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 × 60. 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.
Typically, an AK incision will decrease regular astigmatism while maintaining the spherical equivalent (coupling); however, results of astigmatic enhancements can be unpredictable for patients with irregular astigmatism. For example, a surgeon may be tempted to perform an astigmatic enhancement on a patient who had little preexisting astigmatism but significant postoperative astigmatism despite good uncorrected visual acuity. In such cases, the astigmatic enhancement may cause the axis to change dramatically without substantially reducing cylinder power due to irregular astigmatism.
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 corneal irregularity is then measured and quantified by wavefront analysis.
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. In this case, all the runners travel at the same speed on the ground, but slow down when running through water. Similarly, light rays will travel at the same speed in air but slow down in the lens. 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.
Wavefront analysis is based on the Fermat principle. Construct a circular arc centered on the paraxial image point and intersecting the center of the exit pupil (Fig 7-4A). 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 7-4B). 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.
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.
(Courtesy of Edmond H. Thall, MD; part B modified by C. H. Wooley.)
Another interpretation of the Fermat principle is the point spread function produced by all rays that traverse the pupil from a single object point. This image is perpendicular to the geometric wavefront shown in Figure 7.5B. For example, keratorefractive surgery for myopia using surgical removal procedures reduces spherical refractive error and regular astigmatism, but it does so at the expense of increasing spherical aberration and irregular astigmatism (Fig 7-5). The cornea subsequently becomes less prolate, and its shape resembles an egg lying on its side. The central cornea becomes flatter than the periphery and results in an increase in the spherical aberration of the treated zone. Generally, keratorefractive surgery moves the location of the best focus closer to the retina but, at the same time, makes the focus less stigmatic. Such irregular astigmatism leads to decreased contrast sensitivity and underlies many visual complaints after refractive surgery.
Wavefront aberration is a function of pupil position. For example, coma is a partial deflection of spherical aberration. Figure 7-6 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 saddle. Defocus (myopia and hyperopia) and regular astigmatism constitute the lower-order aberrations.
Figure 7-5 Examples of the effects of (A) coma, (B) spherical aberration, and (C) trefoil on the point spread functions of a light source.
(Courtesy of Ming Wang, MD.)
Figure 7-6 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. After keratorefractive surgery, corneas that become more oblate (after myopic correction) will induce more-negative spherical aberration, while those that become more prolate (after hyperopic correction) will induce more-positive spherical aberration.
Another important 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”). It is commonly observed in the aiming beam during retinal laser photocoagulation; if the ophthalmologist tilts the lens too far off-axis, the aiming beam spot becomes coma shaped. Coma also arises in patients with decentered keratorefractive ablation or keratoconus. These situations may be treatable with intrastromal rings.
Higher-order aberrations tend to be less significant than lower-order aberrations, but the higher-order 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, trefoil or tetrafoil aberrations. These can then be addressed with suture removal, suture addition, or AK. Also, in the manufacture of IOLs, 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.
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. The most popular is based on the Hartmann-Shack wavefront sensor, which uses a low-power laser beam 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; however, in most eyes, the wavefront is not flat. Within the sensor is a grid of small lenses (lenslet array) that samples parts of the wavefront. The images formed are focused onto a charge-coupled-device chip, and the degree of deviation of the focused images from the expected focal points determines the aberration and thus the wavefront error (eg, see Fig 1-1 in BCSC Section 13, Refractive Surgery).
The most frequently used technologies today are those based on measuring wavefront aberrations via a ray-tracing method that projects detecting light beams sequentially rather than simultaneously, using a Hartmann-Shack wavefront sensor, 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 used in many wavefront aberrometers.
To normalize wavefront aberration measurements and improve postoperative visual quality in patients undergoing keratorefractive surgery, ophthalmologists are developing technologies to improve the accuracy of higher-order aberration measurements and treatment by using “flying spot” excimer lasers. Such lasers use small spot sizes (<1-mm diameter) to create smooth ablations, addressing the minute topographic changes associated with aberration errors.
For a more detailed discussion of the topics covered in this subsection, see BCSC Section 13, Refractive Surgery.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.