Optics of Human Eyes

Introduction

Light focused by the human eye is refracted by multiple curved surfaces before falling on the retina, where an electrical impulse is generated, eventually perceived as vision. The corneal tear film, corneal layers, and anterior and posterior lens surfaces all affect the quality of the image formed on the retinal receptors. If the secondary focal plane of the combined refracting elements is at the retina, the eye sees well. If not, a refractive error is present.

Schematic Eyes

Although it is possible to determine with reasonable accuracy the index of refraction and refracting power of all the elements of the average eye, for simple calculations it is useful to represent all refraction as taking place at the corneal surface. The Reduced Schematic Eye is a simplified model of a human eye (Slide 1). The average eye has an axial length 22.6 mm and the index of refraction of the ocular media is 1.333, indicating a refractive power of 1.333/0.0226 = 59 D. The nodal point of this representative eye is located 17 mm in front of the retina.

Slide 1. Reduced schematic eye is shown.

Slide 2. Using the schematic eye permits estimation of retinal image size.

The parameters of the reduced schematic eye allow approximation of the size of the retinal image of a given object (Slide 2), because congruent triangles are formed by the visual axis, the height of the object and the height of the retinal image, and the ray from the object peak through the nodal point to the image peak. By definition, the sides of congruent triangles have the same ratios in both triangles, so the height of the retinal image bears the same ratio to the height of the object as the distance of the nodal point from the retina bears to the distance from nodal point to the object. In such calculations, the distance to the object is measured from the cornea, because the 5.6-mm distance from cornea-to-nodal point is usually insignificant.

Retinal Image

=

Object height Object distance

×

17 mm

In Slide 2, [0.5 ft/20 ft] x 17 mm = 0.425 mm retinal image height. Making such calculations requires memorization of only the 17-mm retina-to-nodal point factor.

Slide 3. When the eye accommodates, the anterior lens surface increases its curvature greater than the posterior surface.

Of course, the human eye is not arranged as simply as the Reduced Schematic Eye, and use of the Reduced Schematic Eye provides only a good estimate of what occurs when light passes to our retinas. The parameters of the Gullstrand schematic eye, which is a more complete representation of the human eye, are offered in the Table. This separates the several refractive elements and allows more accurate estimates of retinal images, but is not necessary for everyday clinical refraction.

Accommodation

When the ciliary muscle constricts in response to parasympathomimetic stimulation, the zonular fibers that keep tension on the lens capsule shorten. The lens changes shape (Slide 3), increasing the surface curvature, predominantly on its front surface. The increased curvature refracts light to a greater degree, adding plus vergence. This process, known as accommodation, can generate an additional +14 D to +15 D vergence in children. The amplitude of accommodation diminishes steadily during the first four decades of life, for reasons still being debated.

Refractive Error

Refractive errors are defined based on how the eye, while its accommodation is maximally relaxed and at minimum vergence, focuses light that originates at a far distance, that is, essentially parallel light with zero vergence. Far distance is known as optical infinity and is considered to be any distance greater than 6 m, which is one sixth of a diopter from true infinity. This is an arbitrary choice, but it is reasonable because spectacles are rarely ground for accuracy less than one quarter of a diopter. An eye that can focus infinity on the retina is termed emmetropic (Slide 4). If it cannot focus infinity on the retina, it is ametropic.

Slide 4. The emmetropic eye, with accommodation relaxed, focuses parallel light from optical infinity on the retina.

If an eye, with its accommodation at minimum, focuses light from infinity anterior to the retina, it is myopic (Slide 5). The myopic eye has too much plus power for its length. Either the eye is too long, or the refractive elements (cornea and/or lens) are too strong. Any increase in accommodative tone will pull the focus forward, toward the lens, and away from the retina, which would further blur the vision of the eye. However, bringing the target closer to the eye would produce negative vergence in the light striking the cornea, and would push the focus away from the front of the eye. A target positioned at the far point of the eye would be focused on the retina and would be seen clearly (Slide 6). The far point plane and the retina are conjugate planes, and light originating at either plane would be focused at the other plane. Myopic patients, therefore, see near targets well (if targets are positioned at the far point or closer), but are blurred for distant targets.

Slide 5. The myopic eye, with accommodation relaxed, focuses light from infinity anterior to the retina.

Slide 6. The far point is conjugate to the retina. An object at the far point would be focused on the retina. The myopic eye has its far point anterior to the cornea.

An eye that has accommodation at minimum power and focuses parallel light from infinity behind the retina is termed hyperopic (Slide 7). Of course, the light does not actually penetrate the retina to come to a focus, but light is still converging when it strikes the retina and produces a blurred image. The far point in hyperopia is located behind the eye (Slide 8). Because light must be focusing on the far point when it strikes the cornea for the nonaccommodating eye to focus the light on the retina, it is obvious that the hyperopic eye requires convergent light to focus on the retina.

Slide 7. The hyperopic eye, with accommodation relaxed, focuses light from infinity behind the retina.

