Raymond A. Applegate,1
William J. Donnelly, III,1
Jason D. Marsack,1
Darren E. Koenig,1
and Konrad Pesudovs2
1Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas 77204, USA
2Department of Ophthalmology, National Health and Medical Research Council, Centre for Clinical Eye Research, Flinders Medical Centre and Flinders University, Bedford Park, South Australia, 5042, Australia
Raymond A. Applegate, William J. Donnelly, III, Jason D. Marsack, Darren E. Koenig, and Konrad Pesudovs, "Three-dimensional relationship between high-order root-mean-square wavefront error, pupil diameter, and aging," J. Opt. Soc. Am. A 24, 578-587 (2007)
We report root-mean-square (RMS) wavefront error (WFE) for individual aberrations and cumulative high-order (HO) RMS WFE for the normal human eye as a function of age by decade and pupil diameter in steps from and determine the relationship among HO RMS WFE, mean age for each decade of life, and luminance for physiologic pupil diameters. Subjects included 146 healthy individuals from of age. Ocular aberration was measured on the preferred eye of each subject (for a total of 146 eyes through dilated pupils; computed for 3, 4, 5, 6, and pupils; and described with a tenth-radial-order normalized Zernike expansion. We found that HO RMS WFE increases faster with increasing pupil diameter for any given age and pupil diameter than it does with increasing age alone. A planar function accounts for 99% of the variance in the 3-D space defined by mean log HO RMS WFE, mean age for each decade of life, and pupil diameter. When physiologic pupil diameters are used to estimate HO RMS WFE as a function of luminance and age, at low luminance HO RMS WFE decreases with increasing age. This normative data set details (1) the 3-D relationship between HO RMS WFE and age for fixed pupil diameters and (2) the 3-D relationship among HO RMS WFE, age, and luminance for physiologic pupil diameters.
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Slope, Intercept, and Coefficient of Determination of the Linear Regression Describing How Pupil Diameter Changes as a Function of Age for Five Luminance Levels for 91 Subjectsa
For Six Different Age Groups, Parameters (a and b), and Coefficient of Determination of the Exponential Regression Describing the Relationship among the Mean HO RMS WFE and Any Given Pupil Diameter and the Corresponding Coefficient of Determination
Mean (Years)
a
b
0.0114
0.5331
0.9875
0.0102
0.5623
0.9972
0.0130
0.5559
0.9952
0.0172
0.5249
0.9967
0.0187
0.5311
0.9881
0.0193
0.5735
0.9950
Table 3
Label for Each Age Range, Age Range Forming Each Group, Mean Age, Standard Deviation (SD), and Minimum and Maximum Age
Shows the number of eyes and individuals in each age group.
Table 5
Mean HO RMS WFE (Third–Sixth Radial Order), Standard Deviation, Minimum and Maximum HO RMS WFE, and Number of Eyes Grouped by Age and Pupil Diametera
Age (years)
Pupil Diameter (mm)
HO RMS WFE
HO RMS WFE Minimum
HO RMS WFE Maximum
No. of Eyes
Eyes Not Fully Dilated
20–29
3
0.022
0.109
20
0
30–39
3
0.017
0.099
18
0
40–49
3
0.027
0.107
32
0
50–59
3
0.027
0.145
32
0
60–69
3
0.047
0.118
21
0
70–79
3
0.044
0.172
23
0
20–29
4
0.050
0.205
20
0
30–39
4
0.038
0.188
18
0
40–49
4
0.063
0.215
32
0
50–59
4
0.053
0.292
32
0
60–69
4
0.108
0.240
21
0
70–79
4
0.115
0.322
23
0
20–29
5
0.097
0.353
20
0
30–39
5
0.067
0.287
18
0
40–49
5
0.125
0.382
32
0
50–59
5
0.099
0.544
32
0
60–69
5
0.193
0.451
21
0
70–79
5
0.218
0.549
23
0
20–29
6
0.170
0.550
20
0
30–39
6
0.127
0.426
18
0
40–49
6
0.200
0.654
32
0
50–59
6
0.158
0.923
31
1
60–69
6
0.287
0.799
20
1
70–79
6
0.312
1.125
23
0
20–29
7
0.261
0.687
18
2
30–39
7
0.227
0.718
15
3
40–49
7
0.334
1.107
29
3
50–59
7
0.324
0.952
18
14
60–69
7
0.429
1.113
16
5
70–79
7
0.576
1.555
16
7
Two eyes did not dilate to , and 34 eyes did not dilate to , as indicated in last column.
