March 2011
Volume 52, Issue 3
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Visual Psychophysics and Physiological Optics  |   March 2011
Evaluation of the Comparability and Repeatability of Four Wavefront Aberrometers
Author Affiliations & Notes
  • Nienke Visser
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • Tos T. J. M. Berendschot
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • Frenne Verbakel
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • Annelie N. Tan
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • John de Brabander
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • Rudy M. M. A. Nuijts
    From the University Eye Clinic, Maastricht University Medical Centre, Maastricht, The Netherlands.
  • Corresponding author: Rudy M.M.A. Nuijts, University Eye Clinic, Maastricht University Medical Centre, P. Debyelaan 25, 6202 AZ Maastricht, The Netherlands; rudy.nuijts@mumc.nl
Investigative Ophthalmology & Visual Science March 2011, Vol.52, 1302-1311. doi:10.1167/iovs.10-5841
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      Nienke Visser, Tos T. J. M. Berendschot, Frenne Verbakel, Annelie N. Tan, John de Brabander, Rudy M. M. A. Nuijts; Evaluation of the Comparability and Repeatability of Four Wavefront Aberrometers. Invest. Ophthalmol. Vis. Sci. 2011;52(3):1302-1311. doi: 10.1167/iovs.10-5841.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To compare total ocular aberrations and corneal aberrations identified with four different aberrometers and to determine the repeatability and interobserver variability.

Methods.: In this prospective comparative study, 23 healthy subjects underwent bilateral examination with four aberrometers: the Irx3 (Hartmann-Shack; Imagine Eyes, Orsay, France), Keratron (Hartmann-Shack; Optikon, Rome Italy), iTrace (ray-tracing; Tracey Technologies, Houston, TX), and OPD-Scan (Automated Retinoscopy; Nidek, Gamagori, Japan). Six images per eye were obtained. Second-, third- and fourth-order spherical aberrations were exported for 5.0-mm pupils.

Results.: Significant differences in measurements were found for several total ocular aberrations (defocus [2,0], astigmatism [2,2], trefoil [3,−3], trefoil [3,3], and spherical aberration [4,0]) and corneal aberrations (defocus [2,0] and astigmatism [2,2]). The Irx3 showed the highest repeatability in measuring total ocular aberrations, followed by the Keratron, OPD-Scan, and iTrace. The repeatability of the corneal aberration measurements was highest for the iTrace, followed by the Keratron and OPD-Scan. The OPD-Scan showed a lower interobserver variability, compared with the Irx3, Keratron, and iTrace.

Conclusions.: Total ocular and corneal aberrations are not comparable when measured with different aberrometers. Hartmann-Shack aberrometers showed the best repeatability for total ocular aberrations and iTrace for corneal aberrations. It would be worthwhile in the future to evaluate aberrometers in patients with more aberrant eyes.

Wavefront analysis allows for a detailed evaluation of imperfections in the optical system of the eye, caused by the refractive surfaces of the anterior and posterior cornea and the lens. It provides an estimation of the optical quality of the eye that extends beyond the description of spherical and cylindrical refractive errors. Measurement of higher-order aberrations has changed from a laboratory or research application to a clinical application and may be used for example in wavefront-guided excimer laser surgery, lens implantation surgery, and contact lens fitting. 1 4 Wavefront analysis may be performed to design an ideal refractive correction, which corrects not only lower-order aberrations (sphere and cylinder), but also higher-order aberrations. In addition, it may be used to evaluate eyes with abnormal optics due to ageing or corneal disorders, such as keratoconus and pellucid marginal degeneration. 5 However, the success of clinical applications of wavefront analysis depends on the accuracy and reliability of the aberrometers. 
Three different wavefront measuring principles are available to measure aberrations: (1) Hartmann-Shack, (2) Tscherning or ray tracing, and (3) automated retinoscopy. A Hartmann-Shack aberrometer is an outgoing wavefront aberrometer. It measures the shape of the wavefront that is reflected out of the eye from a point source on the fovea. An array of microlenslets is used to subdivide the outgoing wavefront into multiple beams which produce spot images on a video sensor. The displacement of each spot from the corresponding nonaberrated reference position is used to determine the shape of the wavefront. 5,6 A Tscherning, or ray-tracing, aberrometer is an ingoing instrument. It projects a thin laser beam into the eye, parallel to the visual axis and determines the location of the beam on the retina by using a photodetector. Once the position of the first light spot on the retina is determined, the laser beam is moved to a new position, and the location of the second light spot on the retina is determined. Aberrations in the optical system cause a shift in the location of the light spot on the retina. 5,7 The third type, automated retinoscopy, is based on dynamic skiascopy. The retina is scanned with a slit-shaped light beam and the reflected light is captured by an array of rotating photodetectors over a 360° area. The time difference of the reflected light is used to determine the aberrations. 8  
Total ocular aberrations are the result of corneal and internal ocular aberrations. Combined wavefront aberrometry and corneal topography can differentiate between aberrations caused by the anterior cornea or by the internal ocular system. In this study, we compare four different wavefront aberrometers, out of which three are combined with a corneal topographer. The purpose of this study is to compare measurements obtained with four different wavefront aberrometers and to determine the repeatability and interobserver variability. 
Methods
In this prospective comparative study, 23 healthy volunteers were recruited from the Department of Ophthalmology, University Hospital Maastricht. Informed consent was obtained from all subjects after the nature of the experiment had been explained. The study adhered to the tenets of the Declaration of Helsinki. 
None of the subjects had a history of ocular surgery or ocular disease. All subjects were measured bilaterally with four different aberrometers. Per eye, six consecutive good-quality images were obtained: three by an expert and three by a nonexpert. An expert was defined as a person who had performed a minimum of 25 measurements with each aberrometer. Nonexperts were medical students with only basic knowledge of ophthalmology and no previous experience with any of the aberrometers. They received an oral instruction and demonstration of the aberrometers. To ensure good-quality images, every nonexpert was supervised while performing the examinations. 
Natural pupil dilation was obtained in all subjects under mesopic light condition (<1 lux). No extrapolation was used and subjects were excluded if the natural pupil diameter was less than 5 mm (measured with all aberrometers). Head positioning and eye alignment were carefully checked before every measurement. Immediately before each measurement, subjects were instructed to blink and then hold their eyes wide open. 
Aberrometers
The Irx3 (Imagine Eyes, Orsay, France) aberrometer (no corneal topography features) uses the Hartmann-Shack principle to measure aberrations of the whole eye. A light source with a wavelength of 780 nm is used. Accommodation is inhibited by automatically adding a fogging of +0.5 D to the measured sphere power. The Irx3 is described in more detail elsewhere. 9  
The Keratron Onda (Optikon, Rome, Italy) is a combined Hartmann-Shack aberrometer and Placido disc videokeratoscope. For the wavefront analysis, an infrared light beam of 840 nm is used. Before aberrometry was performed, the defocus equivalent of the eye was determined, using the autorefraction function of this device, and subsequently +1.0 D of fogging was applied to inhibit accommodation. The Keratron Onda became commercially available in spring 2010 and has not been studied previously. However, the corneal topographer, which is incorporated in the Keratron Onda, is described elsewhere. 10  
The iTrace (Tracey Technologies, Houston, TX) is a combined ray-tracing aberrometer and Placido disc videokeratoscope. It has a laser with a wavelength of 632 nm. Accommodation is inhibited by allowing the patient to view through the device at a target image at optical infinity. It is described in more detail elsewhere. 11  
The OPD-Scan (Nidek, Gamagori, Japan) aberrometer is a combined automated retinoscopy and Placido disc videokeratoscope. It has an infrared light beam with an 808-nm wavelength. Fogging of +1.6 D is used to inhibit accommodation. The details are available in another publication. 12  
Data Analysis
Aberrations were exported for a 5-mm pupil in the form of Zernike coefficients [Z(x,x)], according to the standards of the Optical Society of America and the American National Standards Institute. 13 The following total ocular and corneal aberrations were exported: oblique astigmatism Z(2,−2), defocus Z(2,0), main axis astigmatism Z(2,2), vertical trefoil Z(3,−3), vertical coma Z(3,−1), horizontal coma Z(3,1), horizontal trefoil Z(3,3), and spherical aberration Z(4,0). 
All data were collected in a database (Excel; Microsoft Office 2003; Redmond, WA) and transferred for data analysis (SPSS for Windows, ver. 16.0, SPSS Inc, Chicago, IL). Data were normally distributed and allowed us to use parametric tests. To determine a relationship between measurements of two devices, we performed bivariate correlations to determine the Pearson's correlation coefficient. The agreement between two devices was studied by using the method described by Bland and Altman. 14 This method computes 95% limits of agreement (LoA), defined as the mean difference ±1.96 · SD. A repeated-measures analysis of variance (ANOVA) with Bonferroni correction was used to compare total ocular aberrations and corneal aberrations between devices and to determine whether these are significantly different. The repeatability of the devices was determined by calculating the standard deviation within each series of six repeated measurements per eye (SDwithin). The interobserver variability of each device was determined by comparing the correlations (Pearson's correlation coefficient) measurements (paired t-test), and repeatability (SDwithin) of measurements obtained by experts and nonexperts. P < 0.05 was considered to be statistically significant. 
Results
Twenty-three subjects (12 male and 11 female) underwent bilateral examinations with the Irx3, Keratron, iTrace, and OPD-Scan aberrometers. The mean age was 25.1 ± 6.0 years (range, 21.8–48.9 years). The total ocular aberrations could not be measured in four (9%) eyes with the Irx3, two (4%) eyes with the Keratron, and five (11%) eyes with the OPD-Scan, due to a minor nystagmus in one eye and continuous measurements of smaller pupil size than 5 mm in remaining eyes. All eyes could be measured with the iTrace. 
Correlation of Measurements
Table 1 shows the pair-wise correlations between measurements obtained with the aberrometers. All four aberrometers showed significant correlations for all total ocular aberrations, with P < 0.001 and Pearson's correlation coefficients (r) ranging from 0.574 to 0.975. 
Table 1.
 
