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

This is usually a function of wavelength and temperature. However, for approximate calculations a constant value can be assumed, and values for various materials can be found in the Handbook ofChemistryand Physics (1975).

Maxwellian view

In many visual optical instruments, a small

light source S provides. a uniform f~el~-of­ view. If the entrance pupil of the eye coincides with the image S' of the source, the field-of-

view has maximum width and maximum

uniformity of luminance. This arrangement ~s called Maxwellian view (Figure 13.3).The exit

pupil of the instrument at E' is unifor~ly illuminated, and subtends an angular radius a' to the eye. The eye is focused approxi-

mately on this exit pupil. If S' is much smaller than the entrance pupil of the eye, pupil fluctuations and small eye movements do not

affect retinal illuminance.

Illumination and viewing with Maxwellian

view is optically very different from conventional viewing. For example, the fact that the effective pupil may be much smaller than the normal pupil places limits on expected visual acuity. The illumination may no longer be completely incoherent, so that conventional incoherent image quality criteria such as the point spread and modulation transfer functions may no longer be valid (Westheimer, 1966). Here, only the light levels are considered.

Equivalent luminance of a Lambertian source

Based on equation (13.1), the light in the exit pupil of the instrument produces an illumi-

.II

I

Entrancepupil

LiglIt levellit tileretina 123

nance E1 at the plane of the entrance pupil of the eye, given by

where L is the luminance of the instrument's exit pupil, and this exit pupil subtends an angular radius a' to the entrance pupil of the eye (Figure 13.3). If the image S' of the source S has an area A', the luminous flux Flux; falling on the pla~e of the entrance pupil of the eye is given by

If S' is smaller than the entrance pupil of the

eye, all of this flux falls on the retina, and the exit pupil appears to have a luminance L'.

If the observed bright field of the instrument exit pupil is replaced by a Lambertian source of the same luminance L', the

illuminance Ez in the plane of the entrance pupil of the eye is

Since the new source is Lambertian, light from it fills the pupil of the eye completely. If the

entrance pupil of the eye has area Ap' the luminous flux Fluxz falling on the plane of the entrance pupil of the eye is given by

The illuminated area of the retina is the same in the cases given by equations (13.25) and (13.27), and therefore the ratio of retinal

illuminances and hence luminances is the ratio of the fluxes entering the eye. Since the two luminances are equal, the fluxes are equal, and

ni. 'sinz(aJAp = ni. sinZ( aJA's Therefore

.II

I

Exit pupil

124 Light and tileeye

As an example, if the area of the Maxwellian image is 2 mm2, the area of the entrance pupil of the eye is 10 mm- and the luminance at the

instrument exit pupil is 100 cd/m2, the equivalent luminance of a Lambertian source is 100 x 2/10 =20 cd/rn-,

Adapting pupil size

If the pupil is fully illuminated, pupil size affects retinal illuminance, which in turn controls pupil size. This feedback system cannot operate in Maxwellian view, where the source image is usually smaller than the

smallest pupil size. Palmer (1966) found that, provided the source image in Maxwellian view is smaller than the natural pupil, the

natural pupil is larger than is the case for the same light flux entering the eye in normal

viewing.

The Stiles-Crawford effect

Stiles and Crawford (1933) discovered that the

luminous efficiency of a beam of light entering the eye and incident on the fovea

depends upon the entry point in the pupil. This phenomenon is known as the StilesCrawford effect of the first kind, but more generally as the Stiles-Crawford effect. Later, Stiles (1937) reported that varying the entry of the beam also altered the perceived saturation and hue of the light. This colour effect, called the Stiles-Crawford effect of the second kind,

is not discussed further here.

The Stiles-Crawford effect is important to

visual photometry and retinal image quality, It can be considered both as a neural and as an

optical phenomenon, as it is retinal in origin and is explained as a consequence of the wave-guide properties of the photoreceptors. It is predominantly a cone phenomenon, and hence predominantly a photopic phenomenon, A good review of the Stiles-

Crawford effect is given by Enoch and Lakshminarayanan (1991).

A number of different mathematical functions have been used to describe the Stiles-Crawford effect, with the most popular one being a Gaussian distribution as first used by Stiles (1937). This function is usually an excellent fit to experimental data out to 3 mm

from the peak of the function, and has the addition virtue of simplicity. We describe the

...~ ..

