How does the eye form images?

How does the eye form images?

How does the eye work?

Our pinhole camera is a stripped-down version of an eye that only has a few parts for us to play with. Still, changing those parts around a little and observing what we see goes a long way towards helping us understand what the parts of your eye are doing to record patterns of light in your visual world. First, let’s start by reminding ourselves of the things you saw using your pinhole camera.

Inverted images in the pinhole camera

One of the more conspicuous features of your pinhole camera was that the images produced on the viewing screen in the back were upside-down and backwards. This is a direct consequence of how light gets from the outside world to the viewing screen. Because you sealed your camera up carefully, the only way light can get from an object in the environment to the viewing screen is by passing through the pinhole in the front of the camera. This means that light from the top of a visual scene passes through the pinhole on a downward trajectory, ending up at the bottom of the screen. Light from the bottom of a visual scene passes through on an upward trajectory, ending up at the top of the screen. Thus, patterns of light in the outside world end up reversed after they pass through the pinhole (Figure 1).

Figure 1 - Images are inverted in a pinhole camera because light must pass through the aperture to get to the back of the camera.

This camera is meant to be a model of your own eye, so it’s worth commenting on this observation with regard to how your eye works. Are there inverted images in your eyes as well? Obviously you don’t experience the world as upside-down and reversed, but does the original image of a scene start that way in your eye? There’s a neat trick you can play (see Mini-lab #1) with shadow casting that helps reveal what’s going on in your eye: Briefly, make a small pinhole in a card and look through it at a bright light source. Now, hold a sharp pencil in front of you so that you can “prick” the small circle of light that you see with the pencil tip. There are two things you should see: (1) The pencil tip itself, poking into the circle of light that you see through the pinhole. (2) The shadow of the pencil tip, which you should see creep in from the opposite side of the pinhole! If you have a hard time seeing this, try moving the pencil point top-to-bottom across the pinhole – you should see a corresponding shadow that moves bottom-to-top. What’s going on here? Light rays get inverted through pinhole camera, but shadows don’t! Casting a shadow of the pencil point on your retina gives you a chance to see that your retinal image is indeed inverted, just like your pinhole camera.

Pinhole images are either dim, or kind of blurry

Another conspicuous feature of your pinhole camera is that the images you see on the back of the screen are pretty dim. In fact, you may have needed to make the pinhole a good bit bigger to see much of anything at all! Obviously a small pinhole can only let in a little bit of light, which doesn’t make for a very bright image. A large pinhole is better (more light can get in), but you may have noticed something else happened as the image became brighter: Larger pinholes make for brighter, but blurrier images.

Why should this be the case? Let’s think again about this issue of how light can get from the world outside the camera to the viewing screen. Inverted images resulted from light having limited paths between the world and the screen, and this tradeoff between brightness and blurriness is also a direct result of that same mechanism. Specifically, let’s consider the following situation: Because your pinhole camera was too dim, you decided to make a second hole rather than make one big one. What does this mean for the image formed on the back of the viewing screen? Light now has two ways to get into the camera from a single point on the object: It can through one hole, or it can go through the other. These two points of entry mean that light from one part of the object ends up at two places on the viewing screen. (Figure 2)

Figure 2 - An additional pinhole lets more light in, making a brighter image. Light from two pinholes ends up making two overlapping images in the camera, however, which makes the overall appearance blurry.

This is true for every part of the object, so what you’ll get at the back of the camera is not just one image, but a double image of the object. Twice as bright, but because these images aren’t lined up, things may look a little funny. Now here’s the thing about a large pinhole: It’s more or less just a whole bunch of small holes all lined up next to each other. That means that a large pinhole gives light from one part of the object lots of different ways to get to the viewing screen. The consequence of this is not a double image, but many, many copies of the image all projected on top one another, and each one in a slightly different place. That smearing of the light coming from the object across the screen is the source of the blurriness.

Just like the inverted image phenomenon, we should pause for a second and think about your own eye. Does this happen to you? Remember that we’ve seen that you have a pinhole (your pupil) that changes size depending on the amount of light shining on it, so this business of considering small and large pinholes seems relevant. However, you probably don’t suffer from this problem. The world probably still looks clear to you whether your pupil is large or small. What gives? How are you pulling this off when your pinhole camera can’t do it?

Adding some parts to the eye to get bright AND clear images

Let’s return to that version of the pinhole camera that has two holes in it. The issue we have in that case is that there’s twice as much light coming into the camera (which is good), but the two different images of the object aren’t in the same place on the screen (which is bad). We don’t want to change the amount of light coming in; this is why we poked a second hole in the front of the box in the first place, after all. Instead, it would be nice if we could change the position of these two images on the screen so that they were right on top of each other. But wait! This is something we know how to do. Remember the behaviors of light that we observed in the first lab exercise: Light can be reflected, refracted, and diffracted. Of these, reflection and refraction involve changing the direction of light, which sounds like what we’d like to make happen here. We’d like to be able to change the direction of the light inside the camera so that the images from the two pinholes aren’t misaligned anymore.

