Analysis of Four Aberrometers for Evaluating Lower and
Higher Order Aberrations
Fabiano Cade, Andrea Cruzat, Eleftherios I. Paschalis*, Lilian Espı ´rito Santo, Roberto Pineda
Massachusetts Eye and Ear Infirmary, Harvard Medical School, Boston, Massachusetts, United States of America
Purpose: To compare the measurements of lower and higher order aberrations (HOA) of 4 commonly used aberrometers.
Setting: Massachusetts Eye & Ear Infirmary, Boston, USA.
Design: Prospective, cross-sectional study, in a controlled, single-blinded fashion.
Methods: Multiple readings were obtained in 42 eyes of 21 healthy volunteers, at a single visit, with each of the following
aberrometers: Alcon LADARWaveH, Visx WaveScanH, B & L ZywaveH, and Wavelight Allegro AnalyzerH. Results were
compared and analyzed in regards to the lower and HOA, to the different wavefront sensing devices and software,
Tscherning and Hartmann–Shack and between the Fourier and Zernike algorithms. Statistical analysis included Bland-
Altman plots, Intraclass Correlation Coefficient (ICC), multiple comparison tests with Analysis of Variance and Kruskal-Wallis.
Significant level was set to p,0.05 and alpha level correction was adjusted under the Bonferroni criteria.
Results: Most measurements of all 4 aberrometers were comparable. However, statistically significant differences were
found between the aberrometers in total HOA (tHOA), spherical aberration (SA), horizontal coma and astigmatism (2,2).
LADARwave and Wavescan showed significant differences in tHOA (P,0.001, ICC=0.549, LoA=0.1960.5) and in SA
(P,0.001, ICC=0.733, LoA=0.1660.37). Wavescan showed a significant difference compared to Zywave (p,0.001,
ICC=0.920, LoA=0.0960.13) in SA. Comparisons between Allegro Analyzer and Zywave demonstrated significant
differences in both Horizontal Coma (3,1) (p,0.001, ICC=20.207, LoA=20.1560.48) and Astigmatism (2,2) (P=0.003,
ICC=20.965, LoA=0.262.5). Allegro Analyzer also differed from Wavescan in Horizontal Coma (3,1) (P,0.001, ICC=0.725,
Conclusions: Although some measurements were comparable predominately in the lower order aberrations, significant
differences were found in the tHOA, SA, horizontal coma and astigmatism. Our analysis suggests that sensor design
contributes to agreement in lower order aberrations, and Fourier and Zernike expansion might disagree in higher order
aberrations. Therefore, comparison between aberrometers was generally possible with some exceptions in higher order
Citation: Cade F, Cruzat A, Paschalis EI, Espı ´rito Santo L, Pineda R (2013) Analysis of Four Aberrometers for Evaluating Lower and Higher Order Aberrations. PLoS
ONE 8(1): e54990. doi:10.1371/journal.pone.0054990
Editor: Demetrios Vavvas, Massachusetts Eye & Ear Infirmary, Harvard Medical School, United States of America
Received September 20, 2012; Accepted December 19, 2012; Published January 2 , 2013
Copyright: ? 2013 Cade et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: Financial support: R.P. (Alcon), unrestricted grant. The funders had no role in study design, data collection and analysis, decision to publish, or
preparation of the manuscript.
Competing Interests: The study was funded by Alcon but this does not alter the authors’ adherence to all the PLOS ONE policies on sharing data and materials.
* E-mail: Eleftherios_paschalis@meei.harvard.edu
Last decade technological advancements in aberrometry have
revolutionized wavefront-based corneal refractive surgery [1,2].
Excimer laser technology allowed implementation of wavefront-
guided treatments for correction of both lower and higher order
aberrations, providing additional benefit in highly aberrated eyes.3
Diverse sensor technologies are used in wavefront analysis and
different mathematical techniques are employed for wavefront
error calculations [4,5]. Companies designing wavefront aber-
rometers for the clinical setting implement some of these
techniques and methods . Such systems are routinely used as
part of the refractive surgery consultation and decision making
Aberrometers incorporate wavefront analysis to define the
refractive parameters of the eye . A wavefront aberration is
defined as the deviation of a reflected wave to a reference
unaberrated wave [3,8]. The most common metric in use today is
the Root Mean Square (RMS) wavefront error, which is defined as
the root square of the wavefront variance over the pupil size of
interest . Some visual disturbances such as night vision halos
and glare have been associated with highly aberrated eyes .
