admirer of Maxwell, and the reverse was also true; that had begun with Helmholtz’ study of color mixing. Maxwell was already interested in color vision early in his career; he made a fundamental contribution to the theory of color vision, and was in fact the first to establish the truth of the trichromatic theory by quantitative measurement. Experiments of colour, as perceived by the eye, with remarks on colour blindness was published in 1855. Colorimetry Like Forbes, Maxwell began his study with the color top. He divided the disc into an inner and an outer ring (Fig. 10.6). The outer ring consisted of three colored sectors, the size of which could be measured on a scale calibrated to 100 on the circumference. The inner ring consisted of black

150

Figure 10.7. The ‘trichromatic system’. In the Cartesian co-ordinate system B-G-R the color C has the coordinates B, G, R.

Figure 10.8. The principle of trichromatic colorimetry. Color C can be matched by a mixture of R, G and B. When C is a very saturated color (for example spectral blue-green) C+R can be matched with G+B.

151

Figure 10.9. Maxwell’s color box (from Sherman, 1981). At the ocular a mixture of X, Y and Z (from the slits X, Y and Z) is matched with white. (from the aperture in BC).

Figure 10.10. The color triangle which transects the color space. Color C has the coefficients r, g and b.

152

Figure 10.11. Maxwell’s colorimetric data, compared with the trichromatic distribution curves of the 1931 C.I.E. standard observer (after Judd, 1961).

Figure 10.12. The spectrum locus lies outside the color triangle with spectral primaries B, G and R. In Grassmanns system color C can be specified by its dominant wavelength D and its saturation CW/DW.

153 and white. Maxwell chose for his basic colors – like Young and Helmholtz – red (vermilion), green (emerald green), and violet-blue (ultramarine). With these colors he obtained the color equation: 0.37 green + 0.27 blue + 0.36 red = 0.28 white + 0.72 black. As graphic representation he chose, like Mayer, an equilateral triangle. After much calculation he was able to situate a number of colors on this color plane. In a study with ten subjects he obtained in all cases almost identical results. When the color match had been performed and the outer and inner rings were equally grey, the comparison altered when the arrangement was viewed through a colored glass. The outer grey was therefore objectively not the same as the inner; in other words, which colors are the same is determined by the human eye (an idea which had already been expressed by Young). Maxwell had let himself be persuaded by Helmholtz (in a time when practically nobody believed that blue and yellow could produce white) that green was a suitable primary color, and Grassmann had convinced him of the three-dimensionality of color vision. But Maxwell preferred the ‘trichromatic system’ (Fig. 10.7) to Grassmann’s ‘monochromatic systems’ (Fig. 10.1) and chose red, green and blue as basic colors. As the pigments on his color top were difficult to standardize, he constructed an apparatus with which he could make color comparisons with spectral colors. Maxwell was thus the founder of colorimetry and built the first trichromatic colorimeter. What exactly takes place in colorimetry can perhaps be best explained by describing a modern colorimeter. The subject looks at a field (of diameter 2 degrees, for example), which is divided into two halves. In the right field (in the case that the field is divided vertically) he sees the color C which is to be determined; in the left field the sum of the three ‘primaries’ red, green and blue (Fig. 10.8). The subject has to adjust the amounts of red, green and blue in such a way that the left field cannot be distinguished from the right. In most cases this is possible, but sometimes the color C is too saturated to be equalled by a mixture of xR+yG+zB. In that case equalization of the fields can be achieved in another way: by adding one of the basic colors to the right-hand field. The color equation then becomes, for instance, yG+zB=C+xR, or yG+zB–xR=C. The nature of the test makes clear what a ‘negative component’ of the color C is. By the introduction of negative colors it becomes possible to reproduce every color by adding together the three basic colors. Helmholtz acknowledged this and relinquished his objections to Young’s trichromatic hypothesis. Maxwell’s colorimeter, which was built in 1856, is shown in Fig. 10.9. The slits X, Y and Z can be varied in position and width. The light from the slits is refracted by the prisms P and P0 reflected by mirror S again refracted by the prisms on the way back, and reaches ocular E via mirror e. The other

