VS 117
February 2, 1999
Notetaker: Stacie Low
Announcements:
- Our TA, Erich, needs subjects for his experiment on accomodative
vergence. Subjects will be paid $9/hour and it is for about 3
hours a week. Subjects must have refractive error between 0 to
±3.00D. Please e-mail him or talk to him after class.
- When sending co-ops to Dr. Schor via e-mail, remember not to
send him viruses! Please run your anti-virus programs on your
disks.
- There will be a quiz next week on measuring eye position, measuring
accomodation, and Gaussian equations. Basically, it's everything
including today. The website has old quizzes. Bring a calculator.
Today the first lab will be introduced The lab will be lab number three in the reader on the measurement of accommodation.
Today we're going to start the subject of accommodation.. Accommodation is defined as the ability to adjust the dioptric power of the eye. We do this so that we can focus images over a wide range of viewing distances. Accommodation makes objects in space conjugate to the retina and I wanted to talk to you about this concept.
Consider a simple plus lens and you have a light source on
either side of the lens. You could have a light source at point
1 and the image would be at position 2 or you could have a light
source at position 2 and the image would be at position 1. Your
object planes on either side of the lens in space will be imaged
on each other. These are conjugate planes. Generally, the retina
is one plane and the object in space is the other. What you are
trying to do is make the retina conjugate to some distance in
space and that is what you are doing when you accommodate. You
are changing the power of the eye which then makes a different
set of distances of planes conjugate to the retina. When you
focus a clear image, what you have really done is change the power
of your eye. Your retina is now conjugate to that object distance.
As you increase the power of the eye (accommodate) the retina
becomes conjugate to a nearer object. As you reduce the power
of the eye, the retina becomes conjugate to a more distant object.
Mechanisms controlling accommodation vary greatly among vertibrates.
It is probably the most diversified motor action. I'll talk
more about that at the end of the lecture.
2
1
Let's talk now about how we measure accommodation with a device called an optometer. It is a device used to measure the optical power of the eye. It's the namesake for Optometry ("eye measurer") There are two categories of Optometers, subjective and objective.
SUBJECTIVE OPTOMETERS
Simple optometer
1.5cm
·
focal pt.
EYE
Virtual Real optometer
Lens
Here is our simple optometer. It is a plus lens in the spectacle
plane which is about 1.5 cm in front of the eye. This turns out
to be a very special point. It is the anterior focal point of
the eye, assuming the eye is +60.00D in power. As optometrists,
we want to find the conjugate plane to the retina (refractive
error) which can be anywhere from optical infinity up to the cornea.
If the patient is an emmetrope, the conjugate point of the eye
is at infinity. If the eye is a 10D myope, the conjugate focus
is 10cm away. Here's why we use the optometer. What the optometer
does is it allows us to take a real object and move it small ranges
of distances to form a virtual object that moves over an infinite
range. So when my object is at the focal point of the lens, the
object is at infinity. But as I move the real object closer
to the lens, the virtual image comes in from infinity and gradually
it approaches the lens. When the target is at the lens plane,
the lens doesn't have any power. Basically, as you proceed from
the focal point of the lens to the lens, the image comes from
infinity all the way to the spectacle plane. So this small range
of object positions gives you a large range of power. What you
can do is move a very small Snellen chart over a small range of
distances and then move the image of that chart over an infinite
range of distances. What you are trying to do is to move the
object to form a virtual image conjugate to the retina. The image
will be clear when it is at the far point of the eye. The distance
from the image to the lens is what we use to describe the conjugate
focus. This is the heart of the matter. You need to understand
this to get the basic concepts of the optometers. You are moving
the virtual image around, by moving the object, until it is focused
on the retina and at that point, the image is at the far point
of the eye. The virtual image is conjugate to the retina. That
is similar to what you are doing in optometry with the phoropter.
The phoropter is a simple optometer because a phoropter is in
the spectacle plane only instead of varying the objects distance,
you vary the power of the simple optometer lens with a fixed object
at infinity until objects at infinity are conjugate to the retina.
So if you have a myope, you will use minus lenses and you imagae
objects at infinity at the patient's far point which is conjugate
to the retina. So the phoropter is an example of a simple optometer,
only instead of varying the distance of the object, you are changing
the power of the lens.
So now let's look at the mathematics of this:
Let's say you have a -20D myope. Where do you want virtual image
to be? Well, first of all, let me ask you, where is the patient's
far point? 5cm. So let's say we have a +10D lens in the optometer.