The ability to measure and correct these wavefront abnormalities
can provide a benefit in customizing a refractive procedure and in
the enhancement of iatrogenically induced aberrations after
There are four main techniques for measuring wavefront
aberrations in the eye.[12–15] Three of these are based on
PLOS ONE | www.plosone.org1 January 2013 | Volume 8 | Issue 1 | e54990
objective measuring techniques and include: Hartmann-Shack (the
most popular), Tscherning and Laser Ray Tracing, while one is
based on subjective measurements of the ingoing light, called the
spatially resolved . This study utilized two different techniques,
Hartmann-Shack and Tscherning. The first measures an outgoing
light formed by a laser and reflected by the retina back to a
charged-coupled device (CCD) camera using a lenslet configura-
tion , while the latter measures an ingoing light formed by a
laser grid arrangement reflected by the retina .
Regarding mathematical techniques, Zernike and Fourier
expansion series polynomials are used in modern optics to describe
the optical surface in three dimensions and to quantify these
optical abnormalities, referred to as aberrations [16,17]. Fourier
analysis has been available in engineering since the beginning of
the 19thcentury, while Zernike has been described only in the last
few decades. Advantages and disadvantages are associated with
each technique, mostly related to the processing power and the
magnitude of the optical aberration .
The purpose of this study was to compare the agreement
between 4 different aberrometers using the same reference. All
measurements were undertaken in the same eyes, enabling for
direct comparisons. The aberrometers used were: the Alcon
LADARWaveH, the Visx WaveScanH, the B & L ZywaveH, and
the Wavelight Allegro AnalyzerH. Lower and higher order
aberrations were compared while controlling the co-effect of the
wavefront sensor design, Tscherning (Allegro Analyzer) and
Hartmann–Shack (LADARWave, WaveScan, Zywave) and the
algorithms for wavefront decomposition, Fourier (WaveScan) and
Zernike (LADARWave, Allegro Analyzer, Zywave).
We conducted a prospective, cross-sectional study, in a
controlled, single-blinded fashion. Forty-two eyes of 21 healthy
individuals were included in the study. All subjects were recruited
from the Cornea Service of the Massachusetts Eye & Ear
Infirmary, Boston, Massachusetts, USA. This study was Health
Insurance Portability and Accountability Act (HIPAA)-compliant,
adhered to the tenets of the Declaration of Helsinki, and obtained
approval of the Institutional Review Board (IRB)/Ethics Com-
mittee of the Massachusetts Eye & Ear Infirmary, Boston,
Massachusetts, USA. Written informed consent was obtained
from all subjects after a detailed explanation of the nature of the
All patients underwent a comprehensive eye examination.
Detailed review of ophthalmic history, ocular medication,
refraction, best-corrected visual acuity, slit-lamp biomicroscopy
(with evaluation of the condition of the lid/lashes, conjunctiva,
Figure 1. Representation of aberration maps with all four devices. Left eye examination of a patient. LADARWaveH (a), Visx WaveScanH (b),
ZywaveH (c), Allegro AnalyzerH (d).
Analysis of Wavefront Aberrations
PLOS ONE | www.plosone.org2January 2013 | Volume 8 | Issue 1 | e54990
cornea, anterior chamber, iris/pupil, lens, vitreous, macula, optic
nerve) and corneal topography was performed. Only adult
patients, in generally good and stable health with no ocular
abnormality other than refractive error, were included in the
study. The patients must not have worn contact lens prior to the
study (hard or gas permeable lenses for at least 3 weeks and soft
lenses for at least 3 days) and were able to fixate steadily. Patients
were excluded when they had history of ocular surgery, trauma
and infectious disease, myopia or hyperopia .7.0 D and
astigmatism .3.0 D, abnormal corneal topography (e.g. kerato-
conus), pupil size bellow 6.0 mm under mydriasis, ocular media
opacities, ocular movement abnormalities and pregnancy or
Aberrometry was performed in each eye at a single visit with:
Alcon LADARWaveH (Alcon, Fort Worth, Texas, USA), Visx
WaveScanH (VISX, Santa Clara, CA, USA), B & L ZywaveH
(Baush & Lomb, Rochester, NY, USA), and Wavelight Allegro
AnalyzerH (Wavelight, Erlangen, Germany). A minimum of 3
readings per eye were obtained with each aberrometer. Patients
had a 15 minutes interval between readings with different devices
and one drop of lubricant was applied. Subjects were encouraged
to blink. Also, head positioning and eye alignment were confirmed
before measurements. Natural pupil dilation was achieved under
scotopic light condition. All subjects were dilated after Wavescan
readings and initial LADARwave exam with Tropicamide 1% for
the other three devices, according to the manufacturer’s instruc-
tions, starting with Allegro Analyzer (mid-dilated), followed by
Zywave and LADARwave.
