Chapter 14

Ophthalmoscopy.

In this chapter, we will be looking at various methods for viewing the retina of a patient.

Ophthalmoscopy

You might imagine that it would be quite difficult to clearly see someone else's retina, but in fact it is optically no harder than simply looking straight into their eye. The problem is that the inside of the eye is quite dark - only a small amount of light passes into it through the pupil, and a lot of that gets absorbed by the retina - so the main issue is how to get enough light into the eye to see the retina clearly. We'll address that problem later.

If, somehow, we do get light into a patient's eye, the optics of seeing their retina are fairly straightforward. Once the patient's retina is illuminated, it will diffusely reflect the illuminating light, so bundles of divergent rays will come off all points on the patient's retina (diffuse reflection, Chapter 1). The divergent light coming from a point on the fovea, when it passes through the lens and cornea, emerges from the eye as a parallel beam of light (provided the patient is emmetropic).

This is easiest understood by reversing the direction of light. Under normal circumstances, when an emmetrope views a distant object, parallel bundles of rays from each point of the object are converged onto single points on the retina ( Figure 1(a)). The path a ray takes is the same whether the ray is travelling forwards or backwards along that path. Thus, if we illuminate the retina, each illuimnated point creates divergent light which is like light travelling in the opposite direction from the convergent light in Figure 1(a). This light then emerges in parallel from the eye ( Figure 1(b))

fig1a — **Figure 1(a).** An emmetrope views a bundle of parallel rays from a distant point object. The rays converge to a point on the retina.

fig1b — **Figure 1(b).** The light that isn't absorbed by the retina is diffusely reflected. The reflected rays that hit the lens and cornea leave the eye as a parallel bundle. These rays are essentially the incoming rays in reverse.

fig1c — **Figure 1(c).** If another emmetropic eye (on the left) catches the parallel light leaving the first eye, they can focus the parallel rays to form a sharp image of the point on the retina reflecting that light.

Parallel light thus emerges from an illuminated retina (if the patient is emmetropic). If you place your own eye in the path of this parallel beam of light, you can (if you're also emmetropic) focus it and form an image of the patient's retina on your own retina. ( Figure 1(c))

Field of View

If we looked at a landscape through a small hole in a wall, our field of view - how much we can see - is limited. Two things would increase how much of the landscape we could see. One is to move closer to the hole. The other is to make the hole bigger.

Ophthalmoscopy is similar: we are viewing the patient's retina through a tiny hole - their pupil. We can improve our field of view - in this case, how much of their retina we can see - by moving closer to the pupil, or by making the pupil wider, by using drugs which dilate it. What's not obvious, however, is that the field of view is also limited by our own pupil size.

Figure 2 shows the effect of moving your eye closer to the patient's eye. You can see what happens when you move closer by dragging the left hand eye (the observer's eye, i.e. your eye if you are doing ophthalmoscopy) closer to the patient's eye on the right hand side.

Figure 2. The effect of distance on the field of view. Reflected light from from three points on an illuminated retina emerges from the right hand eye in parallel. By the time the three beams leaving the eye have reached the observer's eye on the left, they have completely separated, so only the centre beam (green) enters the observer's eye on the left. Thus, the observer can't see the parts of the retina where the blue or orange beams come from.

To see all beams simultaneously, the observer must move to where the beams can enter their pupil. You can see where this occurs by dragging the left hand eye closer. (Note that the three points on the illuminated retina are very far apart, so you have to get unrealistically close to see them. In reality, you could never get this close, so your field of view is more restricted.)

Figure 3 shows the effect of changing the patient's pupil size, or changing your own pupil size. The sliders underneath each eye control their pupil. To begin with, both eyes have a \( 3\text{mm} \) pupil. In that case, only the beam of light from the middle of the patient's retina strikes the observer's eye.

If the patient's pupil is widened, the beams of light leaving the eye are also widened, and so some of them overlap the observer's retina. If the observer's pupil is widened, they can then catch some of the beams that would otherwise be stopped by their iris.

Figure 3. Pupil size

We can work out exactly how these factors influence the field of view by analyzing a simple optical system. Figure 4 shows a simplified optical picture of ophthamoscopy. Here, the patient's eye has been reduced to a retina and a positive lens, and the observer's eye has been reduced to another positive lens.