Correlations of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Table 1.
 
Correlations of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Irx3 vs. Keratron Irx3 vs. iTrace Irx3 vs. OPD-Scan Keratron vs. iTrace Keratron vs. OPD-Scan iTrace vs. OPD-Scan
Total Ocular Aberrations
Z(2,−2) 0.960 P < 0.001 0.903 P < 0.001 0.884 P < 0.001 0.903 P < 0.001 0.907 P < 0.001 0.859 P < 0.001
Z(2,0) 0.956 P < 0.001 0.963 P < 0.001 0.984 P < 0.001 0.975 P < 0.001 0.963 P < 0.001 0.965 P < 0.001
Z(2,2) 0.959 P < 0.001 0.911 P < 0.001 0.936 P < 0.001 0.927 P < 0.001 0.932 P < 0.001 0.902 P < 0.001
Z(3,−3) 0.863 P < 0.001 0.869 P < 0.001 0.859 P < 0.001 0.877 P < 0.001 0.883 P < 0.001 0.865 P < 0.001
Z(3,−1) 0.767 P < 0.001 0.772 P < 0.001 0.864 P < 0.001 0.747 P < 0.001 0.759 P < 0.001 0.773 P < 0.001
Z(3,1) 0.944 P < 0.001 0.900 P < 0.001 0.692 P < 0.001 0.909 P < 0.001 0.640 P < 0.001 0.619 P < 0.001
Z(3,3) 0.905 P < 0.001 0.749 P < 0.001 0.773 P < 0.001 0.728 P < 0.001 0.771 P < 0.001 0.574 P < 0.001
Z(4,0) 0.892 P < 0.001 0.897 P < 0.001 0.890 P < 0.001 0.920 P < 0.001 0.906 P < 0.001 0.916 P < 0.001
Corneal Aberrations
Z(2,−2) 0.893 P < 0.001 0.729 P < 0.001 0.776 P < 0.001
Z(2,0) 0.639 P < 0.001 0.216 P = 0.164* 0.373 P = 0.013
Z(2,2) 0.961 P < 0.001 0.719 P < 0.001 0.728 P < 0.001
Z(3,−3) 0.800 P < 0.001 0.281 P = 0.068* 0.309 P = 0.044
Z(3,−1) 0.592 P < 0.001 0.361 P = 0.017 0.347 P = 0.023
Z(3,1) 0.742 P < 0.001 0.701 P < 0.001 0.747 P < 0.001
Z(3,3) 0.788 P < 0.001 0.030 P = 0.848* 0.003 P = 0.986*
Z(4,0) 0.619 P < 0.001 0.246 P = 0.246* 0.337 P = 0.027
Measurements of corneal aberrations obtained with the Keratron and iTrace correlated significantly (P < 0.001) with Pearson's correlation coefficients ranging from 0.592 to 0.961. Measurements between the Keratron and OPD-Scan did not correlate for the defocus (r = 0.216; P = 0.164), trefoil Z(3,−3) (r = 0.281, P = 0.068), trefoil Z(3,3) (r = 0.030; P = 0.848), and spherical aberration (r = 0.246; P = 0.246). In addition, the Pearson's correlation coefficient of the significant correlations ranged from 0.361 to 0.729. Corneal aberrations obtained with the iTrace and OPD did not correlate for the trefoil Z(3,3) Zernike mode (r = 0.003, P = 0.986). Other aberrations showed correlations with Pearson's correlation coefficients ranging from 0.309 to 0.776. 
Agreement of Measurements
The 95% LoA and the span of the 95% LoA of the pair-wise comparisons of the four aberrometers are shown in Table 2. For the total ocular aberrations, the 95% LoA were relatively wide for the defocus Z(2,0) aberration in the comparisons of Irx3 versus Keratron (span 3.61 μm), Irx3 versus OPD-Scan (span 1.97 μm), Keratron versus iTrace (span 2.65 μm), Keratron versus OPD-Scan (span 1.57 μm), and iTrace versus OPD-Scan (span 2.32 μm). All remaining comparisons had 95% LoA with a span of less than 1.0 μm. 
Table 2.
 
Limits of Agreement of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Table 2.
 
Limits of Agreement of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Irx3 vs. Keratron Irx3 vs. iTrace Irx3 vs. OPD-Scan Keratron vs. iTrace Keratron vs. OPD-Scan iTrace vs. OPD-Scan
95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span
Total Ocular Abberations
Z(2,−2) −0.18, 0.29 0.47 −0.36, 0.47 0.83 −0.35, 0.47 0.82 −0.25, 0.46 0.71 −0.33, 0.43 0.75 −0.37, 0.58 0.95
Z(2,0) −1.99, 1.62 3.61 −0.06, 0.10 0.16 −0.85, 1.12 1.97 −1.37, 1.28 2.65 −0.15, 1.42 1.57 −0.78, 1.54 2.32
Z(2,2) −0.26, 0.40 0.66 −0.40, 0.56 0.95 −0.43, 0.56 0.99 −0.25, 0.46 0.71 −0.35, 0.43 0.78 −0.37, 0.55 0.93
Z(3,−3) −0.13, 0.14 0.27 −0.12, 0.15 0.28 −0.21, 0.22 0.43 −0.13, 0.15 0.28 −0.20, 0.20 0.40 −0.20, 0.20 0.39
Z(3,−1) −0.14, 0.19 0.33 −0.14, 0.20 0.34 −0.11, 0.13 0.24 −0.15, 0.21 0.36 −0.13, 0.19 0.32 −0.15, 0.19 0.34
Z(3,1) −0.04, 0.09 0.13 −0.05, 0.12 0.18 −0.12, 0.20 0.32 −0.09, 0.12 0.20 −0.15, 0.21 0.35 −0.17, 0.23 0.40
Z(3,3) −0.03, 0.09 0.12 −0.09, 0.16 0.25 −0.07, 0.16 0.23 −0.10, 0.17 0.27 −0.10, 0.16 0.25 −0.13, 0.22 0.35
Z(4,0) −0.03, 0.09 0.12 −0.06, 0.10 0.16 −0.02, 0.09 0.12 −0.03, 0.09 0.09 −0.05, 0.08 0.13 −0.02, 0.09 0.11
Corneal Aberrations
Z(2,−2) −0.28, 0.40 0.68 −0.55, 0.73 1.28 −0.53, 0.67 1.19
Z(2,0) 0.05, 0.51 0.56 −1.10, 1.30 2.40 −0.66, 1.23 1.88
Z(2,2) −0.29, 0.40 0.69 −0.63, 1.21 1.84 −0.65, 1.19 1.84
Z(3,−3) −0.16, 0.19 0.35 −0.59, 0.81 1.41 −0.59, 0.81 1.39
Z(3,−1) −0.16, 0.28 0.44 −0.66, 0.92 1.58 −0.65, 0.92 1.57
Z(3,1) −0.28, 0.44 0.72 −0.31, 0.42 0.73 −0.20, 0.27 0.48
Z(3,3) −0.07, 0.13 0.20 −0.46, 0.70 1.16 −0.44, 0.68 1.13
Z(4,0) −0.13, 0.14 0.27 −0.29, 0.48 0.76 −0.31, 0.45 0.76
For the corneal aberrations, the 95% LoA were relatively wide in the comparison of Keratron versus OPD-Scan (span > 1.0 μm for Z(2,−2), Z(2,0), Z2,2), Z(3,−3), Z(3,−1), and Z(3,3) and in the comparison of iTrace versus OPD-Scan: span >1.0 μm Z(2,−2), Z(2,0), Z2,2), Z(3,−3), Z(3,−1) and Z(3,3). 
Comparison of Measurements
The results of the comparison of the four aberrometers are shown in Table 3. The total ocular aberrations obtained with the four aberrometers showed significant differences for defocus Z(2,0) (P < 0.001), trefoil Z(3,−3) (P < 0.001), and spherical aberration Z(4,0) (P < 0.001). In addition, minor differences between the aberrometers were found for astigmatism Z(2,2) (P = 0.049) and trefoil Z(3,3) (P = 0.007). No significant differences were found for astigmatism Z(2,−2), coma Z(3,−1), and coma Z(3,1). When we use the different defocus Z(2,0) measurements to calculate the corresponding spherical error, this corresponds to a spherical error of −0.89, −1.91, −1.29, and −1.02 D for the Irx3, Keratron, iTrace, and OPD-Scan, respectively. 
Table 3.
 