Pupil radius (mrn)

Figure 13.4.The Stiles-Crawford function for f3 values of 0.057,0.116 and 0.173, which are 2.5 per cent, 50 per cent and 97.5 per cent population limits, respectively (Applegate and Lakshminarayanan, 1993).

Stiles-Crawford effect function Le(r) as

where r is the distance in the pupil from the peak of the function. The function is normalized to have a value of 1 at the peak. The Stiles-Crawford co-efficient 13 describes the steepness of the function, and is assumed to reflect the directionality (variation in alignment) of the photoreceptor population

being tested. It may not have the same value for measurements in different meridians,

particularly in eyes affected by retinal pathology. Measured 13 co-efficients for the

Light level at tileretina 125

Photometric efficiency and reduced aperture model

Photometric efficiency

Although the Stiles-Crawford effect is a retinal phenomenon, the pupil of an eye with a Stiles-Crawford effect can be treated as being less efficient at transmitting light than a pupil of the same diameter when there is no

Stiles-Crawford effect. We can quantify this using the concept of photometric efficiency. Following Martin (1961), we denote it as 5(15)

and define it as

large-scale study of Applegate and Lakshminarayanan (1993) are given in Table 13.1, and Figure 13.4 shows the Stiles-

Crawford effect function for different 13 coefficients. Combining the data across many

studies gives a mean value of 0.12 (Applegate and Lakshminarayanan, 1993).

In many papers, the Stiles-Crawford effect function is given by equations similar to

We can write this as

P-

If we use equation (13.29) for Le(r),the integral is easily solved to give

The co-efficients in equations (13.29) and (13.29a) are related by

In terms of the entrance pupil diameter D, the photometric efficiency 5(D) is

Peak of the Stiles-Crawford effect

The position of the peak does not usually correspond to the centre of the pupil (which itself varies with pupil size), and it also varies between individuals. Its position is considered to reflect the overall alignment in the

pupil of the photoreceptor population being

tested. The ray distance r in the pupil should be measured from the peak. Measured values of the peak from two large-scale studies are given in Table 13.1. Combining the data across

many studies gives mean values of "" 0.4 mm nasal and "" 0.2 mm superior relative to the pupil reference, whether this be the pupil centre or the pupillary axis (Applegate and Lakshminarayanan, 1993).

Hence, if we express the luminance of an image in terms of the pupil area, we should multiply the latter by the appropriate factor

5(15) or 5(0).

Reduced aperture model

Sometimes we may want to know the diameter D* of the equivalent, but smaller, pupil that would collect the same luminous flux if there was no Stiles-Crawford effect. The relationship is simply

Figure 13.5 shows 0* as a function of 0 for various values of 13.

0+--..----,-----,.---,.--...,...--,---.---+

o246

Pupil diameter D (rnm)

Figure 13.5. The photometric equivalent pupil diameter D' as a function of pupil diameter D for f3 values of

0.057, 0.116 and 0.173.

in the mid-periphery of the visual field (Enoch and Lakshminarayanan, 1991).

Luminance

The Stiles-Crawford effect exists also under scotopic conditions, but is small compared with the effect found under photopic conditions (Crawford, 1937; van Loo and Enoch, 1975). The magnitude of the effect

makes a gradual change over the mesopic range.

Accommodation

Blank et al. (1975) reported that the peak of the Stiles-Crawford effect shifted between 0.4 mm and 1.0 mm nasally in three subjects with a 9 0 increase in accommodative stimulus.

They attributed this to retinal stretch during accommodation.

Some factors influencing the

Stiles-Crawford effect

Wavelength

The Stiles-Crawford effect varies with wave-

length. For the fovea, it shows a minimum in the green and larger effects at both the short

and long ends of the visible spectrum (Stiles, 1937 and 1939; Enoch and Stiles, 1961; Wijngaard and van Kruysbergen, 1975). Parafoveally (50 from the fovea) measured

functions are minimal for blue and green regions of the spectrum, and increase only for the long wavelengths (Stiles, 1939). As an example, Stiles (1937) found for his own eye (foveal vision) that f3 varied between 0.13 and 0.17 over the visible spectrum. If allowance is made for lens absorption, estimates of the

Stiles-Crawford effect increase, particularly at wavelengths less than 450 nm (Weale, 1961;

Mellerio,1971).