Where would the object be so that the image distance is 5cm from
the eye? Use the Gaussian equation.
1/f = 1/v - 1/u
Fv - Ov = Iv In other words, P - U= V
So solving these equations:
1/10 = 1/-5 - 1/u or
U = (-20) - 10 Therefore, object must be
u = -3.33 cm U= -30
3.33 cm in front of the
u= -3.33 cm lens.
These numbers are calculated at the spectacle plane and thus the
vertex distance is irrelevant. If contact lenses are used you
need to compute the effective power at the cornea. At the cornea,
plus lenses take more power and minus lenses less power. That
is why when people lose accommodation, they tend to slide their
glasses down their nose to increase the power of their glasses.
Anyways, this is the simple optometer. The only problem with
this is that the image size changes as you move the object and
image size itself can stimulate accommodation. What we have in
lab is a different type of optometer.
Nagel and Badal Optometers
There is actually a way for us to get a virtual image through
an optometer lens where the virtual image doesn't change size.
One is called the Nagel Optometer. What you do with it is take
the lens and place it so that its focal point is at the nodal
point of the eye. The other is the Badal Optometer where you
take the lens and its posterior focal point is at the anterior
focal point of the eye. So if the Badal Optometer had a +10D
lens, the lens would be placed 10cm from the spectacle plane which
is 1.5cm from the eye. We can change the position of the object
and the will not change size nor will accommodation be stimulated.
When using the Badal Optometer, one thing we need to remember
is that the Gaussian equation can no longer be used because the
Gaussian equation tells us the image distance from the lens.
We want to know the image distance from the spectacle plane.
So we need to derive a slightly different formula so that we
can solve the distance of the image to the spectacle plane using
the optometer.
Consider the following:
X'
EYE
I f O f''
x
Again we are going to be putting targets inside the focal point of the lens so that we can get a virtual image. We want to derive the conjugate focus which is the reciprocal of the distance from the image to the spectacle plane. But the Gaussian equation would tell us the distance from the image to the lens. So what we do is we use Newton's thin lens Equation: ff '=xx'. This equation indicates that the product of the two focal points is equal to the product of the distance between the object to the primary focal point and the distance between the image and the secondary focal point. We want to solve for x' which is 1/CF. (CF is conjugate focus). Conjugate focus is the dioptric vergence of the image at the spectacle plane that is conjugate to the retina. Let's say that this is a -10D myope. We want to set this up so that the image is 10cm away from f '. Remember that the image size and its brightness stays constant. Only the dioptric vergence of the image changes.
Now we will change Newton's equation so that we can use it
in lab:
1 we know that the 1/x' = CF
2 the reciprocal of Newton's equation is 1/xx' = 1/ff '
3 rearranging the equation gives 1/x' = x/ff '
4 substitution results in x/ff ' = xP2
Now I want to show you a stigmascope. Basically the object is the light source and inside is the little plus lens. View the plus lens through the mirror. You are seeing the image of the light source. What you would like to know is the object distance from the anterior focal point of the lens. So to do this you read on the scale of the stigmascope, the distance from the light source to the lens. Then to find the distance from the object to the focal point, use the equation f - o =x (o is the distance from the object to the lens) Now substituting for x in Newton's equation (step 2 above) we get: 1/x' = (f-o) P2. In lab you will actually have a constant for the focal length and you will be measuring o and then you can calculate CF by taking the reciprocal of x'.
We can simplify this a little bit more:
1/x' = P2f - P2 Om (by distributive property)
[ Om =object distance in meters from the lens]
P2f = P (because P = 1/f)
1/x' = P - P2 Om This is the equation that will be used in lab.
Here is an example. There is a +10D lens in the optometer,
the object is at 5cm. What is CF?
CF = 1/x' = 10 - 100(.05)
CF = 5D
Notice we can simplify this to CF = P - Ocm (Ocm is the
object distance in centimeters). This is equation holds only
for the 10D lens.
Suppose we are using a + 8D lens with an object at 5cm:
CF = 8 - (64) (0.05m) (= object distance in
meters)
CF = P - P2Om
We can not simplify this equation further. Thus be sure to note
the dioptric power of your lens during lab so that you can use
the appropriate equation. In lab you will have either a +8D lens
or a +10D lens.
