The sense of vision is marvellously complex; here is a brief compendium of its lore
The visual sense gives us timely knowledge of our spatial surroundings, near and far, identifying all the objects in it to our consciousness. The world we see is inside us, an illusion, but we all share the same internal perception of a real and physical universe outside us. The sense is so well adapted to its purpose that we normally assume that what we perceive are the actual objects, as if by touching, and it was exceedingly difficult for philosophers to overcome this erroneous belief. The visual world is another illusion, like the movement of the sun and moon across the sky, where it is an effort to realize that it is the earth that is moving, not the heavens. What is apparent is not always true. The visual sense intimately combines memory with external stimulation. In this paper, I have endeavoured to collect as much lore on vision as I can find, and to interpret and express it compendiously. The references lead to more detailed discussions.
Eyes are the portals through which electromagnetic radiation from our environment enters the visual system, exciting a flood of information from the distorted, two-dimensional image cast upon the sensitive cells of the retina. Most of vision takes place in the brain, and this begins in the retina, where the signals from neighbouring receivers are compared and a coded message dispatched on the optic nerves to the occipital cortex, behind the ears, where the information is formatted and made available to the processing activities of the brain. The eye is essentially a motion detector, its original purpose when eyes began to evolve from light-sensitive pits in the pre-Cambrian. The compound eye of the flying insect is an extremely sensitive motion detector, and well-suited to its purpose, since only moving things were of any interest. Even here, additional advantage was gained from the ability to receive light, the colours of a flower and the polarization of sunlight proving useful in certain cases. Arthropods, cephalopods, and chordates independently evolved eyes that made images, as the ability to identify objects and understand spatial relations proved valuable. The variety of these evolutionary inventions shows the great advantage of having a visual spatial sense. The most extraordinary eyes are those of the copepod Copilia, which physically scans an image projected by a lens with its light-sensitive organ, or the pinhole pupil of Nautilus.
In spite of the fact that our eyes are now mainly used for the identification of static objects and for establishing spatial relations, their basic functioning still rests on comparison of stimuli from neighbouring cells, which was fundamental to motion detection. When observing a static scene, the eyes perform small repetitive motions called saccades that move edges past receptors. If an image is stabilized on the retina, it soon darkens and disappears, since a motion detector responds only to motion. The same thing happens if the eye is exposed to a neutral, featureless scene, the Ganzfeld. Faint stars soon disappear when stared at, but return as soon as the image moves on the retina. Blood vessels in front of the retina surely cast shadows upon it, but these shadows are never seen. Any constant stimulus is ignored. The eye bears very little resemblance to a camera, except for its power to focus an image on the retina, and none whatsoever after this. Even a digital camera records point-by-point, which the eye does not do. The eye is not a pixel device, though location is very important.
The coded signals sent to the brain down the optic nerves are used to recognize objects, and recognition is necessary, indeed fundamental, for sight. This depends on past experience and learning, so sight is not an instinctive sense. The potential of the system, and its general characteristics are innate, of course, but the complete sense must be developed by experience. This is very easy in the young individual, and is done by comparing the information from other senses, mainly touch and smell, with the corresponding visual perceptions. Even in adults, the sense is not unalterable. An experimenter who wore glasses that inverted his retinal images so they were right-side up instead of the usual upside-down, gradually found that things started to look normal after a while. It is important to realize that vision is principally a function of processing in the brain, and that images and pixels play a very small role. Many objects are recognized from borders, at which changes occur, and the rest is inferred. The orientation of lines, and the directions of movement, are the major sources of information, and are specially coded. Visual sense is a property of consciousness, and is deeply involved in the functioning of the brain.
All of the senses are involved in consciousness and perception, and there are interesting connections between them. It has recently been reported that sound causes vision to become more acute. Faint lights were more reliably perceived when their appearance was preceded by a sound. This work was done at the Univ. of California at San Diego, and was reported in Nature in October 2000.
Light is electromagnetic radiation to which eyes respond. In light of a single wavelength, or spectrally pure light, the extreme range is from 380 nm to 740 nm. The sensitivity of the eye falls off at the ends of this range, so that 400 nm to 700 nm is a good approximation. Infrared radiation cannot enter the eye, and only warms its surface. Long-wave ultraviolet radiation causes fluorescence in the eye (especially in the visual purple), and the fluorescent radiation can be seen. Short-wave ultraviolet again cannot penetrate, but irritates the conjunctiva. Ultraviolet is damaging to the eye, causing irreversible changes. The dark-adapted eye is also sensitive to X-rays, which are not refracted by the eye and pass freely through it. This appears to be a direct sensitivity, since there is little fluorescence, and the stimulus can be moved around on the retina. Gamma rays can also be perceived, but this is again due to fluorescence, so a diffuse glow results. Do not try this at home!
The retina is the light-sensitive part of the eye. There are two systems of receptors in the retina, the rods and the cones. In fact, the retina is actually a dual organ, a rod network and a cone network. Birds and reptiles have only cones, and some nocturnal animals only rods. The rods are sensitive to weak light, inoperative in strong light, and have maximum sensitivity at about 507 nm. The cones are sensitive to strong light, insensitive to weak light, and have a maximum sensitivity at 555 nm. Rod vision is called scotopic (dark-seeing) and cone vision is called photopic (light-seeing). Rods are located in all parts of the retina, and are very sensitive to motion, but give no colour discrimination. Cones are located most densely in a small area called the fovea, a shallow pit 1.5 mm in diameter, to the temporal side of the optic nerve. Their density decreases as one recedes from the fovea. The fovea has no blood vessels. All acute and colour vision is due to the cones. The fovea is surrounded by a pigmented area called the macula lutea, the yellow spot, 2-3 mm in diameter, containing the yellow dye xanthophyll, which absorbs light of wavelengths shorter than 500 nm. This spot cannot be seen in an ophthalmoscope against the living red choroid behind it in normal circumstances. Nerves from the rest of the retina go around it, as do larger blood vessels. It is richly equipped with ganglion cells, which indicates it is a site of signal processing. It plays an important but not clearly understood role in vision.
