For many years, glasses and contact lenses have been used to correct large errors in the optical quality of the eye, namely defocus and astigmatism. However, it has been well known that the human eye also suffers from other subtle optical imperfections, which we refer to as higher order aberrations, in addition to typical defocus and astigmatic errors. Based on the technique devised by Liang et al. (1994), we measure the eye's wave aberration using a Shack-Hartmann wavefront sensor to obtain a picture of the overall optical quality of the eye. The wave aberration may be mathematically represented and broken down into its constituent aberrations (such as defocus, astigmatism, coma, spherical aberration, etc.) using a Zernike decomposition. We are able to measure up to and including the 10th order Zernike modes, or a total of 63 individual aberrations.

We can also compute the eye's point spread function (PSF) from the wave aberration to illustrate our best guess of how well the eye would see a point of light. Fig. 3 shows four typical examples of wave aberrations for normal subjects measured over a pupil diameter of 5.7 mm (top row) and their point spread functions (PSFs) calculated in white light (bottom row). A "perfect" eye would have a flat (uniform grey) wave aberration producing a small, sharp PSF. However, since our eyes are not perfect, we possess wave aberration maps that have several peaks and valleys, as indicated by the contour lines. The higher the density of the contour lines, the more severe the eye's aberrations are at that point. As illustrated in Fig. 3, the pattern and severity of aberration varies widely among normal subjects. Fig. 4 shows the magnitude of the higher order monochromatic aberrations measured with a wavefront sensor in a population of 109 normal subjects for a 5.7 mm pupil size (Porter et al., 2001). As seen in the figure, Zernike defocus (Z,2,0) accounts for 80% of the total variance of the wave aberration and has the largest magnitude of any mode (mean absolute RMS of 3.39 µm or 2.89 D). The next largest contributors to the wave aberration in the population are the astigmatic modes, (Z,2,-2) and (Z,2,2), with the first three modes accounting for over 92% of the total variance of the wave aberration. The magnitudes of the higher order aberrations generally decline with order, except for spherical aberration, which is larger in mean absolute RMS than any third order mode in our population. Even though the remaining higher order aberrations only account for approximately 8% of the total wavefront variance, they are nevertheless very important for improving vision and retinal image quality.

We developed the first fully-automated wavefront sensor (Hofer et al. 2001) capable of measuring the wave aberration in real-time at 25 Hz. With this system, we were able to make the first measurements of the temporal dynamics of the eye's aberrations. It was well known that the eye exhibits temporal fluctuations in focus, with bandwidths less than about 3 Hz (Campbell, Robson, and Westheimer, 1959). However, the stability of the eye's higher order aberrations was unclear. We found that in addition to focus, all of the eye's higher order aberrations exhibit temporal instability. The following images show movies of how Heidi Hofer's wave aberration and pointspread function change while trying to fixate on a target at infinity for a period of 5 seconds. The wavefront sensor was operating at a rate of 25.6 Hz and the videos represent measurements performed over a 5.8 mm pupil in monochromatic light.

The temporal bandwidth of the fluctuations in higher order aberrations dictates how fast an adaptive optics system has to be in order to successfully track and correct higher order aberrations in real time. We also found that the structure of the higher order aberrations changes with accommodation (Williams et al. 2001; Hofer et al. 2001). This means that a higher order correction tailored for distance vision would have limited utility for near viewing and vice versa. The practical significance of these measurements is that fluctuations in higher order aberrations will limit the effectiveness of any static method to correct them, such as a contact lens or refractive surgery.

Liang, Williams, and Miller (1997) calculated how the optical quality of the visual system improves after correcting various aberrations. The Strehl ratio is defined as the ratio of the peak intensity of the eye's PSF to the PSF of an aberration-free eye for the same pupil size. A Strehl ratio greater than 0.8 is considered to be diffraction-limited, or perfect. Fig. 5 shows how the Strehl ratio for two pupil sizes improves as we remove successively higher Zernike orders from the wave aberrations (Liang and Williams, 1997). For 3 mm pupils, only correcting second to fourth-order aberrations will provide a diffraction-limited Strehl ratio. However, for 7.3 mm pupils, Zernike orders up to and including at least eighth order must be corrected to achieve diffraction-limited performance.

Campbell F.W., Robson J.G., & Westheimer G., (1959). Fluctuations of accommodation under steady viewing conditions. Journal of Physiology, 145, 579-594.

Hofer H., Artal P., Singer B., Aragon J.L., & Williams D.R., (2001). Dynamics of the eye's wave aberration. Journal of the Optical Society of America A, 18(3), 497-506.

Liang J., Grimm B., Goelz S., & Bille J., (1994). Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wavefront sensor. Journal of the Optical Society of America A, 11, 1949-1957.

Liang J., & Williams D.R., (1997). Aberrations and retinal image quality of the normal human eye. Journal of the Optical Society of America A, 14, 2873-2883.

Liang J., Williams D.R. & Miller D.T., (1997). Supernormal vision and high-resolution retinal imaging through adaptive optics. Journal of the Optical Society of America A, 14, 2884-2892.

Porter J., Guirao A., Cox I.G., & Williams D.R., (2001). Monochromatic aberrations of the human eye in a large population. Journal of the Optical Society of America A, 18(8), 1793-1803.

Williams D.R., Yoon G.Y., Guirao A., Hofer H., & Porter J., (2001). How far can we extend the limits of human vision. In S. MacRae, R. Krueger, & R.A. Applegate (eds.), Customized Corneal Ablation: The Quest for SuperVision (pp. 11-32). Thorofare: SLACK, Inc.

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