Introduction
Each optical component of the eye contributes to image formation on the retina and its brain interpretation. In order to discuss these components, we must first define the limits of normality considering the best image quality that can be produced by an emmetropic eye (an eye without refractive error). The determination of these limits is important, as they serve as guides for intervention on clinical practice. This chapter discusses individual optical variables that characterize the normal human eye as well abnormal conditions of the refracting apparatus of the eye, also called ametropia.
Cornea
The cornea’s anterior surface is approximately spherical, with a radius of curvature that is typically a bit less than 8 mm. This surface is responsible for about two-thirds of the eye’s refractive power. Technology based in the Scheimpflug principle allows for the detailed analysis of each interface together with the local thickness in estimating the total corneal power for an individual eye before and after corneal surgery. The corneal stroma must be transparent for high-quality image formation on the retina, yet the normal human cornea scatters 10% of the incident light. By comparison, the corneal stroma of the eagle is almost as transparent as glass. This factor (along with the larger pupil size and finer cone diameter) is why the resolution of the eagle eye is better than 120 cycles per degree, which is equivalent to a Snellen acuity of 20/5 (6/1.5).
The aspherical shape of the cornea’s anterior surface affects the quality of the retinal image. Normal corneas have a flatter periphery and steeper center, counteracting the effect of paraxial light that tends to bend more at peripheral areas. The “Q” factor, also named asphericity or eccentricity factor, quantifies this central-periphery flattening and averages −0.25 in normal eyes. A more negative number means that this cornea is steeper than normal (i.e., central keratoconus), and less negative “Qs” are seen, for example, in postrefractive myopic procedures. Such knowledge was built into equipment for new refractive surgeries that allows for the control of final “Q” factor, aiming for better contrast definition after surgery.
Corneal astigmatism is caused by this surface having different radii of curvature along different meridians (directions in the coronal plane). A survey of normal eyes shows that almost every human eye has a baseline corneal astigmatism of at least 0.25–0.50 D. Spherical aberration is caused by the radius of curvature of the corneal surface changing (generally increasing) with distance from the center of the pupil to the pupillary margin. Several devices based on Placido’s ring principle provide quantitative data on corneal aberrations. The amount of spherical aberration contributed by the cornea varies with pupillary aperture and individual corneal shape. For a pupil 4 mm in diameter, spherical aberration varies from +0.21 D to +1.62 D, depending on the specific corneal form.
Pupil
The iris expands or contracts to control the amount of light admitted to the eye. The pupil can range in diameter from 8 mm in very dim light down to about 1.5 mm under very bright conditions. A strong association exists between visual acuity and pupillary diameter. For example, visual acuity has been shown to improve steadily as background illumination increases up to a value of 3400 cd/m 2 . This improvement is due to blockage of paraxial aberrant rays and brain compensation for the resulting dimming of retinal illumination. To deliver more light (larger pupil) without aberration it is necessary to control the peripheral shape of the cornea.
Retinal image quality, as determined by optical aberrations such as spherical aberration, tends to improve with decreasing pupil diameter, because peripheral optical aberrations decrease with decreasing pupil size. On the other hand, retinal image quality is limited by diffraction, which tends to improve with increasing pupil diameter. For most eyes the best retinal images are obtained when the pupil diameter is about 2.4 mm, which is the diameter at which the effects of aberration and diffraction are balanced optimally. Thus the optimal pupillary size seems to be determined by several influences. In fact, Campbell and Gregory have shown that pupil size tends to be adjusted automatically to give optimal visual acuity over a wide range of luminance.
Lens
The crystalline lens, which has about one-third of the eye’s refractive power, enables the eye to change focus. When the eye views nearby objects, the ciliary muscle changes the shape of the crystalline lens by making it more bulbous and, consequently, optically more powerful. The lens of a young adult can focus over a range greater than 10 D. Presbyopia, which begins at about 40 years of age (depending on the environmental factors such as temperature), is the inability of the eye to focus (accommodate) due to hardening of the crystalline lens with age. Experiments that disrupt the hard collagen within the lens are ongoing and may provide new insights in presbyopia correction. When the eye can no longer accommodate at the reading distance, positive spectacle lenses of about 1.5–3 D are prescribed to correct the difficulty.