Eccentricity

Under photopic conditions, the StilesCrawford effect increases from the foveal

centre out to approximately 2-30 eccentricity, where the value of f3 may have doubled, after

which it declines slowly to reach foveal levels

Theory

Since the discovery of the Stiles-Crawford effect, a number of explanations have been offered for it. Most theories are based around

the assumption that the photoreceptors act as wave-guides.

O'Brien's (1946)geometric optical theory of the Stiles-Crawford effect considered that the cones act as wave-guides, using total internal reflection to channel the light to the photo-

pigment. As the ray position in the pupil increases away from the centre, the rays enter

the cones at a larger angle to increase the angle of incidence on the internal wall of the

cones and hence increase the probability of light loss through the walls. His theory does not explain the influence of wavelength adequately. A comprehensive theory was presented by Snyder and Pask (1973). They modified the wave-guide model by using a physical optical approach, which better predicts the Stiles-Crawford effect, including the effect of wavelength.

Measurement

The Stiles-Crawford effect has been measured

by a number of subjective and objective techniques (Enoch and Lakshminarayanan,

1991). The values of f3 and the peak position mentioned in this section are from subjective

methods. Subjective techniques include flicker photometry and photometric matching. Objective methods include fundus reflectometry, consensual pupillary response, the electroretinogram, and the visual evoked

response.

Role of the Stiles-Crawford effect

As mentioned at the start of this section, the Stiles-Crawford effect is important in visual photometry and retinal image quality.

Concerning visual photometry, it reduces the effective retinal illuminance at photopic

lighting levels. As discussed earlier, and as

given by equations (13.32) and (13.33), this is equivalent to having a smaller effective pupil size.

The Stiles-Crawford effect reduces the detrimental effects of scattered light on retinal

image quality at photopic lighting levels, although the extent to which this improves

visual performance is not known (Enoch, 1972). In a similar fashion, it reduces the effects of defocus and aberrations on retinal

image quality and thus reduces their influence on visual performance. The Stiles-

Crawford effect can be included in optical modelling of the eye as an apodization, which means that it can be treated as an optical filter

of variable density placed at the pupil. Its influence in this respect, as discussed further in Chapter 18, seems to be small.

Summary of main symbols

General

dioptres (i.e. rrr")

Lluminance of an extended source in cd/m2

r ray height in pupil

rmean luminous transmittance of ocular media of the eye

Light level at the retina 127

Retinal illuminance: directly transmitted light

E'T retinal illuminance in trolands

Iluminous intensity of a point source in cd

Retinal illuminance: scattered light

Eilluminance in plane of eye

Lv(8) equivalent veiling luminance in a direction ()

Photon density levels

N(A).1A photon density in photons/rn-ys

Maxwellian view

Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality. J. Opt. Soc. Am. A, 10, 1611-23.

Bedell, H. E. and Katz, L. M. (1982). On the necessity of correcting peripheral target luminance for pupillary area. Am. J. Optom. Pilysio/. Opt., 59,767-9.

Blank, K., Provine, R. P. and Enoch, J. M. (1975). Shift in the peak of the photopic Stiles-Crawford function with marked accommodation. Vision Res., 15, 499-507.

Campbell, C. (1994). Calculation method for retinal irradiance from extended sources. Ophthal. Physiol. Opt., 14, 326-9.

Charman, W. N. (1989). Light on the peripheral retina.

Ophtha/. Pilysio/. Opt., 9, 91-2.

Crawford, B. H. (1937). The luminous efficiency of light rays entering the eye pupil at different points and its relation to brightness threshold measurements. Proc. R.

Soc. B., 124, 81-96.

Drasdo, N. and Fowler, C. W. (1974). Non-linear projection of the retinal image in a wide-angle schematic eye. Br.J. Ophtha/., 58, 709-14.

Dunnewold, C. J. (1964). On the Campbell and Stiles-Crawford effects and their Clinical Importance.

128 Light 11Ild Ihl'eye

Institute for Perception. The Netherlands National Defence Research Organisation RVOTNO.

Enoch, J. M. (1972). Retinal receptor orientation and the role of fiber optics in vision. Am. J. Oplom. Arch. Am. Acad. Optom., 49, 455-71.