Lower and higher order aberrations were analyzed and
compared between the 4 analyzers. In particular, refraction
parameters, defocus (2,0), astigmatism (2,22 and 2,2) vertical and
horizontal coma (3,21 and 3,1), trefoil (3,23 and 3,3), spherical
aberration (SA) (4,0) and the root mean square (RMS) error of the
total aberration and the total higher order aberrations (tHOA)
were assessed. Statistical analysis included Bland-Altman plots,
Intraclass Correlation Coefficient (ICC), independent comparisons
with Mann-Whitney test and multiple comparison tests with
Analysis of Variance (ANOVA) and Kruskal-Wallis. Significant
Figure 2. Comparison of aberrations between four aberrometers. Boxplots comparing the distribution of the data. The box contains 50% of
the data, the horizontal line inside the box indicates the median value. The whiskers represent the range of the data. Statistically significant difference
was found between the 4 aberrometers: A) Total Higher Order Aberrations (tHOA), B) Spherical aberration (SA), C) Horizontal Coma D) Astigmatism
(2,2). P-values for multiple comparison tests are represented with connecting lines. RMS=Root mean square.
Analysis of Wavefront Aberrations
PLOS ONE | www.plosone.org3 January 2013 | Volume 8 | Issue 1 | e54990
level was set to 0.05 and alpha level correction was applied under
the Bonferroni criteria for multiple comparisons.
Alcon LADARWaveH uses the Hartmann-Shack principle to
measure aberrations in the eye. The device software measures the
displacement of each focused dot from its ideal location, that is, the
pattern generated by a perfectly flat plane wave, and uses this
information to calculate the slope of the intact wavefront at each
lenslet location. The software then uses this slope data to generate
a mathematical description of the original wavefront profile.
LADARWave uses a light source of 820 nm. For a 6-mm diameter
pupil, it results in 170 wavefront samples at the sensor. This large
body of data permits calculation of wavefront aberrations up to the
eighth order. The device can measure wavefronts between +15.0
and 215.0 D. The unit can also measure up to 8.0 D of
astigmatism. A Zernike expansion series polynomial is used to
describe the complex three-dimensional surface .
Visx WavescanH also measures the refractive error and
wavefront aberrations of the human eye using a Hartmann-Shack
wavefront principle. A small spot of laser light at 785 nm is
projected onto the retina and reflects back through the pupil. The
WaveScan system can measure spherical refractive errors between
212.0 D and +9.0 D, cylindrical refractive errors up to 5.0 D, and
higher-order aberrations up to sixth-order. The WaveScan Fourier
wavefront system is capable of reconstructing very complex three-
dimensional surfaces with little processing power compared to
Zernike expansion. The algorithm provides the ability of
peripheral data representation using a multi term polynomial,
which means it captures wavefront information in patients with
larger pupils with highly aberrated optics and can treat higher and
lower aberrations up to 7-mm diameter pupil .
B & L ZywaveH is another device that measures wavefront
aberrations based on the Hartmann-Shack principle. It uses a
wavelength of 780 nm and measures approximately 75 locations
within the pupil. Up to fifth-order Zernike coefficients are included
in the measurements. The Zywave system automatically measures
the pupil size at the moment the wavefront image is captured and
measures refractive errors over a range of +8.0 D to 214.0 D and
up to 5.0 D cylinder. Similar to LADARWave, Zywave
implements Zernike expansion for three-dimensional representa-
tion of surfaces. [20,21].
Wavelight Allegro AnalyzerH uses a Tscherning sensor archi-
tecture in order to capture the ocular wavefront. The Allegro
Analyzer projects a grid pattern to the retina. This image is
observed using a dot patterned mask and captured by a CCD
camera. The distortion of the grid pattern enables calculation of
the optical aberrations. A sixth-order Zernike expansion series is
utilized using a laser of 660 nm in wavelength. One hundred and
seventy wavefront samples are acquired in a dioptric range of
+6.0D to 212.0 and up to 6.0D of cylinder .
