Thursday 31 January 2013

The Eye has been likened to a camera, in that it has a focussing lens and a light-sensitive medium (the retina) in the focal plane of that lens. But that is about the limit of the similarity. The Eye is really an extension of the brain, and it is the primary source of information for the brain. A rough estimate of the information capacity of the eye-brain link (the optic nerve) is about 1 million bits/second.
Diagram of the Eye
Let's look first at its optical properties. Most of the focussing of incoming light is done by the Cornea, i.e. refraction at the air-cornea interface.
Light path in Eye
The Lens acts as a fine adjustment of the focus. The average refractive index of the Eye is about 1.33, the same as water, because the “humours” are mostly water. The Lens is a flexible structure, like a thick jelly, and has a number of layers in it, so that its refractive index increases towards the centre; this helps to reduce internal reflections, like the “bloom” on a camera lens. It is normally kept under tension by the fibres of the Ciliary Body, but there is a ring of muscle round the lens which acts to take up the tension in these fibres, and allows the lens to relax into a more spherical shape. This in turn increases its optical power, making the eye focus on closer objects.

The Optical Power (F) of a lens is measured in dioptres. There is a simple relationship:
F = 1/f = 1/p + 1/q
Focussing by the Lens
f is called the Focal Length and is equal to the image distance q when the object is at infinity (p = ∞).The ratio q/p is also equal to the object magnification.

The advantage of using F is that if you put two lenses together, the resulting power is simply F1+F2, but only if they are close together; if they are separated, the formula is more complicated. So the cornea and lens powers can be added, and we can regard the variable power of the lens as a range of F, known as the Accommodation of the eye.

The effective power of the eye is about 50 dioptres, i.e. f=20 mm. An object 10 cm long at a distance of 1 metre will give an image 2 mm long on the retina. In children, the range of accommodation is about 10 dioptres (F can vary from 50 to 60), so their eyes can focus from infinity down to 10 cm. The range gradually decreases with age as the lens becomes less flexible. Typically it is down to 5 dioptres at age 40, and less than 2 dioptres at 65. This condition is known as Presbyopia and is quite normal – most older people need reading glasses.

Focussing Defects
However, the focussing of the relaxed eye may actually be wrong. If it is too strong, the image of a distant object is formed somewhere in front of the retina. A closer object would give the correct focus:
Myopia
This condition, when D is too high, is called Myopia, or Short Sight. It can be corrected by a negative lens:
Myopia correction
The opposite condition is called Hypermetropia, or Long Sight. The relaxed eye will not even focus on infinity, and the lens muscle has to be activated to enable any focussing. The continuous need to activate this lens muscle can lead to complaints of eye strain and headaches as the first reported symptoms. Correction is done with a positive lens.

Further focussing faults can arise from Astigmatism. The curvature of the cornea is not the same in all directions; it is slightly ellipsoidal. Typical symptoms are that vertical and horizontal lines have a different focus. It is corrected by a cylindrical lens as shown below:
Astigmatic lens
Response to Light Level
The Iris is the eye's way of “stopping down”, i.e. changing its aperture or f-number. The central hole, the Pupil, normally varies in diameter from about 3 mm in bright light to 8 mm in very dim light. Now this is a range of light-gathering power of only 7 to 1, whereas the eye can cope with a brightness range of 1010 to 1. (You may not believe it, but a sunlit scene is one million times as bright as a full moonlit scene!)
So why bother with an iris?
One reason is that visual acuity and depth of focus are better with a small pupil. But the full answer isn't really known. Most of the light/dark Adaptation occurs in the Retina, which is an interesting structure.

If you look into the eye using an Opthalmoscope, you will see a generally reddish brown surface, with peripheral blood vessels running towards an off-centre dark spot, known as the Blind Spot. This is where the optic nerve converges and leaves the eye. To the centre is an area devoid of blood vessels, called the Macula Lutea, and right in the middle of this is a tiny area (about 300 µm diameter) where all the most detailed vision takes place, called the Fovea. Nowhere else in the body is there such a tiny yet vital piece of tissue!

The Retina covers about half of the inside of the eye. The light-sensitive cells are the rods and thecones. Oddly enough, the light has to pass through several layers of nerve cells, except in the fovea, where they are pushed to the side to improve acuity of vision. There are about 6 million cones and 120 million rods over the retina.
  • Cones are responsible for colour, daytime (photopic) vision. The peak response is around 560 nm (yellow).
     
  • Rods give monochrome, nighttime vision (scotopic). The peak response is nearer 500 nm (green-turquoise).
Rods are much more sensitive to green and blue light (by up to 1000 times). Cones are most abundant in the macula and fovea, but exist over the whole retina. There are very few rods in the fovea; they reach a peak density about 20° away from the fovea. This is why you can often see things better at night if you don't look directly at them. The blind spot is about 15° to the side of the fovea, and covers about 5°.

Dark Adaptation is accompanied by the build-up of a pigment (dye) called Rhodopsin, and takes about 30 minutes to reach full strength. Cones dark-adapt rapidly, but only to a limited extent. Rods increase their sensitivity by a factor of over 1000 within 20 minutes. Subsequent exposure to to bright light bleaches the rhodopsin (gives you a kind of "white-out" vision while it takes place). The two eyes can be dark-adapted independently.

Under optimal conditions, the eye can detect as few as 10 photons landing on the retina within 0.1 seconds. This actually requires nearer 90 photons incident on the cornea.

The ability to resolve brightness differences (contrast) drops substantially at low light levels. At typical reading light level of 100 mL (millilambert), a difference of 1% can be seen. At the levels used in unenhanced fluoroscopy, for example (about 10-6 lambert), it has to be about 20%. [The Lambert is not an SI unit, but is still frequently used. The SI unit of surface illumination is the Lux, or lumen per square metre; 1 mL is 10 lux.]

Much odder is that spatial resolution drops markedly at low light levels. In part this is due to increased pupil size, allowing lens aberrations to have more effect, but it now seems that the answer lies in the behaviour of the nerve cells immediately overlying the retina. These are much more than simple buffer amplifiers, as was once thought. They carry out some local image processing functions such as edge enhancement. At low light levels, they seem to switch over to a smoothing function, averaging the signals from groups of rods.

Cones apparently use three different pigments each having a different spectral response. This accounts for our three-colour vision. In colour-blind people, one of these pigments is missing or altered - usually the red-sensitive one.
Retinal molecule
Rhodopsin works by changing its molecular shape. Part of the molecule is called Retinal, and changes from CIS- to TRANS- configuration when light falls on it (bond 11-12 can twist). The TRANS form is more linear, and allows it to become detached from the rest of the molecule (known as OPSIN), which becomes the bleached form, and activates the rod. Cis-retinal is regenerated, and reforms the full rhodopsin molecule with a time-constant of about 7 minutes. Retinal is closely related to vitamin A (retinol), which has a -CH2OH group (alcohol) instead of the -CHO (aldehyde).

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