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Module 16 Section 2 |
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Module 16: |
Optics | |||
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Section 2: |
Physiologic Optics | |||
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Astigmatism and cylindrical corrections |
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| Physical optics refers to the properties of light itself, such as the electromagnetic spectrum. Geometric optics refers to how light behaves when affected by various media, such as lenses and mirrors. Physiologic optics refers to the mechanics and physiology of the eye. | ||||
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The human eye is a compound lens system consisting of the cornea and lens. The total diopter power of an "average" eye is about 60 diopters. The average diopter power of the cornea, about 43 D, accounts for most of the refractive power of the system.
The human eye functions in a similar manner to a camera. In fact, the camera analogy is useful in explaining eye problems to the patient. Light is focused by a compound lens system (cornea and lens), through an aperture that regulates the amount of light (pupil, iris), onto a light sensitive medium (retina).
The "normal" eye is about 24mm in length. The cornea is the most powerful "lens" in the system with about 43 diopters of plus power. The natural lens has about 20 diopters of plus power. An emmetropic (optically perfect) eye focuses parallel rays (distant) of light on the retina without accommodating (changing the shape of the lens).
Hereditary factors and natural variations in the development of the human body produce imperfect "camera parts". Not everyone can see 20/20 in the distance without a visual aid such as a glasses correction. These eyes with imperfect optics are said to have a refractive error.
A myopic (nearsighted) refractive error results when the cornea is too steep, or the axial length of the eye is too long, or a combination of the two. In this case parallel light is focused in front of the retina. If the patient accommodates (focuses with the lens), the vision is made worse. The myopic eye is corrected optically by using a minus lens to move the focal point back to the retina. The next three illustrations are animations meant to be viewed on a computer screen. If this information is printed, these illustrations will not be effective.
A hyperopic (farsighted) refractive error results from a cornea that is too flat, or an axial length that is too short, or a combination of the two. In this case parallel light is focused behind the retina. The focal point can be moved onto the retina either by using a plus lens in front of the eye (glasses or contacts) or by accommodative effort (focusing of the lens) by the patient. |
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Astigmatism and cylindrical corrections
Corneal astigmatism is created when the cornea is not a perfect sphere. The astigmatic cornea is curved more in one meridian than it is in the other. These meridians are usually 90 degrees apart (regular astigmatism). The lens can have astigmatism also, this is termed lenticular astigmatism. Lenticular astigmatism is evident when there is a significant difference between the astigmatism as measured on the keratometer and refractive astigmatism. However, you must also take into account that corneal astigmatic power as measured by the keratometer does not always translate directly to refractive astigmatic power. The Javal Rule states that for keratometer readings of less than 1.75 D of astigmatism, the refraction will probably need about .25 D less correction if the astigmatism is with-the-rule (see below). For against-the-rule astigmatism of less than 2.5 D as measured by the keratometer, the refraction may yield .75 to 1.00 D more correction.
Most astigmatic corneas have the most curvature, and therefore the greatest power, in the 90 degree (vertical) meridian. This is called with-the-rule astigmatism, and the minus cylinder axis is at or near 180. Against-the-rule astigmatism has the minus cylinder axis at or near 90 degrees. Oblique astigmatism has an axis at an oblique angle, such as 45 degrees.
Astigmatism is corrected optically with a cylindrical lens. A combination of a spherical lens and a cylindrical lens (spherocylindrical lens) is used to correct a spherical error with an astigmatic error. A cylindrical lens is pictured below. It has power (curvature) in one meridian and no power in the other meridian. The axis of the cylinder is lined up with the axis of astigmatism to correct the astigmatic power difference.
Instead of a focal point, the spherocylindrical lens creates two focal lines perpendicular to one another and at different focal distances depending upon the particular curvatures. Half way in between the two lines a blur circle is formed called the "circle of least confusion".
The axis of the cylinder in a spherocylinder is marked according to the optical protractor. It is formed by a half circle with the zero mark at the east point on the compass, the 90 degree mark at the north point, and 180 degrees at the west point.
A spherocylindrical lens power is written in the following manner:
-2.00-2.00x180 or -4.00+2.00x90
The first number represents the sphere power. The second number is the cylinder power notation in plus or minus cylinder. The number after the x is the axis notation. Conversion from plus to minus cylinder notation is accomplished by transposing. The sphere and cylinder values are added together algebraically, the cylinder sign is reversed, and the axis is rotated 90 degrees.
The circle of least confusion is represented by the spherical equivalent of a spherocylinder lens. This is the lens power that would give the best vision if a cylinder correction could not be used. The spherical equivalent is sometimes used in soft contact lens fitting to provide the best vision without using a toric lens. It is calculated by adding half of the cylinder power to the sphere power. The spherical equivalent of –2.00-2.00x180 is –3.00.