The normal 20-year-old crystalline lens scatters about 20% of the incident light. The amount of scatter is more than double this in the normal 60-year-old lens. Such scatter significantly diminishes contrast sensitivity. Also, the normal 20-year-old lens absorbs about 30% of incident blue light. At age 60, this absorption increases to about 60% of the incident blue light. The increase of blue light absorption with age results in subtly decreased color discrimination and decreased chromatic aberration. It is possible that this increased absorption helps to reduce the amount of UV light reaching the older retina, protecting it from oxidative damage, which is seen in age-related macular degeneration.
The variation in index of refraction of the crystalline lens (higher index in the nucleus, lower index in the cortex) is responsible for neutralization of a good part of the spherical aberration caused by the human cornea. A progression toward positive spherical aberration throughout life due to the crystalline lens has been described. Fig. 2.2.1 shows how this variation of index of refraction in the spherical fish lens almost eliminates its spherical aberration compared with a spherical glass lens.
Accommodation
In a convergent optical system, as an object approaches, its formed image moves away from its original position, that is, farther away from the lens. Accommodation is a complex mechanism involving sensory and neuromuscular phenomena by which the human eye, through contraction of the ciliary muscle, changes the optical power of the lens to assist the convergence of the image to the retina, adjusting the focus to different distances between the object of regard and the eye.
According to the von Helmholtz model (the most widely held theory), when the visual target approaches nearer to the eye, there is a stimulus to the contraction of the ciliary muscle that leads to a relaxation of the suspensory ligaments of the lens, increasing its anterior–posterior diameter, and a forward shift of the lens, and, consequently, its dioptric power ( Figs. 2.2.2 and 2.2.3 ). The opposite occurs when relaxation of this musculature occurs.
The precise details of the mechanism of accommodation remain unclear to this day. Discussion of the various hypotheses currently under investigation is beyond the scope of this chapter.
The ability of the lens to change its shape is called physical accommodation, whereas the contraction capacity of the ciliary muscle is called physiological accommodation. Both alter the refractive power of the system and can be measured. If the lens becomes stiffer and unsightly, unable to alter its shape, physical accommodation is impaired even with the strength of the preserved ciliary muscle. A similar process may occur with physiological accommodation if weakness of the ciliary muscle exists.
Range and Amplitude
The greatest distance an object can be clearly seen by the eye with relaxed accommodation is called the “far point.” The nearest point at which an object can be clearly seen is called the “near point,” which is the location of the focus obtained with maximum accommodation. The range of accommodation, by definition, is the distance between these two points. The amplitude, measured in diopters, refers to the refractometric difference between the eye in maximum relaxation and maximum accommodation.
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Far point: The greatest distance at which an object can be seen clearly in the absence of accommodation.
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Near point: The closest distance at which an object can be seen clearly when maximum accommodation is used.
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Range of accommodation: Distance between the far point and the near point.
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Amplitude of accommodation: Difference in dioptric power between the eye at rest and the fully accommodated eye.
The amplitude of accommodation can be measured directly by the method of spheres. In this method, we ask the patient to look at an object 40 cm away and change his/her need for accommodation with the addition of lenses. By adding negative lenses, the accommodation is stimulated until the image begins to blur. For example, suppose the patient accepts −2 D with clear vision. As we add positive lenses, the accommodation will relax until the image begins to blur again. Suppose in this situation, the lens used was +3 D. In this case the patient has a 5 D amplitude of accommodation.
Further information can be obtained with simple examination. Placing an object at the nearest point where the patient can obtain sharp vision will determine the near point. Moving away the object, we define the far point. In the case of a patient with 3 D of amplitude: If he or she is emmetropic, the far point will be in infinity and the near point will be to 33 cm. If the patient is a 3 D hyperope, the near point will be at infinity, because all the accommodation must be used to clarify the acuity at distance. If the patient has a myopia of 3 D, the near point will be 16.7 cm because the accommodation together with the refractive error amounts to a total of 6 D of refractive power.
In a hyperope, the accommodation necessary to see clearly at a distance is the same diopters of the magnitude of their hypermetropia. However, to see a near object 10 cm from the eye, as we saw before, 10 diopters (D) should be added to this value.