Comparison of the Total Ocular Aberrations and Corneal Aberrations Obtained with the Four Aberrometers
Table 3.
 
Comparison of the Total Ocular Aberrations and Corneal Aberrations Obtained with the Four Aberrometers
Zernike Coefficient
Astigmatism Z(2,−2) Defocus Z(2,0) Astigmatism Z(2,2) Trefoil Z(3,−3) Coma Z(3,−1) Coma Z(3,1) Trefoil Z(3,3) Spherical Z(4,0)
Total Ocular Aberrations
Irx3 (I) −0.023 ± 0.341 0.802 ± 1.873 −0.073 ± 0.461 −0.020 ± 0.081 −0.027 ± 0.087 0.003 ± 0.089 0.012 ± 0.068 0.063 ± 0.068
Keratron (K) −0.030 ± 0.350 1.724 ± 1.790 −0.082 ± 0.397 −0.046 ± 0.095 −0.013 ± 0.097 −0.013 ± 0.089 −0.014 ± 0.059 0.034 ± 0.064
iTrace (T) 0.024 ± 0.387 1.160 ± 1.911 −0.025 ± 0.430 −0.026 ± 0.107 −0.027 ± 0.105 −0.022 ± 0.098 −0.004 ± 0.080 0.064 ± 0.076
OPD-Scan (O) 0.012 ± 0.303 0.916 ± 1.674 −0.016 ± 0.335 −0.098 ± 0.133 −0.008 ± 0.083 −0.003 ± 0.078 −0.022 ± 0.084 0.023 ± 0.067
P P = 0.122 P < 0.001 P = 0.027 P < 0.001 P = 0.137 P = 0.076 P = 0.007 P < 0.001
I vs. T; P < 0.001 K vs. O; P = 0.049 I vs. K; P = 0.010 I vs. K; P < 0.001 I vs. K; P < 0.001
I vs. K; P < 0.001 I vs. O; P < 0.001 I vs. O; P = 0.003 I vs. O; P < 0.001
K vs. T; P < 0.001 K vs. O; P < 0.001 K vs. T; P < 0.001
K vs. O; P < 0.001 T vs. O; P < 0.001 T vs. O; P < 0.001
Corneal Aberrations
Keratron (K) −0.009 ± 0.295 0.207 ± 0.08 −0.295 ± 0.460 −0.032 ± 0.106 −0.028 ± 0.113 −0.024 ± 0.201 −0.003 ± 0.071 0.157 ± 0.059
iTrace (T) −0.029 ± 0.281 0.597 ± 0.21 −0.327 ± 0.399 −0.039 ± 0.072 −0.009 ± 0.089 −0.014 ± 0.094 0.009 ± 0.049 0.115 ± 0.041
OPD-Scan (O) 0.056 ± 0.358 0.441 ± 0.45 −0.470 ± 0.586 −0.072 ± 0.285 0.026 ± 0.332 0.005 ± 0.139 −0.002 ± 0.226 0.131 ± 0.160
P P = 0.055 P < 0.001 P = 0.011 P = 0.393 P = 0.341 P = 0.316 P = 0.761 P = 0.142
K vs. T; P < 0.001 K vs. O; P = 0.023
K vs. O; P = 0.003
Most corneal aberrations obtained with the iTrace, Keratron, and OPD-Scan were not significantly different, except for some second order aberrations. Defocus Z(2,0) measurements obtained with the Keratron were significantly lower compared to the iTrace (P < 0.001) and OPD-Scan (P = 0.003). Astigmatism Z(2,2) measurements obtained with the Keratron and OPD-Scan were significantly different (P = 0.023). When we use the different defocus Z(2,0) measurements to calculate the corresponding spherical error, this corresponds to a spherical error of −0.23, −0.66, and −0.49 D for the Keratron, iTrace, and OPD-Scan, respectively. 
Repeatability of the Aberrometers
Figure 1 shows the repeatability of the aberrometers. A smaller SDwithin indicates a higher repeatability. The Irx3 shows the highest repeatability for all total ocular aberrations. The Keratron shows a significantly lower repeatability, compared to the Irx3, for defocus Z(2,0) (P < 0.001). The iTrace shows a significantly lower repeatability, compared to the Irx3, for the following Zernike coefficients: astigmatism Z(2,−2) (P = 0.003), defocus Z(2,0) (P = 0.009), coma Z(3,−1) (P = 0.002), coma Z(3,1) (P < 0.001), trefoil Z(3,3) (P = 0.003) and spherical aberration Z(4,0) (P = 0.015). The OPD-Scan has a significantly lower repeatability, compared to the Irx3, for trefoil Z(3,−3) (P = 0.012), coma Z(3,−1) (P < 0.001), and trefoil Z(3,3) (P < 0.001). 
Figure 1.
 
Repeatability of the Irx3, Keratron, iTrace, and OPD-Scan for total ocular aberrations (A) and corneal aberrations (B). A smaller mean SD within six measurements per eye (SDwithin) indicates better repeatability. Error bars, ±SD; *significant differences between two aberrometers (P < 0.05). Results are shown for 5-mm pupils.
Figure 1.
 
Repeatability of the Irx3, Keratron, iTrace, and OPD-Scan for total ocular aberrations (A) and corneal aberrations (B). A smaller mean SD within six measurements per eye (SDwithin) indicates better repeatability. Error bars, ±SD; *significant differences between two aberrometers (P < 0.05). Results are shown for 5-mm pupils.
The repeatability of the corneal aberrations is shown in Figure 1B. The iTrace shows the highest repeatability for all Zernike coefficients. The Keratron has a significantly lower repeatability, compared to the iTrace, for astigmatism Z(2,−2) (P = 0.001), astigmatism Z(2,2) (P = 0.004), coma Z(3,−1) (P < 0.001), coma Z(3,1) (P = 0.011), and spherical aberration Z(4,0) (P < 0.001). As indicated in Figure 1B, the SDwithin of all corneal aberration measurements obtained with the OPD-Scan was much higher than measurements obtained with the iTrace and Keratron, indicating a lower repeatability. However, due to the large variability of the measurements obtained with the OPD-Scan (indicated by error bars in Fig. 1B), this difference did not reach statistical significance. 
Interobserver Variability
To determine whether operating experience influences measurements, we compared the differences in measurements and the SDwithin of measurement obtained by experts and nonexperts. The results are shown in Table 4. For the Irx3, Keratron, and iTrace, we found high correlations, no significant differences, and a high repeatability of measurements obtained by experts and nonexperts. However, for the OPD-Scan we found a significantly lower repeatability of total ocular aberration measurements, if measurements were obtained by a nonexpert, compared to an expert: trefoil Z(3,−3) (0.040 ± 0.020 μm versus 0.031 ± 0.023 μm; P = 0.007); coma Z(3,−1) (0.039 ± 0.020 μm versus 0.018 ± 0.014 μm; P < 0.001); coma Z(3,1) (0.018 ± 0.010 μm versus 0.013 ± 0.010 μm P < 0.001); and trefoil Z(3,3) (0.041 ± 0.022 μm versus 0.028 ± 0.021 μm; P < 0.001). No differences in interobserver variability were found when measuring corneal aberrations. 
Table 4.
 