Enoch, J. M. and Lakshminarayanan, V. (1991). Retinal fibre optics. In Visual Optics alld 1I1slrumePllalioll, vol. 1 of Cronly-Dillon, J.R. Visioll alldVisual Dysfl/llclicm (W. N. Charrnan, ed.), Macmillan Press.

Enoch, J. M. and Stiles, W. S. (1961). The colour change of

monochromatic light with retinal angle of incidence.

Oplica Acta,8, 329-58.

Fry, G. A. (1954). A re-evaluation of the scattering theory of glare. Illuminating Engineering, 49, 98-102.

Handbook of ClTemislry and Pltusic« (1975). Weast, R. C.

(ed.). 56th edn. CRC Press.

Holladay, L. L. (1927). Action of a light-source in the field of view in lowering visibility. J. 01'1. Soc. Am., 14, 1-15.

Kooijman, A. C. (1983). Light distribution on the retina of a wide-angle theoretical eye. J. 01'1. Soc. Am., 73,

1544-50.

Kooijman, A. C. and Witmer, F. K. (1986). Ganzfeld light distribution on the retina of human and rabbit eyes: calculations and ill vilro measurements. J. 01'1. Soc. Am.

O'Brien, B. (1946). A theory of the Stiles and Crawford effect. J. 01'1. Soc. Am., 36, 506-9.

Palmer, D. A. (1966). The size of the human pupil in viewing through optical instruments. Visioll Rcs., 6,

471-7.

Smith, G. and Atchison, D. A. (1997). ti« Eye alld Visual Oplical IllslrumCllts, pp. 286, 308, 547. Cambridge University Press.

Snyder, A. W. and Pask. C. (1973). The Stiles-Crawford

effect - explanation and consequences. Visioll Rcs., 13,

1115-37.

Stiles, W. S. (1929). The effect of glare in the brightness difference threshold. Proc. R. Soc. 8.,104,322-51.

Stiles, W. S. (1937). The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect. Proc. R. Soc. B., 123,

90-118.

Stiles, W.S. (1939). The directional sensitivity of the retina

and the spectral sensitivities of the rods and cones. Proc.

R. Soc. B., 127, 64-105.

Stiles, W. S. and Crawford, B. H. (1933). The luminous

efficiency of rays entering the eye pupil at different points. Proc. R. Soc. B., 112, 428-50.

van den Berg, T. J. J. P. (1995). Analysis of intraocular straylight, especially in relation to age. Oplom. Vis. Sci.,

12,52-9.

van den Berg, T. J. T. P. and Ijspeert, J. K. (1992). Clinical assessment of intraocular stray light. Applied Oplics, 31,

3694-6.

Van Loo, J. A. and Enoch, J. M. (1975). The scotopic Stiles-Crawford effect. Visioll Res.,15, 1005-9.

Vos. J.J. (1984). Disability glare - a state of the art report.

ClE-I, 3(2), 39-53.

Vos, J. J. and Bouman, M. A. (1959). Disability glare; theory and practice. Proc. CIE,Brussels 1959,298-306.

Walraven, J. (1973). Spatial characteristics of chromatic

induction; the segregation of lateral effects from straylight artefacts. Visioll Res., 13, 1739-53.

Weale, R. A. (1961). Notes on the photometric significance of the human crystalline lens. Vision Res., 1, 183-91.

Westheimer, G. (1966). The Maxwellian View. Vision Rrs.,

6,669-82.

Wijngaard, W. and van Kruysbcrgen, J. (1975). The

function of the non-guided light in some explanations of the Stiles-Crawford effects. In Plwloreceplor Oplics

(A. H. Snyder and R. Menzel. eds), pp. 175-83. Springer-Verlag.

Introduction

As well as the absorption of light by the

retinal photoreceptors, which initiates the neural processes of vision, other interactions of light with the fundus of the eye (a term that

generally includes the retina, choroid and sclera) are important. Light from the fundus

that passes out of the eye is essential for the diagnosis of ocular disease in ophthalmoscopy. Light from the fundus passing out of the eye is also important for determination of

refractive error by retinoscopy and other objective techniques (Chapter 8). The spectral absorption by the fundus is important for understanding the processes of retinal damage by excessive light levels. In this chapter, we examine the specular reflection, scatter and absorption of light at the fundus.

