Spherical aberration and other higher-order aberrations in the human eye: from summary wave-front analysis data to optical variables relevant to visual perception
1Department of Ophthalmology, University Medical Center Groningen, University of Groningen, P.O. Box 30.001, 9700 RB Groningen, The Netherlands (n.m.jansonius@ohk.umcg.nl)
Nomdo M. Jansonius, "Spherical aberration and other higher-order aberrations in the human eye: from summary wave-front analysis data to optical variables relevant to visual perception," J. Opt. Soc. Am. A 27, 941-950 (2010)
Wave-front analysis data from the human eye are commonly presented using the aberration coefficient (primary spherical aberration) together with an overall measure of all higher-order aberrations. If groups of subjects are compared, however, the relevance of an observed difference cannot easily be assessed from these summary aberration measures. A method was developed for estimating various optical variables relevant to visual perception from summary wave-front analysis data. These variables were the myopic shift (the difference in the optimal focus between high and low spatial frequencies, a threat to the simultaneous in-focus viewing of fine and coarse patterns), the depth-of-focus (at 8 cpd), and the modulation transfer at high (16 cpd; reading small print) and low (4 cpd; edge detection) spatial frequencies. The depth-of-focus was defined in two ways: using a relative measure (the full width at half-height of the through-focus curve) and an absolute measure (the range where the through-focus curve exceeds a predefined modulation transfer value). The method was shown to be accurate by using previously published contrast sensitivity data and wave-front analysis data. The applicability of the method was illustrated by applying the method to wave-front analysis measurements performed in pseudophakic patients with aspheric and spherical intraocular lenses.
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MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 4 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.05
1.1
1.4
0.89
0.40
0.85
0.1
0.14
1.1
1.4
0.88
0.38
0.82
0.2
0.24
1.1
1.4
0.86
0.35
0.74
0.3
0.39
1.3
1.5
0.83
0.30
0.66
0
0.50
0.04
1.4
1.6
0.78
0.26
0.75
0.1
0.14
1.5
1.7
0.78
0.25
0.73
0.2
0.22
1.6
1.7
0.76
0.24
0.68
0.3
0.36
1.6
1.7
0.73
0.22
0.62
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Table 2
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 5 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.04
1.0
1.2
0.85
0.33
0.80
0.1
0.19
1.1
1.2
0.83
0.31
0.70
0.2
0.43
1.3
1.4
0.77
0.25
0.53
0.3
0.68
1.5
1.5
0.68
0.22
0.43
0
0.50
0.01
1.4
1.5
0.71
0.22
0.68
0.1
0.17
1.4
1.5
0.70
0.21
0.62
0.2
0.34
1.6
1.5
0.66
0.19
0.55
0.3
0.54
1.7
1.5
0.60
0.17
0.47
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Table 3
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 6 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.04
0.9
1.2
0.81
0.29
0.75
0.1
0.29
1.1
1.2
0.75
0.25
0.55
0.2
0.59
1.3
1.3
0.63
0.20
0.41
0.3
0.68
1.5
1.2
0.52
0.17
0.35
0
0.50
0.02
1.4
1.4
0.65
0.19
0.62
0.1
0.21
1.5
1.3
0.62
0.17
0.55
0.2
0.44
1.7
1.3
0.55
0.15
0.43
0.3
0.58
1.8
1.1
0.47
0.13
0.37
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as calculated from Aberration Coefficient and an Overall Measure of all Higher-Order Aberrations, for Pseudophakic Eyes with Various Types of IOLs [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55], Phakic Eyes [11], and a Hypothetical Eye without Higher-Order Aberrations, for a Pupil Diameter of 5 mm and White Lighta
error; measure of all higher-order aberrations (root of the sum of the squares of all aberration coefficients belonging to Zernike polynomials with radial order ); of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Calculated directly from the original eye model since β (0 D) is well outside the range of the fit (0.25–0.50 D).
Tables (5)
Table 1
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 4 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.05
1.1
1.4
0.89
0.40
0.85
0.1
0.14
1.1
1.4
0.88
0.38
0.82
0.2
0.24
1.1
1.4
0.86
0.35
0.74
0.3
0.39
1.3
1.5
0.83
0.30
0.66
0
0.50
0.04
1.4
1.6
0.78
0.26
0.75
0.1
0.14
1.5
1.7
0.78
0.25
0.73
0.2
0.22
1.6
1.7
0.76
0.24
0.68
0.3
0.36
1.6
1.7
0.73
0.22
0.62
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Table 2
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 5 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.04
1.0
1.2
0.85
0.33
0.80
0.1
0.19
1.1
1.2
0.83
0.31
0.70
0.2
0.43
1.3
1.4
0.77
0.25
0.53
0.3
0.68
1.5
1.5
0.68
0.22
0.43
0
0.50
0.01
1.4
1.5
0.71
0.22
0.68
0.1
0.17
1.4
1.5
0.70
0.21
0.62
0.2
0.34
1.6
1.5
0.66
0.19
0.55
0.3
0.54
1.7
1.5
0.60
0.17
0.47
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Table 3
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as a Function of Spherical and Irregular Aberrations, for a Pupil Diameter of 6 mm and White Lighta
α
β (D)
MS (D)
(D)
(D)
0
0.25
0.04
0.9
1.2
0.81
0.29
0.75
0.1
0.29
1.1
1.2
0.75
0.25
0.55
0.2
0.59
1.3
1.3
0.63
0.20
0.41
0.3
0.68
1.5
1.2
0.52
0.17
0.35
0
0.50
0.02
1.4
1.4
0.65
0.19
0.62
0.1
0.21
1.5
1.3
0.62
0.17
0.55
0.2
0.44
1.7
1.3
0.55
0.15
0.43
0.3
0.58
1.8
1.1
0.47
0.13
0.37
of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
MS, Relative and Absolute DOFs, Maximum MT at 4 and 16 cpd, and MT at 4 cpd with Optimal Focus for Small Optotypes as calculated from Aberration Coefficient and an Overall Measure of all Higher-Order Aberrations, for Pseudophakic Eyes with Various Types of IOLs [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55], Phakic Eyes [11], and a Hypothetical Eye without Higher-Order Aberrations, for a Pupil Diameter of 5 mm and White Lighta
error; measure of all higher-order aberrations (root of the sum of the squares of all aberration coefficients belonging to Zernike polynomials with radial order ); of spherical aberration; of irregular aberration; shift; DOF measure; DOF measure; MT at 4 cpd; MT at 16 cpd; at 4 cpd with optimal focus for small optotypes.
Calculated directly from the original eye model since β (0 D) is well outside the range of the fit (0.25–0.50 D).