The furthest point of the patient's retina that can be seen by the observer is \( x \) in Figure 3(a). Two rays have been drawn from \( x \): one goes through the centre of the patient's lens, and so is not deviated. The other hits the top of the lens and is refracted to come out parallel to the first ray. If \( x \) were any higher, the rays would be slanted down more, and miss the observer's lens. The field of view that the observer has is twice the angle \( \alpha \). In Figure 3(b), the angle \( \alpha \) is also the angle between the yellow middle ray and the imaginary horizontal line running through the centres of the two eyes.

fig3a — **Figure 4(a).** The patient's eye has been reduced to a thin lens and a flat retina on the right of this figure. Rays diverging from \( x \) emerge from the lens in parallel. The point \( x \) is the highest part of the retina that can be seen by the observer, because the (green) ray from \( x \) that hits the top of the patient's lens is refracted to just hit the bottom of the observer's lens. If \( x \) were any higher, this ray would miss the observer. The angle \( \alpha \) is half the field of view.

fig3b — **Figure 4(b).** The angle \( \alpha \) is also the angle between the yellow ray and the dotted line joining the patient and observer.

fig3c — **Figure 4(c).** The aperture of the patient's eye is \( h \) and of the observer's eye \( p \). The tangent of \( \alpha \) is given by the triangle with base \( d \) and height \( h/2+p/2 \).

In Figure 3(c), the angle \( \alpha \) is the angle inside a triangle. The triangle has a base equal to \( d \), the distance between the eyes. If \( p \) is the aperture of the observer's eye, and \( h \) is the aperture of the patient's eye, then the height of the triangle is \( p/2+h/2 \). Thus

\[\tan{(\alpha)}=\dfrac{p/2+h/2}{d}\]

When \( \alpha \) is quite small (which it is in ophthalmoscopy), then \( \tan{\alpha}\approx\alpha \), and so \( \alpha\approx(p/2+h/2)/d \), for \( \alpha \) measured in in radians. Since \( \alpha \) is only half the field of view, doubling it gives the full field of view:

\[\text{field of view (radians)}=\dfrac{p+h}{d}\]

For example, if the patient and observer's pupils are both \( 3\text{mm} \), and their eyes are \( 15\text{cm} \) apart, then the field of view is \( 6/150 = 0.04 \) radians, or about \( 2.3 \) degrees (\( 1 \) radian \( \approx 57 \) degrees). However, the above formula defines the field of view as any point on the patient's retina where even a single ray makes it into the observer's eye. It might be quite hard to see a single ray of light, so the useful field of view is somewhat smaller than this. Since we don't have a precise definition of useful, we can't precisely define how big a useful field of view is, but we can get a rough idea of its size by subtracting one to two mm from both patient and observer pupils. The useful field of view, in the above case, is (very roughly) \( 3/150 = 0.02 \) radians, or \( 1.2 \) degrees.

How big does a \( 1^o \) field of view look in ophthalmoscopy? The central \( 1 \) degree of the retina is about \( 0.25\text{mm} \) wide. A field of view of \( 1 \) degree will also look about twice as wide as the full moon, which has a visual angle of \( 0.5 \) degrees. So ophthalmoscopy will enlarge the central \( 1/4\text{mm} \) of the retina to something looking twice as tall as the moon.

It's often said that the magnification produced by ophthalmoscopy is about \( 15\times \). This isn't a very useful figure however; if you look at Figure 2 you can see that, once the observer's eye is close enough to see all three points on the patient's retina, getting closer doesn't change how far apart the image points are. That is, the size of the image formed in the observer's eye is the same regardless of how close or far from the patient they are.

From the equation for the field of view, there are three ways of improving it:

Reduce the distance \( d \) as much as possible - Figure 2.
Dilate the patient's pupil i.e. increase \( h \) - Figure 2, using the right hand slider.
Dilate the observer's pupil i.e. increase \( p \) - Figure 2, using the left hand slider.

The first two are commonly used in ophthalmoscopy. While the third option is not really practical, it is the motivation behind indirect ophthalmoscopy.

Illuminating the Retina

All the above discussion assumes the patient's retina can be brightly illuminated, so light reflecting off it leaves their eye in sufficient quantity to be seen by an observer. However, the only way we can get light into the patient's eye is through their pupil, which presents a few problems:

The pupil is small, so the quantity of light making it into the eye is limited.
The light going into the eye has the same field-of-view probelm as the light leaving the eye: only a small spot of the retina can be illuminated.
The patient's cornea acts a bit like a convex mirror, and reflects the light, forming a reflection of the light source in front of the patient's retina, thus obscuring part of it.