These properties are affected by the optical properties of the fundus layers (see Figure 1.3). Of particular importance are four absorbing pigments: macular pigment in the retina, visual pigments in the photoreceptors, melanin mainly in the pigment epithelium, and haemoglobin mainly in the choroid. There are individual and racial differences in the amount of the pigments, particularly melanin (Hammond et al., 1997). We will

consider specular reflection, scatter and absorption at the layers along a typical ray

path.

Inner limiting membrane to photoreceptors (six layers>

Light is first incident on the retina at the inner limiting membrane, and there will be some

specular reflection at this boundary. The six

layers between this boundary and the photoreceptors are highly transparent, but the regular array of the fibres in the nerve fibre

layer has some effect on polarized light. There is a yellow pigment called xanthophyll in the macula (the macula pigment), and the amount

of this pigment varies greatly between individuals (Ruddock, 1963; Bone and

Sparrock, 1971).

The photoreceptors

Some light is then absorbed by the visual pigments in the photoreceptors. There is little data available on the proportion of light incident on the retina which is absorbed by the visual pigments and, therefore, contri-

butes to visual perception, but the proportion will vary with state of light adaptation, retinal location and spectral light distribution. Rodieck (1998) made some estimations of the

proportion of light which stimulates vision for a large pupil (0:: 7mm diameter) when looking directly at a star. Ninety-two per cent of the light incident at the inner limiting membrane reaches the cones after absorption by the macular pigment. Of this amount, 53% reaches the cone outer segments which

130 Li~ht and me eye

contain the visual pigments. Of this amount, 38% is absorbed by visual pigment. Finally, 67% of this amount results in a photochemical reaction. Combining these proportions gives a retinal 'efficiency' of 12%. Combining this 12% with the 54% of the light incident on the cornea which reaches the retina, approximately 7%of the light incident at the cornea is responsible for initiating the neural responses in the retina and beyond. Rodieck made estimations at 15° eccentricity to obtain a similar overall result for the rods of the dark adapted retina.

The pigment epithelium

The remaining light passes into the pigment epithelium, where there is strong absorption and scatter by melanin granules. Some light passes through the pigment epithelium and enters the choroid.

The choroid

The thin (350-450 urn) choroid is highly vascularized, but contains some melanin.

Thirty to sixty per cent of the choroid is blood (Delori and Pflibsen, 1989). This contains

haemoglobin, which is mainly oxygenated and strongly absorbs short wavelength light and back-scatters longer wavelengths. A small amount of light penetrates the choroid

to reach the sclera.

The sclera

This dense, whitish tissue back-scatters light strongly, so that most light reaching the sclera passes back through the retina.

Fundus reflectance

The term fundus reflectance refers to the light

specularly reflected and scattered at the fundus and which eventually passes back out

of the eye. Fundus reflectance can be measured by illuminating the fundus with a

light source and analysing the spectrum of

light emerging from the eye. However, this is complicated by a number of factors:

1.III iiioo spectral reflectance measurements involve the passage of light through the ocular media twice. We know from

Chapter 12 that the ocular media absorb light, and that this absorption is not

spectrally neutral. The effect of the spectral absorption of the ocular media is thus doubled.

2.III vivo results are contaminated by specular reflections from the refracting surfaces.

3.Reflectance measurements must use a reference baseline, which is often taken to be a white tile of high, diffuse reflectance, such as one based upon magnesium oxide.

4.Pigment absorption by the photoreceptors depends upon the level of bleaching and hence their immediate previous light exposure.

Measured values of fundus reflectance are shown in Figure 14.1. Reflectance is low at

short wavelengths, and gradually increases with increase in wavelength. The high reflect-

ance at the longer wavelengths is attributed to the blood in the choroid.

60-t-----1---'-----J----l.-__L-_-+

--Geeraets and Berry ( 19681

~Hunold and Malcssa (1974)

50

Delori and Pflihsen (1989)

--<>-- Nasal fundus

40-0-- Parafovea

~Fovea

~c 30 t;"

t;::'"

~ 20

10

Wavelength (nm)

Figure 14.1. Spectral reflectance of the fundus from

Geeraets and Berry (1968)- reflectance of pigment epithelium and choroid, Hunold and Malessa (1974)- derived from their extinction values, and Delori and Pflibsen (1989)- illl'illo measurements on 10 normal

subjects at different retinal locations.

