Axial length

Larsen noted that the axial length of the neonate’s eye was 17 mm and that it increases 25% by the time the child reaches adolescence. Up to 6 months of age, it reaches around 19.7 mm and up to 1 year of age, 20.5 mm. Around 7 years old, on average it reaches 22.4 mm. The size of the normal infant’s eye is about three-quarters that of the adult size. Geometric optics teaches us that the retinal image of the normal infant eye is, therefore, about three-quarters the size of the adult’s image. *

* Specifically, the size of the retinal image depends on an entity known as the nodal distance , which averages 11.7 mm in the newborn and 16.7 mm in the adult emmetropic schematic eye, giving a ratio of adult to infant retinal images of 1.43.

† The infant’s visual acuity is about 20/600, versus the normal visual acuity of an adult, which is 20/20.

Fig. 1.1 shows that visual acuity swiftly improves, and by the age of 12 months, the infant’s level of visual acuity is 25% (20/80) of optimal adult visual acuity. This improvement in acuity seems to parallel eyeball growth. By the age of 5 years, the child usually has 20/20 vision. What other factors beyond eye size account for the young child’s lowered visual acuity? As the eye grows, the optical power of the eye lens and cornea must weaken in a tightly coordinated fashion so that the world stays in sharp focus on the retina. Patients with myopia highlight the developmental process of balancing the growth of the eye while maintaining a sharp retinal image. In most cases of myopia the eye is elongated. The stretching and weakening of the sclera seems to depend on two major factors. First, that the intraocular pressure maintains a constant force on the sclera. Second, there is digestion of sclera architecture (collagen I fibers and extracellular matrix) by metalloproteinase enzymes. This idea of strengthening the sclera to prevent myopic expansion is supported experimentally. In one series of experiments, 7-methylxanthine (a caffeine metabolite) was used to enhance concentration and thickness of collagen fibers in the posterior sclera of animals. In humans, scleral collagen fibers were crosslinked using riboflavin activated by ultraviolet light.

A graph showing the improvement of visual acuity in the infant as it ages. The method of preferential viewing was used to achieve these results. The 30 cycles per degree is comparable to a 20/20 vision in adults.

From Chandna A. Natural history of the development of visual acuity in infants. Eye . 1991;5;20–26.

However, we do not know what activates the process of scleral weakening and stretching in myopia. Some human studies have shown that use of atropine drops in children partially inhibits the development of myopia. The reason is unclear. Some feel that atropine reduces the pull of the ciliary muscle on the sclera, which otherwise allows the sclera to elongate. Another theory suggests that the atropine reduces vitreous pressure, thus reducing the stretching force. However, atropine has the same effect in chickens that have a ciliary muscle unresponsive to the effects of atropine. Another school of thought is that retinal receptors somehow activate the process of scleral weakening (e.g., M1 muscarinic receptors present in the neural retina but not in muscle).

Animal experiments using specific M1 blockers such as pirenzepine show the same effects as atropine, without blockade of accommodation. The presence of pirenzepine-inhibited receptors within the choroid and retina could also explain why elongation in eyes with transected optic nerves is inhibited by pirenzepine. Human use of topical pirenzepine was reported in two studies that showed a small but statistically significant reduction in myopia and axial length. These data suggest that during childhood the retina can record information concerning the sharpness of the retinal image and then use this information to control the eye’s axial length via scleral stretching.

If this tight coordination of growth fails, the infant may become nearsighted or farsighted. Because the coordination of eye length growth and the focusing power of the cornea and eye lens may be imperfect, is there some compensation provided, early in life, guaranteeing that almost every child can process a sharply focused retinal image of the world? Accommodation is the safety valve that can help provide a sharp image, even if all the ocular components are not perfectly matched. In the young child, the range of accommodation is greater than 20 diopters ( d ). This range, in addition to the farsightedness of almost all infants, means that most young eyes can focus almost any object by using part or all of this enormous focusing capacity.

Because of the infant’s smaller pupil, a second factor that helps the infant achieve a sharper retinal image is an increased depth of focus. Photographers use this principle when they use larger F-stops (F32, F64) to keep objects at different distances all in focus.