Table 6
Parameters (a and b) of the Exponential Function Describing the Mean HO RMS WFE for Each Age Group for a Given Pupil Diametera
Pupil Diameter (mm)
Parameter
a
b
3
0.0329
0.0151
0.9683
4
0.0662
0.0148
0.9660
5
0.1109
0.0154
0.9453
6
0.1789
0.0160
0.9359
7
0.2899
0.0157
0.9481
x is the average age of the patients in each decade group as given in Table 3.
Table 7
Mean and Standard deviation (SD) of the RMS WFE is Displayed for Trefoil,a Coma,b Tetrafoil,c Secondary Astigmatism (2nd Astig.),d and Spherical Aberration (Sph. Ab.)e for Each Decade and Pupil Diameter
Age (years)
Pupil Diameter (mm)
RMS WFE Trefoil
RMS WFE Coma
RMS WFE Tetrafoil
RMS WFE 2nd Astig.
RMS WFE Sph. Ab.
20–29
3
30–39
3
40–49
3
50–59
3
60–69
3
70–79
3
20–29
4
30–39
4
40–49
4
50–59
4
60–69
4
70–79
4
20–29
5
30–39
5
40–49
5
50–59
5
60–69
5
70–79
5
20–29
6
30–39
6
40–49
6
50–59
6
60–69
6
70–79
6
20–29
7
30–39
7
40–49
7
50–59
7
60–69
7
70–79
7
. . . . .
Tables (7)
Table 1
Slope, Intercept, and Coefficient of Determination of the Linear Regression Describing How Pupil Diameter Changes as a Function of Age for Five Luminance Levels for 91 Subjectsa
For Six Different Age Groups, Parameters (a and b), and Coefficient of Determination of the Exponential Regression Describing the Relationship among the Mean HO RMS WFE and Any Given Pupil Diameter and the Corresponding Coefficient of Determination
Mean (Years)
a
b
0.0114
0.5331
0.9875
0.0102
0.5623
0.9972
0.0130
0.5559
0.9952
0.0172
0.5249
0.9967
0.0187
0.5311
0.9881
0.0193
0.5735
0.9950
Table 3
Label for Each Age Range, Age Range Forming Each Group, Mean Age, Standard Deviation (SD), and Minimum and Maximum Age
Shows the number of eyes and individuals in each age group.
Table 5
Mean HO RMS WFE (Third–Sixth Radial Order), Standard Deviation, Minimum and Maximum HO RMS WFE, and Number of Eyes Grouped by Age and Pupil Diametera
Age (years)
Pupil Diameter (mm)
HO RMS WFE
HO RMS WFE Minimum
HO RMS WFE Maximum
No. of Eyes
Eyes Not Fully Dilated
20–29
3
0.022
0.109
20
0
30–39
3
0.017
0.099
18
0
40–49
3
0.027
0.107
32
0
50–59
3
0.027
0.145
32
0
60–69
3
0.047
0.118
21
0
70–79
3
0.044
0.172
23
0
20–29
4
0.050
0.205
20
0
30–39
4
0.038
0.188
18
0
40–49
4
0.063
0.215
32
0
50–59
4
0.053
0.292
32
0
60–69
4
0.108
0.240
21
0
70–79
4
0.115
0.322
23
0
20–29
5
0.097
0.353
20
0
30–39
5
0.067
0.287
18
0
40–49
5
0.125
0.382
32
0
50–59
5
0.099
0.544
32
0
60–69
5
0.193
0.451
21
0
70–79
5
0.218
0.549
23
0
20–29
6
0.170
0.550
20
0
30–39
6
0.127
0.426
18
0
40–49
6
0.200
0.654
32
0
50–59
6
0.158
0.923
31
1
60–69
6
0.287
0.799
20
1
70–79
6
0.312
1.125
23
0
20–29
7
0.261
0.687
18
2
30–39
7
0.227
0.718
15
3
40–49
7
0.334
1.107
29
3
50–59
7
0.324
0.952
18
14
60–69
7
0.429
1.113
16
5
70–79
7
0.576
1.555
16
7
Two eyes did not dilate to , and 34 eyes did not dilate to , as indicated in last column.
Table 6
Parameters (a and b) of the Exponential Function Describing the Mean HO RMS WFE for Each Age Group for a Given Pupil Diametera
Pupil Diameter (mm)
Parameter
a
b
3
0.0329
0.0151
0.9683
4
0.0662
0.0148
0.9660
5
0.1109
0.0154
0.9453
6
0.1789
0.0160
0.9359
7
0.2899
0.0157
0.9481
x is the average age of the patients in each decade group as given in Table 3.
Table 7
Mean and Standard deviation (SD) of the RMS WFE is Displayed for Trefoil,a Coma,b Tetrafoil,c Secondary Astigmatism (2nd Astig.),d and Spherical Aberration (Sph. Ab.)e for Each Decade and Pupil Diameter