Interobserver Variability: Differences in Measurements Obtained by Experts and Nonexperts
Table 4.
 
Interobserver Variability: Differences in Measurements Obtained by Experts and Nonexperts
Zernike Coefficients
2, −2 2, 0 2, 2 3, −3 3, −1 3, 1 3, 3 4, 0
Irx3
TOA Correlation (PCC; P) 0.968; P < 0.001 0.994; P < 0.001 0.998; P < 0.001 0.962; P < 0.001 0.962; P < 0.001 0.963; P < 0.001 0.927; P < 0.001 0.960; P < 0.001
Difference in measurement (mean ± SD) 0.008 ± 0.052 −0.025 ± 0.194 0.014 ± 0.045 0.001 ± 0.022 −0.004 ± 0.030 0.001 ± 0.024 −0.002 ± 0.027 0.002 ± 0.016
Expert SDwithin ± SD 0.033 ± 0.020 0.126 ± 0.141 0.050 ± 0.020 0.023 ± 0.015 0.022 ± 0.013 0.018 ± 0.011 0.020 ± 0.013 0.013 ± 0.008
Nonexpert SDwithin ± SD 0.036 ± 0.020 0.097 ± 0.079 0.047 ± 0.025 0.023 ± 0.012 0.020 ± 0.010 0.021 ± 0.013 0.025 ± 0.015 0.014 ± 0.009
Keratron
TOA Correlation (PCC; P) 0.985; P < 0.001 0.981; P < 0.001 0.940; P < 0.001 0.752; P < 0.001 0.650; P < 0.001 0.958; P < 0.001 0.818; P < 0.001 0.833; P < 0.001
Difference in measurement (mean ± SD) 0.013 ± 0.059 0.058 ± 0.362 0.028 ± 0.136 0.005 ± 0.075 −0.011 ± 0.097 0.006 ± 0.026 −0.001 ± 0.038 −0.002 ± 0.039
Expert SDwithin ± SD 0.030 ± 0.019 0.187 ± 0.196 0.040 ± 0.023 0.021 ± 0.022 0.027 ± 0.022 0.021 ± 0.033 0.021 ± 0.021 0.021 ± 0.045
Nonexpert SDwithin ± SD 0.039 ± 0.041 0.211 ± 0.204 0.047 ± 0.041 0.023 ± 0.023 0.025 ± 0.027 0.019 ± 0.016 0.020 ± 0.028 0.017 ± 0.021
CA Correlation (PCC; P) 0.880; P < 0.001 0.473; P < 0.001 0.930; P < 0.001 0.630; P < 0.001 0.804; P < 0.001 0.744; P < 0.001 0.494; P < 0.001 0.505; P < 0.001
Difference in measurement (mean ± SD) 0.031 ± 0.153 0.011 ± 0.095 0.048 ± 0.195 −0.005 ± 0.107 0.002 ± 0.075 −0.024 ± 0.165 0.015 ± 0.084 0.009 ± 0.069
Expert SDwithin ± SD 0.073 ± 0.97 0.039 ± 0.053 0.088 ± 0.138 0.043 ± 0.065 0.073 ± 0.104 0.050 ± 0.078 0.034 ± 0.050 0.030 ± 0.042
Nonexpert SDwithin ± SD 0.116 ± 0.180 0.059 ± 0.076 0.126 ± 0.214 0.059 ± 0.158 0.064 ± 0.072 0.077 ± 0.132 0.041 ± 0.108 0.043 ± 0.055
iTrace
TOA Correlation (PCC; P) 0.834; P < 0.001 0.989; P < 0.001 0.881; P < 0.001 0.910; P < 0.001 0.921; P < 0.001 0.813; P < 0.001 0.856; P < 0.001 0.843; P < 0.001
Difference in measurement (mean ± SD) 0.033 ± 0.102 0.042 ± 0.270 0.025 ± 0.125 −0.011 ± 0.036 0.004 ± 0.045 −0.012 ± 0.049 0.014 ± 0.040* 0.006 ± 0.042
Expert SDwithin ± SD 0.064 ± 0.064 0.164 ± 0.232 0.074 ± 0.044 0.035 ± 0.024 0.038 ± 0.024 0.037 ± 0.026 0.032 ± 0.016 0.023 ± 0.018
Nonexpert SDwithin ± SD 0.057 ± 0.040 0.131 ± 0.119 0.067 ± 0.043 0.036 ± 0.027 0.037 ± 0.025 0.042 ± 0.038 0.027 ± 0.019 0.026 ± 0.20
CA Correlation (PCC; P) 0.828; P < 0.001 0.688; P < 0.001 0.946; P < 0.001 0.765; P < 0.001 0.878; P < 0.001 0.694; P < 0.001 0.872; P < 0.001 0.738; P < 0.001
Difference in measurement (mean ± SD) 0.014 ± 0.090 −0.023 ± 0.086 −0.001 ± 0.077 −0.003 ± 0.039 0.006 ± 0.052 −0.009 ± 0.045 0.006 ± 0.027 0.001 ± 0.025
Expert SDwithin ± SD 0.090 ± 0.064 0.059 ± 0.038 0.184 ± 0.096 0.046 ± 0.031 0.042 ± 0.026 0.049 ± 0.039 0.038 ± 0.029 0.054 ± 0.026
Nonexpert SDwithin ± SD 0.073 ± 0.055 0.073 ± 0.131 0.200 ± 0.093 0.040 ± 0.033 0.045 ± 0.039 0.038 ± 0.028 0.037 ± 0.027 0.059 ± 0.037
OPD-Scan
TOA Correlation (PCC; P) 0.890; P < 0.001 0.958; P < 0.001 0.965; P < 0.001 0.934; P < 0.001 0.928; P < 0.001 0.958; P < 0.001 0.762; P < 0.001 0.961; P < 0.001
Difference in measurement (mean ± SD) −0.024 ± 0.146 0.165 ± 0.484 −0.025 ± 0.089 −0.013 ± 0.050 −0.007 ± 0.034 −0.008 ± 0.022 −0.013 ± .062 −0.002 ± 0.018
Expert SDwithin ± SD 0.078 ± 0.271 0.097 ± 0.191 0.061 ± 0.156 0.031 ± 0.023 0.018 ± 0.014 0.013 ± 0.010 0.028 ± 0.021 0.012 ± 0.010
Nonexpert SDwithin ± SD 0.075 ± 0.185 0.164 ± 0.278 0.061 ± 0.104 0.040 ± 0.020* 0.039 ± 0.020* 0.018 ± 0.010* 0.041 ± 0.022* 0.014 ± 0.007
CA Correlation (PCC; P) 0.501; P = 0.001 0.415; P = 0.005 0.481; P = 0.001 0.182; P = 236 0.228; P = 0.137 0.626; P < 0.001 −0.079; P = 0.610 0.220; P = 0.152
Difference in measurement (mean ± SD) 0.086 ± 0.440 0.046 ± 0.728 −0.149 ± 0.776 −0.049 ± 0.538 0.061 ± 0.614 0.011 ± 0.146 0.029 ± 0.458 0.024 ± 0.292
Expert SDwithin ± SD 0.036 ± 0.024 0.122 ± 0.110 0.048 ± 0.058 0.023 ± 0.032 0.031 ± 0.049 0.023 ± 0.023 0.027 ± 0.026 0.019 ± 0.028
Nonexpert SDwithin ± SD 0.186 ± 0.640 0.331 ± 0.983 0.299 ± 1.233 0.205 ± 0.894 0.208 ± 0.949 0.054 ± 0.184 0.180 ± 0.685 0.110 ± 0.463
Discussion
Effective correction of higher-order aberrations is only possible if high levels of measurement accuracy are achieved. In this study we examined the correlations, agreement, and comparison of measurements obtained with the Irx3 and Keratron (both Hartmann-Shack aberrometers), the iTrace (a ray-tracing aberrometer), and the OPD-Scan (automated retinoscopy). In addition, we determined the repeatability and interobserver variability of these aberrometers. To perform an effective correction of higher-order aberrations, it is also necessary to discriminate between aberrations caused by the anterior cornea or the internal ocular system, such as the lens. The Keratron, iTrace, and OPD-Scan are combined wavefront aberrometers and corneal topographers and can therefore make this discrimination. If wavefront aberrometry and corneal topography are performed separately using different devices, identical head positioning and realignment of the eye may be difficult. By combining these measurements into one device and performing measurements within a short time, potential errors are minimized. However, the Keratron, iTrace, and OPD-Scan still require some form of realignment when switching from the aberrometry to the topography mode. This will not be necessary in the Keratron version available since April 2010, but was not available at the time of this study. 
In the first part of this study we determined the correlations and agreement of total ocular aberrations and corneal aberrations obtained with the the Irx3, Keratron, iTrace, and OPD, and determined whether these values were significantly different. Even though the total ocular aberrations obtained with the different aberrometers showed good correlation, the agreement of all aberrometers for the defocus aberration was relatively low. In addition, significant differences between aberrometers were found in Zernike values. The defocus, trefoil, and spherical aberration measurements were significantly different between most aberrometers. If we use the defocus measurements of the total ocular aberrations to calculate the corresponding spherical error, the spherical errors range from −0.89 (Irx3) to −1.91 D (Keratron). In our opinion, this is a clinically significant difference. The corneal aberrations obtained with the OPD-Scan correlated less well with the iTrace and Keratron and the agreement of these aberrometers was relatively low. In addition, significant differences were found in defocus measurements. Is we use these defocus measurements of the corneal aberrations to calculate the corresponding sphere, the sphere ranges from −0.23 D (Keratron) to −0.66 D (iTrace). The difference is not clinically relevant in our opinion. The comparability of the higher order corneal aberration is good. Since no golden standard is available to measure wavefront aberrations, it is unclear which device better reflects the patients' ocular aberrations. As far as we are aware, only one previous study compared the same aberrometers that we have used in this study. Won et al. 15 compared the iTrace and OPD-Scan and also found significant differences in total ocular spherical aberrations. In addition, the internal aberrations (total ocular minus corneal aberrations) were significantly different for the coma and trefoil Zernike terms. Several other studies have compared wavefront aberrometers, but these studies have used other aberrometer types, which were mostly not combined with a corneal topographer. All these studies show slight differences in aberrometry measurements between the devices. 16 19 For example, Rozema et al. 18 compared the measurements obtained by the OPD-Scan to five other (Hartmann-Shack, ray tracing or automated retinoscopy) aberrometers and found significant differences between the devices when measuring astigmatism, defocus, and coma. 
The monochromatic wavelengths used by the different aberrometers in our study varied from red to infrared (iTrace, 650 nm; Irx3, 780 nm; OPD-Scan, 808 nm; and Keratron, 840 nm). A previous study indicated that this might cause differences in measurements. 17 However, since our data did not show a clear trend between the lowest and highest wavelength aberrometers, we do not believe this difference in wavelength causes differences in measurements. 
Differences in measurements could be explained by errors in converting measurements to smaller pupil sizes. Dai and Schwiegerling 20,21 have both published algorithms for converting Zernike expansion coefficients from one pupil size to another. For all devices, we calculated the aberrations for a 4-mm pupil from the aberrations of a 5-mm pupil using these algorithms. The values were than compared to the values provided by the aberrometers for a 4-mm pupil. The two approaches yielded the same results for the Irx3, Keratron, and iTrace, as expected. However, for the OPD-Scan the results differed significantly. We do not have an explanation for the disparity. We could also not get feedback on this question from Nidek. The issue has been discussed in a study by Rozema et al. 12 The table in the paper by Schwiegerling 21 has an error in the formula for calculating the first-order Zernike coefficients. We therefore added Table 5 to this article, showing the correct conversions up to order eight. 
Table 5.
 
