Introduction
Clinicians are accustomed to thinking in terms of spherocylindrical spectacle correction of naturally occurring refractive errors. We shall review traditional clinical optics and add to this framework current thoughts on the optics of keratorefractive procedures. Wavefront aberrations and wavefront-guided corrections will be discussed in Chapters 5 and 13 .
Geometric Optics
The ray of geometric optics is a line drawn perpendicular to each of a train of light wavefronts. When such a ray passes obliquely from a medium of lower index of refraction to a medium of higher index of refraction, the velocity of the associated waves is reduced and the ray is bent toward the normal (perpendicular) to the refracting interface. The change of direction is governed by Snell’s law: the quotient of the sines of the angle of incidence and the angle of refraction equals the quotient of the indices of refraction of the second and the first media ( Figs. 3.1 and 3.2 ).
nisini=nrsinr,
Prisms and Lenses
When entering, and again when exiting a prism, light is refracted following Snell’s law. This results in deviation of the light rays toward the base of the prism. If one imagines a lens to be a continuous array of prisms of various strengths, Snell’s law describes the passage of rays through each part of the lens.
Images and Vergence
To analyze the behavior of light passing through lenses, one begins with a simplifying assumption, imagining a lens to be spherical and infinitely thin. An optical axis passes perpendicularly through the center of the lens. This central part of the lens has no prismatic power; hence, rays striking it from any direction pass undeviated. Suppose that an extended object stands some distance away from the lens; rays emanating from points on this object strike the lens. To understand the behavior of these rays and thus the formation of images of points on the object, it is helpful to consider two focal points and three cardinal rays. We consider the case of a convex lens and a real image; analysis of other cases is similar ( Fig. 3.3 ). All rays passing through the primary focal point on the optical axis emerge from the lens parallel to the optical axis. Rays parallel to the optical axis come to focus, after refraction by the lens, at the secondary focal point. These useful ray diagrams are approximately correct, assuming that the rays are paraxial, that is, not too far from being parallel to the optical axis. To reveal the formation of an image of a point source of light, rays are drawn from that point (1) through the center of the lens; (2) parallel to the optical axis and, after passing through the lens, to the secondary focal point; and (3) through the primary focal point, continuing to the lens, and exiting the lens parallel to the optical axis. Construction of these cardinal rays enables us to understand and calculate “conjugate” locations of images of objects. Another helpful construct is that of vergence. The inverse of the distance, u , from object point to lens (diopters of divergence) plus the power of the lens, D (diopters), equals the inverse of the distance, v , to the image point (diopters of convergence).
U+D=V,
The validity of this vergence analysis is also derived from Snell’s law. When the simplifying assumption of “thin” lenses is relaxed so that lenses are allowed to have significant thickness or there is a series of lenses, nodal points and principal planes replace the conceptual center of the infinitely thin lens.
Magnification
Magnification characteristics of optical systems may be defined in several ways. Where an image is formed of an object, linear magnification may be defined to be the quotient of the sizes, measuring perpendicular to the optical axis, of image and object. Measuring along the optical axis, the quotient of image and object sizes is called axial magnification and is found to be the square of the linear magnification described earlier. Considering the eye’s view through optical systems, it is useful to speak of angular magnification, the quotient of the angles subtended at the eye, or more precisely at its first principal plane by an object as viewed with and without the optical system, respectively.
Refractive Errors of the Human Eye
Emmetropia
The nonaccommodating emmetropic eye brings any pencil of parallel rays (e.g., from a point on an object at optical infinity) to focus at some point on the retina. The secondary focal plane of such an eye is located on the retina and the far-point plane (defined as the points conjugate to the retina in the nonaccommodating state) is at optical infinity, that is, far away.
Myopia
The myopic eye brings pencils of parallel rays to focus at points anterior to the retina. The secondary focal point of the eye is in the vitreous. Rays diverging from a point on the far-point plane of the eye will be brought to focus on the retina without the aid of accommodation. For instance, a −2.00 D myope who is capable of 1 D of accommodation reads without effort at a half meter and can keep the image clear up to one-third of a meter by accommodating. The spectacle correction of myopia involves placing a diverging lens in front of the eye so that the secondary focal point of the lens coincides with the far point of the eye. Pencils of parallel rays striking the lens will diverge when they leave the lens as though they originated from the far point of the eye; hence, they will be brought to focus on the retina. Refractive surgical correction of myopia is achieved by flattening the front surface of the eye. When the myopic error is fully corrected, pencils of parallel rays are brought to focus on the retina.