Polarized light

Some early workers in ocular polarization concluded that most polarized light incident

upon the fundus is depolarized upon return out of the eye. This was because conversion of

linear polarized light into elliptical polarized light was mistaken as depolarization (van Blokland, 1985). More recent studies have found that most polarization is retained, although the orientation of polarization may

change (birefringence). Van Blokland (1985) found about 90 per cent retention (fovea, 514 nm) and Dreher et al. (1992) found 5O-S0 per

cent retention (close to the optic disc, 633 nm). Van Blokland and van Norren (1986) found that the retained polarization at the fovea decreases with increase in wavelength ("" 90

Guided and unguided light

Some of the light incident on the retinal

pigment epithelium is returned within the outer segments of photoreceptors, and can be considered to be guided or directed (van Blokland and van Norren, 1986). The rest of the returned light may be considered to be unguided. Bums et al. (1995 and 1997) developed and used an objective instrument

for measuring cone photoreceptor alignment by measuring the distribution of light returning from the retina corresponding to different positions of a small light source at the pupil. The distribution is affected by the guiding of light along the photoreceptors. For bleached retinas, this produced functions with

peak pupil positions that match those obtained by psychophysical measurements of the Stiles-Crawford effect (see Chapter 13, The

Stiles-Crawford effect).

Layers responsible for the fundus reflectance

On the basis that different components of reflectance (polarized versus unpolarized, and guided versus unguided) showed similar dependencies on wavelength, van Blokland and van Norren proposed a simple model in

Lixilt interaction untl: tile [undus 131

which one layer is mainly responsible for the fundus reflectance. Because the wavelength

dependence of the fundus reflectance was similar to that of the retinal pigment epithelium, they suggested that the retinal pigment epithelium is this layer. This argument was supported by the fact that the

guided component increased with increased bleaching of retinal pigment, an effect that would not occur if the responsible layer was in front of the receptors. More sophisticated

models have been developed since with van de Kraats etal. (1996) proposing that the outer

aspects of the cones are responsible for the guided component of reflectance.

Veiling glare

Some of the light scattered by the fundus will

contribute to veiling glare, because light that is scattered sideways (halation) and back-

wards can illuminate photoreceptors, some a

long way from the original site of incidence. The Stiles-Crawford effect may reduce the luminous efficiency of this scattered light. Veiling glare is reduced for people with dark irides compared with people with light irides, and this has been attributed largely to the level of fundus pigmentation (IJspeert et al., 1990; van den Berg, 1995).

Absorption

Light that is not specularly reflected or scattered back out of the eye from the fundus is either absorbed or scattered in other directions within the eye. Since scattered light has the potential to excite photoreceptors in other parts of the fundus, one would expect the fundus to preferentially absorb rather than scatter. The layers of the retina in front of the

cones and rods are highly transparent.

Absorption is due mainly to visual pigments in the photoreceptors, melanin in the pigment epithelium, and haemoglobin in the choroid.

Figure 14.2a shows spectral absorption of the pigment epithelium and choroid (Geeraets and Berry,1968). Figure 14.2bshows spectral absorption of oxygenated hemoglobin (van Assendelft, 1970), and Figure

Figure 14.2. Absorption of the fundus:

a.Pigment epithelium and choroid (Geeraets and Berry, 1968).

b.Oxygenated hemoglobin (van Assendelft, 1970).This is for a concentration of 0.00233moles/litre and 0.1 mm thickness.

c.Macular pigment (Wyszecki and Stiles, 1967).

14.2c shows spectral absorption of the macular pigment (Wyszecki and Stiles, 1967).

Birefringence

Birefringence has been discussed in Chapter 12 (Birefringence> with regard to the media of

the eye. In birefringent materials, refractive index depends upon the direction of the light

beam and upon the direction of the electric vector. The retinal nerve fibre layer exhibits

birefringence because of the structure of the

nerve fibres and their regular arrangement (Dreher et al., 1992). The nerve fibres form a radial pattern centred on the optic disc but, because over short distances neighbouring fibres can be regarded as parallel, the nerve fibres can be regarded as a layer of long parallel cylinders perpendicular to the retinal surface. Such an arrangement acts as a

uniaxial crystal, with its optic axis being parallel to the axis of the cylinders and

perpendicular to the incident light. The

refractive index will be at minimum for the electric vector perpendicular to the nerve fibre