Formulas for Calculating the Zernike Expansion Coefficients for Smaller Pupil Sizes
Table 5.
 
Formulas for Calculating the Zernike Expansion Coefficients for Smaller Pupil Sizes
n m New Expansion Coefficient
0 0 b 00 = a 00 − a 20 3 ( 1 − r 2 2 r 1 2 ) + a 40 5 ( 1 − 3 r 2 2 r 1 2 + 2 r 2 4 r 1 4 ) − a 60 7 ( 1 − 6 r 2 2 r 1 2 + 10 r 2 4 r 1 4 − 5 r 2 6 r 1 6 ) + a 80 3 ( 1 − 10 r 2 2 r 1 2 + 30 r 2 4 r 1 4 − 35 r 2 6 r 1 6 + 14 r 2 8 r 1 8 )
1 −1, 1 b 1 m = r 2 r 1 [ a 1 m − a 3 m 8 ( 1 − r 2 2 r 1 2 ) + a 5 m 3 ( 3 − 8 r 2 2 r 1 2 + 5 r 2 4 r 1 4 ) − a 7 m 4 ( 2 − 10 r 2 2 r 1 2 + 15 r 2 4 r 1 4 − 7 r 2 6 r 1 6 ) ]
2 −2, 0, 2 b 2 m = r 2 2 r 1 2 [ a 2 m − a 4 m 15 ( 1 − r 2 2 r 1 2 ) + a 6 m 21 ( 2 − 5 r 2 2 r 1 2 + 3 r 2 4 r 1 4 ) − a 8 m 3 ( 10 − 45 r 2 2 r 1 + 63 r 2 4 r 1 4 − 28 r 2 6 r 1 6 ) ]
3 −3, −1, 1, 3 b 3 m = r 2 3 r 1 3 [ a 3 m − a 5 m 2 6 ( 1 − r 2 2 r 1 2 ) + a 7 m 8 ( 5 − 12 r 2 2 r 1 2 + 7 r 2 4 r 1 4 ) ]
4 −4, −2, 0, 2, 4 b 4 m = r 2 4 r 1 4 [ a 4 m − a 6 m 35 ( 1 − r 2 2 r 1 2 ) + a 8 m 5 ( 9 − 21 r 2 2 r 1 2 + 12 r 2 4 r 1 4 ) ]
5 −5, −3, −1, 1, 3, 5 b 5 m = r 2 5 r 1 5 [ a 5 m − a 7 m 4 3 ( 1 − r 2 2 r 1 2 ) ]
6 −6, −4, −2, 0, 2, 4, 6 b 6 m = r 2 6 r 1 6 [ a 6 m − a 8 m 3 7 ( 1 − r 2 2 r 1 2 ) ]
7 −7, −5, −3, −1, 1, 3, 5, 7 b 7 m = r 2 7 r 1 7 a 7 m
8 −8, −6, −4, −2, 0, 2, 4, 6, 8 b 8 m = r 2 8 r 1 8 a 8 m
To study the repeatability of the aberrometers, we computed the SD within each series of six repeated measurements per eye. The repeatability of aberrometers may be influenced by microfluctuations in accommodation, instability of the tear film, and small eye movements. 22 To minimize variations in measurement conditions we took the repeated measurements in a short period and instructed subjects to blink immediately before each measurement. In our study, the repeatability varied considerably between the different aberrometers. We found that the Irx3 had the highest repeatability in measuring total ocular aberrations, followed by the Keratron, OPD-Scan, and iTrace. In measuring corneal aberrations, the iTrace was found to have the highest repeatability and the OPD-Scan the lowest. The high repeatability of the Irx3 in measuring total ocular aberrations is in accordance with a study that showed only slight variations in repeated measurements that were not considered to be clinically significant. 9 Studies using other Hartmann-Shack aberrometers generally show a high repeatability, with some variations in aberration measurements higher than the fourth order. 19,23,24 No previous study has evaluated the Keratron aberrometer. Repeated measurements obtained with the iTrace in this study showed substantial variation in total ocular aberrations, but an excellent repeatability of corneal aberrations. Win-Hall and Glasser 11 determined the repeatability of the iTrace for total ocular aberrations and found only minor changes during repeatability testing. However, their study focused only on refraction measurements and not on higher-order aberration measurements. In our study, the repeatability of the OPD-Scan in measuring total ocular aberrations was comparable to the other aberrometers, but the repeatability in measuring corneal aberrations was low, with large variations. Previous studies have shown moderate to good results for the OPD-Scan when measuring both total ocular and corneal aberrations. 16,25,26  
We determined the interobserver variability for the aberrometers by comparing measurements obtained by experts and nonexperts. We found good interobserver variability for the total ocular and corneal aberration measurements obtained with the Irx3, Keratron, and iTrace. However, the interobserver variability for the OPD-Scan was not satisfactory, since significant differences in repeatability were found when measuring total ocular aberrations. We believe this may have been caused by technical properties of the OPD, since it was generally easy for nonexperts to perform measurements, but difficult to evaluate if the quality of measurements was satisfactory. 
The iTrace was able to measure total ocular aberrations in all eyes in our study, whereas the Irx3, Keratron, and OPD-Scan could not measure 9%, 4%, and 11% of all eyes, respectively, mainly because of a measured pupil size of less than 5 mm. However, one eye with a minor nystagmus could be measured only by the iTrace and not by the Irx3, Keratron, and OPD-Scan. The Hartmann-shack method uses a lenslet array to sample a large number of points across the pupil. However, Hartmann-shack aberrometry has been shown to be more difficult in highly aberrant eyes due to the crossover of spots from a lenslet to a neighboring lenslet with increasing aberrations. 19 The ray-tracing method uses sequential measurements and may therefore be more suitable to measure highly aberrant eyes. One study showed 14% of normal eyes and 50% of post–laser in situ keratomileusis eyes could not be measured with the Hartmann-Shack aberrometer, whereas the ray-tracing device was able to measure all eyes. 19 Therefore, a limitation of the present study is that only young, healthy subjects were examined. Our study population consisted of subjects with a mean age of 25.1 ± 6 years, ranging from 21.8 to 48.9 years old. In addition, only healthy eyes with no ocular disease or previous ocular surgery were included. It would be worthwhile to compare different wavefront aberrometers in, for example, post–refractive surgery patients, patients with intraocular lenses, and patients with corneal disorders such as keratoconus. 