Hyperopia
The hyperopic eye brings pencils of parallel rays of light to focus at points behind the retina. Accommodation of the eye may produce enough additional plus power to bring a parallel (or even a diverging) pencil of rays to focus on the retina.
Astigmatism
Astigmatism of the eye’s optical system may be caused by asymmetry of the cornea or, less frequently, of the lens. Astigmatism is regular when it is correctable with a spherocylindrical lens so that pencils of light from distant objects can be focused on the retina. Otherwise, the astigmatism of the eye is called irregular . Fortunately, naturally occurring refractive error of the eye tends to be the result of toricity of the cornea and lens and is therefore regular, so that spherocylindrical corrective lenses allow acuity similar to that found in emmetropic eyes. Regular astigmatism is with the rule when the steepest (most refracting) meridian lies near 90°. It is correctable by a spherocylindrical lens with plus-cylinder, whose axis lies near 90°, or minus-cylinder, with axis near 180°. When the steepest meridian is near the 180° meridian, the eye’s astigmatism is termed against the rule and is correctable by plus-cylinder, with axis at 180°, or minus-cylinder, with axis at 90°. When astigmatism is regular, but the principal meridians do not lie close to 90° and 180°, the astigmatism is termed oblique .
Emmetropia
The nonaccommodating emmetropic eye brings any pencil of parallel rays (e.g., from a point on an object at optical infinity) to focus at some point on the retina. The secondary focal plane of such an eye is located on the retina and the far-point plane (defined as the points conjugate to the retina in the nonaccommodating state) is at optical infinity, that is, far away.
Myopia
The myopic eye brings pencils of parallel rays to focus at points anterior to the retina. The secondary focal point of the eye is in the vitreous. Rays diverging from a point on the far-point plane of the eye will be brought to focus on the retina without the aid of accommodation. For instance, a −2.00 D myope who is capable of 1 D of accommodation reads without effort at a half meter and can keep the image clear up to one-third of a meter by accommodating. The spectacle correction of myopia involves placing a diverging lens in front of the eye so that the secondary focal point of the lens coincides with the far point of the eye. Pencils of parallel rays striking the lens will diverge when they leave the lens as though they originated from the far point of the eye; hence, they will be brought to focus on the retina. Refractive surgical correction of myopia is achieved by flattening the front surface of the eye. When the myopic error is fully corrected, pencils of parallel rays are brought to focus on the retina.
Astigmatism
Astigmatism of the eye’s optical system may be caused by asymmetry of the cornea or, less frequently, of the lens. Astigmatism is regular when it is correctable with a spherocylindrical lens so that pencils of light from distant objects can be focused on the retina. Otherwise, the astigmatism of the eye is called irregular . Fortunately, naturally occurring refractive error of the eye tends to be the result of toricity of the cornea and lens and is therefore regular, so that spherocylindrical corrective lenses allow acuity similar to that found in emmetropic eyes. Regular astigmatism is with the rule when the steepest (most refracting) meridian lies near 90°. It is correctable by a spherocylindrical lens with plus-cylinder, whose axis lies near 90°, or minus-cylinder, with axis near 180°. When the steepest meridian is near the 180° meridian, the eye’s astigmatism is termed against the rule and is correctable by plus-cylinder, with axis at 180°, or minus-cylinder, with axis at 90°. When astigmatism is regular, but the principal meridians do not lie close to 90° and 180°, the astigmatism is termed oblique .
Correction of Refractive Errors and Visual Distortions
Eyes with myopia, hyperopia, and largely regular astigmatism are commonly corrected to approximately 20/20 acuity with spectacles. Aside from the cosmetic and practical inconveniences, what are the drawbacks of spectacle correction? Minus lenses minify the perceived image by roughly 2% per diopter. To the extent that the minus power is astigmatic, the minification is meridionally unequal, thereby distorting the image. Minification is somewhat beneficial because the periphery is brought into view. Plus lenses, on the other hand, magnify the image but create a peripheral scotoma between what is viewed inside and what is viewed outside the spectacle frame. The farther away from the optical center the line of sight deviates, the more prism is encountered—hence, the well-known pincushion and barrel distortions encountered with spectacle correction of high myopia and hyperopia, respectively. Off-axis viewing and lens tilt produce changes of the effective sphere and cylinder. These effects are greater with higher-power lenses, of course, and may be particularly disturbing when the two eyes have markedly different refractive errors.
Oblique Astigmatism
Binocular spectacle correction of oblique astigmatism distorts each eye’s view and, when the axes are not the same, tilts the perceived three-dimensional field. The perceived tilt occurs when both eyes are corrected and disappears when either eye is occluded. Differential meridional minification and misperception of tilt can be reduced, at the expense of clarity, by decreasing the cylinder power and by rotating the axis of the correcting cylinders toward 90° or 180°.
