Both the anterior surface of the cornea and the internal optics (the posterior cornea, crystalline lens) contribute to the aberration of a wavefront passing through the eye. Artal, Guirao, Berrio, and Williams (2001) reported that the wavefront aberrations produced by the internal optics offset, or compensate for, the aberrations produced by the cornea to reduce ocular wavefront aberrations. We have investigated the wavefront aberrations of the cornea, internal optics, and complete eye on both the population and individual level to determine which aberrations are compensated and probable paths leading to that compensation. The corneal and ocular aberrations of 30 young subjects at relaxed accommodation were measured with the Topcon Wavefront Analyzer, which simultaneously measures refraction, corneal topography (videokeratoscope), and wavefront aberrations (Hartmann-Shack sensor). We found strong evidence for compensation of horizontal/vertical (H/V) astigmatism (Zernike term Z5) lateral coma (Z8) and spherical aberration (Z12). H/V astigmatism compensation is scaled for each individual, suggesting that it is actively determined by a fine-tuning process. Spherical aberration shows no individual compensation, suggesting that is a passive result of genetically determined physiology. Lateral coma shows individually scaled compensation, some of which may be attributable to eccentricity of the fovea.

^{nd}through 4

^{th}order Zernike wavefront aberrations of the cornea by the internal optics in 30 young subjects. We have examined both sample population means and individual values, which provide clues as to whether compensation arises passively or through an active process, as indicated by compensation scaled to each individual eye.

^{th}order) are fit to the wavefront and reported.

*W*(

*X, Y*)is the wavefront,

*X, Y*, are horizontal and vertical coordinates on the pupil, Δ

*x*, Δ

*y*, are the displacements of the spots from their reference positions on the CCD, and

*f*is the distance between the Hartmann-Shack lenslet array and the CCD (Thibos & Hong, 1999).

^{th}-order, one-dimensional polynomial. This height map is subtracted from a spherical surface with a radius computed from the placido ring image positions. The residual shape for the 7-mm diameter area centered on the corneal pole is then fit with Zernike polynomials up to the 6

^{th}order. The Zernike coefficients are multiplied by n-1, where n is the standard refractive index assigned to the cornea (1.3375), and added to the spherical aberration of the computed spherical surface to generate the aberrated wavefront. The wavefront coordinate plane is then translated so that the origin lies on the pupil center, and corneal wavefront aberration Zernike coefficients up to 6

^{th}order are calculated for a 6mm pupil.

^{nd}through 4

^{th}order aberrations, first considering the sample population’s mean absolute values using a Wilcoxon signed rank test and then considering individual subject values by examining correlations. High-order compensation was compared to ocular high-order RMS wavefront error, inclusive of all 3

^{rd}through 6

^{th}order coefficients. Statistical significance was set to the

*p*< .05 level.

*SD*of only 0.030 ± 0.009 microns RMS wavefront error. The 4

^{th}-order spherical aberration coefficient had a SE of 0.0024 microns for 27 measurements. Measurements were also highly repeatable. For the 30 subjects used in this study, the mean RMS SE of the aberrated ocular wavefront was 0.0601 microns for astigmatism plus 3

^{rd}through 6

^{th}order coefficients, and 0.0467 microns for only 3

^{rd}through 6

^{th}order coefficients. Mean RMS SE of Zernike coefficients Z5, Z8, and Z12, those of interest to this study, were 0.0281 microns, 0.0139 microns, and 0.0107 microns, respectively.

*SD*microns for astigmatism plus all 3

^{rd}through 6

^{th}order coefficients. Corneal wavefront aberrations generated by Code V for the shifted model eye differed from those calculated by the WFA program by a mean RMS of 0.0019 ± 0.0044

*SD*microns for all 3

^{rd}through 6

^{th}order coefficients.

^{rd}through 6

^{th}order coefficients, and 0.0764 microns for only 3

^{rd}through 6

^{th}order coefficients. Mean RMS SE of Zernike coefficients Z5, Z8, and Z12, those of interest to this study, were 0.0415 microns, 0.0190 microns, and 0.0160 microns, respectively.

^{rd}and 4

^{th}order coefficients (excluding defocus) for 13 subjects. We found highly significant Pearson correlations between right and left eye ocular coefficients (

*r*= 0.717, Fisher’s

*p*< .0001) corneal coefficients (

*r*= 0.829, Fisher’s

*p*< .0001) and internal coefficients (

*r*= 0.821, Fisher’s

*p*< .0001). Figure 2 shows the dataset superimposed on the line

*y*=

*x*, which demonstrates perfect symmetry.