Wavefront aberrations are pupil size-dependent and generally increase with increasing pupil diameter. Older aberrometer types generally used visible light to measure aberrations and required pupil dilation to avoid reflex pupil constriction. However, all aberrometers tested in this study use light wavelengths in the infrared spectrum and do not require pupil dilation. In addition, the application of mydriatic agents may cause differences in wavefront analysis. 27,28 Apart from pupil size, the location of the pupil center is also an important factor in wavefront analysis, because it may serve as a landmark for surgical correction of wavefront aberrations. Pharmacologic pupil dilation may erroneously induce a shift in the location of the pupil center, whereas natural pupil dilation resulted in minor changes in the location of the pupil center compared with the pupil center's location in photopic conditions. 29 We therefore performed the wavefront analysis with natural pupil dilation in mesopic light conditions. 
Wavefront aberrations change considerably with accommodation due to the shape changes of the crystalline lens. Aside from changes in lower-order aberrations with accommodation, the most change in higher-order aberrations is noticeable in the spherical aberration, which decreases and may even become negative in young adults. 30 32 It is therefore necessary to eliminate accommodation during measurements. Eliminating accommodation by using cycloplegic agents is not preferable because this has been shown to significantly alter wavefront aberrations. 27,28 The aberrometers we have tested in our study use different methods to prevent accommodation. The Irx3, Keratron, and OPD-Scan use a fogging method that places the target out of focus, so that accommodation will not help one to attain a sharp image. The iTrace aberrometer allows the patient to view through the device at a target image at optical infinity. In our study, we found significant differences between the devices in spherical aberration, the indicator of accommodation. Spherical aberration measurements obtained with the Keratron and OPD-Scan were significantly lower than those obtained with the Irx3 and iTrace. Hence, it is unclear whether the fogging method (Irx3, Keratron, and OPD-Scan) or the method used by the iTrace is most effective in inhibiting accommodation. Even though pharmacologic agents alter wavefront aberrations and should preferably not be used in the clinic, an option in future studies comparing different aberrometers is to eliminate accommodation with cycloplegic agents. This approach would eliminate the influence of the different methods on the inhibition of accommodation and would allow for a more reliable comparison, without the possible influence of accommodation on measurements. 
In summary, combined wavefront aberrometry and corneal topography allow discrimination between aberrations caused by the anterior cornea or by the internal ocular system. We found significant differences in total ocular and corneal aberration measurements obtained with the Irx3, Keratron, iTrace, and OPD-Scan in measuring eyes of healthy volunteers. Hartmann-Shack aberrometers showed the best repeatability for total ocular aberrations and iTrace for corneal aberrations. It would be worthwhile in the future to perform a similar evaluation of aberrometers in more aberrant eyes. 
Footnotes
 Disclosure: N. Visser, None; T.T.J.M. Berendschot, None; F. Verbakel, None; A.N. Tan, None; J. de Brabander, R.M.M.A. Nuijts, None
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Figure 1.
 
Repeatability of the Irx3, Keratron, iTrace, and OPD-Scan for total ocular aberrations (A) and corneal aberrations (B). A smaller mean SD within six measurements per eye (SDwithin) indicates better repeatability. Error bars, ±SD; *significant differences between two aberrometers (P < 0.05). Results are shown for 5-mm pupils.
Figure 1.
 
Repeatability of the Irx3, Keratron, iTrace, and OPD-Scan for total ocular aberrations (A) and corneal aberrations (B). A smaller mean SD within six measurements per eye (SDwithin) indicates better repeatability. Error bars, ±SD; *significant differences between two aberrometers (P < 0.05). Results are shown for 5-mm pupils.
Table 1.
 
Correlations of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Table 1.
 
Correlations of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Irx3 vs. Keratron Irx3 vs. iTrace Irx3 vs. OPD-Scan Keratron vs. iTrace Keratron vs. OPD-Scan iTrace vs. OPD-Scan
Total Ocular Aberrations
Z(2,−2) 0.960 P < 0.001 0.903 P < 0.001 0.884 P < 0.001 0.903 P < 0.001 0.907 P < 0.001 0.859 P < 0.001
Z(2,0) 0.956 P < 0.001 0.963 P < 0.001 0.984 P < 0.001 0.975 P < 0.001 0.963 P < 0.001 0.965 P < 0.001
Z(2,2) 0.959 P < 0.001 0.911 P < 0.001 0.936 P < 0.001 0.927 P < 0.001 0.932 P < 0.001 0.902 P < 0.001
Z(3,−3) 0.863 P < 0.001 0.869 P < 0.001 0.859 P < 0.001 0.877 P < 0.001 0.883 P < 0.001 0.865 P < 0.001
Z(3,−1) 0.767 P < 0.001 0.772 P < 0.001 0.864 P < 0.001 0.747 P < 0.001 0.759 P < 0.001 0.773 P < 0.001
Z(3,1) 0.944 P < 0.001 0.900 P < 0.001 0.692 P < 0.001 0.909 P < 0.001 0.640 P < 0.001 0.619 P < 0.001
Z(3,3) 0.905 P < 0.001 0.749 P < 0.001 0.773 P < 0.001 0.728 P < 0.001 0.771 P < 0.001 0.574 P < 0.001
Z(4,0) 0.892 P < 0.001 0.897 P < 0.001 0.890 P < 0.001 0.920 P < 0.001 0.906 P < 0.001 0.916 P < 0.001
Corneal Aberrations
Z(2,−2) 0.893 P < 0.001 0.729 P < 0.001 0.776 P < 0.001
Z(2,0) 0.639 P < 0.001 0.216 P = 0.164* 0.373 P = 0.013
Z(2,2) 0.961 P < 0.001 0.719 P < 0.001 0.728 P < 0.001
Z(3,−3) 0.800 P < 0.001 0.281 P = 0.068* 0.309 P = 0.044
Z(3,−1) 0.592 P < 0.001 0.361 P = 0.017 0.347 P = 0.023
Z(3,1) 0.742 P < 0.001 0.701 P < 0.001 0.747 P < 0.001
Z(3,3) 0.788 P < 0.001 0.030 P = 0.848* 0.003 P = 0.986*
Z(4,0) 0.619 P < 0.001 0.246 P = 0.246* 0.337 P = 0.027
Table 2.
 
Limits of Agreement of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Table 2.
 