To the nasal side of the fovea is the blind spot, or papilla, where the optic nerve enters the eye, and where there can, therefore, be no receptors. This area is simply ignored by the eye and filled in with the neighbouring field, so that it does not disturb vision. The blind spots in the two eyes do not overlap, of course. It can occasionally be seen as a dark spot when the eye is first opened. At a distance of 7 ft, the blind spot is about 8 inches across, so it is not negligible, and may cause something not to be seen. To demonstrate it, draw two small spots on a card about 60 mm apart. Close the left eye, and fixate the left-hand spot with the right eye. When the card is at the proper distance from the eye, the right-hand spot will disappear. The retinal blood supply enters through the centre of the optic nerve.
The eye is almost a sphere, of 12 mm radius, consisting of three layers. The sclera is the tough white outer hide of the eye, merging into the cornea at the boundary called the limbus. The choroid is a dark absorbing layer, richly supplied with blood vessels. Cats have a reflecting layer of unpigmented fibrous tissue, the tapetum on the choroid. The sensitive cells of the retina are transparent cylinders of higher index of refraction than their surroundings, so they guide the light by total internal reflection. A tapetum causes light to pass through them twice, increasing the sensitivity of the eye to weak light. It also causes the pupil to become luminous, returning light in the direction it arrived, a well-known feature of cat's eyes. The choroid is continuous with the iris, which forms the pupil of the eye, and has radial and circumferential muscles to control its size. The ciliary body contains muscles to control the lens, to which it is connected by fibres called the zonule. The innermost layer comprises the retina and the lens. The ora serrata is the edge of the retina. The insertions of the six extrinsic muscles that move the eye are not shown in the diagram. The very sensitive conjunctiva lines the inner side of the eyelid, and covers the exposed front of the eye, including the cornea.
The size of the pupil changes with different levels of brightness, expanding in dim light, and contracting in bright light, or when an object is held close. This change, over a range from 4 mm to about 8 mm, changes the retinal illumination of an extended object only by a factor of 16, far smaller than the actual dynamic brightness range of the eye of perhaps a factor of one million. A more plausible reason for the change in pupil size is to restrict the entering rays to the centre of the aperture when the illumination is sufficient, reducing aberrations and increasing the depth of field, while allowing the full aperture to be used in dim light. The rim of the lens, where the muscles are attached, is particulary irregular, and may exhibit diffraction at its radial fibres, so it is used only when necessary. Light entering near the edge of the pupil is less effective per unit area in producing retinal illumination than light passing through the centre of the pupil, a fact which could simply follow from optical principles, although there appears to be some controversy. This is known as the Stiles-Crawford effect. The slit pupil of the cat can be closed more completely in bright light than can a round pupil. The spacing of the rods in the fovea is roughly equal to the size of the diffraction pattern produced by the aperture of the pupil when contracted for vision in bright light. Given either the diameter of the pupil or the spacing of the rods, the eye is proportioned so that it could not be more acute, taking diffraction into consideration.
The cornea, the transparent area shown blue in the diagram, has a radius of curvature of about 8 mm, and is the area where light enters the eye. Most of the refraction takes place at the surface of the cornea (43D out of a total power of 59D). This is evident from the great loss of power when the eye is immersed in water when swimming. Light then passes through the aqueous humour to the lens, also shown in blue. The liquid aqueous humour nourishes the cornea and lens, which have no blood supply. The light then travels through the jellylike vitreous humour, which has an index of refraction of 1.336, close to that of water, to the retina at the back of the eye.
The size of the retinal image in mm is given by y' = 16.68 u, where u is the angle in radians subtended by the object at the eye. This gives a field of about 5° for foveal vision. The image is inverted, which caused some disquiet when the fact was discovered. The orientation of the image has nothing to do with its interpretation. To demonstrate the inversion, make a pinhole in a card and put it in front of the pupil, looking at a bright light so that you see a disc of collimated light. Now cast a shadow on the retina by moving a pinhead between the hole and your eye (there will be no image, just the shadow). The pinhead will apparently come from the other side. Phosphenes also demonstrate this. If you press gently on the sides of a closed eye, the pressure will cause the rods there to be stimulated. You will see a bright ring on the opposite side of the eye (the greenish colour of scotopic light). The visual system assumes the rods are detecting a light in that direction.
The centre of the fovea is also sensitive to the polarization of light. This nearly imperceptible sense is perhaps the remnant of an ability that was once important much earlier in evolution. It appears as Haidinger's brush (discovered 1844), a delicate yellow and blue pattern in the centre of the visual field that appears when the light is polarized, and whose orientation shows the direction of polarization. The brush is about the same size as the macula lutea, so this strange region must be doubly refracting and give rise to the phenomenon. The lens is also weakly doubly refracting. In nature, the light of the blue sky is strongly polarized, from which the direction of the sun can be determined. Some insects may make use of this.
The visual system is tolerant of errors in the retinal image, correcting them where possible. The eye has considerable spherical and chromatic aberration, so the image produced on the retina is very poor. The mental image is much sharper, refined by the visual system. The acute vision at the fovea is used to correct the mental image, when the focus is proper. Poor focus, however, makes edges indistinct, and since the system depends on edges, the result is discomfort and lack of sharpness in perception. The most common reason for poor focus is incorrect curvature of the cornea, where the majority of the focussing power of the eye resides (because of the large change in index of refraction at this surface). If the cornea is too steeply curved, which is quite common, distant objects are focussed short of the retina, and myopia is the result. Hypermetropia is the opposite case. An eye with neither is called emmetropic. Lack of sphericity of the cornea causes astigmatism, in which no stigmatic (point) focus exists. These errors of refraction may have other causes, as discussed in Helmholtz (Ref. 1). Young found that his marked astigmatism was not due to corneal curvature, for example. The lens becomes rigid with age, so that the ciliary muscles can no longer give it the curvature required to focus on close objects, a property called accommodation, and presbyopia is the result. All such errors of refraction can be corrected by external lenses, and an approximate correction is usually quite satisfactory. Because of chromatic aberration (the indexes of refraction vary with wavelength) blue and red are normally less well-focused than greenish-yellow. Visual perception contains little hint of this chromatic aberration, another proof that perception is subjective.
