Perception Lecture Notes: The Eye and Image Formation

Professor Davd Heeger

What you should know from this lecture

The Vision Science web site is a good resource for research in human and animal vision.

Vision begins when light enters the eye, focused by the cornea and lens onto the retina, a thin (a few mm) layer of neural tissue at the back of the eye. Photoreceptors, specialized neurons that transduce light into neural signals, respond with graded potentials, pass the signal on to bipolar cells and then to retinal ganglion cells. Retinal ganglion cells are the only neurons in the retina that fire action potentials. Axons of ganglion cells make up the optic nerve.

The Blind Spot.  There is something kind of funky about the setup here. The photoreceptors are at the back of the retina, the ganglion cells are at the front, and the ganglion cell axons make up the optic nerve that goes out through a hole at the back. There can't be any photoreceptors here where the hole is. It's the photoreceptors that transform light energy into a neural signal. No photoreceptors means no sensitivity to light. That means there must be a blind spot here.

Blind spot demo

Here's how to find your blind spot. Close your left eye and keep it closed. Hold your left thumb at arms lenghth and look at it with your right eye. Now hold up you right thumb next to your left thumb. Continue looking only at your left thumb while slowly moving your right thumb to the right. Your right thumb will dissappear when your thumbs are separated by about 6 inches. Remember the whole time to fixate your left thumb with your right eye. The blind spot is surprisingly large. Once you have found your blind spot, move your right thumb around a bit (up/down, right/left) to see how big it is. There is a web site which you can use to map your blind spot more precisely.

It's interesting that you were never aware of your blind spot. Discuss...

Eye Anatomy, Cornea, Glaucoma, and Corneal Transplants

Cornea is living tissue but must be transparent. To make it transparent means that it can have no blood vessels running through it. This has two important practical consequences, glaucoma and corneal transplants.

Glaucoma: Without blood vessels there must be another way to provide nourishment to the tissue to keep it alive.  Nutrients are passed to the cornea and lens through a continual flow of liquids through the eye.

Diagram of flow and blockage

Glaucoma is a disease caused by a blockage of the flow. Normally the nutrients flow around the lens to the anterior chamber of the eye, then out through this little pore call Shlemm's canal. The flow can be blocked (as shown in the right-hand figure) in either of two places. If the blockage is at the pupil, then the problem can be fixed by cutting a hole in the iris. If the blockage is at Shlemm's canal, then it can usually be treated by drugs.

Although the source of the problem is at the front of the eye, the end result of glaucoma is damage at the back of the eye, leading to blindess. There is an increase in the pressure in the eye because the fluids cannot exit from Shlemm's canal. This increase in pressure causes the blood vessels in the eye to compress, sometimes destroying them. In addition, the increase in pressure can crush the optic nerve.

In an advanced state, the loss of blood vessels can lead to retinal detachments. Retinal detachments sometimes also result from an eye injury. They can be fixed by surgery if caught immediately be using heat or a laser to "staple" the retina back in place.

One method of diagnosing glaucoma, called tonometry is quite direct. An old device is called a Shiotz Tonometer. The eye was anaesthesized (using cocaine to stop the pain in the free nerve endings) and this instrument was pressed upon the eyeball. The amounts of weight needed to achieve various displacements of the eyeball were measured and this let the doctor infer the amount of pressure inside the eye ball. There is a normal range, and an out of scale range. These days, this device has been replaced with an instrument that merely delivers an air-puff to your eye. The puff causes a displacement of your eye ball, much as the weights in the Schiotz tonometer.

Corneal transplants: The second consequence of avascularization in the cornea is good news. Because there is no blood, the cornea can be transplanted with a much reduced fear of rejection by the body's auto-immune system. No blood arriving means no anti-bodies and reduced danger of rejection. About eighty-five percent of corneal transplants succeed.

Recent advances in stem cell technology have enabled new procedures for repairing the cornea in patients for whom corneal transplants previously did not work. Mike May is one patient who has received this experimental procedure. He had been blind since the age of 3 due to an accident which seriously damaged the corneas in both of his eyes. Because of the scar tissue, conventional corneal transplants did not work. But the new stem cell procedures have restored limited vision. Mike May's web page includes a first hand account of what he is seeing and how he is feeling about it. So far so good, but...

A cautionary note on miracle cures: In 1963 Gregory and Wallace wrote a monograph describing a miracle cure. As an infant, the patient SB had lost effective sight in both eyes from a corneal disease. At the age of 52, he received a corneal graft that restored his optics. After living most of his life without sight, SB looked upon his wife for the first time. While the case of SB is one of the best studied, there have been a few similar cases described.

Patients who have been blind most of their lives do not see well after their optics have been repaired. Some visual measures, such as acuity and color vision, can be within the normal range, but patients do not perceive depth, motion, or the relationship among features effortlessly. They have difficulty recognizing a face, or judging the movement of traffic. Their visual world is a jumble from which they can only occasionally glean a useful pattern or bit of information. The description of these cases suggests that many patients never acquire a good facility at grouping together features from different positions within the image, nor features at different points in time from different perspectives. They have great difficulty integrating information from different perspectives, over time, into a coherent description of the scene.

The difficulty in integrating information is not a small thing. The restoration of the elements of sight without this integrative ability is a disconcerting emotional experience. Some of the patients experience severe depression. SB ended his life by committing suicide. Even those patients who overcome the depression, wonder whether the returned sight was worth the effort.