Limits of Agreement of the Total Ocular Aberrations and Corneal Aberrations Obtained with Four Different Aberrometers
Irx3 vs. Keratron Irx3 vs. iTrace Irx3 vs. OPD-Scan Keratron vs. iTrace Keratron vs. OPD-Scan iTrace vs. OPD-Scan
95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span 95% LoA Span
Total Ocular Abberations
Z(2,−2) −0.18, 0.29 0.47 −0.36, 0.47 0.83 −0.35, 0.47 0.82 −0.25, 0.46 0.71 −0.33, 0.43 0.75 −0.37, 0.58 0.95
Z(2,0) −1.99, 1.62 3.61 −0.06, 0.10 0.16 −0.85, 1.12 1.97 −1.37, 1.28 2.65 −0.15, 1.42 1.57 −0.78, 1.54 2.32
Z(2,2) −0.26, 0.40 0.66 −0.40, 0.56 0.95 −0.43, 0.56 0.99 −0.25, 0.46 0.71 −0.35, 0.43 0.78 −0.37, 0.55 0.93
Z(3,−3) −0.13, 0.14 0.27 −0.12, 0.15 0.28 −0.21, 0.22 0.43 −0.13, 0.15 0.28 −0.20, 0.20 0.40 −0.20, 0.20 0.39
Z(3,−1) −0.14, 0.19 0.33 −0.14, 0.20 0.34 −0.11, 0.13 0.24 −0.15, 0.21 0.36 −0.13, 0.19 0.32 −0.15, 0.19 0.34
Z(3,1) −0.04, 0.09 0.13 −0.05, 0.12 0.18 −0.12, 0.20 0.32 −0.09, 0.12 0.20 −0.15, 0.21 0.35 −0.17, 0.23 0.40
Z(3,3) −0.03, 0.09 0.12 −0.09, 0.16 0.25 −0.07, 0.16 0.23 −0.10, 0.17 0.27 −0.10, 0.16 0.25 −0.13, 0.22 0.35
Z(4,0) −0.03, 0.09 0.12 −0.06, 0.10 0.16 −0.02, 0.09 0.12 −0.03, 0.09 0.09 −0.05, 0.08 0.13 −0.02, 0.09 0.11
Corneal Aberrations
Z(2,−2) −0.28, 0.40 0.68 −0.55, 0.73 1.28 −0.53, 0.67 1.19
Z(2,0) 0.05, 0.51 0.56 −1.10, 1.30 2.40 −0.66, 1.23 1.88
Z(2,2) −0.29, 0.40 0.69 −0.63, 1.21 1.84 −0.65, 1.19 1.84
Z(3,−3) −0.16, 0.19 0.35 −0.59, 0.81 1.41 −0.59, 0.81 1.39
Z(3,−1) −0.16, 0.28 0.44 −0.66, 0.92 1.58 −0.65, 0.92 1.57
Z(3,1) −0.28, 0.44 0.72 −0.31, 0.42 0.73 −0.20, 0.27 0.48
Z(3,3) −0.07, 0.13 0.20 −0.46, 0.70 1.16 −0.44, 0.68 1.13
Z(4,0) −0.13, 0.14 0.27 −0.29, 0.48 0.76 −0.31, 0.45 0.76
Table 3.
 
Comparison of the Total Ocular Aberrations and Corneal Aberrations Obtained with the Four Aberrometers
Table 3.
 
Comparison of the Total Ocular Aberrations and Corneal Aberrations Obtained with the Four Aberrometers
Zernike Coefficient
Astigmatism Z(2,−2) Defocus Z(2,0) Astigmatism Z(2,2) Trefoil Z(3,−3) Coma Z(3,−1) Coma Z(3,1) Trefoil Z(3,3) Spherical Z(4,0)
Total Ocular Aberrations
Irx3 (I) −0.023 ± 0.341 0.802 ± 1.873 −0.073 ± 0.461 −0.020 ± 0.081 −0.027 ± 0.087 0.003 ± 0.089 0.012 ± 0.068 0.063 ± 0.068
Keratron (K) −0.030 ± 0.350 1.724 ± 1.790 −0.082 ± 0.397 −0.046 ± 0.095 −0.013 ± 0.097 −0.013 ± 0.089 −0.014 ± 0.059 0.034 ± 0.064
iTrace (T) 0.024 ± 0.387 1.160 ± 1.911 −0.025 ± 0.430 −0.026 ± 0.107 −0.027 ± 0.105 −0.022 ± 0.098 −0.004 ± 0.080 0.064 ± 0.076
OPD-Scan (O) 0.012 ± 0.303 0.916 ± 1.674 −0.016 ± 0.335 −0.098 ± 0.133 −0.008 ± 0.083 −0.003 ± 0.078 −0.022 ± 0.084 0.023 ± 0.067
P P = 0.122 P < 0.001 P = 0.027 P < 0.001 P = 0.137 P = 0.076 P = 0.007 P < 0.001
I vs. T; P < 0.001 K vs. O; P = 0.049 I vs. K; P = 0.010 I vs. K; P < 0.001 I vs. K; P < 0.001
I vs. K; P < 0.001 I vs. O; P < 0.001 I vs. O; P = 0.003 I vs. O; P < 0.001
K vs. T; P < 0.001 K vs. O; P < 0.001 K vs. T; P < 0.001
K vs. O; P < 0.001 T vs. O; P < 0.001 T vs. O; P < 0.001
Corneal Aberrations
Keratron (K) −0.009 ± 0.295 0.207 ± 0.08 −0.295 ± 0.460 −0.032 ± 0.106 −0.028 ± 0.113 −0.024 ± 0.201 −0.003 ± 0.071 0.157 ± 0.059
iTrace (T) −0.029 ± 0.281 0.597 ± 0.21 −0.327 ± 0.399 −0.039 ± 0.072 −0.009 ± 0.089 −0.014 ± 0.094 0.009 ± 0.049 0.115 ± 0.041
OPD-Scan (O) 0.056 ± 0.358 0.441 ± 0.45 −0.470 ± 0.586 −0.072 ± 0.285 0.026 ± 0.332 0.005 ± 0.139 −0.002 ± 0.226 0.131 ± 0.160
P P = 0.055 P < 0.001 P = 0.011 P = 0.393 P = 0.341 P = 0.316 P = 0.761 P = 0.142
K vs. T; P < 0.001 K vs. O; P = 0.023
K vs. O; P = 0.003
Table 4.
 
Interobserver Variability: Differences in Measurements Obtained by Experts and Nonexperts
Table 4.
 
