between the pupillary axis and the central corneal apex. If the angle kappa is large, centering an excimer ablation over the geometric center of the cornea will effectively result in a decentered ablation. This can be particularly problematic in a hyperopic correction, in which a large angle kappa can result in a refractively significant “second corneal apex,” causing monocular diplopia and decreased quality of vision. A large angle kappa must be identified before surgery to reduce the likelihood of a poor visual outcome.
Freedman KA, Brown SM, Mathews SM, Young RS. Pupil size and the ablation zone in laser refractive surgery: considerations based on geometric optics. J Cataract Refract Surg. 2003;29(10):1924–1931.
Pupil Size
Pupil size measurement is becoming the standard of care in preoperative evaluations, prompted by observations that some patients with large pupils (>8 mm) reported difficulties with night vision after undergoing keratorefractive surgery. Typical symptoms included the appearance of glare, starbursts, and halos; decreased contrast sensitivity; and poor overall quality of vision. Night-vision problems tended to occur in patients with both large pupils and small treatment zones (≤6 mm). The algorithms used in third-generation lasers, however, incorporate larger optical and transition zones, enabling surgeons to perform refractive procedures on patients with larger pupils. Use of these algorithms has dramatically decreased the incidence and severity of night-vision problems.
Many surgeons use default ablation zones during excimer procedures. The accepted standard transition zone between ablated and unablated cornea is 0.5–1.0 mm larger than the pupil; use of this zone helps minimize night-vision problems. To conserve corneal tissue, smaller optical zones are typically used in higher myopic corrections. In patients who require such corrections, the incidence of night-vision problems increases in part because of the mismatch between the size of the pupil and that of the optical zone.
Although pupil size does not affect surgical outcome as significantly as it once did, pupil size measurement continues to be the standard of care in preoperative evaluation. Patients with extremely large pupils (≥8 mm) should be identified and counseled about the potential for increased risk of complications. Spherical aberration may be increased in these patients. Clinical management of postoperative night-vision problems includes the use of a miotic such as brimonidine (0.2%) or pilocarpine (0.5%–1%).
Freedman KA, Brown SM, Mathews SM, Young RS. Pupil size and the ablation zone in laser refractive surgery: considerations based on geometric optics. J Cataract Refract Surg. 2003;29(10):1924–1931.
Klyce S. Night vision after LASIK: the pupil proclaims innocence. Ophthalmology. 2004;111(1):1–2.
Lee YC, Hu FR, Wang IJ. Quality of vision after laser in situ keratomileusis: influence of dioptric correction and pupil size on visual function. J Cataract Refract Surg. 2003;29(4):769–777.
Schallhorn SC, Kaupp SE, Tanzer DJ, Tidwell J, Laurent J, Bourque LB. Pupil size and quality of vision after LASIK. Ophthalmology. 2003;110(8):1606–1614.
Irregular Astigmatism
The treatment of postoperative irregular corneal astigmatism is a substantial challenge in refractive surgery. The diagnosis of irregular astigmatism is made by meeting clinical and imaging criteria: loss of spectacle best-corrected vision but preservation of vision with the use of a gas-permeable contact lens, coupled with topographic corneal irregularity. An important sign of postsurgical irregular
astigmatism is a refraction that is inconsistent with the uncorrected visual acuity. For example, consider a patient who has –3.50 D myopia with essentially no astigmatism before the operation. After keratorefractive surgery, the patient has an uncorrected visual acuity of 20/25 but a refraction of +2.00 –3.00 × 060. Ordinarily, such a refraction would be inconsistent with an uncorrected visual acuity of 20/25, but it can occur in patients who have irregular astigmatism after keratorefractive surgery.