The refraction of the eye (determined by the curvature of the cornea, shape of the lens, and the indexes of refraction of the media) must be closely matched to the size of the eyeball in order that an image be focused on the retina. This does not just "happen," but must be arranged. This is mediated by a protein in the retina, recent study shows, which takes part in a feedback relationship during the growth of the eyeball. When this mechanism works properly, the result is emmetropia; when it is hindered, the result is myopia. It is not a case of eyeballs being different lengths, as was once thought. Most of the refraction occurs at the cornea. Since the length of the eyeball is about 2.5 cm, the power of the eye is about 44 D. In young individuals, the lens creates an accommodation of as much as 10 D, decreasing to 2 D in mature individuals, and to a very small value in elderly ones.
Properly focussed eyes can resolve two sources separated by about 6' of arc in everyday life. Exceptionally good observers can resolve down to about 4' or 3', but this is not common, and depends on the object viewed. The absolute limit of acuity, under laboratory conditions with fine gratings, seems to be between 1' and 2'. The Snellen chart for assessing visual acuity uses small characters (often E's or other hook-shaped patterns in various orientations) that subtend 5' at specified distances, and the width of whose lines are 1/5 the size of the pattern. The chart contains lines of patterns that subtend 5' at, say, 10 ft, 20 ft, 30 ft and 40 ft. If the chart is placed 20 ft from an observer, and the line subtending 5' at 20' can be resolved, the visual acuity is called 20/20. If the line subtending 5' at 40' can be resolved, the visual acuity is now 20/40, and so on.
The pupil of another person's eye appears black to the observer. We have noticed that cat's eyes, and those of dogs and horses, reflect light that enters them back in the same direction because of the tapetum. In flash snapshots, the pupil often shows a fuzzy redness, caused by light entering the eye through the choroid and its blood vessels, then being scattered out the pupil. It is practically impossible to observe the back of the eye, as for medical purposes, by looking in the pupil, for three reasons. First, illumination of the retina is difficult, since it must enter via the pupil, and the light is not regularly scattered, but preferentially normal to the retina. Second, the eye is a refracting instrument, and the image of the retina produced by light going the reverse direction may not be in a suitable place for observation, and moves around as the subject's eye accommodates. Thirdly, the field of view limited by the iris is very restricted when the observer's eye is far enough away to see the retina clearly. These difficulties are overcome by the ophthalmoscope, invented by Helmholtz. The retina is illuminated by a light to the side, reflected into the pupil by a mirror with a small hole through it for viewing. The observer's eye can be brought close to the pupil by using a lens to place the image at a suitable distance for viewing. There are many possible arrangements, which have resulted in the design of small, portable instruments. A minimum ophthalmoscope can be assembled from a penlight held beside the observer's eye to illuminate the subject's pupil, and a converging lens for observation. The retina is still not easy to observe, since it is a thin transparent layer seen against the dark red choroid. It is possible to examine one's own retina by using a mirror (plane or convex) with a tiny hole in the centre. Hold the hole before the pupil and look at a source of light that is not too bright. The field of view is small, but may be moved about by moving the eye.
The refractive index of the eye medium varies with wavelength similiarly to water, so that n = 1.3318 at 656 nm (red) and n = 1.3435 at 405 nm (blue). This gives the eye a difference in power of about 1.5 D over the visual spectrum. The effect is to focus blue light at a shorter distance than red light, as shown at (a) in the diagram at the left. E is the entrance pupil, the image of the actual pupil formed by the iris in the cornea. C is the cornea and R is the retina. Light rays stop at the retina, of course, but are continued in the diagram for clarity. Since the sensitivity of the eye varies with wavelength, the focus is adjusted (when possible) for green light at which the sensitivity is maximum. This image will be surrounded by a violet patch which is not normally evident. An absence of chromatic aberration would give very little advantage.
The chromatic aberration can be made evident by looking at the image of a bright spot, or better, a bright line, as the pupil of the eye is partially covered by a screen, as at (b). This destroys the symmetry, and the edges of the image will be tinged with color, red on the side of the screen (remember the inversion of the retinal image) and blue on the other. This effect is small, but can rather easily be seen when conditions are right. The bright image is, in effect, spread out into a spectrum.
Dispersion in the eye can be made to exhibit the phenomena of chromatic parallax. For clearest viewing, a bright line image, perhaps from a slit, and screens also made from accurate slits, should be used. In principle, small point apertures can also be used. At the left in the diagram, there is a screen S that can be moved across the entrance pupil of the eye. Light from a bright source to the left passes through a cobalt-glass screen F that admits red and blue rays, blocking the others. As the screen is moved back and forth, the red and blue images change sides, giving an impression like that of parallax. This is called internal chromatic parallax, since the paths of the rays coincide outside the eye, the differences being purely internal.
Now suppose we have two identical sources, one red and one blue, located on the axis of the eye at distance that bring them to a common focus on the retina, as shown in the upper diagram at the right. The paths of the rays are identical inside the eye in this case, but differ externally. Moving an aperture in front of the eye has no effect on the image in this case. If the two sources were white sources, their images would show the usual parallactic displacements as the aperture was moved.
If, however, we move the eye instead, principal rays through the nodal point N of the eye will locate red and blue images on the retina as shown. The locations of these images will not be affected if an aperture is moved in front of the eye, as they would be in the case of normal parallax. This phenomenon is called external chromatic parallax.
It is wonderful that the optic nerve in vertebrates enters the eyeball, turns, and connects with rods and cones that are facing toward the back of the eye. Light must penetrate the relatively transparent network of blood vessels and retinal nerves before it is detected. The evolutionary advantage of this arrangement may be that it holds the sensitive cells in fixed relative positions. The transparency and complexity made microscopic study of the structure of the retina extremely difficult. Its structure was first accurately described by Ramón y Cajal (1852-1934), who found that it was not as simple as light-sensitve cells directly wired to the optic nerve. Neurons in the eye have a body with dendrites (inputs), and a long axon with an arborization at the end (outputs). Communication is through synapses between neurons, in which the receiving neurons are either stimulated or inhibited by chemicals diffusing across the interface. The optic nerves begin as bundles of axons from the ganglion cells on one side of the retina. The rods and cones, on the other side, are connected to the ganglion cells by bipolar cells, and there are also horizontal nerve cells making lateral connections. The retina extends from the pigment epithelium at the back to the hyaline membrane separating it from the vitreous humour at the front.