In hyperopia, there is no object distance for which a clear retinal image can be obtained without accommodation (or optical correction)—the optical apparatus of the eye has too little dioptric power at rest to focus an object on the retina. In this case we may define the far point of the eye as the (virtual) point, located behind the eye, which is imaged by the relaxed optics of the eye on the retina. Additional plus lens power, either from accommodation or supplied by a spectacle lens, is necessary to obtain a clear image.
For example, assuming a 4 D hyperope with amplitude of accommodation of 8 D, the (virtual) far point is at 25 cm behind the eye. With an accommodating effort of 4 D, the parallel rays from an object at infinity converge to the retina. Note that with an 8 D effort, this hyperope can converge divergent rays from a point 25 cm away from the eye. Assuming that this is the maximum available accommodation, by definition this is the near point ( Fig. 2.2.4 ). It is important to note that this hyperope needs to accommodate between 4 D and 8 D to see objects ranging from infinitely distant to the near point. In other words, in some situations, the hyperope can have the same range as an emmetrope but the required amplitude of accommodation is necessarily greater, that is, the hyperope needs a greater accommodative effort. The prescription of lenses for this patient should take into account maintaining a more physiological accommodative effort. This process is discussed in the next chapter.
In myopes, the far point is at a finite distance in front of the eye. In a myopic eye that sees objects at most up to 20 cm distant from the eye, a myopia of 1/0.2 = 5 D exists. Remember that the accommodation of an eye when viewing an object at the far point is fully relaxed. If the near point is at 10 cm, the accommodation range will be α = 20 − 10 = 10 cm. As at this point, as we saw before, the added refractive power of the system is 10 D. The amplitude of accommodation will be the difference of the power in the two points, that is, A = P − R = 10 − 5 = 5 D. Notice that a 5 D myopic eye accommodates 5 D to focus an image at 10 cm. Therefore, although myopes cannot see objects at distance clearly, they have the advantage of being able to see objects at closer range with a smaller effort of accommodation ( Fig. 2.2.5 ).
Range and Amplitude
The greatest distance an object can be clearly seen by the eye with relaxed accommodation is called the “far point.” The nearest point at which an object can be clearly seen is called the “near point,” which is the location of the focus obtained with maximum accommodation. The range of accommodation, by definition, is the distance between these two points. The amplitude, measured in diopters, refers to the refractometric difference between the eye in maximum relaxation and maximum accommodation.
- •
Far point: The greatest distance at which an object can be seen clearly in the absence of accommodation.
- •
Near point: The closest distance at which an object can be seen clearly when maximum accommodation is used.
- •
Range of accommodation: Distance between the far point and the near point.
- •
Amplitude of accommodation: Difference in dioptric power between the eye at rest and the fully accommodated eye.
The amplitude of accommodation can be measured directly by the method of spheres. In this method, we ask the patient to look at an object 40 cm away and change his/her need for accommodation with the addition of lenses. By adding negative lenses, the accommodation is stimulated until the image begins to blur. For example, suppose the patient accepts −2 D with clear vision. As we add positive lenses, the accommodation will relax until the image begins to blur again. Suppose in this situation, the lens used was +3 D. In this case the patient has a 5 D amplitude of accommodation.
Further information can be obtained with simple examination. Placing an object at the nearest point where the patient can obtain sharp vision will determine the near point. Moving away the object, we define the far point. In the case of a patient with 3 D of amplitude: If he or she is emmetropic, the far point will be in infinity and the near point will be to 33 cm. If the patient is a 3 D hyperope, the near point will be at infinity, because all the accommodation must be used to clarify the acuity at distance. If the patient has a myopia of 3 D, the near point will be 16.7 cm because the accommodation together with the refractive error amounts to a total of 6 D of refractive power.
In a hyperope, the accommodation necessary to see clearly at a distance is the same diopters of the magnitude of their hypermetropia. However, to see a near object 10 cm from the eye, as we saw before, 10 diopters (D) should be added to this value.
In hyperopia, there is no object distance for which a clear retinal image can be obtained without accommodation (or optical correction)—the optical apparatus of the eye has too little dioptric power at rest to focus an object on the retina. In this case we may define the far point of the eye as the (virtual) point, located behind the eye, which is imaged by the relaxed optics of the eye on the retina. Additional plus lens power, either from accommodation or supplied by a spectacle lens, is necessary to obtain a clear image.