Another important sign is the difficulty of determining axis location during manifest refraction in patients with a high degree of astigmatism. Normally, determining the correcting cylinder axis accurately in a patient with significant cylinder is easy; however, patients with irregular astigmatism after keratorefractive surgery often have difficulty choosing an axis. Automated refractors may identify high degrees of astigmatism that are rejected by patients on manifest refraction. Because their astigmatism is irregular (and thus has no definite axis), these patients may achieve almost the same visual acuity with high powers of cylinder at various axes. Streak retinoscopy often demonstrates irregular “scissoring” in patients with irregular astigmatism.
Results of astigmatic enhancements (ie, astigmatic keratotomy, LASIK) are unpredictable for patients with irregular astigmatism. Avoid “chasing your tail” in keratorefractive surgery. For instance, a surgeon may be tempted to perform an astigmatic enhancement on a patient who had little preexisting astigmatism but significant postoperative astigmatism. If, however, the patient is happy with the uncorrected visual acuity (despite irregular astigmatism), avoiding further intervention may be preferable. In such cases, the stigmatic enhancement may cause the axis to change dramatically without substantially reducing cylinder power.
Irregular astigmatism can be quantified in much the same way as is regular astigmatism. We think of regular astigmatism as a cylinder superimposed on a sphere. Irregular astigmatism, then, can be thought of as additional shapes superimposed on cylinders and spheres. This approach is widely used in optical engineering.
Application of Wavefront Analysis in Irregular Astigmatism
Refractive surgeons derive some benefit from having a thorough understanding of irregular astigmatism, for 2 reasons. First, keratorefractive surgery may lead to visually significant irregular astigmatism in a small percentage of cases. Second, keratorefractive surgery may also be able to treat it. For irregular astigmatism to be studied effectively, it must be described quantitatively. Wavefront analysis is an effective method for such descriptions of irregular astigmatism.
An understanding of irregular astigmatism and wavefront analysis begins with stigmatic imaging. A stigmatic imaging system brings all the rays from a single object point to a perfect point focus. According to the Fermat principle, a stigmatic focus is possible only when the time required for light to travel from an object point to an image point is identical for all the possible paths that the light may take.
An analogy to a footrace is helpful. Suppose that several runners simultaneously depart from an object point (A). Each runner follows a different path, represented by a ray. All the runners travel at the same speed in air, just as all rays travel at the same (but slower) speed in glass. If all the runners reach the image point (B) simultaneously, the “image” is stigmatic. If the rays do not meet at point B, then the “image” is astigmatic.
The Fermat principle explains how a lens works. The rays that pass through the center of a lens travel a short distance in air but slow down when they move through the thickest part of the glass.
Rays that pass through the edge of a lens travel a longer distance in air but slow down only briefly when traversing the thinnest section of the glass. The shape of the ideal lens precisely balances each path so that no matter what path the light travels, it reaches point B in the same amount of time. If the lens shape is not ideal, however, some rays reach point B at a certain time point and other rays do not; this focus is termed astigmatic.
Wavefront analysis is based on the Fermat principle. Construct a circular arc centered on the image point with a radius approximately equal to the image distance (Fig 6-5A). This arc is called the reference sphere. Again, consider the analogy of a footrace, but now think of the reference sphere (rather than a point) as the finish line. If the image is stigmatic, all runners starting from a single point will cross the reference sphere simultaneously. If the image is astigmatic, the runners will cross the reference sphere at slightly different times (Fig 6-5B). The geometric wavefront is analogous to a photo finish of the race. It represents the position of each runner shortly after the fastest runner crosses the finish line. The wavefront aberration of each runner is the time at which the runner finishes minus the time of the fastest runner. In other words, it is the difference between the reference sphere and the wavefront. When the focus is stigmatic, the reference sphere and the wavefront coincide, so that the wavefront aberration is zero.
Figure 6-5 A, The reference sphere (in red) is represented in 2 dimensions by a circular arc centered on point B and drawn through the center of the exit pupil of the lens. If the image is stigmatic, all light from point A crosses the reference sphere simultaneously. B, When the image is astigmatic, light rays from the object point simultaneously cross the wavefront (in blue), not the reference sphere. (Part B modified b y C. H. Wooley.)