154 half of the colorimetric field is white. White light enters the colorimeter at BC and reaches the ocular via mirrors M and M0 . Maxwell repeatedly altered the position of one of the slits while the comparison with white was being made. The technique is mathematically more complicated than shown in Figure 9.9, but gives the same results. Maxwell arranged his measurements in a scheme, the color triangle. A short explanation is needed of how a color triangle is obtained. The threedimensionality of the color collection actually demands a color space with three axes. Color C in Figure 10.7 has the color coordinates R, G and B. A color triangle is obtained when the color space is cut by a plane (Fig. 10.10). In the color triangle the color C is determined by the color coefficients r, g and b. The color triangle is easier to visualize and reproduce than the color space. Brightness is intentionally left out of consideration. The color triangle only shows the ratios of the coefficients r, g and b. As in an equilateral triangle r+g+b=1, C can be determined on the plane by two variables. Maxwell made a graph of the quantities of R, G and B needed to imitate every wavelength in the spectrum. It was the first ‘calibration’ of the spectrum by the three ‘primaries’. His own data and those of his wife (K) are shown in Figure 10.11. The results have been converted by Deane B. Judd in order to be able to compare them with modern data (1961). The three curves are called ‘spectral distribution curves’. The fact that there are three of them forms the experimental proof of Young’s trichromatic theory. The negative components of the three curves can be clearly seen in the figure. In the color triangle (Fig. 10.12) it can also be seen that the spectral colors are too saturated to be able to be consistently produced by mixing two primary colors. Thus spectral bluegreen lies far outside the triangle. The color match (with three fixed primaries) was thus only possible if blue and green were on one side of the colorimetric field and blue-green, with red as negative color, on the other side. The fundamental sensation curves After Maxwell had proven that Young had been right, Helmholtz could summarise Young’s theory in the well-known scheme of Figure 10.13. The three curves of Young’s sensations (in other words: the absorption curves of Young’s three ‘sensitive retinal fibers’) have no negative components, as negative light absorption does not exist. The curves are entirely conjectural as far as their shape and the location of their maxima are concerned. On the other hand, Helmholtz’s curves should not be at variance with Maxwell’s empirical spectral distribution curves. How was one to picture negative color sensations within the framework of Young’s hypothesis? Such negative color sensations (Figs. 10.11, 10.12) arise when spectral primaries are chosen as the

155

Figure 10.13. Helmholtz 1866). There is a long-wave, a middle-wave and a short-wave receptor. The absorption curves overlap.

corners of the color triangle. When, however, angular points of a new triangle are placed outside the original color triangle, the whole spectral curve falls inside the new triangle (Fig. 10.5). The new corner – if they are well chosen – can represent the ‘fundamental sensations’ which arise when one of the three receptors is stimulated separately. As the corners lie outside the spectral curve, the corresponding sensations are virtual, ‘oversaturated’ in comparison with the spectral colors. It is possible to conjure up this ‘oversaturation’: by intensive adaptation to a complementary color. As Helmholtz expresses it: Thence it follows that there must be a series of color sensations still more saturated than those invoked by the spectrum. And, as a matter of fact, when we come to the theory of after-images, produced by fatiguing the eye by the complementary colors, we shall see how to produce color sensations beside which the colors of the spectrum look pale [11]. In this way a framework for a trichromatic theory is constructed which does justice to both Young’s hypothesis and Maxwell’s experimental findings. But it is nothing more than a framework; it needs physiological proof. And for this, it is necessary that Helmholtz’ hypothetical curves are replaced by receptor sensitivity curves obtained by experiment. These curves must be linear transformations of the distribution curves deduced by Maxwell from color mixing experiments, on the basis of which the laws of color mixing have been laid down.