Fig. 1.2 shows the importance of the nodal point in determining the size of the retinal image in a typical human eye. To help us appreciate the basic optical principles operating within the human eye and avoid being confused by their many details (e.g., the many different radii of curvature, the different indices of refraction), an all-purpose, simplified eye was developed. Such model eyes have many names (e.g., reduced, schematic, simplified eye) and were developed by some of the true giants of physiologic optics. *

* A partial list of giants of physiologic optics who have created schematic or reduced eyes includes Listing, Helmholtz, Wüllner, Tserning, Matthiessen, Gullstrand, Legrand, Ivanoff, and Emsley.

A diagram of a reduced human eye. F , Focal points; n , nodal point; p , principal point. The dotted line represents the retina of an enlarged eye.

Fig. 1.2 depicts such an eye with its cardinal points (the principal points, focal points, and nodal points). Knowing the location of the cardinal points of a lens system, the optical designer can calculate all of the relationships between an object and an image. For example, to determine the image size of the reduced eye, one simply traces the ray, starting from the top of the object, which goes undeviated through the nodal point and lands on the top of the inverted retinal image. As the distance between the nodal point and the retina increases, the image size increases. The addition of a plus spectacle lens to the eye’s optic system moves the nodal point of the new system forward (increasing the nodal point to retina distance), thus magnifying the retinal image. The reverse is true with a negative spectacle lens. Therefore, a contact lens or a refractive cornea on which surgery has been performed enlarges the image size for a person with myopia who previously wore spectacles. The change in retinal image size should be taken into account when evaluating the visual acuity results after corneal refractive surgery. From an optical point of view, an 8- d hyperope exchanges a larger image produced by their +8 spectacle lens for a smaller image after corneal refractive surgery. Thus, they should theoretically lose a line of visual acuity after refractive surgery, but instead often gain a line. A possible reason is that the aberrations of the high plus spectacle lens cancel the effects of the larger retinal image, but this area requires further study.

Emmetropization

The overall refractive state of the eye is determined by four components:

• •
  

  Corneal power (mean, 43 d )

  
  
• •
  

  Anterior chamber depth (mean, 3.4 mm)

  
  
• •
  

  Crystalline lens power (mean, 21 d )

  
  
• •
  

  Axial length (mean, 24 mm)

The coordination of the power of these components to process a sharp retinal image of a distant object is known as emmetropization .

Essentially, with age, cornea and lens must lose refractive power as the anterior chamber depth and axial length increase so that a sharp image remains focused on the retina.

The cornea, which averages 48 d of power at birth and has an increased elasticity, loses about 4 d by the time the child is 2 years of age. One may assume that the spurt in growth of the sagittal diameter of the globe during this period pulls the cornea into a flatter curvature. The fact that the average corneal diameter is 8.5 mm at 34 weeks of gestation, 9 mm at 36 weeks, 9.5 mm at term, and about 11 mm in the adult eye supports this “pulling, flattening” hypothesis.

However, other coordinated events also occur, such as the change of lens power and the coordinated increase in eye size (most important, an increase in axial length). The crystalline lens, which averages 45 d during infancy, loses about 20 d of power by age 6 years. To compensate for this loss of lens power, the axial length increases by 5 to 6 mm in that same time frame. (In general, 1 mm of change in axial length correlates with a 3- d change in refractive power of the eye.)

Now let us examine a possible mechanism that could account for most of the data. As the cross-sectional area of the eye expands, there is an increased pull on the lens zonules and a subsequent flattening of the lens (the anterior lens surface is affected a bit more and the posterior lens surface a bit less), thus decreasing the overall lens power. There also may be a related decrease in the refractive index of the lens, which also contributes to the reduction in lens power. It seems, at final, that the various components cooperate to achieve a higher-than-expected incidence of refractive state between 0 and +2 d . It is now known that not only genetics but also the environment play an important role in regulating the final refractive state of human eye development. In other words, the genetic program can be tuned by environmental and intrinsic (i.e., intraocular) factors. Koretz et al., Laties and Stone, and Stone et al. have provided further insights into the biophysical and biochemical controls of emmetropization and their failure. The role of the environment is mainly demonstrated by three factors: deprivation myopia, deprivation myopia recovery, and lens-induced defocus compensation.