The first problem can be solved by using a bright light, although this is uncomfortable for the patient and tends to make the third problem worse. We can however do some clever things with the light beam to minimize the reflections and to maximize the area of the retina that is illuminated. Figure 5 shows some of the things that can be done to get light into the patient's eye.

fig4a — **Figure 5(a).** One way to introduce light into the patient's eye is to shine a light into it. Because of the limited space, the light is usually directed into the eye by a mirror between the patient and observer. There are three problems with this approach: First, the mirror blocks the observer's view of the eye. This can be fixed by cutting a hole in the middle of the mirror or by using a half-silvered mirror which both reflects and transmist light. Second, there is a strong reflection right in the middle of the cornea, obscuring the view of the retina. Third, the parallel beam of light is focused to a point by the patient, so it doesn't illuminate much of the retina at all.

fig4b — **Figure 5(b).** We can solve some of these problems by moving the mirror and tilting it. Here the light beam is sent upwards into the patient's eye. This moves the reflection of the light downwards, allowing a beter view of the retina. But the light is still focused to a point, so it doesn't cover much of the retina at all.

fig4c — **Figure 5(c).** The problem with the light beam focussing can be overcome by introducing a positive lens. This lens causes the light beam to converge strongly within the patient's eye. The convergence of the light is so much that the patient's cornea and lens hardly change it at all. The light then spreads out over a larger area of the retina.

fig4d — **Figure 5(d).** The ophthalmoscope handle contains a light source, although the beam does not usually come out at such an angle from the viewing axis.

A way of thinking about the reflection caused by the illuminating light is to think of the cornea as a spherical mirror, with a radius of \( 7.8\text{mm} \) (Chapter 8). This gives a power of \( F=-64\text{D} \) (Chapter 7), because it is a convex (diverging) mirror. The reflection of the light is the virtual image of the light rays hitting the cornea.

The cornea will cause a troublesome reflection if

the position of the virtual image is between the observer's eye and the patient's eye.
rays reflected from the cornea manage to get into the observer's eye.

The illumination shown in Figure 5(c) is idealized - it would generally not be possible to get the light beam so far out of the way. Still, it shows what ophthalmoscope designers might be aiming form.

Correcting Ametropia during Ophthalmoscopy

In the figures above, the assumption was that the patient is emmetropic. Thus, light leaving the patient's eye is parallel, and can be easily focused by an emmetropic observer. This simple situation becomes more complicated if the patient or observer (or both) are not emmetropic. However, this problem is easily solved by putting an extra lens between the patient and the observer, whose purpose is to adjust the vergence of the light to suit the observer's eye.

For example, if the patient is myopic, then light reflected off their retina will leave the eye converging rather than parallel. In this case, a negative lens of the appropriate power (in fact, the power used to correct their vision) will make the light parallel.

Indirect Ophthalmoscopy

The field-of-view equation shows that if the viewing eye aperture \( p \) is large, the field of view is increased. This is the main idea behind indirect ophthalmoscopy (opthalmoscopy using only our own eye is called direct ophthalmoscopy). We can use a large positive lens instead of our own eye to image the retina. This large lens will create an image of the patient's retina floating in space (what's called an aerial image). Because the lens can be made much larger than our own pupil, the field of view is greatly increased compared to direct ophthalmoscopy ( Figure 5).

fig5a — **Figure 5(a).** The principle behind indirect ophthalmoscopy. Instead of using their eye, the observer uses a strong positive lens to form an aerial image of the patient's retina. Comparing this to Figure 2 , the field of view is greatly increased. However, the light rays leaving the three points shown in the aerial image don't overlap here, so it isn't possible to see the three points simultaneously.

fig5b — **Figure 5(b).** The solution is to view the aerial image at some distance. If you put your eye at point (a), you get light from both the top and middle of the aerial image (and all points in between) and so can see that entire stretch of the image. At (b) you can see the entire bottom of the aerial image. By moving even further back, you can see even more. Of course, moving back makes the aerial image appear smaller, which is a disadvantage compared to direct ophthalmoscopy.

You might think that it would be simple to view the aerial image formed by the ophthalmoscopy lens. However, in Figure 5(a), the diverging rays leaving each point in the aerial image form a narrow cone of rays, and they don't overlap. That means you can't see both the top point in the aerial image and the bottom one simultaneously within Figure 5(a). However, the narrow cones do spread out a bit, so if you move further away from the aerial image ( Figure 5(b)) there are areas where the light cones from different points in the aerial image do overlap. In the places where the cones overlap, it is possible to see both points in the aerial image at the same time. That is why, when doing indirect ophthalmoscopy, the observer cannot view the aerial image up close, but needs some distance between themself and the image to see most of it.