156 These conditions limit the collection of possible curves considerably. But still, of all the possible only three are the curves of ‘elementary excitation’ (Helmholtz’ Elementarerregungen or Donders’ fundamental curves: the absorption curves of the three hypothetical ‘receptors’. If these curves are known, it is possible to find the precise locus of the ‘fundamental sensations’ (Helmholtz’ Grundempfindungen) in the plane of the color triangle.

Trichromatism and dichromatism More than a century ago, there was no possible means of measuring the spectral absorption of the retinal receptors and discovering directly in this way their sensitivity curves. The problem had therefore to be tackled from the other end, and a start was made with the determination of the fundamental sensations in the color triangle. It was Young who pointed the way, with his suggestion that Dalton lacked one of the color-sensitive fibers (as he thought, the red-sensitive one). Maxwell, in his turn, proved the possible truth of Young’s suggestion experimentally [12]. He examined a colorblind subject (of type Seebeck II, i.e., with shortening of the spectrum at the red end) with his color box and demonstrated that all the colors of the spectrum could be reproduced by the two spectral lights green and blue (Fig. 10.14). White could be matched by a mixture of green and blue, or by a precisely selected spectral blue-green: at that position there was a narrow ‘neutral zone’ in the spectrum, as seen by the redblind subject. Young was thus right: red-green blind persons lack one fundamental sensation; in Maxwell’s case, the sensation of red. Redgreen blind persons are dichromats: they have one less variable in their color sense than normal trichromats.

Figure 10.14. Maxwell’s spectral mixture curves from a red-blind observer (1860). All spectral colors can be matched with a suitable mixture of the primaries G and B. The spectrum has been calibrated by means of the Fraunhofer lines.

157

Figure 10.15. Helmholtz’s ‘fundamental sensations’ P, D and T in the chromaticity diagram (modified after Konig & Dieterici, 1893). The thick line represents the spectrum locus. Red-blinds confuse red with green, and white with blue-green (N0 ). The missing fundamental sensation is located at the intersection of the lines GP and N0 W, i.e. at P. Green-blinds confuse red with green, and white with N2 . They therefore lack the sensation D. Blue-blinds confuse violet with yellowish green (N3 ) Point T is located just outside the violet end of the spectrum.

Maxwell tried to locate the missing sensation in the color triangle. It had to be possible to find that point because all the lines that radiate from it in the color triangle are ‘isochromatic’. All the colors on one isochromatic line must look the same, because the distance from the color point to the point of the absent fundamental sensation can have no meaning. Let PDT (Fig. 10.15, adapted from König) be a color triangle which includes the locus of the spectral colors RGV. The color point of the absent red-receptor R must lie on the red-green line (because red and green are confused with each other) and also on the WN1 line (the line through the neutral point in the spectrum

158 and the white point). The point P lies outside the spectral plane and therefore has a higher saturation than a color on the spectral curve or the purple line. The reader will gradually be asking himself why the trichromatic theory is usually called the Young–Helmholtz theory and not the Young–Maxwell theory. There is certainly a good deal to say for Sherman’s suggestion to speak of the Young–Maxwell–Helmholtz theory. Helmholtz put the finishing touch to the job. He appreciated the significance of the dichromatism discovered by Maxwell and set himself the task of finding further evidence for Young’s theory. Ideally there should be three forms of dichromatism: red-blindness, green-blindness and violet-blindness. Helmholtz assumed that the red-greenblind persons of Seebeck’s type I were green-blind. Blue-blind persons were also reported, but there were so few of them that reliable information was not available.