Interobserver Variability: Differences in Measurements Obtained by Experts and Nonexperts
Zernike Coefficients
2, −2 2, 0 2, 2 3, −3 3, −1 3, 1 3, 3 4, 0
Irx3
TOA Correlation (PCC; P) 0.968; P < 0.001 0.994; P < 0.001 0.998; P < 0.001 0.962; P < 0.001 0.962; P < 0.001 0.963; P < 0.001 0.927; P < 0.001 0.960; P < 0.001
Difference in measurement (mean ± SD) 0.008 ± 0.052 −0.025 ± 0.194 0.014 ± 0.045 0.001 ± 0.022 −0.004 ± 0.030 0.001 ± 0.024 −0.002 ± 0.027 0.002 ± 0.016
Expert SDwithin ± SD 0.033 ± 0.020 0.126 ± 0.141 0.050 ± 0.020 0.023 ± 0.015 0.022 ± 0.013 0.018 ± 0.011 0.020 ± 0.013 0.013 ± 0.008
Nonexpert SDwithin ± SD 0.036 ± 0.020 0.097 ± 0.079 0.047 ± 0.025 0.023 ± 0.012 0.020 ± 0.010 0.021 ± 0.013 0.025 ± 0.015 0.014 ± 0.009
Keratron
TOA Correlation (PCC; P) 0.985; P < 0.001 0.981; P < 0.001 0.940; P < 0.001 0.752; P < 0.001 0.650; P < 0.001 0.958; P < 0.001 0.818; P < 0.001 0.833; P < 0.001
Difference in measurement (mean ± SD) 0.013 ± 0.059 0.058 ± 0.362 0.028 ± 0.136 0.005 ± 0.075 −0.011 ± 0.097 0.006 ± 0.026 −0.001 ± 0.038 −0.002 ± 0.039
Expert SDwithin ± SD 0.030 ± 0.019 0.187 ± 0.196 0.040 ± 0.023 0.021 ± 0.022 0.027 ± 0.022 0.021 ± 0.033 0.021 ± 0.021 0.021 ± 0.045
Nonexpert SDwithin ± SD 0.039 ± 0.041 0.211 ± 0.204 0.047 ± 0.041 0.023 ± 0.023 0.025 ± 0.027 0.019 ± 0.016 0.020 ± 0.028 0.017 ± 0.021
CA Correlation (PCC; P) 0.880; P < 0.001 0.473; P < 0.001 0.930; P < 0.001 0.630; P < 0.001 0.804; P < 0.001 0.744; P < 0.001 0.494; P < 0.001 0.505; P < 0.001
Difference in measurement (mean ± SD) 0.031 ± 0.153 0.011 ± 0.095 0.048 ± 0.195 −0.005 ± 0.107 0.002 ± 0.075 −0.024 ± 0.165 0.015 ± 0.084 0.009 ± 0.069
Expert SDwithin ± SD 0.073 ± 0.97 0.039 ± 0.053 0.088 ± 0.138 0.043 ± 0.065 0.073 ± 0.104 0.050 ± 0.078 0.034 ± 0.050 0.030 ± 0.042
Nonexpert SDwithin ± SD 0.116 ± 0.180 0.059 ± 0.076 0.126 ± 0.214 0.059 ± 0.158 0.064 ± 0.072 0.077 ± 0.132 0.041 ± 0.108 0.043 ± 0.055
iTrace
TOA Correlation (PCC; P) 0.834; P < 0.001 0.989; P < 0.001 0.881; P < 0.001 0.910; P < 0.001 0.921; P < 0.001 0.813; P < 0.001 0.856; P < 0.001 0.843; P < 0.001
Difference in measurement (mean ± SD) 0.033 ± 0.102 0.042 ± 0.270 0.025 ± 0.125 −0.011 ± 0.036 0.004 ± 0.045 −0.012 ± 0.049 0.014 ± 0.040* 0.006 ± 0.042
Expert SDwithin ± SD 0.064 ± 0.064 0.164 ± 0.232 0.074 ± 0.044 0.035 ± 0.024 0.038 ± 0.024 0.037 ± 0.026 0.032 ± 0.016 0.023 ± 0.018
Nonexpert SDwithin ± SD 0.057 ± 0.040 0.131 ± 0.119 0.067 ± 0.043 0.036 ± 0.027 0.037 ± 0.025 0.042 ± 0.038 0.027 ± 0.019 0.026 ± 0.20
CA Correlation (PCC; P) 0.828; P < 0.001 0.688; P < 0.001 0.946; P < 0.001 0.765; P < 0.001 0.878; P < 0.001 0.694; P < 0.001 0.872; P < 0.001 0.738; P < 0.001
Difference in measurement (mean ± SD) 0.014 ± 0.090 −0.023 ± 0.086 −0.001 ± 0.077 −0.003 ± 0.039 0.006 ± 0.052 −0.009 ± 0.045 0.006 ± 0.027 0.001 ± 0.025
Expert SDwithin ± SD 0.090 ± 0.064 0.059 ± 0.038 0.184 ± 0.096 0.046 ± 0.031 0.042 ± 0.026 0.049 ± 0.039 0.038 ± 0.029 0.054 ± 0.026
Nonexpert SDwithin ± SD 0.073 ± 0.055 0.073 ± 0.131 0.200 ± 0.093 0.040 ± 0.033 0.045 ± 0.039 0.038 ± 0.028 0.037 ± 0.027 0.059 ± 0.037
OPD-Scan
TOA Correlation (PCC; P) 0.890; P < 0.001 0.958; P < 0.001 0.965; P < 0.001 0.934; P < 0.001 0.928; P < 0.001 0.958; P < 0.001 0.762; P < 0.001 0.961; P < 0.001
Difference in measurement (mean ± SD) −0.024 ± 0.146 0.165 ± 0.484 −0.025 ± 0.089 −0.013 ± 0.050 −0.007 ± 0.034 −0.008 ± 0.022 −0.013 ± .062 −0.002 ± 0.018
Expert SDwithin ± SD 0.078 ± 0.271 0.097 ± 0.191 0.061 ± 0.156 0.031 ± 0.023 0.018 ± 0.014 0.013 ± 0.010 0.028 ± 0.021 0.012 ± 0.010
Nonexpert SDwithin ± SD 0.075 ± 0.185 0.164 ± 0.278 0.061 ± 0.104 0.040 ± 0.020* 0.039 ± 0.020* 0.018 ± 0.010* 0.041 ± 0.022* 0.014 ± 0.007
CA Correlation (PCC; P) 0.501; P = 0.001 0.415; P = 0.005 0.481; P = 0.001 0.182; P = 236 0.228; P = 0.137 0.626; P < 0.001 −0.079; P = 0.610 0.220; P = 0.152
Difference in measurement (mean ± SD) 0.086 ± 0.440 0.046 ± 0.728 −0.149 ± 0.776 −0.049 ± 0.538 0.061 ± 0.614 0.011 ± 0.146 0.029 ± 0.458 0.024 ± 0.292
Expert SDwithin ± SD 0.036 ± 0.024 0.122 ± 0.110 0.048 ± 0.058 0.023 ± 0.032 0.031 ± 0.049 0.023 ± 0.023 0.027 ± 0.026 0.019 ± 0.028
Nonexpert SDwithin ± SD 0.186 ± 0.640 0.331 ± 0.983 0.299 ± 1.233 0.205 ± 0.894 0.208 ± 0.949 0.054 ± 0.184 0.180 ± 0.685 0.110 ± 0.463
Table 5.
 
Formulas for Calculating the Zernike Expansion Coefficients for Smaller Pupil Sizes
Table 5.
 
Formulas for Calculating the Zernike Expansion Coefficients for Smaller Pupil Sizes
n m New Expansion Coefficient
0 0 b 00 = a 00 − a 20 3 ( 1 − r 2 2 r 1 2 ) + a 40 5 ( 1 − 3 r 2 2 r 1 2 + 2 r 2 4 r 1 4 ) − a 60 7 ( 1 − 6 r 2 2 r 1 2 + 10 r 2 4 r 1 4 − 5 r 2 6 r 1 6 ) + a 80 3 ( 1 − 10 r 2 2 r 1 2 + 30 r 2 4 r 1 4 − 35 r 2 6 r 1 6 + 14 r 2 8 r 1 8 )
1 −1, 1 b 1 m = r 2 r 1 [ a 1 m − a 3 m 8 ( 1 − r 2 2 r 1 2 ) + a 5 m 3 ( 3 − 8 r 2 2 r 1 2 + 5 r 2 4 r 1 4 ) − a 7 m 4 ( 2 − 10 r 2 2 r 1 2 + 15 r 2 4 r 1 4 − 7 r 2 6 r 1 6 ) ]
2 −2, 0, 2 b 2 m = r 2 2 r 1 2 [ a 2 m − a 4 m 15 ( 1 − r 2 2 r 1 2 ) + a 6 m 21 ( 2 − 5 r 2 2 r 1 2 + 3 r 2 4 r 1 4 ) − a 8 m 3 ( 10 − 45 r 2 2 r 1 + 63 r 2 4 r 1 4 − 28 r 2 6 r 1 6 ) ]
3 −3, −1, 1, 3 b 3 m = r 2 3 r 1 3 [ a 3 m − a 5 m 2 6 ( 1 − r 2 2 r 1 2 ) + a 7 m 8 ( 5 − 12 r 2 2 r 1 2 + 7 r 2 4 r 1 4 ) ]
4 −4, −2, 0, 2, 4 b 4 m = r 2 4 r 1 4 [ a 4 m − a 6 m 35 ( 1 − r 2 2 r 1 2 ) + a 8 m 5 ( 9 − 21 r 2 2 r 1 2 + 12 r 2 4 r 1 4 ) ]
5 −5, −3, −1, 1, 3, 5 b 5 m = r 2 5 r 1 5 [ a 5 m − a 7 m 4 3 ( 1 − r 2 2 r 1 2 ) ]
6 −6, −4, −2, 0, 2, 4, 6 b 6 m = r 2 6 r 1 6 [ a 6 m − a 8 m 3 7 ( 1 − r 2 2 r 1 2 ) ]
7 −7, −5, −3, −1, 1, 3, 5, 7 b 7 m = r 2 7 r 1 7 a 7 m
8 −8, −6, −4, −2, 0, 2, 4, 6, 8 b 8 m = r 2 8 r 1 8 a 8 m
×
×

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