Slide 8. The hyperopic eye has its far point "behind the eye." Light converging to a focus at the far point would be focused on the retina by the eye's optics.

As in any eye, an increase in accommodative tone above its minimum will pull the focus toward the front of the eye. If the hyperopic eye accommodates, it may add enough plus vergence to bring the light from infinity into focus on the retina. Unlike the myope, however, bringing the target closer to the hyperopic eye does not help, because this creates negative vergence at the cornea and pushes the focus of the light further behind the retina. Greater accommodation is required to see the closer target clearly than if the target were at infinity. However, if the eye can exercise enough accommodation, it can clearly see targets at any distance. Therefore, hyperopic patients see well without assistance when they are young and have significant accommodative amplitude. But images may be blurred for both near and far later in life when accommodation is lost.

Myopia and hyperopia are "spherical" refractive errors, focusing light from a point source as a point. An astigmatic eye focuses a point source of light as a conoid of Sturm. This is a three-dimensional structure of light with thin lines at the anterior and posterior ends, a circle in the dioptric middle, and ovals of varying dimensions between the lines and circle (Slide 9).

Slide 9. The astigmatic eye focuses light as a conoid of Sturm, with focal lines at each end and a circle in the dioptric middle. The image of a point source of light at several planes within the conoid is shown below the eye.

The astigmatic interval is the space between the two focal lines and the amount of astigmatism is the dioptric difference between the two lines. The circle in the middle of the Conoid is known as the circle of least confusion, and it increases in diameter with increasing amounts of astigmatism. An astigmatic eye sees best when the circle of least confusion is positioned at the retina, such that a point source of light is imaged as a circle, rather than an oval or line as would be the case if any other plane of the Conoid was imaged on the retina. There is no far point that is conjugate to the retina, but the two focal lines can be considered "far lines," and the circle of least confusion the "far circle" of the astigmatic eye. The position of the circle of least confusion relative to the retina is a measure of the amount of myopia or hyperopia present in addition to the astigmatic error (Slide 10). The dioptric distance of the circle of least confusion from the retina is known as the spherical equivalent of the total refractive error. (In algebraic lens representations, the spherical equivalent is the sphere power plus half the cylinder power, including its sign. For example, spherical equivalent of -3.00 + 2.00 x 180 = -2.00.)

In "regular" astigmatism the two focal lines are positioned perpendicular to each other. Regular astigmatism is a common refractive error in normal, healthy eyes. "Irregular" astigmatism, in which the focal lines are not perpendicular, is often the result of pathology (e.g., corneal scar, cataract, globe distortion from chalazion). Regular astigmatism can be compensated with cylindric spectacle lenses, but irregular astigmatism is not correctable by spectacles.

Slide 10. The spherical equivalent is the position of the circle of least confusion relative to the retina, and describes the myopic or hyperopic component of the astigmatic refractive error.

Corrective Lenses

Refractive errors may be compensated by spectacles, contact lenses, intraocular lenses, or refractive surgery on the cornea, or even pinhole. This Tutorial will be limited to discussing spectacle correction. See other Tutorials for the optics of contact lenses, intraocular lenses, and refractive surgery.

Spectacle lenses change the vergence of the light before it reaches the cornea. Plus spectacle lenses increase the convergence of incident light (Slide 11), thus increasing the plus vergence inside the eye behind the lens. Plus spectacle lenses always pull the focus closer to the lens, and when placed before an eye plus spectacles always pull toward the front of the eye. Minus lenses diverge light (Slide 10), decreasing the plus vergence inside the eye behind the lens. Minus spectacle lenses always push the focus farther from the lens, and when placed before an eye, minus spectacles always push the focus away from the front of the eye.

Slide 11. Plus lenses pull the focus closer to the lens, while minus lenses push it farther from the lens. (Slide adapted from Optics for Clinicians by Mel Rubin, MD, with permission of the author.)

Simple cylindric lenses have curvature in one meridian on their surface and are uncurved (plano) in the meridian 90° away (Slide 12). Therefore, the full refractive power of the lenses is exerted along the curved meridian and there is no effect along the flat meridian. The axis of a cylindric lens is perpendicular to the plane of the curved surface, and the cylindric lens will act maximally on a line parallel to its axis and not at all on a line perpendicular to its axis. Cylindric power may be combined with spherical power (plus or minus) in one spectacle lens, in which case there are two major meridians on the lens surface, one of maximum curvature and one of minimum curvature. Each meridian will have its full vergence effect on a line parallel to the axis of that curvature and perpendicular to the plane of the curvature (Slide 13).

Slide 12. Simple plus and minus cylindric lenses have curvature in one meridian and are flat in the opposite meridian. Light is refracted by the curved surface, but is not by the flat one.

Slide 13. A spherocylindric lens has a surface curvature of maximum strength and of minimum strength, perpendicular to each other. Each major meridian will exert its power on lines perpendicular to the plane of that meridian.

