Ординатура / Офтальмология / Английские материалы / Optics of the Human Eye_Atchison, Smith_2000

Several colleagues have commented on drafts or provided references and advice. In particular, we thank Brian Brown, Niall Strang and Tom Raasch, who read substantial

sections of drafts. Others include Ray Applegate, Pablo Artal, Harold Bedell, Arthur Bradley, Neil Charman, Nicolas Chateau, Michael Doughty, Dave Elliot, Richard Guy, Douglas Homer, Tony [oblin, Phil Kruger, Barbara Pierscionek, Katrina Schmid, Lawrence Stark, Peter Swann, Christopher Tyler, Barry Winn, Joanne Wood and Russell

Woods.

Weare grateful to Pablo Artal, Michael Cox, Larry Thibos and Barry Winn for providing data for some figures; these are also acknowledged at the appropriate figure captions. We thank the American Academy of Optometry, the Optical Society of America, Elsevier Press and the Association for Research in Vision and Ophthalmology for permission to use previously published data; again, these are acknowledged at the appropriate figure captions.

Finally, we thank our wives, Janette and Yolette, for their support.

The purpose of this book is to describe the optical structure and optical properties of the human eye. It will be useful to those who have an interest in vision, such as optometrists,

ophthalmologists, vision scientists, optical physicists, and students of visual optics. An understanding of the optics of the human eye is particularly important to designers of ophthalmic diagnostic equipment and visual optical systems such as telescopes.

Most animals have some sort of eye structure or sophisticated light sense. Like humans, some rely heavily on vision, including predatory birds and insects such as honeybees and dragonflies. However, many animals rely much more on other senses, particularly hearing and smell, than on vision. The visual sense is very complex and is able to process huge amounts of information very rapidly. How this is done is not fully understood; it requires greater knowledge of how the neural components of vision (retina, visual cortex, and other brain centres) process the retinal image. However, the first stage in this complex process is the formation of the

retinal image. In this text, we investigate how the image is formed and discuss factors that

affect its quality.

The majority of animal eyes can be divided

into two groups: compound eyes (as possessed by most insects), and vertebrate eyes (such as the human eye). Compared with

vertebrate eyes, there is considerable variation in the compound eyes. Compound eyes contain a large number of optical elements (ommatidia), each with its own aperture to the

external world. Vertebrate eyes have a single aperture to the external world, which is used by all the detectors. A number of other animals have simple eyes, which can be

described as less developed versions of the vertebrate eye. All eyes, of whatever type, involve compromises between the need for detection (sensitivity), particularly at low light levels, and spatial resolving capability in terms of the direction or form of an object.

Although this book is about the optics of the human eye we do not wish to consider the optics in complete isolation from the neural components, as otherwise we cannot appreciate what influence changes in the retinal image will have on vision performance. As an example, altering the optics has considerable influence on resolution of objects for central vision but not for peripheral vision. This is because the retina's neural structure is fine enough at its centre, but not in the periphery, for large changes in optical quality to be of importance (Chapter 18). Thus, the neural components of the visual system, particularly the retinal detector, rate some mention in the

book. The neural structures of the retina themselves produce optical effects. As an

example, the photoreceptors exhibit waveguide properties that make light arriving from some directions more efficient at stimulating vision than light arriving from other directions. Another example is that the regular arrangement of the nerve fibre layers produces polarization effects.

While image formation in the eye is similar to that in man-made optical systems such as

xii Introduction

cameras and must obey the conventional optical laws, there are some interesting

differences because of the eye's biological basis. Perhaps the greatest difference is that,

as a living organ, the eye responds to its environment, often in an attempt to give the

best image under different circumstances. Also, it grows, ages and suffers disease.

Unlike most man-made optical systems, the eye is not rotationally symmetrical about a

single axis, and different axes must be used to define image formation.

There are many interesting and important optical effects associated with ocular diseases such as keratoconus (conical cornea) and cataract. Furthermore, the balance between optical and neural contributions to overall vision performance changes with diseases of

the retina and beyond. Although there are some passing references to cataract, we have

concentrated on the healthy human eye. We give some prominence to age-related changes

in the optics of the eye throughout the book, and devote Chapter 20 to this topic.

