Physics of Eyes and Vision

مدرس المادة Sub.Medical physics Physics of Eyes and Vision
ناهدة حمود الجراح Lec.4


Sense of vision
- Eyes (Fig.1).
- Millions of optic nerves.
- Visual cortex.


Figure 1: Cross-section of the left eye as seen from above.

Analogy with CCTV (Fig.2).

Figure 2: The sense of sight is in many ways similar to a closed circuit color TV system.

Special features.
- Large viewing angle (Fig.3).
- Blinking built-in lens cleaner and lubricator for the front lens (cornea).
- A rapid automatic focusing system permits viewing objects as close as 20 cm one second and distant objects the next. Under relaxed conditions the focus for normal eyes is set for "infinity" (distant viewing).
- Range of light intensity: brilliant daylight to very dark night (1010 to 1).
- Iris: automatic aperture adjustment
- Built-in scratch remover in cornea
- Self-regulating pressure system for internal pressure of about 20 mmHg keeps the eye in shape.
- Bone provides protection and fat provides cushion.
- Automatic image correction from the upside down image in retina.
- Three-dimensional viewing using two eyes.
- Flexible eye movement by muscles.
1. Focusing Elements of the Eye

Two major focusing elements
- Cornea: clear, transparent, 2/3 of focusing, fixed focusing.
- Lens: fine focusing, 1/3 of focusing, variable in shape.
The cornea focuses by bending (refracting) the light rays. The amount of bending depends on the curvatures of its surfaces and the speed of light in the lens compared with that in the surrounding material (relative index of refraction). When the cornea is under water it loses most of its focusing power because the index of refraction of the water (1.33) is close to that of the cornea (1.37). (Fish have a similar problem out of the water.
2. Some Other Elements of the Eyes

Iris and pupil
- Pupil: opening in the center of iris.
- Light enters the lens through the pupil.
- Diameter of the pupil.
1. Average light: 4mm. 2. Bright light: 3 mm. 3. Dim light: 8 mm.
- Response time of the iris.
1. Fully open: 300 s 2. Minimally open: 5 s
Aqueous humor
1. Fluid filling the space between the lens and the cornea.
2. Mostly water and contains many components of blood.
3. Supply nutrients to nonvascularized cornea and lens.
4. Surplus escapes through drainage tube (the canal of Schlemm).
5. Blockage of the drainage tube increased eye pressure glaucoma
Vitreous humor (vitreous body)
1. Clear jelly-like substance filling the large space between the lens and the retina. 2. Keep fixed shape of the eye. 3. Permanent.
Sclera
1. Tough, white, light-tight covering over all of the eye except the cornea.
2. Protected by a transparent coating called the conjunctiva.

3. The Retina – the Light Detector of the Eye

Convert light image into action potentials

Light photon (3 eV) photochemical reaction in photoreceptor action potentials.
IR has insufficient energy to produce action potential not seen.
UV are absorbed before the retina not seen.
Most vision is restricted to a small area called the macula lutea, or yellow spot. All detailed vision takes place in a very small area in the yellow spot (~ 0.3mm in diameter) called the fovea centralis (Fig. 1). In Fig. 4, 0 is the object size, I the image size, P the object distance, and Q the image distance, usually about 2 cm. Thus we can write 0/P = 1/Q or 0/1 = P/Q. I = (QIP) O (Example.1).


Figure4: There is a simple relationship between the object and image sizes and the object and image distances. The image on the retina is small because of the short image distance of about 2cm.



Example 1:
How big is the image on the retina of a fly on a wall 3.0 m away? Assume the fly is 3 mm(0.003 m) in diameter and Q=0.02 m.
I = 0.02/3 ? 0.003= 2 ?10-5 m = 20 ?m

Photoreceptors: Fig.5, 6, 7, and 8.
There are two general types of photoreceptors in the retina: the cones and the rods.
1- Rods
- Vision in dim light, photopigment is rhodopsin night or scotopic vision.
- Peripheral vision.
- ~ 120 million in each eye in most of the retina.
- Hundreds of rods are connected to one optic nerve better sensitivity.
- Maximal sensitivity at 510 nm (blue-green light).
2- Cones
- Color vision in bright light, 1 to 3 photopigments daylight or photopic vision
- ~ 6.5 million in each eye in the fovea centralis.
- One cone is connected to one optic nerve detail.
- Maximal sensitivity at 550 nm (yellow-green): Fig.7.