Image Formation

The simplest kind of focussing mechanism, the pin-hole camera, was discovered by Leonardo Da Vinci. Imagine an eye with no cornea nor lens but with a very tiny hole for the pupil. Light that passes through this hole forms an image on retina. Starting with a point in the world, light will be reflected in many different directions. From the point of view of our pin-hole pupil, however, most of these directions will be irrelevant. The only direction that will matter will be the direction that lies between the object and the tiny pin hole. There is only a single ray of light from each point in the scene that makes it into the pin hole, that is, each point on the retina receives light from a single point in the scene. Note that image on retina is upside-down. Does this mean that processing in the brain must turn it upright again? Discuss...

Note that two objects of different sizes and at different distances can project through the pin hole to make precisely the same image. This has two important consequences. The first is that there is an inherent ambiguity in the way that images form in the eye, and it makes the visual system's job of estimating size and distance rather difficult. We'll cover more about depth and size perception later in the course.

The second consequence of this ambiguity between an object's size and its distance from the observer is that we need some way of specifying the size and position of a visual stimulus independently of its distance. What we do is to specify stimulus position and size in terms of its visual angle. The visual angle is the angle subtended by an object. If two objects have the same visual angle, they project onto the same retinal area. Your thumbnail at arm's reach is about 2 deg of visual angle.

For a pin-hole camera to work properly the pin hole must be very small. The image gets blurred if the hole is large. But when the pin hole is too small, that causes other problems. First, only a small fraction of the light can make it through the opening - a small pin hole cannot operate well in medium or low light level conditions. Second, as many of you know, there is a process called diffraction that occurs when you try to stuff light through a little hole.

The above figure shows an image of a lightbulb filament taken with pin-hole cameras with three different aperture sizes. In the first one, on the left, the pin hole was too large so it looks blurry because a wide circle of light rays from a given object point enter through different parts of the pin hole, resulting in a blurry image. For the one on the right, the pin hole was too small so it looks blurry due to diffraction. The middle one is just right (that is, for imaging a light bulb filament). For imaging other things that aren't so bright, there wouldn't be enough light because the pin hole is so small.

The way around this trade-off is to open up the pin hole a bit (to let enough light in and avoid diffraction) and add a lens (to avoid the blurring). There are actually two structures in your eye that help focus the light through your pupil. The cornea in your eye has the effect of bending the light rays that are incident on your eye. Thus, it acts, in part, like a lens. Behind the cornea is the lens itself, and it bends the light rays even further. The combined effect of the cornea and lens (if you have 20-20 vision) is that they focus the light rays onto the surface of your retina.

Accomodation. You know that when you take a picture with a camera, you need to adjust the focus depending on the distance to your subject. In your eye, you have an analogous mechanism.

The focusing power of the cornea is fixed - it can not be adjusted. But the focusing power of the lens can be adjusted. The lens has muscles attached to it that change its shape and focusing power. When the muscles are relaxed the lens has the shape shown at the top of the figure. In this state the lens has little curvature and serves for viewing distant objects. When we wish to have a sharp focus on points that are nearby, we adjust the shape of the lens by pulling the muscles taut. This process of adjusting the lens in your eye for different viewing distances is called accommodation. And, it doesn't work equally well in all people. Some of us have lenses that don't properly focus distant objects. That's why many of you wear eyeglasses or contact lenses.

There are two main failures of focusing. The first, myopia (or near-sightedness) involves an eye that is too long (or a lens that is too fat), so that even with relaxed accommodation, far objects are focussed in front of the retina. Such a person can not focus on distant objects, but has no problem focussing on close objects. This is corrected with a concave lens. The opposite condition, hyperopia (or far-sightedness) results from an eye that is too short (or a lens that is too thin). With relaxed accommodation, distant objects are focussed behind the retina, so that some degree of accommodation is required to bring distant objects into focus, so that  there is less remaining accommodative power for focussing on near objects. This is corrected using a convex lens. The other main failure of focus is astigmatism, which means typically that your cornea is somewhat football-shaped (with more curvature in one direction than in the other). It is corrected by adding a cylindrical correction (90 deg rotated from that in your eye), which is specified in your eyeglass prescription as a cylindrical lens power plus the angle at which that cylindrical correction should be oriented.

The lens of your eye tends to get more rigid with age and it gets to the point where the muscles can no longer bend it. That's why people who have had perfect vision all their lives usually find themselves in need of reading glasses by age 50 or so. This condition is called presbyopia ("aging vision"). A typical early sign of this is that people complain of having difficulty seeing under low light levels (e.g., reading a menu in a spiffy restaurant). The reason for this is that the eye tries to compensate for the failure of lens accomodation by closing down the pupil a bit. A smaller pupil means better focus even without a lens (pinhole camera), but suffers from not having enough light.

Another condition often associated with aging (although not always) is cataract: Cataract is the clouding of the lens. It may be present at birth or caused by eye infection or injury.  The most common cause is old age (it is not understood why cataracts form but 95% of people over the age of 85 have them).  If serious enough, surgery is the only treatment available.  The surgical intervention is to break up and remove old lens and install a new plastic one with a fixed focus (i.e., no ability to accommodate).

Eye Movements

Each eye has three pairs of muscles that can move the eye left/right, up/down, and rotate it about the line of sight (a torsional movement). The first two are used to direct the gaze to objects of interest. The last is used to ensure that the torsional state of the eye is the same no matter what sequence of eye movements resulted in that choice of fixation.

There are several types of eye movements:


Copyright © 2006, Department of Psychology, New York University
David Heeger