Wavefront aberration is a function of pupil position. Figure 6-6 shows some typical wavefront aberrations. Myopia, hyperopia, and regular astigmatism can be expressed as wavefront aberrations. Myopia produces an aberration that optical engineers call positive defocus. Hyperopia is called negative defocus. Regular (cylindrical) astigmatism produces a wavefront aberration that resembles a cylinder. Defocus (myopia and hyperopia) and regular astigmatism constitute the lower-order aberrations.
Figure 6-6 Second-, third-, and fourth-order wavefront aberrations (indicated by n values 2, 3, and 4, respectively) are
most pertinent to refractive surgery. (Reproduced with permission from Applegate RA. Glenn Fry Award Lecture 2002: wavefront sensing, ideal corrections, and visual performance. Optom Vis Sci. 2004;81(3):169.)
When peripheral rays focus in front of more central rays, the effect is termed spherical aberration. Clinically, spherical aberration is one of the main causes of night myopia following LASIK and PRK.
Another common wavefront aberration is coma. In this aberration, rays at one edge of the pupil cross the reference sphere first; rays at the opposite edge of the pupil cross last. The effect is that the
image of each object point resembles a comet with a tail (one meaning of the word coma is “comet”). Coma also arises in patients with decentered keratorefractive ablation. It is commonly observed in the aiming beam during retinal laser photocoagulation; if the ophthalmologist tilts the lens too far offaxis, the aiming beam spot becomes coma shaped.
Higher-order aberrations tend to be less significant than lower-order aberrations, but the higherorder ones may worsen in diseased or surgically altered eyes. For example, if interrupted sutures are used to sew in a corneal graft during corneal transplant, they will produce higher-order, clovershaped aberrations. Also, in the manufacture of intraocular lenses, the lens blank is sometimes improperly positioned on the lathe; such improper positioning can also produce higher-order aberrations.
Optical engineers have found approximately 18 basic types of astigmatism, of which only some— perhaps as few as 5—are of clinical interest. Most patients probably have a combination of all 5 types.
Wavefront aberrations can be represented in different ways. One approach is to show them as 3- dimensional shapes. Another is to represent them as contour plots. Irregular astigmatism can be described as a combination of a few basic shapes, just as conventional refractive error represents a combination of a sphere and a cylinder. The approach used by ophthalmologists does not use graphs or contour plots to represent conventional refractive errors. Instead, ophthalmologists simply specify the extent of sphere and cylinder that make up the refractive error. Similarly, once ophthalmologists are comfortable with the basic forms of irregular astigmatism, they have little need for 3-dimensional graphs or 2-dimensional contour plots. They simply specify the degree of each basic form of astigmatism in a given patient. Prescriptions of the future may consist of 8 or so numbers: the first 3 may be sphere, cylinder, and axis; and the remaining 5 may specify the irregular astigmatism as quantitated by higher-order aberration.
Currently, wavefront aberrations are specified by Zernike polynomials, which are the mathematical formulas used to describe wavefront surfaces. Wavefront aberration surfaces are graphs generated using Zernike polynomials. There are several techniques for measuring wavefront aberrations clinically, but the most popular is based on the Hartmann-Shack wavefront sensor. In this device, a low-power laser beam is focused on the retina. A point on the retina then acts as a point source. In a perfect eye, all the rays would emerge in parallel and the wavefront would be a flat plane. In reality, the wavefront is not flat. An array of lenses sample parts of the wavefront and focus light on a detector. The wavefront shape can be determined from the position of the focus on each detector (eg, see Fig 1-6 in BCSC Section 13, Refractive Surgery).
Another method of measuring wavefront aberrations is a ray-tracing method that projects detecting light beams sequentially rather than simultaneously, as in a Hartmann-Shack device, further improving the resolution of wavefront aberration measurements. The application of Zernike polynomials’ mathematical descriptions of aberrations to the human eye is less than perfect, however, and alternative methods, such as Fourier transform, are being utilized in many wavefront aberrometers.