The signals from neighboring receptors in the retina are grouped by the horizontal cells to form a receptive field of opposing responses in the centre and the periphery, so that a uniform illumination of the field results in no net stimulus, but a difference in illumination of the center and the periphery does. Some receptive fields use colour differences, such as red-green or yellow-blue, so the differencing of stimuli applies to colour as well as to brightness. There is further grouping of receptive field responses in the lateral geniculate bodies and the visual cortex for directional edge detection and eye dominance. This is low-level processing preceding the high-level interpretation whose mechanisms are unclear. Nevertheless, it demonstrates the important role of differencing in the senses, which lies at the root of contrast phenomena. If the retina is illuminated evenly in brightness and colour, very little nerve activity occurs.
There are 6 to 7 million cones, and 110 to 130 million rods, in the average human retina, but only some 800,000 fibres in the optic nerve. The connections cannot, therefore, be simple, and the amount of information sent to the brain for interpretation is huge. By contrast, the auditory nerve has only about 15,000 fibres. The optic nerves cross at the optic chiasma, where all signals from the right sides of the two retinas are sent to the right half of the brain, and all signals from the left, to the left half of the brain. Each half of the brain gets half a picture. This ensures that loss of an eye does not disable the visual system. The optical nerves end at the lateral geniculate bodies, halfway back through the brain, and the signals are distributed to the occipital (visual) cortex from there. The visual cortex still has the topology of the retina, and is merely the first stage in perception, where information is made available. Visual regions in the two cerebral hemispheres are connected in the corpus callosum, which unites the halves of the visual field. The connections of the visual cortex are complete at birth, and are highly ordered, not random, but surprisingly uniform. A study of all this wiring reveals remarkably little about visual perception, and it is not known how it all works.
Although the study of vision has always been pursued mainly in an empiric tradition, especially by physicists, during the 19th century a school of intuitionists gained considerable following, especially among psychologists, of which significant traces remain. The intuitionist postulates an inherent sense of space and movement, in which retinal points were mapped onto physical space. In their view, the visual system only correlates external objects with pre-existing concepts. This view gave rise to elaborate mathematical theories of the correlation of the retinal images in binocular vision, as one example. The observation that when sight was restored to individuals blind from birth, they could not make any correlation between the knowledge of objects gained by touch and their new visual apperceptions argues strongly against intuition, as do many other observations showing that mental processes and learning are important. The original intuitivist concept seemed to be that there existed a conscious, nonphysical ego, for which the body was only a vehicle, and the senses were a means of communication with it. The external universe was conceived as a material expression of a similar ego, so the correlation would naturally be close. A modern echo of intuitionism is the discovery that some basic properties of vision, such as edge perception, are to be found in the arrangement and structure of the sensory nervous system, independently of higher brain functions, and do not need to be learned or developed.
When the optic nerves of young mammals were surgically rerouted from the optical cortex to the auditory cortex, sight was preserved, at least partially. This clearly shows the adaptability of the brain, and that a large part of its functioning results from learning, not from genetically imposed organization. It also shows that the higher visual functions are not localized in the visual cortex, which must only be a kind of switchboard supplying data. In people blind from birth, it has been found that the visual cortex assumes other functions.
Rhodopsin, or visual purple, was the first light-sensitive visual protein to be recognized, in the rods. The absorption of a quantum or two of light causes a structural change that makes the protein uncomfortable in its usual position, and in shifting to relieve this triggers a nerve impulse. The protein returns to its normal sensitive structure with a certain half-life, of the order of 15 minutes. When the light is too strong, all the rhodopsin is in the modified, or bleached, form and the rod cell is insensitive to light. The search for similar proteins in cones was protracted and difficult, but three relatives of rhodopsin with different spectral absorption were eventually identified. When bleached, these return to normal in about 7 minutes. The dark adaptation of eyes is mainly about restoring the sensitive forms of these proteins. Purkinje (Pur-KIN-yee), the remarkable Czech observer, reported in 1825 that the relative intensity of the red and blue in some signs he saw was different under high and low illumination. Blues can become quite vivid in dim light, while reds become black. There is no Purkinje effect in foveal vision, where there are no rods; the area simply becomes insensitive at low light levels.
The presence of three photosensitive proteins in the eye (the cones are of three types) is the reason that colours can be matched by mixtures of three monochromatic lights. Unlike the ear, the eye does not perform a Fourier analysis of its stimulus, but merely interprets the relative stimulation of cones that possess the three different proteins. Light of many different compositions can produce the same perception of colour. That there were three coordinates in colour was first recognized by Thomas Young (1801), reiterated and studied by James Clerk Maxwell, and placed on a firm foundation by Hermann von Helmholtz. It became the basis of colour measurement and specification, because it was empirically validated. There were dissenting views, remarkably by Goethe, and more recently by Edwin Land (who, incidentally, had anomalous colour vision). The final discovery of the three optical proteins firmly established the trichromatic theory (1959).
Once, when I developed a peripheral floater in one eye, the annoyance was compensated by the opportunity to study my eye motions while performing visual tasks. A floater is a piece of opaque substance in front of the retina, usually a small blood clot escaped from a capillary. While reading a book, vision fixated on one side then the other. The leftward motion was obvious when the floater suddenly jerked into view before the visual sense cancelled it. There was one scan for every one or two lines. It was not line by line, and was not a continuous scan. When reading the narrower columns of a newspaper, there was no such scan, and one fixation did the job. This clearly shows the superiority of narrow columns in facilitating reading. When the fixation jumped from one point to another, the perceived view did not change in the least, not even blinking. This clearly shows that the perceived view is not the picture projected on the retinas. The retinas merely collect information that is used to create the view.