Correction of Refractive Errors

The ametropic eye's retina clearly sees a target at its far point. Several approaches may be used to neutralize the eye's refractive error so that distant targets can be seen sharply. One may imagine the corrective lenses moving the far point to infinity. Alternatively, one may view the corrective lens as imaging infinity at the far point, since the retina focuses well on any object at the far point. Lastly, one may perceive the lenses as moving the focus of light from infinity within the eye until it is on the retina.

To correct myopia, a minus lens is required. This pushes the focus away from the lens, toward the back of the eye. It also pushes the far point away from the lens and eye, toward infinity.

In myopia, the far point is between infinity and the eye, in front of the eye. If an eye's far point is 20 cm anterior to the cornea (Slide 14), a corrective lens at the corneal plane must focus infinity 20 cm (0.2 m) away from the lens, on the same side as the incident light. A minus lens would accomplish this, if it had a power of 1/0.2 m = -5.00 D (Slide 14). Of course, if the eye were under water, the numerator of the equation would be the refractive index of water.

Slide 14. The minus lens before the myopic eye focuses light from infinity on the far point, which is conjugate to the eye's retina, and is therefore seen sharply.

In hyperopia, a convergent plus lens is required to focus infinity at the far point behind the eye, unless the hyperope has already accommodated to bring the focus to the retina. If a hyperopic eye cannot accommodate enough to focus for infinity, the minimum plus lens power required to achieve that eye's best visual acuity is a measure of absolute hyperopia (Slide 15). As additional plus power is added before the eye, accommodation is relaxed to maintain maximum acuity. The additional plus power that does not reduce acuity is a measure of facultative hyperopia. Absolute plus facultative is manifest hyperopia. The eye may have more hyperopia than the manifest, but cannot relax accommodation to allow measurement of this latent hyperopia. Cycloplegia is required to "bring out" the latent component of hyperopia.

When astigmatism is present, cylindric (toric) lenses are used to collapse the conoid of Sturm. Each focal line in an astigmatic eye has a corresponding far line, the position of each being determined by the dioptric distance of the focal line from the retina. A simple cylindric lens is used to focus infinity at one far line (or push that far line out to infinity), and a second to adjust for the other far line (Slide 16). Each cylindric lens acts on the far line (and focal line) parallel to its axis. Then, the two simple cylinders are combined in one spherocylindric lens. Alternatively, one may picture using a cylindric lens to move one far line (and focal line) to the other, collapsing the astigmatic interval, and then using a spherical lens to focus infinity on the resultant far point (Slide 17). Of course, the end result is the same.

Astigmatic eyes are often referred to as "with the rule" or "against the rule." With the rule astigmatism is corrected by plus cylinder lenses with axis near 90°. Against the rule astigmatism is corrected by plus cylinder with axis near 180°. With the rule astigmatism is typically found in younger patients with corneas more steeply curved in the vertical meridian. Against the rule astigmatism is typically found in older patients with corneas more steeply curved in the horizontal meridian.

Slide 15. The "pyramid" of hyperopia.

Slide 16. Each cylindric lens focuses light from infinity as a line at the far plane of one focal line of the conoid in the eye. Combining the two cylinder lenses creates the corrective spherocylindric lens.

Slide 17. Collapsing the astigmatic interval by moving one focal line to the other leaves a spherical error. Combining the corrective lens for that spherical error with the cylindric lens gives the spherocylindric correction.

Visual Acuity and Refractive Error

The farther from the retina the image is focused, the larger the blur circle of any image point on the retina will be. Therefore, the greater the refractive error, the greater the distortion of vision will be. There is variation in the visual acuity of patients with the same degree of refractive error, but the refractionist can predict the degree of uncorrected refractive error from the visual acuity with some modest accuracy. A patient with a refractive error of 1 D will have approximately 20/40 vision, or sometimes slightly better. A patient with a refractive error of 2 D will result in vision ranging from 20/100 to 20/200. When a patient reads the chart at 20/25 but the refraction indicates 2.5 D of uncorrected error, the refractionist or the patient may have made a mistake.

Bibliography

The American Academy of Ophthalmology. The Revised 2000-2001 Basic and Clinical Science Course. Section 3: Optics, Refraction, and Contact Lenses. San Francisco, Calif: The Foundation of the American Academy of Ophthalmology.

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Michaels D. Basic Refraction Techniques, Raven Press. New York

Miller D. Textbook of Ophthalmology. Vol. 1. Optics and Refraction. New York, NY: Gower Medical Publishing; 1992.

Rubin M. Optics for Clinicians, 2nd ed. Gainesville, Fla: Triad Publishing; 1993.

Sloane A, Garcia G. Manual of Refraction, 3rd ed. Boston, Mass: Little Brown and Co; 1979.

Tasman W, Jaeger E, eds. Duane's Foundations of Clinical Ophthalmology. Vol 1: Refraction and Clinical Optics. Philadelphia, Pa: Lippincott-Raven Publishers; 2000.