Arthur König The fact that Helmholtz’s aim: to base the fundamental sensations (the corners of the physiological color triangle) and the fundamental receptor curves on the symptomatology of dichromatism, was achieved, was largely due to Arthur König [13], who continued the physiological-optical work after Helmholtz had begun to concentrate solely on theoretical physics. Arthur König (1856–1901) had, like Helmholtz, a great talent for mathematics. In 1882 he became Helmholtz’ assistant, and in 1884 professor of physiological optics at Berlin University. He was a master in the art of experimenting. Together with Conrad Dieterici he completed in 1886 the theoretical edifice whose foundation had been laid by Maxwell. The precision of their measurements was not to be surpassed until many decades later. König and Dieterici first examined a number of normal subjects in order to obtain precise calibrating of the spectrum with three primaries, and constructed on the basis of these data a color triangle with a spectral curve. Then they calibrated the spectrum of green- and red-blind persons and looked for the isochromes and their point of convergence in both groups. The convergence point of the isochromes in blue-blindness was dubious, but had to lie somewhere close to the blue or violet part of the spectral curve. The physiological color triangle is shown (slightly updated) in Figure 10.15. It can be seen that the fundamental sensation P, which is lacking in red-blind persons, is oversaturated red with a touch of purple. The missing fundamental sensation in green-blind persons (point D) lies far outside the spectral curve and is very strongly oversaturated. König and Dieterici were not able to localize point T; in Figure 10.15 it has been added on the grounds of later experiments.

159

Figure 10.16. The three fundamental curves (Helmholtz, 1896). W1 , W2 : spectral sensitivity of the ‘warm’ color receptor, respectively in green-blinds and red-blinds. K: the receptor of the ‘cold’ colors in the red-green blind. Abscissa: wavelength. Ordinate: tristimulus values. The surfaces under the three curves has been made equal.

With these data and some calculations, König and Dieterici were able to convert the spectral distribution curves, which they had obtained from normal subjects, to the three hypothetical sensitivity curves R, G and B (Fig. 10.16) of the three receptor types. (W1 and W2 are the ‘warm’ – longwave – curves of the red- and green-blind subjects, respectively.) It has later appeared that the three curves, found by indirect means, only differed slightly from the spectral absorption curves found by a direct method in the middle of the twentieth century. The trichromatic theory may certainly be regarded as a magnific creation of human ingenuity. It was essentially the creation of Maxwell and Helmholtz. Anomalous trichromatism With Maxwell and Helmholtz’ trichromatic theory, the two forms of redgreen-blindness became the pillars of the theory of color vision. Seebeck (p. 132) had also signalized the existence of a number of persons with a slight disturbance of color vision. It was to take nearly fifty years for any insight to be obtained into this (congenital and hereditary) ‘color weakness’. John William Strutt, Lord Rayleigh (1842–1919) was one of England’s most important physicists. His investigations of sound and light are classic. He was the first to explain why the sky is blue: through dispersion of light in

160 the upper atmosphere, where it is mainly the shortwave rays which are reflected (the blue sky is the opposite of the red sunset, where it is the unreflected, longwave rays which are seen). In 1882 he published Experiments on Colour in which he demonstrated that there are great differences in the proportions of red and green light needed to produce yellow in persons with (as it seemed) normal color vision. He let his subjects match spectral yellow with a mixture of red and green. Subjects with ‘anomalous color vision’ needed either too much red or too much green to match the yellow. All but one of his subjects had ‘normal color vision’. Franciscus Cornelis Donders (1818–1889), the most important Dutch physician in the nineteenth century (famous through his monograph On the Anomalies of Accommodation and Refraction in the Eye) repeated Rayleigh’s experiment and found that persons with an abnormal red-green ratio matching yellow, formed a separate group with variable degrees of reduction in their ability to distinguish colors [14]. They were, in fact, the ‘color-weak’ subjects described by Seebeck. König and Dieterici demonstrated that one of the three fundamental curves runs an abnormal course in persons with ‘green weakness’ (who need more green than normal to make the color equation). The green curve is shifted in the direction of the red curve. In persons with the less common ‘red weakness’ the red curve is shifted in the direction of the green curve. Rayleigh’s and Donders’ experimental method, embodied in Nagel’s anomaloscope (1907), is still used to verify the diagnosis of anomalous trichromatism and dichromatism. It was also Nagel who introduced the terms ‘protanomaly’ and ‘deuteranomaly’ for red and green weakness respectively.