Stereopsis and colour sense are interesting and fundamental aspects of vision that are subject to experimental study and understanding. Let us first consider colour. Burnham, Haynes and Bartleson (Ref. 3) defined colour in the following terms:
"Colour is the attribute of visual experience that can be described as having quantitatively specifiable dimensions of hue, saturation, and brightness."
This is a highly unsatisfying definition for an artist, or even for a psychophysicist trying to understand the whole fabric of visual sensation. It is, however, of great utility in the practical application of colour, and includes the most remarkable property of colour. If you take any three different monochromatic or spectral lights, then any given colour in a limited range, depending on the choice of the three stimuli, can be matched by mixing certain amounts, measured as physical intensities, of the three monochromatic lights. This does not refer to all the ways in which colour can appear, but only to this matching under standard conditions. If the normalized fractions (defined in the next paragraph) of the three monochromatic stimuli are represented by x, y and z, so that x + y + z = 1, then a colour can be plotted in two dimensions, say x and y. The location of this point represents hue and saturation. Saturation increases with the distance from a point representing white, and hue is determined by the azimuth from this point. Spectral colours plot on a horseshoe-shaped curve of maximum saturation called the spectral locus, and complementary colours are at the opposite ends of line through the point representing white. In this way, colour is expressed in terms of hue, saturation, and brightness. There are some colours that do not correspond to any spectrally pure colour. An example are the purples, formed by mixtures of red and blue, occupying the triangle in the diagram whose vertices are the white point, and the red and blue limits of the spectral colours. White and black are also true colour sensations. Black is not the same as seeing nothing, as in the case of scotomas (areas of no sensation) and blindness. In fact, limited scotomas, like the blind spot, are not normally noticed.
The CIE (Commission Internationale d'Éclairage) system of colour specification uses primaries at 700 nm, 546.1 nm (Hg), and 435.8 nm (H), which are related by a mathematical transformation to three standard stimuli. The corresponding tristimulus values X, Y and Z are weighted averages of the radiant flux, weighted by standard functions of wavelength that represent the standard observer. The normalized values or chromaticity coordinates are x = X / (X + Y + Z), y = Y/(X + Y + Z), and z = Z/(X + Y + Z). Y represents the luminance of the colour, since the weighting factor is simply the spectral sensitivity of the eye. These primaries are essentially red, green and blue, the same colours used in a colour video screen.
Aristotle's theory of colour was based on interplay of light and darkness, in which colour was a result of the modification and attenuation of light. The visual sense was a form of feeling, of active perception, not the passive reception of stimuli. Descartes (1637) considered light as a pressure communicated through a medium, and color a rotary motion. To others, light was a stream of particles from source to eye, modified by the bodies which it encountered on the way. De la Hire (1711) ascribed colour to the impact of the particles of light on the optic nerve. Newton (1666) showed that the colours from a prism were not changed by further refraction and could be recombined to form white light. Colour was associated with the refrangibility of the rays, dependent on the particle velocity. This was the beginning of the modern distinction between the objective physical light, and the subjective perception of colour. Essentially, Newton said that the light was not red, only its perception (and Helmholtz explains this at length). Newton was opposed by many thinkers, such as Brewster (1831), who claimed light was of three kinds: red, yellow and blue, each of which was variously refrangible. This idea ascribed Young's trichromatic explanation of colours to the physical light itself. Hooke (1665), Huygens (1679) and Euler (1746) adopted a vibrational wave model of light. Euler initially made red the short wavelength and blue the long, but soon got it the right way round. Goethe, in Zur Farbenlehre (1810), also vigorously attacked Newton's ideas, returning to Aristotle's concepts, holding perception to be objective, not subjective, and colour the result of the modification of light by the natures of the bodies it encountered. His science was superficial and confused, but artistically expressed, and attracted much amateur support. Young established the wave nature of light (1801), which was finally accepted after its consequences were elaborately worked out by Fresnel (1819). Helmholtz and Maxwell then constructed the modern theory of colour, which has been verified by all subsequent investigations, notably by the long-awaited discovery of three different photosensitive proteins in the cones. There were many other recent theories, such as Hering's four-colour theory, that are now discredited though possessing a degree of plausibility.
A recent discussion involving the roles of Goethe and Land in colour theory well demonstrates the muddle that arises when the objective and subjective aspects of colour are mixed (See References). We understand the physical basis of the spectral composition of light, which Newton studied, very well indeed. He showed that colour was not an acquired condition of light, but was dependent on its physical nature. The physiological aspects of vision, such as visual pigments, are now mainly understood. The sensory aspects are poorly known, except for superficial properties, like all mental processes. It should always be remembered that equal visual stimuli do not produce uniform and equal results, although this is true to a certain approximation, as evidenced by the success of the CIE colour specification. Land's experiments show clearly the limitations of a dogmatic physical view, but vision is physiologically a tristimulus affair after all. Goethe's experiments, however intelligent and interesting, led nowhere, either in the physical basis of colour or in the subjective. Newton's theory of colours is, indeed, quite defective, but it is the ancestor of our modern understanding.
As one perambulates the locus of spectral colours, the colour names are blue, green, yellow, orange, red, and then purple on the line between red and blue. Some authors say that the extreme blue has a slight reddish tinge that makes the traditional name of violet appropriate. When people are asked about their colour preferences, there is a great disparity of opinion, but weighted averages of the responses rank the colours in the order blue, red, green, violet (purple), orange, and yellow, for both sexes. Youth prefers warmer colours, maturity cooler ones. Yellow was the Chinese imperial colour, and violet the colour of Japanese royalty. Black was the colour of life and warmth in China, white the colour of death and cold. In Europe, it was the opposite. Saffron and black are the colours of hell in Pakistan, but saffron is the colour of Buddhist monks' robes. Ideas on colour harmony vary greatly. There are four psychological primaries that probably have no fundamental significance, other than retaining a hue invariant under changes in intensity. The yellow is produced by monochromatic 577 nm, green by 513 nm, blue by 473 nm. The red is a mixture of red and blue complementary to 495 nm. The spectral colours are called simple or homogeneous because they consist of a single wavelength. They have no special significance in colour perception, except for providing the most saturated possible hues. The same colour sensation can be produced by a wide variety of stimuli; no one-to-one relationship exists, as there is between frequency and pitch in hearing. There is no harmonic relation between colours, as in music, though many investigators have sought for such relations, beginning with Newton. In fact, colour is a secondary character of light, like timbre in music. The primary character of light is its spatial distribution, as the primary character of sound is its temporal distribution.