Table 1. Descriptive statistics.
WF Rx Sph
WF Rx Cyl
tHOA RMS0.503±0.2550.399±0.1540.401±0.1320.332±0.132 .001*
Defocus (2,0) 2.94663.2552.28662.9561.82162.6992.08962.408 .189
Astigmatism (2, 22) 0.01760.3590.06060.364
Coma (3, 21)
Trefoil (3, 23)
Trefoil (3,3) 0.00360.160 0.01760.158 0.07560.119 0.00360.107 .065
SA RMS (4,0)0.293±0.2270.182±0.156 0.252±0.126 0.157±0.144.001*
Summary of four aberrometers with comparison of wavefront measurements. WF=wavefront; Rx=Refraction; Sph=Spherical; Cyl=Cylinder; RMS=Root mean square;
tHOA=Total Higher Order Aberration; SA=Spherical Aberration.Data is shown as the mean 6 SD (in micrometers).
Table 2. Statistical significant differences between
aberrometers for total higher order aberrations (tHOA),
spherical aberration (SA), horizontal coma and astigmatism
P-Value ICCCI 95%
LADARWave (HS,Z) vs Wavescan
.001 .549 0.161 to 0.757
LADARWave (HS,Z) vs Wavescan
.001.7330.504 to 0.857
Zywave (HS,Z) vs Wavescan
.001.920 0.849 to 0.958
Allegro Analyzer (T,Z) vs Zywave
21.302 to 0.367
Allegro Analyzer (T,Z) vs Wavescan
.001.725 0.485 to 0.853
Allegro Analyzer (T,Z) vs Zywave
29.834 to 20.927
Significant P-Value ,0.01 by Mann-Whitney (Bonferroni adjusted).
ICC=Intraclass correlation coefficient. CI=Confidence interval. HS=Hartmann-
Shack, T=Tscherning, Z=Zernike, F=Fourier.
Analysis of Wavefront Aberrations
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We compared the measurements of lower and higher order
aberrations between the 4 analyzers. Displays of the different
aberrometers are illustrated in Figure 1. The summary data of four
aberrometers with comparison of wavefront measurements is
presented in Table 1. Lower order aberrations between the 4
aberrometers were in agreement with no significant difference in
defocus(2,0) (p=0.189) and
(p=0.853), with the exception of astigmatism (2,2) (P=0.011).
Higher order aberrations such as vertical coma (3,21) (p=0.209),
trefoil (3,23 and 3,3) (p=0.170 and p=0.065) and the root mean
square (RMS) error of the total aberration (p=0.621) did not show
a significant difference. However, statistically significant differenc-
es were measured between the aberrometers regarding total HOA
(p,0.001), SA (4,0) (p,0.001), and horizontal coma (3,1)
(p,0.001). Graphic representation of the comparison of aberra-
tions between the four aberrometers is shown in Figure 2 with
Table 2 outlines the significant differences between aberrometer
data acquisition and data analysis showing independent compar-
isons and ICC. Figure 3 shows Bland Altmann difference plots
with Limits of agreement (LoA, mean difference 61.96 SD) of
each significantly different independent comparison. LADARwave
and Wavescan showed significant difference in tHOA (p,0.001,
ICC=0.549, LoA=0.1960.5) (Table 2, Figure 3A) and in SA
(p,0.001, ICC=0.733, LoA=0.1660.37) (Table 2, Figure 3B).
Although there was a difference between Wavescan and Zywave
measurements (p,0.001, LoA=0.0960.13), they showed good
agreement (ICC=0.920) in SA (Table 2, Figure 3B).
Comparisons between Allegro Analyzer and Zywave demon-
strated significant differences in both horizontal coma (3,3)
Figure 3C) and astigmatism (2,2) (p=0.003, ICC=20.965,
LoA=0.262.5) (Table 2, Figure 3D). Allegro Analyzer also
differed from the Wavescan in horizontal coma (3,3) (p,0.001,
ICC=0.725, LoA=20.0760.25) (Table 2, Figure 3C).
There are few studies comparing aberrometers in the literature,
and most of those have emphasized the differences amongst them.
