The eye : how does it work ?
Ophthalmic Optics for beginners
I wish to thank A.Meyer (Science &Vie)
for the eye's illustration and Caroline, my English teacher, for checking
the English language of this page.
The eye : how does it work ?
The light emitted by the object you are looking at enters the eye through the cornea. The light rays then pass through the pupil (which regulates the amount of light entering the eye) and then cross the (crystalline) lens. Finally, the light rays are focused on the retina which is a thin layer covered with light receptor cells. Thanks to electrochemical reactions, the light is converted into electrical impulses transmitted to the brain by the optic nerve.
About at the center of the retina is a small depression known as the macula. At the center of the macula, in an area called fovea, cells are densely packed and provide the sharpest colored and most detailed information. But, despite the importance of the fovea, the other parts of the retina are also very useful to detect motion, to see in dim light ...
From an optical point of view, the eye may be compared to a camera. On the one hand, the lens combination of the camera forms an image on the sensitive film and on the other hand, the eye forms an image on the retina.
An eye is said to be normal or emmetropic if the image of a distant object falls on the retina :
But the normal eye is also able to see near objects thanks to a fine focusing mechanism, known as accommodation. Through changes in its shape, the (crystalline) lens gives a variable focal length to the eye. With this accommodation mechanism, the normal young human eye is able to see near objects, say 25 cm in front of him. In this way, the human eye may be more precisely compared to an autofocus camera, adjusting continuously in order to bring the image into focus.
But with age, accommodation begins to fail and the image of near objects can't be focused on the retina : the increase of power produced by the accommodation is not important enough. This phenomena is known as presbyopia and begins to affect people at the age of 40.
Nearsightedness, short-sightedness or myopia
Farsightedness, long-sightedness or hyperopia
Why ophthalmic lenses ?
Correction of myopia
Correction of hyperopia
This is the task of your optometrist to
define the characteristics of the lenses you need to wear : the prescribed
lenses.
One common way to characterize this prescribed
lens is to give its vertex power. Let's have a look at the definition of
the vertex power of a lens :
As you know, for an object at infinity,
the image is formed in f' : image focus point. By definition, the vertex
power of a lens is the inverse of the distance between the vertex of the
rear surface and f'. This quantity is given in m-1 or diopter
(D).
For example, in the case of myopia you
may need a -3 D diverging lens, or a +3 D converging in the case of hyperopia.
Let's now suppose an emmetrope person. At this point, he can clearly see objects at different distances, but only objects which are just in front of him. If the object he is looking at moves in the field of vision, what happens ?
First, you can move the object (as a jeweller looking at a diamond) or turn around it, in order to put it just in front of your eye. Of course, this may not always be very easy, particularly if you are looking at stars in the sky. Another simpler and common way is to move the head or to turn the eyes (or both). In the following we will only consider motion of the eyes, for a given position of the head :
A schematic representation of the eye is as follows. The eyeball rotates around a fixed point known as Eye's Center of Rotation (ECR), in order to focus image on the fovea. This is obtained when the (main) light ray passes through the center of the pupil and through the eye's center of rotation, defining in this way a position of gaze.
However, what does it mean for the wearer of ophthalmic lenses ?
Vision through ophthalmic lenses
| Myopic eye and diverging lens | Hyperopic eye and converging lens |
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But at this time there is a last problem : ophthalmic lenses provide a good vision only while one looks through their centers. This is not the case as the position of gaze is non null, and the vision may be affected. One way to quantify the quality of vision would be to analyze the image formed on the retina. But, on the one hand, it is difficult to make ray tracing inside the eye because of it's complex structure and, on the other hand, it is not easy to interpret how the brain "sees" this image. How to avoid this ?
We are going to analyze the image formed by the lens because, in fact, this is the image the eye is looking at : one speak about virtual image. But one thing is sure : the best the image produced by the lens, the best the quality of vision for the wearer.
For a null position of gaze, we know that the image formed by the prescribed lens must be at a distance 1/D m from the vertex of the back surface. By extension for the other positions of gaze, and because of the rotational symmetry around the ECR, the image should be formed on a sphere centered on ECR, and known as far point sphere.
As you can imagine, the image formed by the lens is not always perfectly focused on the far point sphere. One way to know if the image is exactly positioned, is to measure the distance between the intersection of the ray with the vertex sphere (which a sphere centered on the ECR and tangent to the back surface) and the focus point. This quantity is defined for each position of gaze and should always be 1/D m.
Aberrations introduced by the ophthalmic lenses
Two kinds of aberrations may deteriorate the image :
This is a schematic view with the eye, the lens and the astigmatic foci :
Let's now define different quantities :
These quantities are defined for each position of gaze and can be represented on such a graph :
Eight parameters may be modified :
There are 2 different ways to run this
applet.
Documentation of the program
Everything about the java language
http://java.sun.com
Everything you want to know about the eye
http://webvision.med.utah.edu/
A lot of interesting links about optics
http://members.xoom.com/joelzahn/lightoptics/index.html
American Optometric Association
http://www.aoanet.org/
A nice animation
http://www.vision1to1.com/