Danger (Ref. 2) gives a great deal of the lore of colour applications. He says that colour means pigments to an artist, an internal perception to a psychologist, the response of a neural system to a physiologist, an aspect of radiant energy to a physicist, and a property of objects and lights to the man in the street. We have mentioned all of these meanings so far except the first. The mixing of colours had been difficult to explain since ancient times. When pigments are mixed, the usual result is an obscure dark colour, not what one might expect (confirming Aristotle). Mixing pigments is subtractive mixing. Here, magenta subtracts green, cyan subtracts red, and yellow subtracts blue. My watercolours in primary school were red, yellow, and blue, which some stolid educationalist believed were 'primary.' Mixing these, you get black or any number of obscure browns, not the colours you need for painting. These paints were an ignorant attempt to demonstrate long-discredited ideas on colour. The yellow and blue contained enough green, and the red and yellow enough orange, to show the resulting colour to some degree, but the whole concept was very confused. The idea that yellow and blue lights make green refuses to die. It appears in a recent article in Nature (V. 404, p. 457). Colour slides have suitable subtractive primaries, video screens suitable additive primaries. Both produce very effective images that are interpreted by the visual sense to contain a full range of colour.
Mixing of lights was first effectively demonstrated by Maxwell's colour top (before 1855), in which segments of coloured paper provided quantitative amounts of colour that were mixed in the eye by spinning the top. It is very easy to make a Maxwell top for yourself. Such experiments cleared up the confusion about additive and subtractive colour mixing that had confused painters for a long time. There are no true primary colours that can be mixed to produce all colours, but three properly chosen lights can be mixed to produce a very wide range of colours, as we have already mentioned above. Maxwell's colour top was also used to study and diagnose colour blindness.
It should always be remembered that colour is a perception, not a physical property. It exists only in the mind, and is not mapped in any one-to-one way on the characteristics of, say, radiation. The colour yellow is excited by monochromatic radiation of wavelength 600 nm, but also by a mixture of 550 nm and 650 nm. A green thing has no "green" in it. The colour of a solid body can be a body colour, the usual case, or a surface colour. A body colour is produced by absorption in the light that penetrates into the body and travels a ways before it is diffusely reflected. A substance that absorbs blue and red will appear green, as does a leaf. A surface colour is produced by selective reflection caused by a strong absorption in the substance. In the region of the absorption band, the substance exhibits very high reflectance that resembles that of metals, except that it only occurs over a more or less narrow band. This is "seen" mostly in the far infrared, where many crystalline substances, such as quartz or rock salt, have extremely strong absorption. Quartz, for example, shows a metallic reflection at 8.5 μm and 20 μm. In the visible range, many aniline dyes exhibit this behavior. For example, the dye in purple ink, while having a body colour of purple (since it absorbs green very strongly), also shows a greenish metallic reflection, which is easily seen, especially in dried ink. Selective reflection colours always have this strange metallic-appearing lustre. It is due to the extravagant behaviour of the index of refraction and coefficient of absorption in the region of a resonant line.
Curious is the association of colours with shapes, shown on the left, as given in Danger (Ref. 2). Danger also points out that if a room is illuminated by 100 light bulbs, and then 90 are extinguished, objects in the room will appear very much the same. This constancy of colour perception is remarkable. Land showed that patches sending light of exactly the same spectral character to the eye could appear as very different colours, depending on the general illumination of the scene. This demonstrates that perceived colour depends on colour contrasts, explaining in part the remarkable colour constancy of visual perception. The existence of metallic colours with lustre, such as copper and gold, as well as browns and other hues that cannot be excited by a pure spectral light is further evidence of the complex nature of colour. Brown is, in fact, a sensation produced by contrast in a yellow colour surrounded by a brighter field. Lustre or gloss is attributed to surfaces that reflect regularly, making the images in the two retinas different. It automatically arises in stereoscopic viewing of images in contrasting brightnesses or colours. It is seen in monocular vision when a surface is recognized as one that normally shows lustre in binocular vision, or gives traces of variable appearance. It is not a direct effect of binocular vision, but of interpretation.
Something called chromostereopsis has been reported, where it is said that red appears closer to the eye, blue more remote. A popular science magazine (Discover, Nov. 2000) had a page on this that claimed the effect was due to chromatic aberration, which somehow put red and blue images in different positions on the retina as a result of the change of index of refraction with wavelength. Not only does this explanation rely on an erroneous conception of stereopsis as due to retinal position, but shows a lack of understanding of optical imaging. The diagram accompanying the article is totally erroneous, showing rays refracted as if at a prism, and implying that images are carried with the rays. Chromatic aberration causes images to be at different axial distances, and at different sizes, but does not separate red and blue images when the images are stigmatic, as a prism would do. The diagrams purporting to show the effect are concentric rings of blue and red, the blue, incidentally, of much less luminosity than the red. When I view them, the blue actually appears nearer than the red, and the effect is not changed by closing one eye. The article further claims that lack of seeing the effect implies some defect of the observer's stereopsis, which is absurd. There may be a true subjective effect here, but there is probably no physical cause, as is claimed. The theory is doubtless due to some psychologist with little knowledge of optics. This is not to say that chromatic aberration might not produce some such effect in certain cases, only that this article has not presented the argument believably.
