The purpose of this study was to evaluate some of the methods used to calculate objective refractions from wavefront aberrations, to determine their applicability for accommodation research. A wavefront analyzer was used to measure the ocular aberrations of 13 emmetropes and 17 myopes at distance, and 4 near target vergences: 2, 3, 4, and 5 D. The accommodative response was calculated using the following techniques: least squares fitting (Zernike defocus), paraxial curvature matching (Seidel defocus), and 5 optical quality metrics (PFWc, PFSc, PFCc, NS, and VSMTF). We also evaluated a task-specific method of determining optimum focus that used a through-focus procedure to select the image that best optimized both contrast amplitude and gradient (CAG). Neither Zernike nor Seidel defocus appears to be the best method for determining the accommodative response from wavefront aberrations. When the eye has negative spherical aberration, Zernike defocus tends to underestimate, whereas Seidel defocus tends to overestimate the accommodative response. A better approach is to first determine the best image plane using a suitable optical quality metric and then calculate the accommodative error relative to this plane. Of the metrics evaluated, both NS and VSMTF were reasonable choices, with the CAG algorithm being a less preferred alternate.

_{E}): 0.21 ± 0.20 D, range: plano to +0.50 D) and 17 were myopic (mean S

_{E}: −3.47 ± 1.47 D, range: −1.25 to −5.75 D). Astigmatism was limited to ≤1.00 D, and anisometropia to <2.00 D. All subjects had normal corrected visual acuity (20/20 or better) and no binocular vision anomalies. Prior to data collection, binocular accommodative amplitudes and facility were assessed to be within normal parameters based on age.

*c*

_{2}

^{0}is the second-order Zernike coefficient for defocus and

*r*is the pupil radius.

*c*

_{2}

^{0}is the second-order Zernike coefficient for defocus,

*c*

_{4}

^{0}is the fourth-order Zernike coefficient for spherical aberration, and

*r*is the pupil radius.

*M*needed to maximize optical quality for the accommodating eye was determined. The OQM we evaluated were 5 identified as reasonably accurate and among the most precise: PFWc, PFSc, PFCc, NS, and VSMTF (Thibos et al., 2004).

Acronym | Description |
---|---|

PFWc | Pupil fraction for wavefront when critical pupil is defined as the concentric area for RMS _{w} < criterion ( λ/4) |

PFSc | Pupil fraction for slope when critical pupil is defined as the concentric area for RMS _{s} < criterion (1 arcmin) |

PFCc | Pupil fraction for curvature when critical pupil is defined as the concentric area for B _{ave} < criterion (0.25 D) |

NS | Neural sharpness |

VSMTF | Visual Strehl ratio for MTF |

*c*

_{2}

^{2}and

*c*

_{2}

^{−2}are the second-order Zernike coefficients for astigmatism and

*r*is the pupil radius.

*p*< 0.001) across metrics. An all-paired comparisons test, using the Tukey–Kramer method (

*α*

_{FW}= 0.05), identified the results for Zernike defocus as significantly different from the results for Seidel defocus, PFSc, CAG1, and CAG2 for the distance target. At the 2-and 3-D stimuli, there were no significant differences in the values calculated by the different metrics. With the 4- and 5-D stimuli, there were significant differences in accommodative responses (

*p*< 0.001) across metrics. The all-paired comparisons for the 4-D stimulus found the results for Zernike defocus to be significantly different to the results for Seidel defocus and CAG2, and the results for Seidel defocus also significantly different to the results for NS and VSMTF. The all-paired comparisons for the 5-D stimulus found the results for Zernike defocus to be significantly different to the results for Seidel defocus, PFSc, CAG1, and CAG2.

*p*< 0.001) across metrics. The all-paired comparisons, for all near vergences, found the results for Zernike defocus to be significantly different to the results for all other metrics. For the 5-D stimulus, there were also significant differences between the results for NS and the results for both Seidel defocus and PFSc, and between the results for VSMTF and the results for PFSc.

*t*-tests were used to compare the results for the two groups. For Zernike defocus, myopes had marginally higher accommodative responses than emmetropes, being significantly different only for the 3-D stimulus (

*p*< 0.05). For Seidel defocus, myopes again recorded higher accommodative responses; here the differences reached statistical significance for all vergences (

*p*< 0.05).

Metric | Slope | Correlation | ||
---|---|---|---|---|

Emmetropes | Myopes | Emmetropes | Myopes | |

Zernike | −0.211 ^{†} | −0.171 ^{†} | −0.657 | −0.495 |

NS | −0.139 ^{†} | −0.147 ^{†} | −0.445 | −0.406 |

VSMTF | −0.113 ^{†} | −0.110 ^{†} | −0.327 | −0.341 |

PFWc | −0.038 | −0.065 | −0.135 | −0.212 |

PFSc | −0.071 | −0.076 | −0.205 | −0.218 |

CAG1 | −0.064 | −0.074 ^{†} | −0.208 | −0.277 |

CAG2 | −0.055 | −0.067 ^{†} | −0.174 | −0.250 |

Seidel | −0.030 | −0.032 | −0.085 | −0.092 |

*t*-test. For both emmetropes and myopes,

*J*

_{45}, vertical coma, and horizontal coma were not significantly different from zero for any stimulus condition. This was also the case for

*J*

_{0}for the emmetropes, except for the 2-D stimulus, where the average astigmatism increased slightly to 0.12 ± 0.03 D (

*p*< 0.005). The myopes showed significant amounts of negative astigmatism (

*J*

_{0}) for all stimulus vergences, ranging from −0.14 ± 0.06 D to −0.21 ± 0.12 D (

*p*< 0.05). This was not unexpected as the inclusion criterion for astigmatism allowed up to 1 D, which was not corrected by the spherical soft contact lenses.

*J*

_{45}and vertical coma for any stimulus vergence. For the 3-D stimulus, there was a small, statistically significant difference in horizontal coma between emmetropes and myopes (0.07 ± 0.03 D,

*p*< 0.05). For

*J*

_{0}, there was also a small but significant difference between the two refractive error groups at all stimulus vergences ranging from 0.18 ± 0.07 to 0.31 ± 0.08 D (

*p*< 0.05).

*p*< 0.05), with the myopes recording more negative values in all cases.

*p*< 0.05) for the 2- and 3-D stimuli only.

*t*-test was used to compare the DOFs for the two refractive error groups, except for the 2-D stimulus where the Aspin–Welch unequal variance test was used. Differences between the two groups were significant only for the 2-D and 4-D stimuli (

*p*< 0.05).

*J*

_{45}) between emmetropes and myopes. The myopes had, on average, significantly larger amounts of astigmatism (

*J*

_{0}) compared to the emmetropes, although in magnitude this difference was very small. Myopes also had smaller pupil sizes ( Figure 6) compared to emmetropes, significantly different for the 2- and 3-D stimulus conditions. Both of these findings imply that the myopes should have a larger DOF compared to the emmetropes, which was supported by the results of the DOF estimates from the neural sharpness metric ( Table 3).