Visual performance is defined by how well a visual task of interest can be performed by a given individual or group of individuals. A classic but not the only test of visual performance is high-contrast visual acuity.
Recently, the link between visual performance and optical quality of the eye has enjoyed a renewed interest, due largely to the development of clinically viable wavefront aberrometers and the popularization of wavefront guided refractive surgery. Currently, the most common method for describing the wavefront error of the eye is the normalized Zernike expansion (Thibos, Applegate, & Schweigerling,
2000). The Zernike expansion is in common use for several reasons. First, it provides an efficient way to specify an entire wavefront aberration map with a relatively small set of Zernike coefficients. Second, individual Zernike basis functions (i.e., modes) correspond to classical optical aberrations, such as defocus, astigmatism, coma, and spherical aberration. Third, when normalized by the recommended OSA system, the Zernike functions are mutually orthogonal, and the root mean squared (RMS) wavefront error of each function is given by its coefficient. Consequently, a Zernike expansion provides a convenient accounting scheme in which the total RMS wavefront error is equal to the square root of the sum of the squares of the individual coefficients in the Zernike spectrum of a wavefront aberration map.
Over a large range of RMS errors (an equivalent dioptric range of around 3 diopters), visual acuity decreases with increasing RMS error of the corneal first surface (Applegate et al.,
2000). However, at low levels of whole eye aberrations (less than 0.25 equivalent D), the RMS wavefront error cannot account for an observed two-line variation in visual performance (Applegate, Marsack, Ramos, & Sarver,
2003). Closing this gap in our understanding of the visual consequences of low levels of residual wave aberration is important to fully realize the potential of custom refractive surgery as well as customized contact lens corrections.
The complex interactions of wave aberrations at low levels of optical error and how these interactions impact visual performance are being systematically investigated by our laboratory (Applegate, Ballentine, Gross, Sarver, & Sarver,
2003; Applegate, Sarver, & Khemsara,
2002; Applegate, Marsack et al.,
2003) and others (Cheng, Bradley, Thibos,
2004). We typically perform these experiments using the Zernike expansion to describe wave aberration and keep the amount of wave aberration purposely low (RMS < = 0.25 µm over a 6-mm pupil — a dioptric equivalent of equal or less than 0.19 D) (G. Pettit, personal communication). We first explored the visual impact of low levels of aberration by observing how a fixed amount of RMS error loaded into single Zernike modes (2
^{nd} through 4
^{th} radial orders) impact letter acuity of an individual (Applegate et al.,
2002). In these experiments, each subject served as his or her own control. That is, we measured how a change in aberration altered visual performance as measured by high-contrast logMAR acuity. These experiments revealed that 0.25 µm of aberration over a 6-mm pupil reduced visual acuity by an amount that depended on which Zernike mode contained the wavefront error. Modes near the center of each radial order have a greater impact on visual performance (more letters lost) than modes near the edge of the pyramid. This result is seen in
Figure 1.
In a second experiment, 6 levels of RMS wavefront error (0.00 µm, 0.05 µm, 0.10 µm, 0.15 µm, 0.20 µm, and 0.25 µm) were loaded one at a time into the same 12 Zernike modes to determine how they affected high-contrast logMAR acuity (Applegate, Ballentine et al.,
2003). The results showed that within any given Zernike mode, performance decreased linearly with increasing RMS wavefront error and reconfirmed the results of the first experiment by demonstrating that Zernike modes near the center of each radial order impacted acuity more (increased slopes of the linear fit) than modes near the edge of each radial order.
However, real eyes do not exhibit single-mode aberrations (Howland & Howland,
1977; Porter, Guirao, Cox, & Williams,
2001; Thibos, Hong, Bradley, & Cheng,
2002). To individually study all or even most of the possible or even relevant combinations of aberrations and magnitudes present in a normal population would be impractical. Instead, we chose to systematically approach the problem one step at a time by exploring interactions of various combinations of two aberration modes. Accordingly, a third experiment was conducted to investigate how low levels of RMS wavefront error split between two Zernike modes affect visual acuity (Applegate, Marsack et al.,
2003). The experiment was performed by varying the relative proportion of the wavefront error attributable to each of two Zernike modes while keeping total RMS wavefront error constant at 0.25 micrometers over a 6-mm pupil used in the previous experiments.
Figure 2 illustrates the relative proportions of each Zernike mode used in the combination.
The experimental result revealed a variation in high-contrast visual acuity of nearly two lines on a log MAR chart, despite the fact that the total RMS error was held constant at 0.25 micrometers over a 6-mm pupil (a fixed equivalent dioptric error of 0.19 D). The magnitude of the loss was dependent on which aberration modes were combined and in what ratio. This finding demonstrates that the manner in which the Zernike modes are combined significantly impacts measured acuity in a way that RMS wavefront error and equivalent dioptric error cannot predict. The likely reason is that RMS wavefront error specifies only the standard deviation of the wavefront error over the pupil. It does not contain any information as to how this wavefront error was distributed within the pupil, the resulting effect on the point spread function in the spatial domain, or the impact on the modulation transfer function or the phase transfer function in the frequency domain.
That equivalent diopters and RMS error cannot account for any of the two-line changes in acuity induced in this study and that these combinations are challenging due to interactions between Zernike modes that affect visual perception make this data set an interesting step in developing single-value metrics predictive of visual performance.
The study reported here uses this latter data set (Applegate, Marsack et al.,
2003) to investigate the ability of 31 scalar metrics derived from wave aberration maps to predict changes in high-contrast logMAR acuity. Phrased as a question, we ask, “Can the change in visual acuity induced by different combinations of Zernike modes be well predicted by one or more of the 31 metrics derived from the wavefront aberration map?”