            To change the direction of the light at each pinhole, we might want to be able to put a small prism (which could be made of glass or acrylic) right in front of each pinhole so that the light gets refracted (bent) at the right angle to get to the middle of the screen. If we know Snell’s Law, we can make sure we pick the right angles for the prism’s sides so that we bend the light by just the right amount to line up our two images (Figure 3).

 Figure 3  - We can fix our two-pinhole problem with prisms. Each prism is placed at the right angle so that the light from the two pinholes is aligned in the camera. The image is now brighter and not blurry!

OK, now imagine we want to let in even more light. We poke some more holes, but now we need to make sure that the light that comes in through those openings also gets bent by the right amount to get to the middle of the screen. That’s not a problem; we can just put a prism with a different angle in front of that pinhole. Specifically, the further away the pinhole is from the center of the camera, the further the prism’s faces will have to tilted away from vertical. Light coming in at the center doesn’t need to be bent at all, so we’ll just put a vertical prism there, for example, but as we move away from the center, we’ll need prism faces with more tilt to get the light to bend the correct amount. If we keep poking holes and keep putting these prisms in front of them, you’ll see that after a while we poke enough holes to have one big opening, and also that we’ve put down enough prisms with different tilts to have…a lens (Figure 4).

 Figure 4 - A big hole is really lots of little holes in a row. Each one requires a prism at a different angle, so a convex lens lets us vary the angle continuously.

So here’s how you balance the need to let more light into your camera with the blurriness caused by large apertures: You install a lens in front of your opening.  Remember that the convex lenses you used in the first lab exercise had a focal point where incoming horizontal light rays met after they were bent by the lens. This means we can’t just put any old lens in there – we need one that has a focal length that’s appropriate to the size of our pinhole camera. However, let’s see what happens if I put such a lens in front of the opening of a pinhole camera with a very large aperture.

Figure 5 - A large aperture makes an incredibly blurry image (left), but installing a convex lens with the appropriate focal length yields a bright and clear image. Note that inverted image, too. 

It works! More importantly, this helps us get a handle on the functional relationships between different parts of your eye. What we’ve just done for the pinhole camera in the figure above is a lot like what’s going on in your eye, courtesy of two structures called the cornea and the crystalline lens. The cornea is a mostly spherical bit of tissue that does most of the actual bending of light so the world continues to look focused even when your pupil changes size. Behind the cornea, the lens is able to change it’s shape (or accommodate) to help provide a modifiable amount of bending after the light is already refracted by the cornea. This secondary bit of refraction is necessary because the cornea is limited in its ability to focus incoming light onto the back of your eye. By itself, one convex lens can't focus objects at all distances from the camera, so we have to do something else to cope with that variation in image quality. Objects that are close to you require divergent light rays to be bent more on the way in, for example, and so they require more bending than the cornea can offer. Objects that are far away won’t require this, so the cornea may be enough. By having a second opportunity to refract light, your visual system can be responsive to these changing demands, too: If something is nearby, make the lens more spherical so light is bent more when it passes through. If something is far, let the lens relax into a nearly flat shape so nothing much happens to the path of the light as it goes through.

There are a lot of fun things to be said about the rest of the eye. For one, the muscles that control the shape of the crystalline lens are called the “Zonules of Zinn,” which is just fantastic. There are also different humours or liquids in the eye that are very important for eye structure and eye health, but can also end up contributing to various vision problems and eye diseases. Probably the most well-known of these is glaucoma, which results from a build-up one of the two humours due to faulty drainage mechanisms in the eye. The build-up of liquid leads to increased pressure within the eye itself, which can cause the retina to die. If you’ve been to an eye doctor and had to stare into a blue light after they put some rather nasty drops in your eye, you’ve had your cornea nudged a bit with a puff of air to see how much it deflects when pushed. If you have too much liquid in the eye, that nudge will be like poking at an over-inflated balloon, and your optometrist may need to tell you how to manage the situation so you don’t end up with vision loss.

These other anatomical features of the eye won’t really concern us a whole lot, however, though they are interesting in their own right. Our emphasis is on developing a simple computational model of the visual system and one way we’re keeping it simple is by leaving a lot of things out. For now, we will therefore conclude that we have worked out how to get light into our eye AND keep it in focus, and that this represents an honest day’s work. 

Figure 6 - That'll do pinhole camera. That'll do.

Our next step involves actually measuring that light now that we’ve managed to get it into our eye, and turning it into an electrical signal that cells in our nervous system can work with. This process is called transduction. How do we do it? How does a light shining on something turn into electricity? To get a handle on some of the principles of this process, now is a good time to work on Lab #3.