TRICHROMACY AND OPPONENCY

Figure 3.1. Responses of the three human cone types to light of different wavelengths. Please note that the points where the curves cross depend on the way the data is presented - these curves are normalized to have peak sensitivity at the same level. Image source:
Maxim Razin, after Bowmaker J.K. and Dartnall H.J.A., "Visual pigments of rods and cones in a human retina." J. Physiol. 298: pp501-511 (1980). http://commons.wikimedia.org/wiki/Image:Cone-response.png

Why three primaries? Well, the number three comes ultimately from the fact that there are three kinds of colour-discriminating receptor cells, called cones, in the human retina. This trichromatic model of colour vision was in fact first prompted by the evidence of the three painter's primaries. The three cone types have broadly overlapping ranges of sensitivity, and are designated L, M and S according to the location of their peak sensitivities in the long, medium and short wavelength parts of the spectrum respectively (Figure 3.1). We will see in a later section exactly how these three cone types result in our three primary colours.

The continuous circular arrangement of hues, on the other hand, is believed to derive from the way the inputs from these three cone types are subsequently processed. According to the widely held opponent model of colour vision, proposed in the late nineteenth century by Ewald Hering and subsequently quantified in particular by Hurvich and Jameson (1957), inputs from the three cone types are added and subtracted together to create three signals: total brightness, redness vs greenness (r/g), and yellowness vs blueness (y/b). All the hues we experience are thought to result from the various possible combinations of positive and negative r/g and y/b signals (Figure 3.2).

Figure 3.2. Brightness ("achromatic"), y/b and r/g opponent signals for light throughout the spectrum. Hurvich and Jameson showed that by using a blue or yellow AND a red or green light they could match by hue cancellation all wavelengths of the visible spectrum, thus determining quantitatively the r/g and y/b components of the colour sensation induced by each wavelength. Image source: http://webvision.med.utah.edu/imageswv/KallColor15.jpg

The broad outline of the opponent model seems firmly founded based on the evidence (1) that there are just four unique hues - hues that we can experience as unmixed with other colours, and (2) that these four are arrayed in these opponent pairs, such that no colour can be red and green, or yellow and blue, at the same time. Details of the neurological mechanisms enabling this process are still uncertain however, and earlier claims of discoveries in this area are now disputed.

Different sources vary somewhat on the way the visual system calculates opponent signals, but Kuehni (2005) gives the following account as representative (other sources give brightness as L+M+S).

• Brightness	L + 0.5 M
  r/g (redness vs greenness) signal	L - M
  y/b (yellowness vs blueness) signal	L + M - S

Figure 3.3 below is meant to clarify the meaning of Figure 3.2. At the long-wavelength end of the spectrum, high L, low M, and zero S responses create positive r/g and y/b signals, and we experience a broad zone of orange-red colours. Moving left towards shorter wavelengths, the L response peaks before the M response (Figure 3.1), so that r/g begins dropping. At wavelengths around 577 nanometers the L and M cone influences effectively balance out, the r/g signal passes through zero, and we experience unique yellow, that is, a yellow that is neither reddish nor greenish. Past this point, negative r/g signals result in a series of greenish colours. At around 513 nm the influence of S effectively balances (L+M), so that the y/b signal drops to zero, and we experience unique green, neither yellowish nor bluish. Throughout the remainder of the spectrum, S predominates over (L+M), so that the y/b signal is negative, and all of the colours are bluish in character. Near the short wavelength end of the spectrum the M response drops below the L response, and we get positive r/g signals and reddish colours again, to which we apply the name violet. The second point of zero r/g, which we experience as unique blue, occurs at wavelengths around 475 nm. All of the wavelengths quoted here are subject to considerable individual variation. Note that unique yellow, unique green and unique blue do not occur at the peaks of the y/b and r/g curves, but at the point where the other signal is at zero.

The circular range of the colour wheel results from the 360^o range of possible combinations of positive and negative r/g and y/b values. However, spectral wavelengths can not create the full 360^o range. Unique red, for example, does not occur in the visible spectrum, because all long wavelengths create a positive y/b component. Colours from unique red through magenta to red-violet can only be induced by a mix of wavelengths from the red and violet ends of the spectrum.

Figure 3.3. Interactive demonstration of changing y/b and r/g signals throughout the spectrum. Push the slider from the long to the short wavelength end of the spectrum to understand how the colours of the spectrum result from different combinations of positive and negative r/g and y/b signals. Copyright David Briggs and Ray Kristanto, 2007.

The L, M and S cones are sometimes described as being red-, green-, and blue- sensitive respectively. Many authors have been quick to point out that these descriptions are not strictly correct, since all three cone types have broadly overlapping ranges of sensitivity, and the L and M cones are sensitive throughout the visible spectrum (Figure 3.1). Nevertheless, these descriptions are not entirely incorrect either, if we take into account the way the inputs from these cones are processed in the opponent model. The three cone types effectively divide the visible spectrum into three bands, in each of which the response of one cone type predominates over the other two (Figure 3.3). At the short wavelength end is a band of blue to violet colours, where S > (L + M) gives negative y/b values. The remainder of the spectrum is divided into a middle band of greenish colours, where M > L gives negative r/g values, and a long-wavelength band of reddish colours, where R > M gives positive r/g values. The first two bands overlap in the cyan part of the spectrum, while the second and third meet at yellow. This division of the spectrum into a reddish, a greenish and a blue-violet band is quite evident on visual inspection (Figure 3.4).

Figure 3.4. Solar spectrum. The orange-red, green and violet-blue bands, in which the responses of the L, M and S cones respectively predominate over the other two, are clearly evident on visual inspection of spectra such as this complete solar spectrum. Image source: http://www.adlerplanetarium.org/cyberspace/sun/learning.html (Credit: Nigel Sharp, NOAO/NSO/Kitt Peak FTS/ AURA/NSF).

The importance of these spectral bands with high redness, greenness and blueness respectively is that if we were to mix in varying proportions three lights, one from each band, we could make mixtures with any possible combination of strongly positive and negative r/g and y/b signals, and thus create strongly coloured mixtures throughout the full 360^o range of hues. These three lights would therefore make optimal primary colours for additive colour mixing. Both the division into a reddish, a greenish and a blue-violet band, and the derivation of other colours by mixture of these colours, were recorded in the rainbow in antiquity in Aristotle's Meteorologica.

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