To make the book easy to read it is divided into a number of short chapters, with each

chapter dedicated to a single theme. The most commonly useful topics are at the beginning,

and topics with narrower appeal (such as ocular aberrations) are placed towards the

end. Section 1 covers the basic optical structure of the human eye, including the

refracting components, the pupil, axes and simple models of the eye. Section 2 is about image formation and refraction of the eye.

This includes the refractive errors of the eye, their measurement and correction, and

paraxial treatments of focused and defocused

image sizes and positions. Section 3 deals with the interactions between light and the

eye, considering transmission, reflection and scatter in the media of the eye and at the fundus. Section 4 deals with aberrations and retinal image quality. As well as considering these for real eyes, it covers the modelling of eyes and the performance of a range of schematic eyes of different levels of sophistication. Section 5 considers the topics

of depth-of-field and age-related changes in the optics of the eye. While depth-of-field

effects could possibly have been placed earlier

in the book, understanding them well requires some knowledge about aberration and

diffraction. The book concludes with 4 appendices, three of which (Appendices 1, 2

and 4) cover some mathematics relating to paraxial optics, aberrations theory and image

quality criteria. Appendix 3 lists construction data, optical parameters and the aberrations of a number of schematic eyes.

Introduction

This chapter is a short overview of the optical structure and function of the human eye. It

mentions briefly some important aspects such as the cornea, the lens and ocular axes, which

are covered in more detail in later chapters. Other important topics, such as the passage of light, aberrations and retinal image quality, are also discussed in later chapters.

The structure of the human eye is shown in

Figure 1.1. The outer layer is in two parts: the anterior cornea and the posterior sclera. The

cornea is transparent and approximately spherical with a radius of curvature of about 8 mm. The sclera is a dense, white, opaque,

fibrous tissue that is mainly protective in function and is approximately spherical with a radius of curvature of about 12 rom. The centres of curvature of the sclera and cornea

4 Basic optical structureof thehuman eve

are separated by about 5 mm. More accurate measures of shapes are given in subsequent

chapters.

The middle layer of the eye is the uveal tract. It is composed of the iris anteriorly, the

choroid posteriorly, and the intermediate ciliary body. The iris plays an important

optical function through the size of its aperture, the ciliary body is important to the process of accommodation, and both the

ciliary body and choroid support important

vegetative processes.

The inner layer of the eye is the retina, which is an extension of the central nervous system and is connected to the brain by the

optic nerve.

The inside of the eye is divided into three compartments:

1.The anterior chamber, between the cornea and iris, which contains the aqueous fluid.

2.The posterior chamber, between the iris, the ciliary body and the lens, which contains the aqueous fluid.

3.The vitreous chamber, between the lens and the retina, which contains a transparent colourless and gelatinous mass called the vitreous humour or vitreous body.

The internal pressure of the eye must be higher than that of the atmosphere in order to maintain the shape of the cornea, and must be maintained at an approximately constant level in order to maintain the transparency of the ocular media. The pressure is controlled

by the production of aqueous fluid in the ciliary body and by drainage of this aqueous

fluid from the eye. This drainage is through the angle of the anterior chamber (between

the cornea and the iris) to the canal of

Schlemm (not shown in Figure 1.1) and, finally, to the venous drainage of the eye.

The eye rotates in its socket by the action of six extra-ocular muscles.

More detailed anatomical descriptions of the human eye can be found in books such as those by Hogan et al. (1971) and Snell and

Lemp (1997).

Optical structure and image formation

The principles of image formation by the eye are the same as for man-made optical systems such as the camera lens. Image-forming light enters the eye through the cornea, and is

refracted by the cornea and the lens to be

focused at the retina. Of the two refracting elements, the cornea has the greater power. However, whereas the corneal power is

constant, the power of the lens can be changed when the eye needs to focus at different distances. This process is called accommo-

dation, and occurs because of an alteration in the lens shape. It is discussed further in

Chapter 20. The diameter of the incoming beam of light is controlled by the iris, which forms the aperture stop of the eye. The opening in the iris is called the pupil. As with all optical systems, the aperture stop is a very important component of a system, affecting a wide range of optical processes, and it is discussed in more detail in Chapter 3.

Figure 1.2 shows two light beams from object points forming images on the retina. The image is inverted, as it is for a camera. We discuss this image formation in more detail in

Chapter 6.