If illumination is intermittent, flicker is produced in a certain range of frequencies. At low frequencies, the light simply goes on and off. At higher frequencies, the flicker becomes less, and eventually disappears at the critical flicker frequency or CFF. The CFF for foveal vision varies from 5 to 55 Hz, about proportional to the logarithm of the product of the intensity and area (Ferry-Porter law). It is greater for peripheral vision. At high flicker rates, and beyond the CFF, the brightness is the same as the average brightness of the fluctuating light (Talbot-Plateau law), but at low flicker rates may be as much as twice as high. If the chromaticity varies, the CFF is higher for brightness than for chromaticity (that is, the fluctuation in colour disappears first as the frequency is increased). At about 5 Hz, a flickering black-and-white image can cause Fechner's colours, which are inappropriately also called subjective colours. All colour is, of course, subjective.
The temporal properties of the visual sense are very complicated and elaborate. A delay of some 80 milliseconds between stimulation and perception has recently been demonstrated. This processing time is involved in flicker, as well as in the direct perception of motion and the cinema illusion. This delay is in addition to the effects of colours and brightness on speed of perception. The Pulfrich Effect is the lag of a dim image with respect to a bright one, which can give a stereoptic effect when a neutral filter is held before one eye. The two images are effectively seen at different times, and therefore at different positions of a moving object, automatically creating a stereopair. A pendulum swinging in a plane will appear to be moving in an ellipse. A BBC televison program was once made using this effect for 3D viewing. We note that the stereo fusion occurs after the Pulfrich delay.
After-images remain when a stimulus is removed. A negative after-image is latent, or hidden, for about a second, and lasts about 30 seconds. Positive after-images have small latency, and are flash-like in duration. The colours in after-images can be complementary or similar in colour (homochromatic). The series of after-images when the illumination is flash-like is called recurrent vision. First is the bright Hering image with latency and duration of about 0.05 second, a positive image. Next is the Purkinje image, complementary and with latency and duration of about 0.2 seconds. Finally comes the Hess image, lasting several seconds, and is again a homochromatic image, but is dim.
The subjective impression of brightness depends on the spectral distribution of the physical energy flux in the light. It is measured by the luminous flux F in lumens, which is the integral of the spectral energy flux in watts weighted by the visual efficiency as a function of wavelength, taken as unity at 555 nm, times the luminous efficiency at this wavelength, which is arbitrarily set at 680 lumens per watt (Ref. 4). A uniform point source of an intensity I of one candela emits one lumen per unit solid angle, or 4p lumens in all directions. The illuminance E (illumination) of a surface is the incident luminous flux per unit area. One lux is a lumen per square metre, one foot-candle is a lumen per square foot. The illumination one metre from a 100 W bulb is about 100 lux. Good office illumination is 500 lux. Luminance L (brightness) is the luminous flux per unit area of extended source normal to a given direction, per unit solid angle. A nit (a seldom-used unit) is a luminance of one candle per square metre. A candle flame has a luminance of about 1 candela per square centimetre, a Welsbach mantle 6.2 times larger. If the radiation from the surface is Lambertian, that is, proportional to the projected area in any direction, then the total radiation is p lumens per square metre, called an apostilb or metre-lambert. The foot and the centimetre are more commonly used as length units, giving a lengthy and confusing list of luminance units. This is best summarized by saying that if one lumen per square metre falls on a perfectly diffusing surface, then its luminance is 1/p lumens per square metre per unit solid angle in any direction. If you integrate this over all directions on one side of the surface, you will get the one lumen back. The method of setting up an ideal illumination calculation is shown in the figure above, without actually integrating over the areas involved. If I is in cd, r is in m, and A in m2, E will be in lux. The lambert itself, a commonly-used unit, is lumens per square cm, and the foot-lambert is lumens per square foot.
It is possible to compare the brightnesses of different colours reliably with the eye, in spite of the difference in colour. The comparison can be done by simultaneous presentation, where the intensities are varied until the boundary disappears, or by successive (alternate) presentation, in which equality is shown by the absence of flicker. The eye is always used as a null detector, since it cannot be calibrated as a quantitative one. To compare the brightnesses of two colours, each is compared separately with white. Talbot's Law, that the apparent brightness of an intermittent light bears the same ratio to the uninterrupted brightness as the time of exposure to the total time, is of use in comparing brightnesses.
Fechner (1858) found that the minimum difference of brightness that can be sensed is a ratio of physical intensity of about 1-2%. He discovered this by observing just distinguishable clouds through a dark glass, observing that they were still visible, and measured it by illuminating an object with two candles at different distances. At very low or very high levels of illumination, this property fails. Stars disappear in daylight because the illumination ratio declines as the sky becomes bright, though the absolute difference remains the same (the same amount of illumination is added to sky and stars by the scattering of sunlight). The veil effect is also explained. Shadows in a moonlit scene become profound because of the failure of Fechner's Law at low levels of illumination. Fechner's Law should not be thought of as exact, especially over large ranges of illumination, but only as a useful approximation. More exact results can be obtained by psychophysical experiments, fraught as usual with difficulty and uncertainty.
Sources of illumination can be thermal, such as candles, incandescent lamps or the sun, or non-thermal, such as fluorescent lamps. Thermal sources can be given a colour temperature, which is the temperature of an ideal black-body (not spectrally selective) radiator with the closest similar intensity as a function of wavelength. This spectrum peaks at a wavelength given by lT = 2 896 000, where the wavelength is in nm and the temperature in K (Wien's law). A candle has a colour temperature of 2000K, an incandescent bulb 3000K, afternoon sunlight 4000K, noon sunlight 5000K, and a cloudy sky 6500K. The visual sense adapts to make anything from 2800K to 10 000K appear white. Complementary colours are relative to the ambient white illumination. Differences in colour matching under different illuminants are well known.
Colours are often produced by absorption in dyes dissolved in a liquid or solid medium. If the decrease in intensity in an infinitesimal distance is proportional to the intensity, the absorption is exponential, for light of a given wavelength. The transmittance of a medium is the ratio of the final to initial intensity, but it is much more convenient to work with the optical density, which is the common logarithm of the transmittance. The optical density is the product of the concentration of the absorber, the thickness of the medium, and the spectral extinction coefficient (optical density for unit concentration and unit thickness) of the absorber. This attenuation applies to the physical intensity, in watts per square metre, at individual wavelengths, not to the total brightness or luminous flux.