In addition, direct comparison between aberrometers is not
possible prior to establishing a common measuring reference. In
the current study, we used the same sample to compared 4
different aberrometers according to manufacturer’s recommenda-
tions. This is the first study to simultaneously assess the agreement
between aberrometers while assessing for the effect of the
Aberrations were evaluated according to the two types of
wavefront sensors: Hartman-Shack (LADARWave, WaveScan,
Zywave) and the Tscherning based wavefront analyzers (Allegro
Analyzer). Furthermore, evaluation was undertaken between
Fourier (WaveScan) and Zernike (LADARWave, Allegro Analyz-
er, Zywave) expansion series polynomials, which are used to
describe the optical geometry of the visual system in three
dimensions and are represented as lower and higher order
aberrations. Due to the lack of a gold standard method to
measure ocular aberrations, this study did not focus on determin-
ing which device exhibited the most objective measurements.
Figure 3. Bland-Altman plots. Diagrams of agreement between the aberrometers. The x-axis represents the mean aberration of two
aberrometers, while the y-axis shows the mean difference between the two same aberrometers. The upper and lower horizontal lines represent the
upper and the lower limits of agreement (mean difference 61.96 SD), respectively. The middle line represents the mean difference between the
aberrometers. Figure 3A. Correlation between Aberrometers for Total Higher Order Aberrations HOA). Figure 3B(i)(ii). Correlation between
Aberrometers for Spherical Aberration (SA). Figure 3C(i)(ii). Correlation between Aberrometers for Horizontal Coma. Figure 3D. Correlation between
Aberrometers for Astigmatism (2,2).
Analysis of Wavefront Aberrations
PLOS ONE | www.plosone.org5January 2013 | Volume 8 | Issue 1 | e54990
In general, there was good agreement between both lower and
higher order aberrations for all 4 wavefront analyzers in this study,
summarized in Table 1. The 4 aberrometers showed similarities in
the lower order aberrations including defocus (2,0) (p=0.189), and
oblique astigmatism (2,22) (p=0.853). Also, higher order
aberrations such as vertical coma (3,21) (p=0.209), trefoil
(3,23 and 3,3) (p=0.170 and p=0.065) and the root mean
square (RMS) error of the total aberration (p=0.621) showed to
be comparable. However, significant differences were found
between the aberrometers in regards to tHOA, SA, horizontal
coma and astigmatism (2,2) (Table 2). These differences were then
analyzed and graphically represented as Bland Altmann plots
(Figure 3). Such graphics provide the mean difference and the
standard deviation of the differences between devices. Different
from correlation coefficients, where any comparison can be highly
correlated even when there is a consistent bias in measurements,
our analysis showed a wide spread sample distribution of
independent comparisons for each one of the aberrations that
were statistically different.
The overall analysis showed that the Allegro Analyzer
measurements were different compared to Zywave and Wavescan
for lower order astigmatism aberration and horizontal coma. It is
important to note that Allegro Analyzer uses Tscherning sensor
architecture while the other two aberrometers employ Hartmann-
Shack, suggesting that the sensor design particularly contributes to
agreement in lower order aberrations.
Some studies have tried to compare measurement acquisition
with different devices focusing their analysis on either repeatability
or interchangeability. Most of these studies have shown good
correlation between aberrometers, although some parameters had
poor agreement [21–24]. Visser et al., showed that Hartmann-
Shack aberrometers had the best repeatability in regards to total
ocular aberrations comparing measurements
(Hartmann-Shack), Keratron (Hartmann-Shack), iTrace (Tshcern-
ing), and OPD-Scan (Automated Retinoscopy) analyzers. Howev-
er, in direct comparison of measurements, the ocular aberrations
obtained with the four analyzers showed significant differences in
astigmatism (2,2), defocus (2,0), trefoil (3,23 and 3,3), and
spherical aberration (4,0) . In another study by Rozema et al.,
with six different aberrometers, similar results were obtained
One explanation for this discrepancy might be the differences in
the algorithm to locate either the chief ray of each lenslet image or
the pupil center. Consequently, any disparity of mathematical
calculation, used by each device, can give slightly different results
The comparison between Fourier and Zernike was done in
order to elucidate possible differences in the mathematical
reconstruction of the three-dimensional surface. The Wavescan
was the only device using Fourier expansion among the four
aberrometers in our study. Interestingly, Wavescan showed
statistically significant differences compared to LADARwave and
Zywave, in tHOA and SA (p,0.001), raising the idea that
mathematical analysis may contribute to differences in higher
order aberration measurements among aberrometers. Although
some authors have been advocating that these differences are more
important in engineering rather than in clinical setting, this
observation allows us to suggest that Fourier and Zernike analysis
might differ in regards to higher order aberrations.