It is important to identify this situation prior to surgery. When tailoring refractive surgery for a patient whose spectacle adaptation has required such compromises, the surgeon needs to know what the actual refractive error is rather than the compromise prescription that is in the spectacles.
It may be that some patients who have long-standing adaptation to spectacle-induced distortion and tilt experience discomfort for some time when they have these distortions removed through surgery or contact lens wear. Until readaptation occurs, absence of optical distortion may be perceived by the patient as a disturbing change in binocular spatial sense.
Image Magnification
Anisometropic patients may seek refractive surgery because their spectacles produce symptoms related to aniseikonia and anisophoria. By reducing the anisometropia, surgery may give long-term relief.
Regarding myopic spectacle minification, when optical correction is moved from the spectacle plane to the cornea by contact lenses or surgery, a larger retinal image of the Snellen chart is formed on the retina so that if the optical resolving power (i.e., clarity of image) is preserved, there should be an artifactual improvement of Snellen acuity. One may therefore reason that postoperative acuity should be compared with preoperative rigid contact lens correction in order to judge the effect of the surgery on the optical quality of the eye. This is not a new idea; recall that the preimplant cataract surgeon could hold a plus lens several inches in front of an aphakic eye so that the patient could read hugely magnified 20/20 letters, viewed one at a time, through the resulting telescope.
Oblique Astigmatism
Binocular spectacle correction of oblique astigmatism distorts each eye’s view and, when the axes are not the same, tilts the perceived three-dimensional field. The perceived tilt occurs when both eyes are corrected and disappears when either eye is occluded. Differential meridional minification and misperception of tilt can be reduced, at the expense of clarity, by decreasing the cylinder power and by rotating the axis of the correcting cylinders toward 90° or 180°.
It is important to identify this situation prior to surgery. When tailoring refractive surgery for a patient whose spectacle adaptation has required such compromises, the surgeon needs to know what the actual refractive error is rather than the compromise prescription that is in the spectacles.
It may be that some patients who have long-standing adaptation to spectacle-induced distortion and tilt experience discomfort for some time when they have these distortions removed through surgery or contact lens wear. Until readaptation occurs, absence of optical distortion may be perceived by the patient as a disturbing change in binocular spatial sense.
Image Magnification
Anisometropic patients may seek refractive surgery because their spectacles produce symptoms related to aniseikonia and anisophoria. By reducing the anisometropia, surgery may give long-term relief.
Regarding myopic spectacle minification, when optical correction is moved from the spectacle plane to the cornea by contact lenses or surgery, a larger retinal image of the Snellen chart is formed on the retina so that if the optical resolving power (i.e., clarity of image) is preserved, there should be an artifactual improvement of Snellen acuity. One may therefore reason that postoperative acuity should be compared with preoperative rigid contact lens correction in order to judge the effect of the surgery on the optical quality of the eye. This is not a new idea; recall that the preimplant cataract surgeon could hold a plus lens several inches in front of an aphakic eye so that the patient could read hugely magnified 20/20 letters, viewed one at a time, through the resulting telescope.
Image Magnification
Anisometropic patients may seek refractive surgery because their spectacles produce symptoms related to aniseikonia and anisophoria. By reducing the anisometropia, surgery may give long-term relief.
Regarding myopic spectacle minification, when optical correction is moved from the spectacle plane to the cornea by contact lenses or surgery, a larger retinal image of the Snellen chart is formed on the retina so that if the optical resolving power (i.e., clarity of image) is preserved, there should be an artifactual improvement of Snellen acuity. One may therefore reason that postoperative acuity should be compared with preoperative rigid contact lens correction in order to judge the effect of the surgery on the optical quality of the eye. This is not a new idea; recall that the preimplant cataract surgeon could hold a plus lens several inches in front of an aphakic eye so that the patient could read hugely magnified 20/20 letters, viewed one at a time, through the resulting telescope.
Lens Effectivity
Two lenses of unequal power at unequal distances from the eye may each give exact distance correction of that eye so long as each focuses parallel pencils of rays at the eye’s far point. When a near object is viewed through the same two lenses, vergence calculations show that the amount of accommodation required to focus the diverging rays on the retina is quite different. For instance, a spectacle-corrected myope accommodates less to read a book at 25 cm than the same myope corrected with contact lenses. This notion, that the near effectivity of distance-corrective lenses depends on vertex distance, is of great interest to the practitioner considering the advisability of contact lenses or refractive surgery for the incipiently presbyopic myope who stands to lose the benefits of the near effectivity of minus spectacles.