Dark adaptation: Fig.8
Dark adaptation is apparently the time needed for the body to increase the supply of photosensitive chemicals to the rods and cones.
The cones adapt most rapidly; after about 5 min the fovea centralis has reached its best sensitivity. The rods continue to dark adapt for 30 to 60 min, although most of their adaptation occurs in the first 15 min.
Blind spot: Fig.6
This is the point at which the optic nerve enters the eye. The blind spot is on the side toward the nose.










Figure 5: The light must pass through various cell layers to reach the rods and cones. In the fovea centralis much of this tissue is pushed to the side, permitting better detail vision in this area. Blood vessels also the light to some rods and cones.






Figure 6: The distribution of the rods and cones in the retina of the left eye; notice the blind spot with no sensors. A parametric angle of 300 to the left or right when the eye is looking straight ahead










Figure 7: The rods are much more sensitive than the cones. The vertical axis is a log scale; each division represents a factor of 10 in sensitivity. The best sensitivity of cons is at about 550 nm, while the best sensitivity of rods is at about 510 nm.


Figure 8: The eye dark adapts in two phases. The phase for the cones is completed in 5 to 10 min; the phase for the rods lasts for over 30 min. The increase in sensitivity is a factor of over 10,000.


4- How Little Light Can You See?

Two photons absorbed in the rods generate visual signal.
Typical flashlight: 1018 photons per second.
Absorption of photons:-
1- About 3%: reflected at the surface of the cornea.
2- About 50%: absorbed in the cornea, lens, and humors.
3- About 40%: absorbed in the backstop.
4- About 10%: absorbed in the rods.

5- Diffraction Effects on the Eye

Light waves passing through a small opening diffraction (point light source rings on the retina)
Diffraction pattern on the retina due to the iris: Fig.9.
All lenses have defects (aberrations). The effect of such aberrations is reduced if the lens opening is made smaller. In the eye, a small pupil improves visual acuity. However, if the pupil is made very small the acuity becomes worse due to diffraction effects. There is an optimum size for the pupil; best acuity for an emmetropic eye is obtained with a pupil size of 3 to 4 mm its normal size under good illumination.


Figure 9: Diffraction in the eye. (a) Monochromatic light from a distant point source is brought to a focus at the fovea centralis in the retina. (b) The diffraction pattern on the retina produced by a pupil 3.0 mm in diameter consists of a central bright spot 8 ?m in diameter surrounded by a ring of light of reduced intensity.





6- How Sharp Are Your Eyes?

The familiar eye charts used to determine whether we need corrective lenses test the property of our eyes called visual acuity. A physicist calls visual acuity the resolution of the eyes.
The optometrist usually uses a Snellen chart (Fig.10) to test visual
acuity.
The visual acuity or resolution of the eye is primarily determined by the characteristics of the cones in the fovea. A common way of testing resolution is to use a pattern of alternating black and white lines that become increasingly narrower. A combination of one white line and one black line is called a line pair (lp). Under optimum conditions, the eye can just barely resolve as separate lines a pattern of about 3o lp/mm; when the eye is twice as far away, it can only resolve 15 lp/mm. The resolution is often given in terms of the angle subtended from the eye. The minimum angle between two black lines that can be seen as separate is about 0.3 milliradians.
The resolution rapidly gets worse as the image moves away from the fovea centralis. At IOo from the fovea, the acuity is worse by a factor of 10. If the lighting is not optimum the resolution also deteriorates (Fig.11).
- One test of acuity used often by scientists is aligning two lines so that they appear to be a single continuous line (Fig .11). This is involved in using a slide rule and also in using a Vernier scale, and it is referred to as Vernier acuity. It is possible for a trained person to align two fine lines under optimum conditions to within 9 x I0-6 radians, much less than the 3x1o-4 radians needed to resolve two lines.

Background
- Resolution of bright on dark = about 10-3 radians of arc.
- Resolution of dark on bright = about 3?10-4 radians of arc.
- Light letters on dark background are harder to be read.








Figure10: A Snellen chart to test vision is usually viewed from 20 ft.