As shown by Klyce et al., Zernike appears to clinically
underestimate the amount of higher order aberrations in highly
aberrated eyes, such as Keratoconus . Fourier polynomials
were suggested as an alternative to decompose wavefront maps
and its expansion is felt to be more reliable and efficient in
representing the overall wavefront map. Liang et.al have also
found differences between Wavescan (Fourier)-Zywave (Zernike),
and between Wavescan (Fourier)-LADARWave (Zernike) in
tHOA and SA . Similar findings were shown in subsequent
studies where data comparison between LADARWave (Zernike)
and Wavescan (Fourier) have also demonstrated differences in
terms of tHOA and SA [19,27].
Advantages of Fourier analysis can be attributed to the
simplicity of mathematical calculations, but clinically, minimum
differences can be seen between the two methods. Zernike
expansion conveniently represents tilt, prism, sphere, cylinder,
spherical aberration and coma, traditionally used in ophthalmol-
ogy. Fourier transform does not have such single term represen-
tation (Zernike polynomials) and requires the sum of multiple
Fourier terms to represent aberrations. However, Fourier has the
capability to calculate complex and highly irregular surfaces with
more precision than Zernike, while Zernike exhibits difficulties in
mapping surface irregularities in the periphery of the analyzed
area. Additionally, Zernike requires a higher amount of computing
power relative to Fourier [4,18].
Another parameter that can interfere with results is the need for
pupillary dilation for wavefront aberrometry by some analyzers.
The location of the pupil center and the pupil size are essential
factors in wavefront analysis [28,29]. Pupil importance relies in the
control of light intensity, which defines the point spread function of
the visual system.30Therefore, either pharmacologic pupil dilation
or pupil displacement can contribute to the increase of higher
order aberrations, with third-order coma and higher order
spherical aberration induction [29,30]. In addition, increase of
aberration in the optical system can be attributed to changes of
lens’ accommodation . Beside the expected differences that
theoretically should be found between a dilated pupil compared to
a mesopic pupil acquired aberrometry, we decided to follow the
manufacturer’s recommendation in order to obtain ‘‘real life’’
results similar to the clinical setting, and compare them to how a
refractive surgeon would evaluate them.
In summary, the purpose of this study was to evaluate which
variables were comparable and which were different between 4
aberrometers using the same eyes. It has been previously
documented that data comparison across aberrometers is not
straightforward and requires careful analysis, even when assessing
related devices. Our analysis showed similarities between all
aberrometers, particularly measuring lower order aberrations.
However, significant differences found in total HOA, SA,
horizontal coma and astigmatism suggest that certain measure-
ments are not always consistent between devices, and hence,
should be interpreted carefully. We believe that these differences
can be attributed to design variations between the aberrometers,
such as sensor architecture and the wavefront decomposition
What was Known
N There are few studies comparing aberrometers in the
literature, most of them have tried to compare measurement
acquisition with different devices focusing their analysis on
either repeatability or interchangeability.
N Poor agreement between different devices has been shown to
occur when comparing higher order aberrations
Analysis of Wavefront Aberrations
PLOS ONE | www.plosone.org6 January 2013 | Volume 8 | Issue 1 | e54990
What this Paper Adds
N This is the first study to simultaneously assess the agreement
between these 4 specific aberrometers while also assessing for
the effect of the aberrometers design.
N In general, there was good agreement between both lower and
higher order aberrations for all 4 wavefront analyzers in this
N However differences were found, and our analysis suggests that
sensor design (Hartmann-Shack and Tscherning) contributes
to agreement in lower order aberrations, and Fourier and
Zernike expansion might disagree in higher order aberrations.
Conceived and designed the experiments: FC AC EIP LES RP. Performed
the experiments: FC AC EIP LES RP. Analyzed the data: EIP FC.
Contributed reagents/materials/analysis tools: FC AC EIP LES RP.
Wrote the paper: FC AC EIP RP.
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Analysis of Wavefront Aberrations
PLOS ONE | www.plosone.org7 January 2013 | Volume 8 | Issue 1 | e54990