Preoperative Optical Considerations for Refractive Surgery
Contact Lens Wear
For the cornea to return to its natural shape, soft contact lens wear should be discontinued for 3 to 7 days and rigid lens wear for 3 weeks prior to conventional refractive procedures. A longer period of contact lens discontinuation may be needed prior to wavefront-guided surgery.
Vertex Distance
For refractive error over 5 D, vertex distance should be measured from the rear surface of a corrective lens in order to calculate the refractive power at the cornea. Frames are often not actually worn at 13.75 mm, the reference distance for the phoropter.
Anisometropia and Aniseikonia
Knapp’s rule tells us that with purely axial anisometropia, which may occur in cases of unilaterally high myopia, equal image sizes on the two retinas are achieved when each refractive error is corrected with a spectacle lens placed at the anterior focal point of the eye, which is about 16 mm in front of the cornea. The geometric-optics argument for this does not consider the possibility that the highly myopic eye may have stretched-apart spacing of photoreceptors, which would tend to minify the view. If these anisometropes do not have disturbing aniseikonia with spectacles, might they after keratorefractive surgery? Placement of a corrective contact lens should allow preoperative investigation of this possibility and adequate counseling to the unilaterally high-myopic patient about possible postoperative discomfort and adaptation.
Aniseikonia may be unavoidable in refractive surgery of the preoperatively iseikonic bilateral high myope. After surgery of one eye, the other eye may require contact lens wear as the only remedy for aniseikonia until the second eye has similar surgery. Thus when discussing the risks of surgery preoperatively, contact-lens-intolerant patients with high myopia should be apprised of the difficulties they might face.
Cycloplegic Refraction
Refraction is repeated after cycloplegia to discover whether accommodation has been active during the previous “dry” refraction, in which case the cyclopleged eye will show less myopia. For example, a young person with spasm of accommodation would in this manner be identified before surgery; thus the surgical plan would be based on the true refractive error. However, there may be a shift with cycloplegia toward greater myopia, which is caused by spherical aberration as the peripheral optics of the eye are exposed by dilation ( Fig. 3.4 ).
Hyperopia
When cyclopleged, the hyperopic eye has insufficient plus power to focus the image of a distant object on the retina. Gazing at distance without cycloplegia, the least plus required for clear distance vision is termed absolute hyperopia . The most plus the eye can accept without blurring of the image is the manifest hyperopia . The diopters between the least and most accepted plus constitute the amount of hyperopia that is facultative. If accommodation is not as relaxed after fogged refraction as it is with cycloplegia, the difference between the manifest and cycloplegic refractions is considered the amount of hyperopia that is latent. As a hyperopic patient advances in age, absolute hyperopia approaches manifest hyperopia (which, in turn, increases to approach the cycloplegic hyperopia). Under ideal circumstances, surgery for hyperopia should aim at correcting most of the cycloplegic refractive error, the difficult point here being the assessment of the tenacity of the accommodative tone that constitutes the latent portion of the hyperopia.
Diabetes
The diabetic lens may fluctuate in size and curvature with changes in blood sugar. Diabetic candidates for keratorefractive surgery need to be identified to assess the stability of refractive error and rule out the existence of diabetic retinopathy. Diabetes is a relative contraindication for elective corneal surgery given that a duplicated basement membrane, recurrent erosions, and persistent epithelial defects occur more frequently in the diabetic corneal epithelium than in the nondiabetic one.
Pupil Size
The size of the entrance pupil (the image of the pupil transmitted through the cornea) should be estimated in brightly and dimly lit conditions. If the entrance pupil is larger than the postsurgical optical zone in dim but photopic conditions, then an annulus of cornea surrounding the optical zone will transmit light waves to the fovea. We may then be concerned that focus through this annulus is significant and is not the same as it is through the central cornea. The wavefront error due to peripheral irregularity may degrade the foveal image. This is represented by abnormal foveal point spread function. The Styles–Crawford effect gives the notion that the orientation of photoreceptors favors reception of light passing through the central cornea, encouraging hope that the noncentral cornea will cause little image degradation even when the entrance pupil is large enough to allow these photons to reach the fovea obliquely.