Figure11: Visual acuity improves with better lighting .The top curve shows the acuity for the Landolt C ring, where the gap direction must be recognized .Vernier acuity (the ability to align two lines) is much better than acuity for the Landolt C.


7- Defective Vision and Its Correction
In order to discuss the strength of a corrective lens for a defective eye we need to review the basic equations of simple lenses. There is a simple relationship between the focal length F, the object distance P, and the image distance Q of a thin lens (Fig.12).
1/F=1/P+1/Q
IF F is measured in meters, then 1/F is the lens strength in diopters (D). That is, a positive (converging) lens with a focal length of 0.1 m has a strength of 10 D. The focal length F of a negative (diverging) lens is considered negative. A negative lens with a focal length of -0.5 m has a strength of -2 D.


Figure12: (a) The distance from the lens to the object P and the distance from the lens to the place where the image is formed Q are related to the focal length F of a positive lens by the equation 1/F=1/P+1/Q .(b) Light coming from a great distance to a positive lens converges at the focus of the lens; the image distance Q is equal to the focal length F.(c) Light from a great distance striking a negative lens diverges. The light appears to diverge from the focal point on the left side of the lens. No image is formed.
Example:
Assume lens A with focal length FA= 0.33 m is combined with lens B with focal length FB = 0.25 m. What is the focal length of the combination? What is the dioptric strength of the combination?
1/F= 1/FA+1/ FB=1/o.33+1/0.25=1/0.143
or F = 0.143 m. Note that lens A is 3D and lens B is 4 D. The combination is simply the sum, or 7 D.

Let us consider the image distance Q of the cornea and lens of the eye to be 2 cm, or 0.02 m (17 mm is a more correct value but the arithmetic is harder). When the normal eye is focused at a great distance (infinity), the focal length F of the eye is the same as Q, or 1/F = 1/Q = 1/0.02 m, or the eye has a strength of 50 D. If the eye focuses on an object at P = 0.25 m, then 1/F = (1/P) + (1/Q) gives us 1/F = (1/0.25) + (1/0 .02) = 4 +50=54 D.
Focusing (refractive) problem: Fig.13 and Table 1.
Ametropia affects over half of the population of the United States. It is often possible to correct it completely with glasses. – - There are four general types of ametropia: myopia near -sightedness), hyperopia or hypermetropia (far-sightedness) astigmatism (asymmetrical focusing), and presbyopia (old sight), or lack of accommodation.
1- The myopic individual usually has too long an eyeball or too much curvature of the cornea; distant objects come to a focus in front of the, retina, and the rays diverge to cause a blurred image at the retina (Fig.14b). This condition is easily corrected with a negative lens.
Table1: A summary of various focusing problems and Their characteristics.



Figure13: Schematic of normal and defective focusing. Wavy lines indicate a blurred image on the retina.
Example:
Let us determine the strength of a lens needed to correct a myopic eye with a far point of 1.0 m. We consider the image (lens to retina) distance to be 2 cm (0.02 m).
A person who is focusing an object at 1.0 m has a lens strength of 1/F= (1/1.0) + (1/0.02) = 51D. An eye able to focus at infinity has a strength of (1/?) + (1/0.02) =50 D Thus a myopic person with a far point at 1.0 m has 1 D too many, and a negative lens of – 1.0 D will correct his vision.





A hyperopic eye has a near point further away than normal and uses some of its accommodation to see distant objects clearly. The usual cause of hyperopia is too short an eyeball (Fig .14 c). A positive lens is used to correct this condition.

Example
Let us consider a far-sighted eye with a near point of 2 .0 m .What power lens will let this person read comfortably at 0.25 m?
The strength of a good eye focused at 0.25 m is given by (1/0.25) + (1/0.02) = 4 +50=54 D. An eye focused at 2m has a strength of (l /2.0) + (1/0.02)=0.5+50=50.5 D. A corrective lens of 54-50.5= +3.5 D would be prescribed for this eye.



Figure 14 : Focusing properties of the eye. (a) The normal, or emmetropic, eye
focuses the image on the retina. (b) The near-sighted, or myopic, eye focuses the image in front of the retina. This problem is corrected with a negative lens. (c) The far-sighted, or hyperopic, eye focuses the image behind the retina. This problem is corrected with a positive lens.