Psychophysics The reader who leafs back in this book will be amazed at the giant strides with which color theory in a couple of decades became a branch of exact science. The trichromatic theory was able to make astounding statements about the function of the retina, while at that time knowledge of the retina had not progressed very far. In this paragraph we shall try to get our breath back and pay attention to the scientific context in which color theory was able to develop in this way. The problem which we have to consider, is: how can one possibly localize ‘fundamental sensations’ on a piece of paper and make complicated calculations with them? The science that claimed that it could quantify and make calculations with psychological, perceptual, data, was given the name ‘psychophysics’. We have to ask ourselves what this new science really signifies.

161 The evolution of color science in the second half of the last century is the result of the introduction of quantitative methods. If one wants to make calculations with colors, as Grassmann and Maxwell did, one has to work with precisely defined colors. The two most important steps in that direction had been taken: Helmholtz had pointed the way to working with monochromatic (spectral) light, and Young’s work had indicated how the spectral colors could be specified by their wavelengths. How to quantify a certain amount of color was an unsolved problem at that time, but it was possible to cope by always using the same source of light (the sun), which might or might not be reflected by a white surface, and by reading off the amount of light on an arbitrary scale: the slit-width of the spectral apparatus. The scales covering the three calibration lights could be adjusted so that white was composed of equal parts of red, green and blue. (The areas under König’s R, G and B curves are therefore all the same). It is important to realize what one is doing when working with quantitative methods in color science, because ‘calculating with colors’ is a paradoxical occupation. Colors are – according to Young and, in fact, almost everyone – sensations. Can sensations, psychological qualities thus, be added, subtracted, or treated like vectors, as if they were physical powers? With these questions, we come face to face with the ‘psychophysical problem’, the relationship between the physical and the perceptual. Color theory is an interdisciplinary science with elements of physics, biology and psychology. There are therefore great methodological problems. Natural science is interested in the anatomy and physiology of the organism, and is far advanced in the quantitative analysis of the physico-chemical processes which are the foundation of color vision. Psychology studies a wealth of subjective color phenomena, which can be described but are practically inaccessible to quantitative analysis. Thus natural science and psychology produces two flows of valuable information, which are recorded in two different languages. The problem of communication between science and psychology is often underestimated. In the previous century, when natural science made a great leap forwards, a well-known physicist put forward the proposition that all real knowledge is based on measurement. When the science of the special senses also began to flourish, it was natural that, thinking along physical lines, perceptual qualities, like the colors, should also be regarded as measurable. It was the physicist Fechner who laid the foundations of a new science: psychophysics. Gustav Theodor Fechner (1801–1887), professor in Leipzig, was both a hard-headed physicist and a romantic with touches of mysticism. His philosophical starting-point was ‘psychophysical parallelism’: in the science of the

162 special senses, the same process can be described ‘from the inside’ by the psychologist and from the ‘outside’ by the physicist. He found that the processes thus had a ‘diurnal’ and a ‘nocturnal’ aspect (Die Tagesansicht gegenüber der Nachtansicht, 1879). In this line of reasoning of psychophysical parallelism it is clear that psychological issues can be subjected to quantitative treatment in the same way as material issues. Fechner made it his aim to prove this. He had the support of experiments carried out by his colleague Ernst Heinrich Weber (1795–1878). Weber had investigated what the difference in weight between two weights must be for it to be just perceptible (1834). He discovered that the difference was not constant, but became proportionally greater as the weights being compared became heavier. If it was possible to distinguish between weights of 20 and 25 grams, it was also possible to distinguish between weights of 200 and 250 grams. According to Weber the same law applied to sound, and for light it had already been discovered by Bouguer in 1729. From Weber’s law Fechner deduced his basic psychophysical law, which states that the magnitude of the sensory sensation is proportional to the logarithm of the power of the sensory stimulus. Fechner presented his psychophysical formula and its mathematical derivation in a book with the mystical title: Zendavesta, oder über die Dinge des Himmels und des Jenseits vom Standpunkt der Naturbetrachtung (1851). Fechner’s basic psychophysical law has not survived. It has a weak theoretical basis and experimental data often fail to agree with its premises. Weber’s law is to a large extent applicable to color science, but only as an indication of an empirical relationship between color stimulus and color sensation. Thus little remains of the quantification of mental experiences (although magnitudes may to a certain degree be estimated). It is not surprising. How can one say that one rose is three times as red as another? That is an assertion which has no meaning. On these grounds, psychophysics might well be thought to have little chance of survival. But that is not the case: it is a flourishing branch of science which, in the field of color, as elsewhere, has produced an inestimable wealth of information, and is still doing so today. The fact that this is possible is the result of a simple agreement: on the physical side one may quantify as much as one likes, but on the psychological side one is restricted to fundamental categories of quality: identity and difference. If this is the starting-point, two perfectly legitimate questions regarding color science may be asked: 1. The question of identity. Which physically different, quantified stimuli produce an identical sensation? The procedure is a subjective comparison of stimulus patterns. In this way Newton discovered the existence of metameric colors. It is the method of colorimetry, as introduced by Maxwell.