The conjugate focus of the eye depends on three things:
1. How much the eye is accomodating
2. The refractive error of the eye
3. The lens value in front of the eye (pt. is wearing glasses
or contacts)
Therefore, CFdiopters = ARdiopters + L diopters + RE diopters
CF = conjugate focus
AR = accomodative response (more accommodation is more positive)
L = lens value
RE = refractive error (A myopic eye is given a plus value, hyperopic
eye is given a minus value. This is because RE refers
to the refractive error of the eye, not the power of the glasses)
On the day of lab, know your refractive error, don't wear glasses, otherwise you will be considered an emmetrope. Rather, lenses will be placed in front of your eyes on that day. Try not to be dialated. If you do get dialated, use phenylephrine only because that doesn't affect accommodation. We will stimulate accommodation in one eye and measure the consensual accomodative response in the other eye. We will see that we have a limited ability to accommodate slightly differently in both eyes. It's something that takes practice, but usually draftsmen and musicians are good at this because they need they need to see things clearly at a distance and up close at the same time.
Apparatus for the lab:
OBJECTIVE OPTOMETERS (used in autorefractors)
Scheiner Pupil
Christopher Scheiner was the first to measure refractive error
with this principle. The Scheiner pupil is simply placing two
pinholes ("pupils") in front of your eyes.
Contrast of retinal image: The Canon and the Bausch & Lomb devices do this. It images a grid on the back of the eye and then varies the distance of the target until you get the highest contrast of the grid. When the target is focused on the retina, it has the greatest contrast. If it is defocused, it is spread out across the retina resulting in lower contrast. Many of these devices adjust the object distance and try to get the retinal image clear.
Purkinje III: Purkinje III is the image that reflects from the front surface of the lens of the eye. When you accommodate, the front surface of the lens becomes more curved and this curvature causes a shrinkage of the third Purkinje image. The same amount of light exists in a reduced area and so we have an increased intensity at each point in the image. This was exploited by Professor Stark who developed an optometer on this principal. He put a photodetector in space to measure the infrared reflection off the front surface of the lens. And as the eye accommodates, a smaller, more intense third Purkinje image is formed and accommodation is measure using the light intensity of the image.
Retinoscopy: As you rotate your retinoscopic image you are
actually sweeping the image across the fundus and if your retinoscope
is at a point conjugate to the retina, that image will move infinitely
fast at the plane of the retinoscope. If you are behind or in
front of that point, you will get a with or against motion.
-Bell and MEM Retinoscopy (for kids): Have a near point card
attached to the retinoscope which has a hole in it for you to
scope through. You scope the eye as the kid looks at the near
point card so you measure the power of the eye. This will help
you to find kids with low accommodation or accommodative lag.
Of these kids, some may have ciliary body problems, but many
of then probably are just bored or sleepy and not accommodating
accurately.
NEW TOPIC: Comparative mechanisms of accommodation
What are the possible mechanisms for accommodation? How do different
vertibrates accommodate?
In all vertibrates there is a retina (image plane) and two lenses
- the cornea and the crystalline lens. Every vertibrate wants
to adjust the power of the eye to clearly image object on retina.
pupil
Lens retina
What are the options for accomodating?
1. Use the pupil to image the paraxial bundle of rays on the retina.
Some animals do this with a slit pupil. The disadvantage of a
round constricted pupil is that is cuts out so much light that
the image may be too dim to see. For the most part, the pupil
is a slit pupil so that you get a lot of light in one meridian
and very little light in the other. You have vertical pupils
often in reptiles, horizontal pupils in grazing animals such as
horses. Slit pupils are basically a modification of a pinhole.
2. Vary the power of the cornea or of the lens inside the eye.
The power can be changed by altering the shape or the index of
refraction of them.
3. Vary the distance of the image screen. The retina can be moved
back and forth in some animals. These are accordian eyes or moving
screens.
4. A static system such as astigmatism with two different focal
axes. If you are a seal, you have high astigmatism so that above
water you use one axis and below water you use another.
Examples
1. Slit pupil is seen in nocturnal animals. Big pupils at night
and smaller pupils in the day time.
2. A picture of an eel's eye
The eel has an accordian eye. There is a muscle in the front
of the eye that pulls the optics of the lens back towards the
retina to shorten the eye. The length of the retina to the optics
(lens) is what is varied. If we have a target up close, the image
is far behind the optics and an image far away will be in closer
to the optics. So you would want to make the eye short to view
a distant object and long to view a near object. An owl also
has a moving eye and has a muscle to make the eye short.