The relationship between sphere and cylinder powers can be understood graphically by constructing an optical cross. The technique is useful when performing retinoscopy with loose lenses and when calculating the need for a slab-off. There are two types of optical crosses, the axis cross and the power cross (also called a meridian cross). Our example -2.00-2.00x180 can be illustrated as follows on the axis cross:
The line can be marked with the meridian or the axis of power, you just have to be consistent. Remember that the axis of a cylinder has no power, and the power is along the meridian (90 degrees to the axis). A power cross of the same lens would look like the figure below:
It takes a –2.00 lens to correct the eye at axis 90 degrees (in the 180 degree meridian) and a –4.00 lens to correct the eye at axis 180 degrees (in the 90 degree meridian). The axis cross is more useful when performing retinoscopy and the meridian (power) cross is more useful when calculating a slab-off. Minus cylinder notation: The more plus number is taken as the sphere power (-2.00). The difference on the number line from the sphere power to the other power is taken as the cylinder power (-2.00 to –4.00 is –2.00), and the axis of the more minus number is used as the axis value (180). The result is –2.00-2.00x180. Plus cylinder notation: The more minus number is taken as the sphere power (-4.00). The difference on the number line from the sphere power to the other power is taken as the cylinder power (-4.00 to –2.00 is +2.00), and the axis of the more plus number is used as the axis value (90). The result is –4.00+2.00x90. You may recognize this as the same procedure used to perform lensometry with a lensometer.
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Astigmatism can be classified according to where light is focused for each primary meridian. This can be demonstrated using a schematic of the eye, or an optical cross. In these illustrations, a power cross is used. Simple hyperopic astigmatism: One meridian is focused on the retina, the other behind the retina, as in an eye needing the following correction: plano+2.00x90. |
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Compound hyperopic astigmatism: Both meridians are focused behind the retina: +2.00+2.00x90. |
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| Simple myopic astigmatism: One meridian is focused on the retina, the other in front of the retina: -2.00+2.00x180 | ||||
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| Compound myopic astigmatism: Both meridians are focused in front of the retina: -4.00+2.00x180 | ||||
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Mixed astigmatism: One meridian is focused in front of the retina and the other behind the retina: -2.00+4.00x180 |
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Many manufactured lenses have a circular contour. Some manufactured lenses and most naturally occurring lenses have a flatter curvature at the edge making the lens curvature a parabola instead of a circle. This is called an aspheric lens. Aspheric lens designs help reduce aberrations (distortion). The cornea is an aspheric lens with the central cap having a steeper curvature than the periphery. The average radius of curvature of the corneal cap is 7.7 mm, which translates to about 43.00 diopters. The crystalline lens is an aspheric lens with the ability to change shape (accommodate). When the fibers (zonules) holding the lens are relaxed by the ciliary muscle, the lens assumes a fatter shape and the radius of curvature is decreased, increasing the plus power. As we get older the lens becomes more and more stiff and less able to change shape. When this affects our near vision, usually around age 45, it is called presbyopia.
The pupil is like the aperture in a camera. It dilates and constricts to regulate the amount of light entering the eye, so as to provide the proper exposure of light to the retina. The pupil also has some optical functions. Constriction of the pupil increases the depth of field (the pinhole effect) and decreases aberrations from the cornea. Pupillary constriction is stimulated by light intensity and by accommodation.
The size of the image projected onto the retina is affected by the type of correction needed. A minus lens makes an image smaller and a plus lens makes an image larger. This is not a problem unless there is a significant difference in refractive error between the two eyes (anisometropia). A difference of more than 3 diopters may produce a problematic image size difference (aniseikonia). This problem can be minimized by wearing contact lenses.
If an object is viewed through a moving plus lens, the object will appear to move in the opposite direction from the direction of movement of the lens. This is termed "against motion".
If an object is viewed through a minus lens, the object will appear to move in the same direction as the movement of the lens. This is termed "with motion".
Neutralizing a lens with loose trial lenses
This phenomenon can be used to identify the sign and approximate power of a lens without the use of a lensometer. The power can be estimated by holding a trial lens against the unknown lens and observing apparent motion. The power of the trial lens is changed until there is no apparent motion detected. The power of the unknown lens is equal in diopter value and opposite in sign to the trial lens. This method can be used to approximate the lens power of a sphero-cylinder by moving the lens along different axis lines. The axis of the sphero-cylinder is 90 degrees from the line that provides the most diopter power.
Compounding and canceling prism
If a patient looks through a base-in prism with the left eye and base-in prism with right eye, the effects are said to be compounding. Since the image appears to be deflected toward the apex of the prism, this prism orientation will move the eyes in opposite directions. The diopter powers of the prisms would be added together to get the total prismatic effect (4 + 2 = 6).
If a patient looks through a base-out prism with the left eye and a base-in prism with the right eye, the effects are said to be canceling. The image is displaced toward the apex of the prism. In this case, the images will be moved in the same direction, thus the canceling effect. The difference between the diopter powers of the prisms would be taken to get the total prismatic effect (4 - 2 = 2).
If a patient looks through a base-down prism with one eye and a base-up prism with the other eye, then again we have images moving in opposite direction and we have compounding prisms.
If the patient looks through a base-up prism with one eye and a base-up prism with the other eye, the images are moving in the same direction and it is a canceling situation with the prism powers.
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