163 2. The question of difference: how much difference must there be between physical stimuli for the difference to be just discernible? This procedure is the determination of threshold values, which will be considered later in this book (p. 196). It is important to realize that the person being tested is not asked to give a verbal account of his subjective feelings. Registration of his actions, for instance the turning of a knob, is sufficient. Exact psychophysics is really a sort of animal psychology, psychology which is not directed towards feelings but towards behavior; the eye functions in psychophysics as a ‘null-instrument’. The question asked at the beginning of this chapter: can one calculate with colors?, must be answered in the negative. In psychophysics, attention is not focussed on the quality of colors as such, but on the stimuli which produce identical qualities, which are thus metameric. When one speaks of the ‘laws of color mixing’, one really means the ‘laws of the synthesis of color stimuli’. The corners of the triangle in Figure 10.16 are actually the (virtual) stimuli, each of which starts a single physiological process in the organ of sight. König defined Helmholtz’ Grundempfindungen as follows: A fundamental sensation is a sensation which corresponds to a simple (not by any further stimulus decomposable) process in the periphery of the optic nerve [15]. To our ears that sounds strange, but in nineteenth-century Germany there was no sharp cartesian distinction between extensio and cogitatio. The divorce of physiology and psychology was still very incomplete. In 1873 Wilhelm Wundt, the ‘father of experimental psychology’, still equated the boundary between the physical and the perceptual with the boundary between sensation and perception. Aubert and Mach: color as subjective quality The tremendous success of the trichromatic theory had as result, that few voices were heard declaring that color sensations were really psychological qualities, which should be analysed on their own merits. Hermann Aubert, physiologist in Halle, wrote in 1864 in his Physiologie der Netzhaut: There can be no doubt that our color sensations are entirely different from their objective causes and the processes in the nerves ... Thus the sensations alone remain. If we are to reach an agreement about them, the following words are sufficient for the main specification of our sensations: black, white, red, yellow, green and blue, which I therefore call the principal sensations or principal colors. They are the same sensations which Leonardo da Vinci called ‘simple colors’ [16].

164 Ernst Mach, from 1870 professor of physics in Prague, said in 1865 exactly the same thing. Analysis of color sensations led him also to the specification of four principal colors and white and black. Speaking of white, he said: Even if several excitations in the retina correspond to it, the last process in the physiological chain, which causes the single sensation of white, must – like the sensation – be thought of as single [17]. And sensations are ‘the ultimate elements of reality’ for Mach [18]! That does not prevent him from adhering to the ‘heuristic principle of psychophysical investigation’: that every psychical event corresponds with a physical event (and vice versa). It was Ewald Hering, longtime professor of physiology in Prague, who was to consistently apply Mach’s heuristic principle, and elaborate the idea of the singularity of white (and the four main colors) into a completely new theory of color vision.