3. A static mechanism can be found in the horse.
Is this genetic or is it an adaptation? It looks like the eye
has adapted. Take a chick and put a lens that causes a negative
refractive error (or hyperopia) on one side of the retina and
not the other. What you find is that eye that has developed a
myopic refractive error such that it is longer and the part without
the error remains short. For the horse with the static eye looking
out into space, the area of the retina that sees near objects
stimulate growth and far objects stimulate less growth. The horse
can focus on near and far objects without actually having to change
the power of the lenses or the distance of the image screen (retina).
This adaptation is thought to be one of the reasons why some eyes
develop myopia it they have too much retinal image blur during
accommodation When you accommodate more and more an error of
accommodation called the Lag increases and may cause your eyes
grow longer and longer. There seems to be susceptible period
where the growth of the axial length is stimulated by the blurry
retinal image in our eyes. Myopic children tend to have larger
lags in accommodation than emmetropic children.
4. You can also change the shape of the cornea and the lens.
That is done in a variety of ways. The same muscle that shortens
the eyes also flattens the cornea. Anyone can accommodate by
flattening the cornea by squinting. In doing so you take your
lids and flatten the cornea. The lamprey and the owl do this
all the time. They flatten the cornea via a muscle that pulls
back into the. So if they want to look far, they flatten the
cornea and at the same time shorten the eye bringing retina up.
We squint when we want to see far away too.
5. Power changes of the lens. For amphibious birds, they change
the power of the lens by pinching the front surface with the iris-ciliary
body. We don't do this. When we accommodate we relax zonules
supporting the lens and allow our lens to round up. The birds
have to pinch the lens in order to make the anterior lens go forward.
This is especially true for aquatic birds. They can get up to
+50D of accomodation. This is necessary because below the surface
of the water, they lose the power of the cornea and as you know,
the cornea adds +40D to the power of the eye. So an aquatic bird
in water has to have this extra accommodation since the cornea
is not longer a refracting surface, however in air, the cornea
refracts light and adds about 40D power to the eye. Underwater,
they must pinch the lens.
6. There is also a static counterpart to the aquatic birds' method
of accomodation
It is seen in the South American trout called the Anablep, "four
eyed fish." They used to be at the Steinhardt Aquarium.
They look like bullfrogs with huge eyes swimming on the surface
of the water. Half the eyes sit above the water and half the
eye looks below the water. Looking at the eye, you see a figure
eight and two pupils. And inside the eye you see a lens with
an elliptical shape with very curved lens surface for the water
and a smaller curvature for seeing in the air. These are physiological
bifocals. Things seen in air go through a less powerful optical
device.
7. Index of refraction changes. The lens of the eye has many
internal refracting surfaces. It is not like a uniform glass
lens. Normally a glass lens refracts light at the anterior and
posterior surfaces only. Everytime light goes through a change
of index of refraction it is bent or refracted. This is analagous
to driving a car with two wheels on asphalt and the other two
on sand. Your car just won't go straight. The same thing happens
to light when it goes through different indicies of refraction.
The index of refraction increases as you go from the lens cortex
to the lens nucleus. Remember the Gullstrand Schematic Eye model?
Cortex : n=1.386
Nucleus: n=1.406
As light travels through, it is refracted many times. There are 6 refractive surfaces in the illustrated crystalline lens, thus light is bent a lot more here than light going through a piece of glass with an index of 1.406. Through the crystalline lens, light is constantly being bent as it travels through the lens. At the nucleus, light is bent more than when it passes through the cortex. This lens has more power than if it had the 1.406 index throughout with no variations of index. With age, the index of refraction of the lens becomes more uniform. Then there will be less overall refraction by the lens. Even though the index of refraction is higher it will refract light less internally. So as we get older the power of the lens actually decreases because the lens is becoming more uniform. That's actually a good thing because as we grow older, the lens continues to grow and so the lens becomes more and more curved with age. And so the power increase caused by the increase in surface curvature is actually offset by the uniform index of refraction of the lens. This is called "the lens paradox". The lens is becoming less powerful even though its outer surface is becoming more curved. The regions of constant index of refraction are called isoindical surfaces. With age, isoindical surfaces become more similar or alike. In young lens, the cortex has a lower index than the nucleus.
Today we covered chapters 16 and 18 from the reader.