2.4 Vision in Action

For a fixed distance, the vergence varies approximately linearly with the aperture size and approximately, inversely with the distance for a fixed aperture size.

Image formation by a lens results from refraction of light due to the fact that the speed of light varies with the medium it is in. Light moves more slowly in matter, such as the lens of the eye, than it does in a vacuum. The degree of reduction in speed depends on the type of material, with the ratio of the speed of light, c, in a vacuum to its speed in another medium, ν, equal to the refractive index, n, of the medium. i.e.

n = c /ν > 1

The speed of light in air is very close to that in a vacuum and therefore the refractive index of air is generally taken to be 1.0. The refractive index is also dependent on wavelength and greater for shorter wavelengths than longer ones. The change in speed with the change in medium generally also results in a change in direction. This change in direction leads to a bending of the light rays. The change in direction can be expressed in terms of Snell’s law which states that the ratio of the sines of the directions (θi and θr for the incident direction and direction after refraction respectively) in two different media is equal to the ratios of the respective refractive indices (ni and nr):

Since the degree of bending or refraction is determined by the difference between the refractive indices of the two media, the air-cornea interface has the greatest effect on the eye’s optical power. Vision is blurred underwater due to the reduced difference between the refractive indices of the cornea and water as compared to the cornea and air. Any scarring of the surface of the cornea or asymmetrical curvature can significantly reduce image quality, whereas the small loss in power due to removal of the lens can be compensated for by spectacles, contact lens or intraocular lens implants.

In general, the optical properties of the eye can be modelled by a lens of negligible thickness. Parallel rays striking the lens are made to converge towards a point on the axis called the focal point of the lens. A ray of light passing through the centre of a thin lens does not change direction. The nodal point is the point on the axis of the lens where rays of light pass through without changing direction. The eye is a compound optical system that has two nodal points. However, since the two nodal points are close together relative to the distance from the eye to the object being viewed, they can be treated in practice as one nodal point about 15–17 mm in front of the retina. This distance is called the posterior nodal distance and varies slightly between people. Using the one nodal point approximation makes it easier to calculate the size of the image on the retina. From Figure 2.6, the angle φ is given by

78 2 Perception, the Eye and Assistive Technology Issues

When light makes contact with an object, it can be absorbed (and the energy converted to heat), transmitted and/or reflected. In many cases, some light is absorbed and some reflected, with the proportions depending on the wavelengths. A pigment absorbs energy in some wavelengths and reflects others. Pigments appear to be coloured if the refracted energy is in the visible light range. However, the colour perceived depends on the properties of the visual system as well as the wavelengths reflected.

Rods contain rhodopsin, which has a peak sensitivity at about 510 nm in the green part of the spectrum. Rhodopsin is sometimes called visual purple, as it reflects blue and red, making it look purple. There are three different types of cones with peak absorptions at about 430, 530 and 560 nm. These types of cones are therefore referred to as blue, green and red cones. However, these names refer to the peak absorption sensitivities rather than how the pigments appear and monochromatic light with wavelengths of 430, 530 and 560 nm are violet, bluegreen and yellow-green rather than blue, green and red. In addition, the three cones have overlapping sensitivity curves. Light at 600 nm will have the greatest response from red cones with their peak sensitivity at 560 nm, but will also have a weaker response from the other two cone types (see Figure 2.8).

The presence of three different types of cones allows colour and brightness to be distinguished, and coloured light to be distinguished from white light. If there were only two types of cones, the monochromatic wavelength that stimulated the two cone systems in the same ratio as white light would be indistinguishable from white light. Therefore, colour-blind people with only two types of cones have a wavelength of light that they cannot distinguish from white light.

The cones function together, whereas the rods work on their own. Although rods and cones may both be functioning in intermediate levels of light intensity, the effects are not combined. People are able to distinguish shapes fairly well in dim light, but are unable to see colours.

Theories of colour vision need to account for the colours of the rainbow, the purples obtained by stimulating the red and blue cones or combining long and short-wavelength light, the pale or desaturated colours obtained from adding white to any other colour and the browns. There are two main theories: the Young- Helmholtz-Maxwell trichromatic theory (see Figure 2.9) and the opponent theory due to Hering (see Figure 2.10). These two theories were originally thought to be contradictory, but it is now realised they are complementary. According to the trichromatic theory, the perception of colour is the result of unequal stimulation of the three types of cones. Light with a broad spectrum of wavelengths, such as light from the sun or a candle, will stimulate all three types of cones approximately equally, giving white. The appearance of white light can also be obtained by using two complementary beams of narrow-band light, such as yellow and blue or red and blue-green which give white when they are mixed together (see Figure 2.9).

The trichromatic theory can predict and explain many, but not all, colour phenomena. For instance, it does not explain why the colour of an object depends on simultaneous and successive colour contrasts, that is, the colours surrounding it and the colours seen immediately before it respectively. According to the opponent colour theory, there are two chromatic visual pairs, comprising yellow and blue,

Figure 2.8. Sensitivity of the cones to different wavelengths of light

and red and green and an achromatic pair, white and black. Opponency means that the colours of an opponent chromatic pair cannot be seen together and therefore there are no reddish green or bluish yellow colours (see Figure 2.10).

Some retinal ganglion cells are excited by one colour in the pair and inhibited by the other, for instance, excited by red light and inhibited by green light, and only fire when there is no green light. These cells have a {red-on, green-off} receptive field and do not respond to a combination of red and green lights if the excitatory and inhibitory effects are approximately equal and therefore cancel each other. There are also cells with {green-on, red-off}, {blue-on, yellow-off} and {yellowon, blue-off} responses. Some cells have centre-surround receptive fields, such as a {red-on centre, green-off surround}.

A {red-on, green-off} cell receives excitatory input from an L (red) cone and inhibitory input from an M (green) cone, whereas a {yellow-on, blue-off} cell receives excitatory input from both M and L cones and inhibitory input from S (blue) cones. When the input is a combination of red and green light, {red, green} cells do not fire due to the opponency of the M and L cone inputs. However, the {yellow-on, blue-off} cells are excited by the M and L cone inputs, whereas the {blue-on, yellow-off} cells are inhibited, so that yellow is transmitted and the combination of green and red is perceived as yellow.

When the input is a combination of yellow and blue light, the yellow light affects the M and L cones and inhibits the {red, green} cells due to opponent input from these cones. The blue light affects the S cones and the {blue, yellow} system is

80 2 Perception, the Eye and Assistive Technology Issues

Figure 2.9. Response of the cones to different mixtures of coloured light

inactivated due to the opponent nature of the S and M+L cones. The black channel is also inhibited and therefore white is perceived. When looking at a grey or white background after a bright colour, such as red, people see the contrast colour, in this case green. A bright red flash or prolonged view of red makes the L cones adapt and reduces their sensitivity compared to the M cones. Therefore, subsequent viewing