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An evaluation of the Bausch & Lomb Zywave aberrometer

Clinical and Experimental Optometry

May 2009
92(3):238 - 245

DOI:10.1111/j.1444-0938.2009.00360.x

Source
PubMed

Authors:

Michael Twa

University of Houston

Mark A Bullimore

University of Houston

Purpose: The Bausch & Lomb Zywave uses Shack-Hartmann aberrometry to determine wavefront aberrations of the human eye and provide an estimate of refractive error. We investigated the effect of pupil size on the repeatability and validity of refractive errors estimated by the Zywave and the repeatability of higher-order aberrations. Methods: Twenty-three subjects were measured with the Zywave under natural and cycloplegic conditions on two occasions separated by at least one week. Refractive error was also measured using a Nidek ARK-700A autorefractor. At one visit, a cycloplegic subjective refraction was performed. Measured ocular wavefront aberrations were expressed as the polynomial coefficients from a least-squares fitted fifth-order Zernike polynomial expansion over three, five and seven millimetre diameters. Repeatability and validity were evaluated by calculating the difference between pairs of refractive estimates or Zernike terms, determining the mean and standard deviation of these differences and calculating the 95% limits of agreement (LoA = mean +/-1.96 x SD). Results: The repeatability of refractive error estimated by the Zywave was better than that of the Nidek autorefractor for both manifest and cycloplegic conditions. Manipulating the pupil size on the Zywave from three to seven millimetres changed the mean cycloplegic spherical equivalent from -1.91 D to -2.60 D, a shift that was negatively correlated with spherical aberration. As expected, the magnitude of the Zernike coefficients increased with increasing pupil diameter, as did their corresponding 95% LoA. The 95% LoA decreased for higher-order terms but the magnitude of the terms and the variation between subjects also decreased with increasing order. To compensate for these factors,the ratio of the SD between sessions to the SD across subjects was calculated. The ratios were lowest for second-order terms (less than 0.08 for 7.0 mm pupil), intermediate for the C4,0 spherical aberration term (0.14) and third-order terms (approximately 0.25) but approached and exceeded 1.0 for many fourth- and fifth-order terms. Conclusions: The Zywave provides valid and repeatable estimates of refractive error. We attribute the myopic shift for larger pupils to the eye's spherical aberration. The repeatability of the Zernike terms measured with the Zywave was acceptable for the second-order and spherical aberration terms but for other higher-order terms, the variation between sessions may exceed the variation between subjects indicating unacceptable repeatability. This may have important ramifications for wavefront-guided LASIK.

The ratio of within-subject SD to between-subject SD for all Zernike aberration terms measured with the Zywave for 7 mm pupil. A smaller ratio represents better repeatability.

…

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ORIGINAL PAPER

An evaluation of the Bausch &

Lomb Zywave aberrometer

Clin Exp Optom 2009; 92: 3: 238–245 DOI:10.1111/j.1444-0938.2009.00360.x

Michael J Dobos*ODMS

Michael D Twa†OD PhD

Mark A Bullimore* MCOptom PhD

* The Ohio State University College of

Optometry, Columbus, Ohio, USA

†University of Houston, College of

Optometry, Houston, Texas, USA

E-mail: dobos.10@osu.edu

Purpose: The Bausch & Lomb Zywave uses Shack-Hartmann aberrometry to determine

wavefront aberrations of the human eye and provide an estimate of refractive error. We

investigated the effect of pupil size on the repeatability and validity of refractive errors

estimated by the Zywave and the repeatability of higher-order aberrations.

Methods: Twenty-three subjects were measured with the Zywave under natural and

cycloplegic conditions on two occasions separated by at least one week. Refractive error

was also measured using a Nidek ARK-700A autorefractor. At one visit, a cycloplegic

subjective refraction was performed. Measured ocular wavefront aberrations were

expressed as the polynomial coefﬁcients from a least-squares ﬁtted ﬁfth-order Zernike

polynomial expansion over three, ﬁve and seven millimetre diameters. Repeatability and

validity were evaluated by calculating the difference between pairs of refractive estimates

or Zernike terms, determining the mean and standard deviation of these differences and

calculating the 95% limits of agreement (LoA =mean ⫾1.96 ¥SD).