Experiments have shown that, after depriving an animal’s eye of vision, for example, by suturing monkey eyelids, it was possible to induce axial myopia. After this experiment, it was found that the phenomenon occurred in several other animal species, including humans with unilateral eyelid ptosis, unilateral congenital cataract, or other pathologies that could deprive the vision of only one eye, generating axial anisometropia. However, when removing the factor that generated the deprivation of sight, this eye tended to gradually reduce its myopia. This happened by the abrupt decrease in the growth rate of the vitreous chamber, while the cornea and lens followed their common flattening unaffected by the experiment. Another curious fact is that correcting deprivation-induced myopia with negative lenses prevented the expected hypermetropization after stopping vision deprivation. It was also demonstrated in several species such as primates, pigs, and rats that the induction of hyperopia with negative lenses in emmetropic eyes caused an increase in the axial diameter and consequent induction of myopia equivalent to the power of the lens placed. Despite the limited evidence in humans, the fact that the human eye behaves similarly in other optical experiments suggests that the same occurs in our species. This is important knowledge that can be applied to address the increasing rates of myopia around the world.

Retinal receptors

The cone photoreceptors of the retina are responsible for sharp vision under daylight conditions. For comparison and didactic purposes, an iPhone 13 Pro (Apple, California, EUA) has a resolution of 1170 × 2532 pixels, approximately 3 million pixels in total (460 pixels per inch), whereas the old iPhone 5 (Apple, California, EUA) had 1136 × 640 pixels, approximately 730,000 pixels (326 pixels per inch). Although it is not the only determining factor in image quality, it is known that the greater the number of pixels in a given space, the higher the quality of the screen image tends to be. Something similar happens in our retina. We have about 7 million cones, with a size of around 2.5 µm (micron), distributed irregularly. The areas where the denser number of cones are packed provide better image quality.

The most sensitive part of the retina is the fovea, the central region where the cones are even finer and are packed together even tighter. The fovea of the infant eye is packed less than one-quarter of the density of that of the adult. Furthermore, the synapse density in the neural portion of the retina, as well as the visual brain, is low at birth. The combination of these two anatomic configurations means that fewer fine details of the retinal image are recorded and sent to the brain.

Neural processing

Finally, the nerves that transmit visual information to the brain, as well as the nerve fibers at the various levels within the brain, are poorly myelinated in the infant. Myelin is the insulating wrap around each nerve fiber. A normally myelinated nerve can transmit nerve impulses swiftly and without static or “cross talk” from adjacent nerves. To use a computer analogy, one might think of the infant brain as being connected with poorly insulated wires. Therefore, sparks, short circuits, and static all slow or interfere with perfect transmission, and only the strongest messages get through. Fig. 1.3 represents an appropriate analogy. The face of a woman is shown with larger and larger pixels. The infant’s early vision might be comparable to the picture with the biggest block pixels. With maturation of the brain-processing elements, the neurologic equivalent of pixel size gets smaller and more details can be registered. Thus, the equivalent of the photographic film grain size in the retina and the equivalent of pixel size in the brain processor both get smaller as the child grows. The immaturity of the infant’s memory capacity may be one reason why its visual images have less detail. In other words, the coarseness of the infant visual system does not overtax the immature memory system.

A computer display of the face of a woman, with pixels of different sizes.

Courtesy of Gabriela Martines, MD.

Recognizing faces

The remarkable thing about the infant’s eyesight is that the relatively poor level of resolution just described still allows the infant to recognize different faces and different facial expressions. We know this to be true in some newborn infants, who can accurately imitate the expressions of an adult ( Fig. 1.4 ), almost as if the baby uses his or her own face as a canvas to reproduce the facial expression of the onlooker.

These photos shows a recently born infant ( D–F ) mimicking the expression of psychologist Dr. A Meltzoff ( A–C ). The baby is obviously able to perceive the different expressions to mimic them.