Stereopsis is the direct sensing of the distance of an object by comparing the images received by the two eyes. This is possible only when the eyes of a creature look in the same direction, and have overlapping fields. The placing of the two eyes this way gives up the opportunity of a wide field of view obtained with eyes on the sides of the head. Predators find it best to have eyes in front, prey to have them on the sides. Stereopsis yields benefits for close work, such as fighting for cats and hand work for humans. Note that normal binocular vision is single, so that the two images have been fused by the brain. There is no evidence that the image resulting from the many simple eyes of an insect is not also fused in a similar way.
Visual perception makes use of a large number of distance clues to create its three-dimensional picture from the two-dimensional retinal images. Strong clues are the apparent sizes of objects of known size, overlapping and parallax, shadows and perspective. Weaker clues are atmospheric perspective (haze and scattering), speed of movement, and observed detail. The strongest clue of all, however, is stereopsis, which overrides all other evidence save touch itself. The convergence of the optic axes of the two eyes, and their distance accommodation, when fixated on an object, do not seem to be strong clues, though some have believed them to be. Although we have two eyes, we usually have only one visual world, which is a remarkable and important fact calling for explanation. Stereopsis gives a reliable distance clue as far away as 450 metres, Helmholtz estimated. The fineness of the comparison that must be made by the visual system is remarkable.
The interpretation of retinal images to produce stereopsis is entirely mental, and must be learned. When the images on the eyes are consistent with the observation of a single object, the two flat images fuse to form a vivid three-dimensional image. With practice, fusion can be achieved with two pictures side by side and the eyes voluntarily diverged so that each eye sees its picture straight ahead, though accommodated for the actual distance. Both the original pictures remain in view, but a third, fused, image appears before them when the concentration is diverted to it that appears strikingly solid. The brain regards this fused image as the real one, the others as mere ghosts. This skill is called free fusion, and requires considerable practice to acquire. In free fusion, both the convergence of the eyes, and their distance accommodation, are inconsistent with the actual location of the image, and must be overridden by stereopsis. It shows, incidentally, that convergence of the optic axes is not a strong depth clue. By the use of a stereoscope, one can achieve fusion without diverging the eyes, or focusing on a close object with the eyes so diverged, so no practice or skill is required. A stereoscope mainly changes the directions in which the two images are seen so that they can both be fixated by normally converged eyes. The two images are called a stereopair.
When the images on the retinas are too different to be views of the same object, rivalry occurs, and either one image is favoured and the other suppressed, or a patchwork of parts of the two images is seen. When everything corresponds except the illumination or colour, the fused image exhibits lustre.
The fundamentals of stereopsis were discovered by Charles Wheatstone in 1836, when stereopairs had to be created by drawing (this could be aided with the camera obscura, but was very difficult except for stick images). The methods of descriptive geometry can be used to create stereopairs. He designed the mirror stereoscope, which directs the view of the images into the eyes with plane mirrors and reflection at about 45°. David Brewster invented the prism stereoscope, which used prisms to deviate the light, which made a more compact and convenient apparatus. Lenses can also be used to decrease the viewing distance and make fixation easier. Photograpy was the natural way to create stereopairs. A stereopair can also be drawn in two colours with the views superimposed. When this anaglyph is viewed through coloured filters that present one image to each eye, fusion is easy. A similar method is to project the two images in orthogonal polarizations, and to view them through polarizing filters. Both of these methods have been used to project 3D films and transparencies before an audience. A small fraction of people, perhaps 4%, have defective stereopsis.
The pattern above demonstrates the stereoscopic wallpaper illusion, which was first discovered by H. Meyer in 1842, and also noted by Brewster. When viewed with the eyes parallel, a strong stereoscopic effect is seen. The green fleurs-de-lis are farthest away, the blue discs closest, and the red crosses at an intermediate distance. This is an autosterogram, a single figure that gives stereoscopic images to the two eyes. Since the figures in a line are identical, when the eyes are turned for free fusion, two different figures are assumed to be parallactic views of the same object. The eye finds it preferable to fuse the images rather than report double vision. It is easier to fuse this autostereogram than a normal stereopair, so it is good practice for developing the useful skill of free fusion.
The mind does not have to recognize the object in a stereopair for fusion to occur. The pattern can be random, but the stereopair must represent the same random pattern as seen from the different positions of the eyes (Julesz, 1960). Even more strikingly, a single apparently random pattern can be fused autostereographically to give a three-dimensional image. No image is seen until fusion occurs. Each point on the image must be capable of interpretation as two different points of a stereopair. These random-dot autostereograms were widely enjoyed in the 1980's. An autostereogram requires free fusion, which must be learned in order to appreciate them. Many people found this difficult, so the autostereograms were usually presented as a kind of puzzle.
Psychologists have argued about stereopsis for many years, but most of their musings are not worth repeating. A widely-held theory was that the two retinas were somehow mapped point-by-point, and differing image positions with respect to this reference frame was interpreted stereoptically. It seems more likely to me that the images are compared by the visual sense for differences, than by their absolute locations on the retina. In the past, psychologists have preferred mechanical explanations, where the brain and retina are created with built-in specializations and functions, spatially localized, rather than regarding the organs as canvases which the cognitive powers organize as necessary.
I have not discussed the broad and interesting field of optical illusions here, since they tell us nothing definite about the inner workings of the visual sense, only give examples of its operation, and also because the 'reasons' for them are controversial, and the arguments are not especially enlightening. Illusions are discussed at length in another article on this website. The oldest and most widely known illusion is the horizon illusion, in which the moon appears larger on the horizon than at the zenith. This illusion was known and discussed in antiquity, and is still the subject of much study. Its explanation is not known. For the application of the visual sense to investigation and appreciation of the world around us, Minnaert's book is outstanding.
I have carried out most of the simple experiments described above to verify that they work as stated. The remaining ones I shall perform when I again have access to the necessary properties. I believe it is quite important to do things like this whenever possible, and not to rely on mere plausibility. It is a great deal of fun to detect a pompous swindle. The experiments are both enlightening and entertaining.
Composed by J. B. Calvert
Created 5 April 2000
Last revised 4 November 2003