Results: The repeatability of refractive error estimated by the Zywave was better than that

of the Nidek autorefractor for both manifest and cycloplegic conditions. Manipulating

the pupil size on the Zywave from three to seven millimetres changed the mean cyclople-

gic spherical equivalent from -1.91 D to -2.60 D, a shift that was negatively correlated with

spherical aberration. As expected, the magnitude of the Zernike coefﬁcients increased

with increasing pupil diameter, as did their corresponding 95% LoA. The 95% LoA

decreased for higher-order terms but the magnitude of the terms and the variation

between subjects also decreased with increasing order. To compensate for these factors,

the ratio of the SD between sessions to the SD across subjects was calculated. The ratios

were lowest for second-order terms (less than 0.08 for 7.0 mm pupil), intermediate for

the C4,0 spherical aberration term (0.14) and third-order terms (~0.25) but approached

and exceeded 1.0 for many fourth- and ﬁfth-order terms.

Conclusions: The Zywave provides valid and repeatable estimates of refractive error. We

attribute the myopic shift for larger pupils to the eye’s spherical aberration. The repeat-

ability of the Zernike terms measured with the Zywave was acceptable for the second-

order and spherical aberration terms but for other higher-order terms, the variation

between sessions may exceed the variation between subjects indicating unacceptable

repeatability. This may have important ramiﬁcations for wavefront-guided LASIK.

Submitted: 1 November 2008

Revised: 6 January 2009

Accepted for publication: 23 January

2009

Key words: aberrations, aberrometer, evaluation, wavefront optics, Zernike polynomials

CLINICAL AND EXPERIMENTAL

OPTOMETRY

Liang and colleagues1were the ﬁrst to

use a Shack-Hartmann aberrometer on

human eyes and mathematically explain

the wavefront maps to the fourth-order

Zernike terms from the local derivatives of

the centroid patterns.2The laboratory

Shack-Hartmann aberrometer of Liang

and colleagues1provided adequate mea-

surements of higher-order aberrations

described by Zernike terms and conven-

tional refractive error measurements. In

the subsequent decade, Shack-Hartmann

wavefront measurement has been used

extensively in the clinical setting to

measure ocular aberrations in keratoco-

nus, dry eye, before and after refractive

surgery and cataract.3,4

Bausch & Lomb Zywave

The Zywave (Bausch & Lomb Zywave,

Rochester, NY) is a Shack-Hartmann aber-

rometer used to measure ocular aberra-

tions.2The Zywave focuses an infrared

laser beam of 785 nm on the retina, which

serves as a point source for light propa-

gated out of the eye. The Zywave provides

an adjustable optical system to compen-

sate for patient’s refractive errors and

adjusts for the subject’s far point by

fogging the image to control for accom-

modation. As a wavefront is propagated

back out of the eye, a lenslet array in the

Zywave that is conjugate with the pupil

plane focuses the wavefront into a

76-point centroid pattern on a CCD detec-

tor. The spatial displacement of each cen-

troid from its ideal location is used to

determine the slope of the aberrated wave-

front. The shape of the wavefront is deter-

mined by integration of the slopes for

each location in the pupil plane. The

Zywave uses Zernike terms to ﬁt the slope

data and the coefﬁcients can be used to

mathematically reconstruct the wavefront.

The Zywave measures total wavefront aber-

rations and mathematically represents

them up to the ﬁfth-order Zernike terms.

Each Zernike term represents a speciﬁc

aberration with a speciﬁc mathematical

deﬁnition and predetermined shape.5

Each Zernike term has a corresponding

coefﬁcient that represents the magnitude

of the wavefront shape in microns and is a

quantitative measure that represents how

much of that aberration is present.

The Zywave can give an estimate of

refractive error, representing the second-

order aberrations of the eye. The Zywave

was designed to measure refractive errors

over a range of +6.00 to -12.00 DS and up

to 5.00 D of cylinder. The Zywave is part of

the Zyoptix Diagnostic Workstation (along

with the Orbscan IIz corneal topogra-

pher) for wavefront-guided refractive

surgery.