From Klaus MH, Klaus PH. The Amazing Newborn . Reading, MA: Addison Wesley, 1985.

Experiments with infants demonstrate that infants prefer to look at faces or pictures of faces rather than look at other objects. Among the faces, the most important is that of the mother. Bushnell et al. have reported that even newborns prefer to look at their mother’s face than at strangers’ faces. By the age of 6 weeks, infants can discern specific features of the face. For example, they can lock in on the mother’s gaze. By age 6 months, they can also recognize the same face in different poses. In fact, they are experts at recognizing a face, be it upside down or right side up, till the age of 6 years. After age 6, infants actually lose their skill at quickly recognizing upside-down faces.

A closer examination of the eye at 6 months of age is worthwhile because an unusual change has started to take place in the optics of the eye at this time. Gwiazda et al. found that a significant amount of astigmatism develops in 56% of the infants studied. The degree of astigmatism is even greater in preterm babies and seems to be inversely related to birth weight. This condition remains for only 1 to 2 years.

The transient astigmatism just described tends to elongate tiny dots of the retinal image into lines. In essence, these create the equivalent of a line drawing of the retinal image. For example, think of a mime (i.e., a painted face with a few dark lines and spots for eyes and nose) as creating different line drawings of the face. What is astonishing is that, although made of only a few dark lines, the mime can recreate most human expressions. It seems reasonable to imagine that the mime presents faces similar to those seen by the young child or found in a child’s drawing. The faces have no texture, no shadowing, and no creases—only a line for a mouth, circle for eyes, and occasionally a dot for a nose. Is it not then possible that infant astigmatism helps represent faces as line drawings to the infant visual system? Line drawings also save memory storage space, which would be an advantage for the small infant brain. *

* This idea was suggested by David Marr in “Early Processing of Visual Information,” published in Transactions of the Royal Society of London, Series B , 1976; 275:483.

A series of computer simulations of the face of a woman with an extensive gray scale on the left and only a two gray scale on the right, the latter being similar to a line drawing.

Courtesy of Gabriela Martines, MD.

Another theory is that transient astigmatism would diminish the “dead zone” of accommodation. The “dead zone” is a range of small defocus or loss of image contrast that is not enough to stimulate accommodation. In other words, an eye with astigmatism would always be in constant accommodative effort, in order to seek the best focus, inducing an activation and a “learning” of the accommodation mechanism in the first years of life.

Line orientation receptors

As noted earlier, in many infants the amount of astigmatism can rise to a level of greater than 2 d in the first year of life. The orientation of the distortion is usually horizontal (180 degrees) initially. In the course of the next 2 years, the meridian of distortion rotates to the vertical and the amount of the astigmatism diminishes. This slow rotation of the axis of exaggeration can help activate different groups of brain cells, which become sensitive to features in the retinal image with different tilts. In fact, the discovery of these brain cells with orientation selectively leads to a ground-breaking understanding of the functional architecture in the higher brain. In 1958 Torsten Wiesel and David Hubel, working in their laboratory at the Harvard Medical School, implanted electrodes in the visual cortex of an anesthetized cat to record cortical cell responses to patterns of light, which they projected onto a screen in front of the cat. After 4 hours of intense work, the two scientists put the dark spot slide into the projector, where it jammed. As the edge of the glass slide cast an angled shadow on the retina, the implanted cell in the visual cortex fired a burst of action potentials. Torsten Wiesel described that moment as the “door to all secrets.” The pair went on to prove that cells in the cortex responded only to stimuli of a particular orientation. Similar responding cells were all located in the same part of the cortex. This work opened up the area of how and where the brain encodes specific features of the retinal image. Fittingly, Drs. Hubel and Wiesel were awarded the Nobel Prize for Medicine in 1981.

Monitoring other’s eye movements

Another function of great survival value to the infant is the ability to follow the eye movements of his or her caretakers. Consider this a near task involving the contrast discrimination of a 12-mm dark iris against a white sclera framed by the palpebral fissure; such a task can be accomplished with a visual acuity of 20/200.