The retina

The light-sensitive tissue of the eye is the retina. It is shown in Figure 1.3, and consists

of a number of cellular and pigmented layers and a nerve fibre layer. These layers have

reflected and scattered by each layer being of particular importance. This aspect is dis-

9. Nervefibre layer '\I'I'

10.Innerlimiting membrane --~

Thehumall eye: alloverview 5

cussed in greater depth in Chapter 14. The thickness of the retina varies from 50 urn(0.05

mm)at the foveal centre to about 600 um (0.6

mm)near the optic disc.

There is a layer of light-sensitive cells at the back of the retina, and the light must pass through the other layers to reach these cells.

These receptor cells are of two types, known as rods and cones. The names refer to their

shapes, but considerable variations in shape occur with location, and it is not always

possible to distinguish between the two types on this basis. Figure 1.4 shows their distribution along the horizontal temporal

section of the retina. There are about 100 million rods in the retina, and they reach their maximum density at about 20° from the fovea.

{....'r5. Outer plexiform layer Outer nuclearlayer

,3. Outer limiting membrane

2. Photoreceptors

(rodsand cones)

1.Pigmentepithelium Bruch's membrane

6 Basic optical structure of the human"ye

There are approximately 5 million cones in the

retina.

In general, rods are longer and narrower than cones. Rods are sometimes described as

highly sensitive low-level light detectors in comparison with cones. However, much of this is due to the neural wiring that occurs rather than differences between the receptors. The retinal neural network of rods is such that the output of about 100 rods can combine on the way to the brain, so that the rod system

has very high sensitivity to light but poor spatial resolution. In contrast, the output of fewer cones is combined, so the cone system functions at higher light levels and is capable of higher spatial resolution. Cones recover

from exposure to light more quickly than rods. The first stage in colour vision is the existence of three types of cones, each with

different wavelength sensitive properties: L (long), M (medium) and 5 (short) cones.

The cones predominate in the fovea, which is 1.5 mm or approximately 5° wide as subtended at the back nodal point N' of the eye. The fovea is free of rods in its central 1°

160

Angle from fovea (deg.)

Figure 1.4. The density of cones and rods across the retina in the temporal direction. From 0sterberg (1935), Curcio and Hendrickson (1991). The data from Curcio and Hendrickson (1991) have been converted from distances along the retina to angles relative to the back nodal point of the eye, assuming a spherical retina of diameter 12 mm and a distance between the back nodal point and retina of 17.054 rnm.

field. At high light levels the best resolution is attained by the cones in the fovea, which occupies only about l/lOOOth of the total retinal area. Despite the predominance of cones at the fovea, it contains only a small proportion (1 per cent) of the total cones (Tyler, 1996), and an even smaller proportion (0.05 %) of cones is found in the highresolution foveola. Therefore, the vast majority of cones are distributed throughout the peripheral retina. At low light levels the

cones at the fovea do not operate; thus the centre of the fovea is 'night blind', and it is necessary to look eccentrically to see objects using the rods. At very low light levels, maximum visual acuity and detection ability occur about 10-15° away from the fovea.

The location of the fovea is shown in Figure 1.1. When the eye fixates on an object of interest, the centre of its image is formed on the foveal centre, which is inclined at about 5° from the 'best fit' optical axis. At the fovea, the layers overlying the receptor cells are thinner than elsewhere in the retina (Figure 1.3) and, as a result, the fovea has a pit-like structure. The bottom of this pit is about 1° wide, and corresponds to the rod-free region. The foveola is the approximately O.5°-wide avascular centre of the foveal pit, and is the region

of highest resolution.

The diameters and packing of the foveal

cones affect visual acuity, and we examine this relationship briefly in Chapter 18. Estimates

of the diameters of foveal cones are given in Table 1.1.

The off-axis position of the fovea is most intriguing since aberration theory predicts that the best image of an optical system is usually formed on the optical axis. Therefore

the retinal image quality at the fovea should be worse than at the posterior pole. The offaxis position of the fovea has some interesting visual effects which we discuss in Chapter 17.

Table 1.1. Diameters of foveal cones. The angular values are calculated assuming the distance between the back nodal point and the fovea is 17 mm,

..Actually centre-to-centre spacing between cones.