E6 Ocular Aberrations and Wavefront

Topic

As described by the model of the eye as an optical system, when the cornea and lens precisely refract light rays emanating from a single point on an object, those rays converge at the same point on the retina; the wavefront—the surface connecting all points of that light sharing the same phase—then exits the eye in a perfectly spherical shape centered on that convergence point. In a real eye, however, the exact shapes of the cornea and lens are never perfect, and the wavefront exiting the eye deviates—to a greater or lesser extent—from that ideal spherical shape; this deviation between the actual wavefront shape and the ideal spherical shape is known as the eye's optical aberration.

Since the deviation between the actual wavefront and the ideal spherical wavefront is not uniform across the pupil but rather exhibits a complex, unique shape, this model decomposes it into a sum of simpler, elementary shapes known as Zernike polynomials. Each polynomial has an associated coefficient measuring the extent to which that specific elementary shape contributes to the total wavefront deviation. The higher the coefficient corresponding to a given elementary shape, the greater that shape's weight within the total wavefront deviation and the greater the optical aberration it individually introduces.

Among these elementary shapes, low-order ones are those that vary smoothly and uniformly across the entire pupil: defocus, which shifts the wavefront away from the ideal spherical shape equally in all directions, and astigmatism, which causes a shift that varies according to orientation within the pupil, as described by the model of ametropias. In contrast, higher-order elementary forms vary in a more irregular and localized manner across the pupil: coma, trefoil, and spherical aberration each introduce a deviation with a distinct, more complex shape than that of defocus or astigmatism; consequently, no simple lens with a single, uniform curvature can correct them in the same way it corrects defocus or astigmatism.

Each of these elementary forms degrades the retinal image in a unique way: defocus spreads the point of light—which should converge on the retina—into a blurred circle that is uniform in all directions; astigmatism spreads it unevenly, creating more blur in one orientation than in the perpendicular one; coma spreads it asymmetrically, with a tail extending to one side; trefoil spreads it into three lobes distributed around the point; and spherical aberration causes rays passing through the center of the pupil and those passing through its periphery to converge at different points along the optical axis, rather than all converging together on the retina. The larger the pupil, the more peripheral rays enter the eye and the more pronounced these higher-order aberrations become in the retinal image; conversely, with a small pupil, those same peripheral rays are blocked, and the image more closely approaches the limit imposed solely by diffraction.

The sum of all these elementary forms—both low-order and high-order—reconstructs the total deviation of the actual wavefront from the ideal spherical wavefront, thereby defining the eye's overall optical quality, beyond the limit imposed by pupil diffraction itself according to the diffraction and resolution limit model. It is this same decomposition of the wavefront into Zernike polynomials that allows the aberrometry model to be reconstructed from data captured by a Hartmann-Shack sensor or a Tscherning disk; it also guides wavefront-guided refractive surgery, reshaping the cornea in a personalized manner to cancel out—component by component—the specific optical aberration of each eye.

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