The British psychologist Simon Baron-Cohen, in his book Mindblindness , * suggests that a major evolutionary advance has been the human’s ability to understand and then interact with others in a social group (e.g., playing social chess). He further suggests that we accomplish this social intelligence primarily by following the eye movements of others, which begins at a young age. For example, an infant of 2 months begins to concentrate on the eyes of adults. Infants have been shown to spend as much time on the eyes as on all other features of an observer’s face.

* In his book Mindblindness: An Essay on Autism and Theory of Mind , published by MIT Press in 1995, Baron-Cohen ferrets out the key features of “eye following” in the normal child by comparing them with those of the autistic child.

By 6 months of age, infants look at the face of an adult who is looking at them two to three times longer than an adult who is looking away. We also know that when infants achieve eye contact, a positive emotion is achieved (i.e., infants smile). By age 14 months, infants start to read the direction in which an adult is looking. Infants turn in that direction and then continue to look back at the adult to check that both are looking at the same thing. By age 2 years, infants typically can read fear and joy from eye and facial expression.

Recognizing movement

Infants are capable of putting up their arms to block a threatening movement. This act tells us that infants appreciate both movement and the implied threat of this particular movement. Admittedly, infants cannot respond if the threat moves too quickly, probably because the immature myelinization of the nerves slows the neural circuits. Nevertheless, a definite appreciation of movement and threat exists.

For movement to be registered accurately, the infant retina probably records an object at point A. That image is then physiologically erased (in the brain and/or retina), and the object is now seen at point B. This physiologic erasure is important because without it movement would produce a smeared retinal image. Researchers think that the infant probably sees movement as a smoothed series of sharp images, not smears. This hypothesis is supported by other experiments demonstrating that the infant can appreciate the on/off quality of a rapidly flickering light at an early age. It seems logical that the movement of an image across the retina (with the inherent erasures) is physiologically related to the rapid on/off registration of a flickering light.

A related reflex, the foveal reflex, is triggered by stimulation of the peripheral retina, activating the eye movement system so that the fovea is directed to the visual stimulus.

Rhodopsin

The rods and cones are made up of a biologic molecule that absorbs visible light and then transluces that event into an electrical nerve signal. The rhodopsin molecule is an example of Einstein’s photoelectric effect. *

* Some wavelengths of light are powerful enough to knock electrons of certain molecules out of their orbits, thereby producing an electric current. Einstein was awarded the Nobel Prize for explaining the “photoelectric effect.”

† In 1942, Selig Hecht and his coworkers in New York first proved that only one quanta of visible light could trigger rhodopsin to start a cascade of biochemical events eventuating in the sensing of light.

‡ Photoactivation of one molecule of rhodopsin starts an impressive example of biologic amplification, in which hundreds of molecules of the protein transducer each activate a like number of phosphodiesterase molecules, which in turn hydrolyze a similar number of cyclic guanine monophosphate (cGMP) molecules, which then trigger a neural signal to the brain.

The internal structure of the molecule allows the wavelengths of visible light to resonate within its electron cloud and within 20 million millionths of a second, inducing the change in the molecule that starts the reaction.

Probably the earliest chemical relative of rhodopsin is to be found in a primitive purple-colored bacteria called Holobacterium halobium . Koji Nakanishi, a biochemist at Columbia

University, in an article titled “Why 11-cis-Retinal?”, notes that this bacteria has been on the planet for the last 1.3 billion years. Its preference for low oxygen and a salty environment places its origin at a time on earth when there was little or no oxygen in the atmosphere and a high salt concentration in the sea. Although found in primeval bacteria, bacteriorhodopsin is a rather complicated molecule, containing 248 amino acids. It is thought that this bacteria probably used rhodopsin for photosynthesis, rather than light sensing. Time-resolved spectroscopic measurements have determined that this molecule changes shape within one trillionth of a second after light stimulation. This early form of rhodopsin absorbs light most efficiently in the blue-green part of the spectrum, although it does respond to all colors.