Extraocular Motility Examination
Extraocular muscle examination, including measurements of the amplitudes of convergence and divergence, can prove helpful prior to keratorefractive surgery. Distance and near cover and alternate cover tests reveal tropias and phorias. Polarized lens stereopsis tests and tests such as red–green Worth lights, which give less stimulus to fusion, may be used to evaluate the degree and stability of fusion and presence of suppression. Keratorefractive surgery may result in reduction or increase in accommodative demands in various circumstances. The spectacle-corrected myope brought to emmetropia by surgery will experience increased demand at near because of the loss of near effectivity of distance-corrective minus lenses. To the extent that myopia is undercorrected, accommodative demand at near will be reduced, giving relief to the presbyope but possibly constituting a cause of concern for someone less presbyopic who has convergence insufficiency. A young esophore with a low reserve of fusional divergence might become symptomatic if overcorrection of myopia, resulting in hyperopia, creates an increased demand for accommodation with its associated accommodative convergence. Measuring the amplitudes of convergence and divergence (far and near, with or without accommodation) with prisms helps to predict whether a change of accommodative demand is likely to stress a weakness of convergence or divergence. If the patient is to function without glasses after surgery, there will be no spectacles in which to grind prisms.
Accommodation
Assessment of the amplitude of accommodation before surgery allows the refractive surgeon to formulate a plan for near vision that may include, for instance, the undercorrection of myopia of one or both eyes. In general, the difference in diopters between least and most spheres accepted with clear vision while gazing at a distant target is the amplitude of accommodation. Measuring the near point while wearing myopic spectacles will tend to overestimate the amplitude of accommodation because of the near effectivity discussed earlier. Unequal or unusually small amplitudes suggest traumatic injury, drug effects, third cranial nerve paresis, lack of effort, spasm of accommodation, or erroneous distance refraction. One may expect a myope or anisometrope with natural monovision who has not bothered to wear glasses to have developed lower amplitude of accommodation than usual, whereas a long-time uncorrected hyperope will probably have built up greater amplitude than usual.
Spectacle Overcorrection of Myopia
The spectacle overminused myope with presbyopic symptoms may become nonpresbyopic when the unnecessary minus is removed. Discovery of the overminused state may require cycloplegia or at least prolonged fogging with plus lenses during refraction, as the patient may have sustained the extra accommodative tone for years. The patient should be given a new pair of lenses, and surgery should be delayed if the excess minus power of the previous spectacle lens has been a diopter or more. Patients will find that the correct glasses are not as functionally impairing as the overminused lenses were, but they may still desire surgical correction. The surgery should be based on the cycloplegic refraction if the cycloplegic manifest is accepted. This situation requires great care in choosing the amount of correction; even after surgery, some of these patients will be unable to relax accommodative tone so that correction based on the cycloplegic preoperative refraction may persistently be felt to be insufficient. The surgeon may then be faced with the patient’s demand for further surgery based on this residual accommodative tone, leading to the patient being deliberately converted from an overcorrected myope to a latent hyperope! The overminused bifocal wearer similarly will complain at a younger age of blur in the middle distance and will regain use of the amplitude of accommodation with a corrected distance prescription.
Contact Lens Wear
For the cornea to return to its natural shape, soft contact lens wear should be discontinued for 3 to 7 days and rigid lens wear for 3 weeks prior to conventional refractive procedures. A longer period of contact lens discontinuation may be needed prior to wavefront-guided surgery.
Anisometropia and Aniseikonia
Knapp’s rule tells us that with purely axial anisometropia, which may occur in cases of unilaterally high myopia, equal image sizes on the two retinas are achieved when each refractive error is corrected with a spectacle lens placed at the anterior focal point of the eye, which is about 16 mm in front of the cornea. The geometric-optics argument for this does not consider the possibility that the highly myopic eye may have stretched-apart spacing of photoreceptors, which would tend to minify the view. If these anisometropes do not have disturbing aniseikonia with spectacles, might they after keratorefractive surgery? Placement of a corrective contact lens should allow preoperative investigation of this possibility and adequate counseling to the unilaterally high-myopic patient about possible postoperative discomfort and adaptation.
Aniseikonia may be unavoidable in refractive surgery of the preoperatively iseikonic bilateral high myope. After surgery of one eye, the other eye may require contact lens wear as the only remedy for aniseikonia until the second eye has similar surgery. Thus when discussing the risks of surgery preoperatively, contact-lens-intolerant patients with high myopia should be apprised of the difficulties they might face.
Cycloplegic Refraction
Refraction is repeated after cycloplegia to discover whether accommodation has been active during the previous “dry” refraction, in which case the cyclopleged eye will show less myopia. For example, a young person with spasm of accommodation would in this manner be identified before surgery; thus the surgical plan would be based on the true refractive error. However, there may be a shift with cycloplegia toward greater myopia, which is caused by spherical aberration as the peripheral optics of the eye are exposed by dilation ( Fig. 3.4 ).