*n*= 30, Figure 3). A decrease in magnitude between corneal and ocular coefficient means indicates compensation by internal optics to reduce overall aberrations, as corneal and internal coefficients add to give ocular coefficients. Because we are examining absolute values, overcompensation and undercompensation are indistinguishable. However, any reduction in corneal aberration will, in general, improve the optical quality of the eye.

*p*= .0429), lateral coma (Z8,

*p*= .009), and spherical aberration (Z12,

*p*= .004). The mean coefficient values, listed in Table 1, show that H/V astigmatism was reduced by 41%, lateral coma reduced by 51%, and spherical aberration reduced by 36%. All other Zernike terms, including oblique astigmatism (Z3), did not show significant compensation. However, ocular vertical coma (Z7) was significantly larger than corneal vertical coma (

*p*= .003).

Aberration | RMS Mean ± SE [microns] | Reduction (corneal to ocular) | p value | ||
---|---|---|---|---|---|

Corneal | Ocular | RMS [microns] | % C coef | ||

H/V Astigmatism (Z5) | 0.634 ± 177; 0.097 | 0.372 ± 177; 0.077 | 0.262 | 41% | 0.043 |

Lateral coma (Z8) | 0.171 ± 177; 0.016 | 0.084 ± 177; 0.011 | 0.087 | 51% | 0.009 |

Spherical aberration (Z12) | 0.207 ± 177; 0.012 | 0.132 ± 177; 0.017 | 0.075 | 36% | 0.004 |

^{rd}– 6

^{th}order RMS [microns]) that compensation introduced was 0.087 microns by lateral coma compensation and 0.075 microns by spherical aberration compensation, totaling 0.114 microns of compensation by the two combined. The mean total high-order RMS wavefront error values measured by the Wavefront Analyzer were 0.371 ± 0.015 SE microns for the cornea and 0.318 ± 0.023 SE microns for the total eye, a total high-order compensation of 0.053 microns. Therefore, roughly half of the reduction in RMS wavefront error introduced by compensation of lateral coma and spherical aberration was seen in the reduction of the total RMS wavefront error, which includes all 3

^{rd}through 6

^{th}order aberration coefficients.

*y*= −

*x*and

*y*= −2

*x*shows if that individual eye exhibits perfect compensation, overcompensation, undercompensation, or augmentation. We have included the reference line

*y*= −

*x*on the scatter plots of Z5, Z8, and Z12 internal against corneal coefficients (Figures 5, 6, and 7).

*df*= 29,

*r*= −0.524,

*p*= .0025) between internal and corneal horizontal/vertical astigmatism (Z5), as shown in Figure 5. The subject responsible for the obvious outlier has a cylinder of −2.3D, but a sphere of +1.0D, so her equivalent sphere, −0.167D, falls within our chosen range of acceptable deviation from emmetropia. Her large degree of astigmatism is seen in the horizontal/vertical Z5 astigmatism coefficient. When this outlier is excluded, the result is still significant (

*df*= 28,

*r*= −0.669,

*p*< .001).

*r*= −0.886,

*p*< .001), but not with ocular oblique astigmatism, coefficient Z3. When the 3 subjects with oblique cylindrical refractive error are examined separately, 2 show both Z3 and Z5 compensation, and 1 shows both Z3 and Z5 augmentation. Three subjects is not a sufficient pool to draw conclusions concerning the ties between oblique refractive error meridians and possible oblique astigmatism Zernike wavefront compensation.

*df*= 29,

*r*= −0.381,

*p*= .0372) between internal and corneal lateral coma (Z8), as shown in Figure 6.

*df*= 29,

*r*= −0.289,

*p*= .123).

^{rd}through 6

^{th}order terms) was significantly negatively correlated with increasing total ocular wavefront error (

*r*= −0.749,

*p*< .0001, Figure 8b). There is no correlation between ocular total high-order RMS error and corneal total high-order RMS error (Figure 8c).

*df*= 29,

*F*= 4.858,

*p*= .036,

*r*

^{2}= 0.148). Internal lateral coma coefficients decreased significantly with increasing distance (regression coef = −0.374,

*df*= 29,

*F*= 6.125,

*p*= .0196,

*r*

^{2}=.179).

^{rd}through 6

^{th}order), roughly half of the RMS reduction introduced by compensation of corneal lateral coma and corneal spherical aberration (0.114 microns) was still detected in the reduction in total RMS wavefront error (from 0.371 microns corneal RMS to 0.318 microns ocular RMS). That only half is seen is probably attributable to wavefront error introduced by the noncompensated aberration terms, such as vertical coma (Z7), which are included in total RMS.

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