To function as the transducer for vision, the photopigment must capture light and then signal the organism’s brain that the light has registered. As noted earlier, one molecule needs only one quanta to start the reaction. Even more amazing is the molecule’s stability. Although only one quanta of visible light is necessary to trigger it, the molecule will not trigger accidentally. In fact, it has been estimated that spontaneous isomerization of retinal (the light-sensing chromophore portion of rhodopsin) occurs once in a thousand years. If this were not so, we would see light flashes every time there is a rise in body temperature (a fever). To better understand the rhodopsin mechanism, one may picture a hair trigger on a pistol that takes only the slightest vibration (but only a special type of vibration) to be activated. As noted, the activating quanta must be of the proper energy level to “kick in” the reaction, that is, the quanta of light must be made of wavelengths of visible light.

Receptor size and spacing

Retinal receptor factors that influence the optical limits of visual acuity occur in the foveal component of the macula. The fovea itself subtends an arc of about 0.3 degrees. It is an elliptical area with a horizontal diameter of 100 µm. The area contains more than 2000 tightly packed cones. The distance between the centers of these tightly packed cones is about 2 µm. The cone diameters themselves measure about 1.5 µm (a dimension comparable to three wavelengths of green light) and are separated by about 0.5 µm. Therefore, the fine details of the retinal image occupy an elliptical area only about 0.1 mm in maximum width.

A discussion of the diffraction limits of resolution, in a theoretical emmetropic human eye, must involve the anatomic size of the photoreceptors and the pupil. A point or an object is focused on the retina as an Airy disc because of diffraction ( Fig. 1.9 ). The angular size of the Airy disc is determined as follows:

Light passing through an aperture. Note that it “bends” into a spreading wavefront pattern, and the image captured by the screen is a grating pattern produced by alternating constructive and destructive interference of light rays. The same phenomena occurs when light encounters a circular aperture, and now the grating pattern emerges as a series of concentric rings—the Airy disc.

Let the wavelength be 0.00056 mm (560 nm; yellow/green light). Then

For a pupil of 2.4 mm (optimal balance between diffraction and spherical aberration in the human eye):

Given this angle of 1 minute, the actual size of the Airy disc can be calculated if the distance from the nodal point to the retina is known. The optimal distance depends on the diameter of the photoreceptors. Because these act as light guides, the theoretical limit is 1 to 2 µm. To obtain the maximum visual information available, Kirschfield calculated that more than five receptors are required to scan the Airy disc. Assume that each foveal cone is 1.5 µm in diameter and that there is an optimal space of 0.5 µm between receptors. The following equation describes the situation for three cones and two spaces (5.5 µm):

Substituting 0.0003 from equation (2) into equation (3) gives equation (4):

From equation (4) the distance from the nodal point to the retina can be rounded off to 18.00 mm, which is close to the distance between the secondary nodal point and the retina in the schematic human eye.

How closely does optical theory agree with reality? The average visual acuity for healthy eyes in the age group younger than 50 was better than 20/16. In the distribution within the group younger than 40, the top 5% had an acuity of close to 20/10.

Another related factor must be kept in mind. The fixating eye is in constant motion, as opposed to a camera on a tripod. Presumably, these movements prevent bleaching or fading within individual photoreceptors. These small movements, called either tremors , drifts , or microsaccades , range in amplitude from seconds to minutes of angular arc. Such movements tend to smear rather than enhance our traditional concept of visual resolution. It can only be presumed that to maintain high resolution within the context of this physiologic nystagmus, the visual system takes quick, short samples of the retinal image during these potentially smearing movements and then recreates an image of higher resolution.

The unique essence of the vertebrate retina is that the structure of the transparent optical components, the rhodopsin molecule, and the size of the foveal cones are all tuned to interact optimally with wavelengths of visible light. It is earth’s unique atmosphere and its unique relationship to the sun that have allowed primarily visible light, a tiny band from the enormous electromagnetic spectrum of the sun, to rain down upon us at safe energy levels. Our eyes are a product of an evolutionary process that has tuned to these unique wavelengths at these levels of intensity.

With this basic science background, we can discuss how functions such as visual acuity and contrast sensitivity are monitored in a clinical setting.