For example, assuming a 4 D hyperope with amplitude of accommodation of 8 D, the (virtual) far point is at 25 cm behind the eye. With an accommodating effort of 4 D, the parallel rays from an object at infinity converge to the retina. Note that with an 8 D effort, this hyperope can converge divergent rays from a point 25 cm away from the eye. Assuming that this is the maximum available accommodation, by definition this is the near point ( Fig. 2.2.4 ). It is important to note that this hyperope needs to accommodate between 4 D and 8 D to see objects ranging from infinitely distant to the near point. In other words, in some situations, the hyperope can have the same range as an emmetrope but the required amplitude of accommodation is necessarily greater, that is, the hyperope needs a greater accommodative effort. The prescription of lenses for this patient should take into account maintaining a more physiological accommodative effort. This process is discussed in the next chapter.
In myopes, the far point is at a finite distance in front of the eye. In a myopic eye that sees objects at most up to 20 cm distant from the eye, a myopia of 1/0.2 = 5 D exists. Remember that the accommodation of an eye when viewing an object at the far point is fully relaxed. If the near point is at 10 cm, the accommodation range will be α = 20 − 10 = 10 cm. As at this point, as we saw before, the added refractive power of the system is 10 D. The amplitude of accommodation will be the difference of the power in the two points, that is, A = P − R = 10 − 5 = 5 D. Notice that a 5 D myopic eye accommodates 5 D to focus an image at 10 cm. Therefore, although myopes cannot see objects at distance clearly, they have the advantage of being able to see objects at closer range with a smaller effort of accommodation ( Fig. 2.2.5 ).
Scattering
Another significant optical factor that degrades vision is intraocular light scatter. The mechanism of light scatter is different from the aberrations discussed earlier, each of which deviates the direction of light rays coming from points in object space to predictable and definite directions in image space. With light scattering, incoming light rays are deflected from their initial (i.e., prescattered) direction into random (postscattered) directions, which generally lie somewhere within a cone angle of approximately a degree or so. Therefore a dioptric value cannot be placed on the blur caused by light scatter. A glaring light worsens the effect of light scatter on vision. Thus a young, healthy tennis player may not see the ball when it is nearly in line with the sun. Light scattering is the mechanism associated with most cataracts and causes significant degradation of vision due to image blur, loss of contrast sensitivity, and veiling glare.
Aberrations
Aberrations are changes in image formation that do not occur in a classically paraxial system. In other words, in specific situations, such as when light incidence occurs at an angle far above the reference axis of the system, no formation of an image exists at a single point. In practice, an optical system never makes a perfect point image and this does not depend only on the regularity of the surface. With the advent of wavefront aberrometry, several new types of aberrations—especially those of high orders—can be classified and today become major challenges for optical system manufacturers and refractive surgeons.
The aberrations are divided into monochromatic and chromatic. The monochromatic aberrations can be further subdivided into several types: astigmatism, defocus, tilt, spherical aberration, among others.
Monochromatic Aberrations
Monochromatic aberrations of a geometrical nature are also called figure aberrations. In spherical aberration, for example, light rays that refract at the extreme periphery of a convergent lens have a different focus from those that enter the eye more centrally, better aligned with the optical axis. Thus between them, many of the rays will cross at intermediate points, degrading the nominal point image (see Fig. 2.2.1 ). A comet-like tail or directional flare appearing in the retinal image is a manifestation of another aberration called coma. This occurs due to the obliquity of the system, resulting from misalignment of the various refracting surfaces in the eye. A large amount of coma (0.3 µm of coma alone) may point to specific corneal diseases such as keratoconus or a decentered intraocular lens. Several other forms of monochromatic aberrations are induced by differences in the axial curvature of the lens and inclination of the light beams, among others.
Chromatic Aberrations
Because the index of refraction of the ocular components of the eye varies with wavelength, colored objects located at the same distance from the eye are imaged at different distances with respect to the retina. This phenomenon is called axial chromatic aberration. In the human eye the magnitude of chromatic aberration is approximately 3 D. However, significant colored fringes around objects generally are not seen because of the preferential spectral sensitivity of human photoreceptors. Studies have shown that humans are many times more sensitive to yellow–green light with a central wavelength at 560 nm than to red or blue light. Amber spectacles used to enhance night vision partially block the blue light, lowering the effect of chromatic aberration.
