The basis of colours

Colour is a human sensation which has little to do with plain physics and a lot with biology. Every very small (part of an) object around us emits electro magnetic energy, which meets the eye. Its image is projected onto the retina. Because of the rapid elliptical movements of the eye, the image describes an elliptical trajectory on the retina. Let be the energy density at wavelength of the image, so is the total amount of energy between wave lengths and . Due to the ellitical movements of the eye, the image meets different sensors for electromagnetic radiation, that have different sensitivities for the different wave lengths. For simplicity's sake we here assume that the signal output of the sensor is proportional to the input. Let be the energy signal conversion of sensor $i$ at wavelength , so is the signal of sensor $i$, if all the separate contributions of the different wave lengths just add up. The actual signal is approximately hyperbolically transformed, like , but this is at present of no importance. It seems that most of us have got three different types of sensors. So, the total signal we receive can be represented as , which we call sensation.

The lower end of the sensitivity range is around 420nm, where we have a sensation which we call violet, and an upper limit of 67nm, where we have a sensation which we call red. The range has no sharp limits. Every possible sensation can be represented by a point in the three dimensional sensation space. The sensors have a considerable overlap in sensitivities. Therefore it is not possible to stimulate only one sensor, without stimulation the others to some extend. This means that not all points in the sensation space can be reached in practice. Suppose that there exists a fixed minimum threshold of the signal we can detect, the range depends on the energy input , which we experience as intensity. The relative firing rate of the three sensors we experience as colour. Any choice of three different colours (i.e. sensations)

can in principle be used as a basis for the sensation space, as long the corresponding three vectors are not in the same plane. So all colours, like white, can be obtained by a linear combination of that three colours. That is to say, when we admit subtraction. The sensation in fact means when we use the sensors , , as a basis. It is equivalent to the sensation , which means when we use the three colours , , as a basis. Because both expressions are equivalent, we must have that , or , where

However, not every choice of the colours as a basis is equally usefull. In the first place, subtraction is cumbersome from a physical point of view. Small errors in the signals of the three sensors are enlarged when the colours are close to each other. It is useful to realize that the eye reduces the energy density function , consisting of an infinite number of "data- points" to just three values collected in . Therefore many different energy density functions are mapped into the same sensation (i.e. colour). It also implies that there are many ways to combine different colours to produce a particular one. The study of different types of colour blindness has contributed a lot in our understanding of colour perception. A particular type is the absence of one sensor, which means that the perception is in two rather than three dimensions. Some species of animals have more than three sensors for electro magnetic radiation. They must be able to distinguish between different sources, that look the same for us.
Filename: ex018; Date 1991/04/24; Author: Bas Kooijman