8- Testing for myopia or hyperopia:

You can check to see if you are myopic or hyperopic. Look through a pinhole in a well-illuminated distinct object, for example, a streetlight (Fig.15).Move the pinhole up and down in front of your eye. If you are an emmetrope, you will not see any motion; if you are myopic, the image on the retina will move in the direction opposite that of the card and will be interpreted by the brain as moving in the same direction; and if you are hyperopic, the motion of the image on the retina will be in the same direction as the card and will appear to be moving in the oppositive direction.
You can also easily check whether glasses have positive or negative lenses by looking at an object through one lens held some distance away. When you move the lens, the object also lens, it is a negative lens; if it moves in the opposite direction, it is a positive lens. Another test is to hold the lens over some printing. If it enlarges the printing, the lens is positive; if it makes the printing smaller, the lens is negative.

Testing for astigmatism and presbyopia:
- In astigmatism, the curvature of the cornea is uneven. Astigmatism cannot be corrected by a simple positive or negative lens. A simple test for astigmatism is to look at a pattern of radial lines (Fig. 16). An astigmatism eye will see lines going in one direction more clearly than lines going in other directions. Astigmatism is corrected with an asymmetric lens in which the strength is greater in one direction than in the perpendicular direction (Fig.17). If you wear glasses to correct astigmatism, hold your glasses some distance from your head and rotate them while looking at an object through one lens. You will notice that the object appears to change shape as you rotate the glasses.
- Often a person older than 50 notices that he has trouble reading fine print; when he holds the book far enough away to focus clearly, the print is too small for him to distinguish the letters. Although reading in a bright light helps because it narrows the pupil and gives him a better depth of focus, he will need reading glasses. If he already wears glasses to correct a vision defect, he will need bifocals. This problem is due to the loss of accommodation with age (Fig.18). The lens becomes less pliable, and when the tension on it is released, its dimensions change only slightly. As you can see in Fig.18, this loss of accommodation starts at an early age.
















Figure 15: Moving a pinhole in front of the ametropic eye while it is looking at a distant object causes apparent motion of the object. Emmetropes see no motion.


Figure16: A simple test for astigmatism. An eye with astigmatism sees lines
going in one direction more clearly than lines going in other directions.













Figure 17: Astigmatism is corrected by adding a cylindrical lens to a spherical lens. (A) Converging or (B) diverging.



























Figure 18: Loss of accommodation with age. The decrease in accommodation usually becomes noticeable after age 40.

9- Use contact lens :

1- Contact lenses are used primarily for cosmetic reason by young people.
The direct contact between a contact lens and the cornea, however, noticeably affects the prescription. A myopic person switching from glasses to contact lenses would need weaker negative lenses, and a hype rope would need stronger positive lenses. The image size on the retina produced by contact lenses is different from that produced by ordinary glasses; it is larger in myopia and smaller in hyperopia. Wearing contact lenses requires more accommodative effort or myopia and less for hyperopia.
2- A contact lens does not have a fixed orientation, the question of correcting or astigmatism must be resolved. The hard contact lens is made to fit the curve with the largest radius; when it is worn, the space left in the region of the higher curvature fills with tear fluid. The tears correct for astigmatism by making a symmetrical "new cornea".
• Soft plastic contact lenses wear developed in 1950s.They are much more comfortable to wear than hard plastic lenses. Also, soft lenses are permeable to gases so that oxygen can reach the cornea directly. With hard plastic lenses, the oxygen is dissolved in the tear layer, and each blink carries a fresh supply under the lens to the cornea.
• The main disadvantages of soft contact lenses are (1) they cost more; (2) they require a special daily cleaning procedure; and (3) since they conform to the cornea, they do not correct for astigmatism.
3- Contact lenses are sometimes used for other than cosmetic reasons. In rough sports such as football and soccer, players often wear contact lenses for safety reasons. Soft plastic lenses are also used to administer medication directly to the cornea over a period of hours. The lens is soaked in the medication before it is put in the eye.



10- Instruments Used in Ophthalmology

1- Ophthalmoscope: to examine the interior of the eye
2- Retinoscopy: to determine the prescription of a corrective lens
3- Keratometer: to measure the curvature of the cornea
4- Lensometer: to measure the focal length of a lens
5- Tonometer: to measure eye pressure, applanation tonometer