The specific types of each monochromatic and chromatic aberration are discussed in Chapter 2.6 .
Monochromatic Aberrations
Monochromatic aberrations of a geometrical nature are also called figure aberrations. In spherical aberration, for example, light rays that refract at the extreme periphery of a convergent lens have a different focus from those that enter the eye more centrally, better aligned with the optical axis. Thus between them, many of the rays will cross at intermediate points, degrading the nominal point image (see Fig. 2.2.1 ). A comet-like tail or directional flare appearing in the retinal image is a manifestation of another aberration called coma. This occurs due to the obliquity of the system, resulting from misalignment of the various refracting surfaces in the eye. A large amount of coma (0.3 µm of coma alone) may point to specific corneal diseases such as keratoconus or a decentered intraocular lens. Several other forms of monochromatic aberrations are induced by differences in the axial curvature of the lens and inclination of the light beams, among others.
Chromatic Aberrations
Because the index of refraction of the ocular components of the eye varies with wavelength, colored objects located at the same distance from the eye are imaged at different distances with respect to the retina. This phenomenon is called axial chromatic aberration. In the human eye the magnitude of chromatic aberration is approximately 3 D. However, significant colored fringes around objects generally are not seen because of the preferential spectral sensitivity of human photoreceptors. Studies have shown that humans are many times more sensitive to yellow–green light with a central wavelength at 560 nm than to red or blue light. Amber spectacles used to enhance night vision partially block the blue light, lowering the effect of chromatic aberration.
The specific types of each monochromatic and chromatic aberration are discussed in Chapter 2.6 .
Retina
An image may be considered as made up of an array of pointlike regions. When a picture on the video screen is viewed with a magnifying glass, these small regions, called pixels, are seen clearly. Technological evolution has produced screen resolution above the human vision threshold in the new generation of smartphones or monitors with so-called retina display. Likewise, the pixel elements comprising a retinal image are the cone and rod photoreceptors. It is the finite size of these photoreceptors that ultimately determines the eye’s ability to resolve fine details.
The finest details in a retinal image can be resolved only within the foveal macular area. This elliptical zone of about 0.1 mm in maximal width ( Fig. 2.2.6 ) has an angular size of approximately 0.3° about the eye’s visual axis. It contains about 30,000 tightly packed light-sensitive cones. The cones themselves have diameters of 1–2 µm (a dimension comparable to 3–4 wavelengths of green light) and are separated by about 0.5 µm. Cone size is an important factor in determining the ultimate resolution of the human eye. No nerve fiber layer, ganglion cell layer, inner plexiform layer, or inner nuclear layer is present in much of the fovea, and in the very center of the fovea no outer nuclear layer is present. Only the so-called Henle’s fiber layer, consisting of the axons between the cones and their synaptic pedicles, and the cones themselves are found.
Another important aspect of the cone receptors is their orientation. Each cone functions as a “light pipe” or a fiber optic that is directed to the second nodal point of the eye ( Fig. 2.2.7 ). This orientation optimally receives the light that forms an image and, together with the black pigment epithelium of the retina, partially prevents this light from scattering to neighboring cones. Müller cells may also be considered living optic fibers in the retina, preventing light scatter.
Another retinal factor that helps to improve vision is the configuration of the foveal pit, which is a small concavity in the retina. This recessed shape acts as an antiglare device in which the walls of the depression prevent stray light within the internal globe of the eye from striking the cones at the center of the depression. Finally, the yellow macular pigment may be considered to act as a blue filter that limits chromatic aberration and absorbs scattered light, which is predominantly of shorter wavelength (i.e., the blue end of the spectrum).
Resolution and Focal Length
A derivation of the theoretical diffraction-limited resolution of a normal emmetropic human eye must consider the eye’s optimal pupil diameter, its focal length, which is associated with its axial length, and the anatomical size of the photoreceptors. A point object imaged by a diffraction-limited optical system has an angular diameter in radians (diameter at one-half the peak intensity of the Airy disc) given by Eq. 2.2.1 .
Angular diameter=1.22(wavelength)pupil diameter
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