Previous studies of the Zywave have paid

little attention to the effect of pupil size

and control of accommodation on the

repeatability and validity of estimates of

refractive error and Zernike terms. The

goals of this study were:

• to determine the repeatability and

validity of the refractive error measured

by the Zywave under manifest and

cycloplegic conditions for a range of

pupil sizes (three, ﬁve and seven milli-

metres plus the instrument’s default)

and in comparison to a conventional

autorefractor

• to determine the repeatability of

higher-order aberrations under cyclo-

plegic conditions, speciﬁed as Zernike

coefﬁcients, measured by the Zywave

for a range of pupil sizes (three, ﬁve

and seven millimetres) and compared

with the range of values found across

subjects.

METHODS

The tenets of the Declaration of Helsinki

were followed and all procedures were

approved by the Ofﬁce of Research Risks

and Protection at The Ohio State Univer-

sity. Written informed consent was ob-

tained from each subject prior to any

procedures being performed. Subjects

were recruited from The Ohio State Uni-

versity College of Optometry. Subjects

were required to be at least 18 years of age

and have correctable visual acuity of at

least 6/6 in the right eye. Contact lens

wearers and patients with any ocular

disease or pathology that could affect

vision, for example, keratoconus or cata-

ract, were excluded.

Patients attended for two visits sepa-

rated by at least one week. On each occa-

sion, three refractive error measurements

were taken of the right eye with the Zywave

(Bausch & Lomb, Rochester, NY) and a

Nidek ARK–700A autorefractor (Nidek,

Fremont, CA). One drop of 1% tropicam-

ide was instilled into the subject’s right

eye and 30 minutes later, the Zywave

and autorefractor measurements were

repeated. Zywave measurements were

taken immediately after a blink to limit

tear ﬁlm disruption. On one of the two

visits, the subject’s refractive error was

determined using standard subjective

techniques under cycloplegia by one of

two authors (MDT or MAB). No artiﬁcial

pupil was used. All measurements were

referenced to the spectacle plane.

The Zywave Version 3.21 software also

allows manipulation of the pupil diameter

by limiting the area of the wavefront used.

Among the data provided is an estimate of

the subject’s refractive error. Refractive

error was determined for the default pupil

size of 3.5 mm for both manifest and

cycloplegic measurements along with

pupil diameters of three, ﬁve and seven

millimetres under cycloplegia. The Zywave

software also calculates complete wave-

front aberration data in Zernike terms.

These data were determined and exported

for pupil diameters of three, ﬁve and

seven millimetres under cycloplegia. The

exported data are normalised Zernike

polynomial coefﬁcients but do not strictly

conform to OSA, ANSI, and ISO stan-

dards. Speciﬁcally, the Zywave uses the

opposite reference for the direction of

wavefront propagation, where positive

propagation is toward the eye. As a conse-

quence, the sign of the coefﬁcients was

reversed and the preferred notation used

(Znmfor the polynomial and Cnmfor the

corresponding coefﬁcient).6

Data analysis

Refractive error data from the Zywave

and autorefractor were converted to the

Fourier components M, J0, and J45 for

further analysis.7Repeatability of refrac-

tive error data was assessed by comparing

the mean values for each session and for

each subject. The mean and standard

TheB&LZywave aberrometer Dobos, Twa and Bullimore

deviation of the differences were deter-

mined along with the 95% limits of

agreement (LoA) consistent with the rec-

ommendations of Bland and Altman.8The

validity of Zywave and autorefractor mea-

surements was assessed by comparing

values to the subjective refraction using

the same methods.

The repeatability of the higher-order

Zernike terms was assessed using the same

methods. The mean, SD and 95% LoA

were calculated for each Zernike term and

for each pupil size. To further assess the

impact of these values, the calculated

between-session standard deviation for

each Zernike term was compared to the

between-subject standard deviation. In

this way, the repeatability of each Zernike

term could be placed in the appropriate

context by comparing the value to the

variation across subjects.

RESULTS

Twenty-three subjects met the eligibility

criteria and completed the study. Ten

were male and 13 (57 per cent) were

female. Subjects ranged in age from 20

to 48 years (mean: 27.6 ⫾6.8 years). The

mean spherical equivalent for subjective

refraction under cycloplegia was -2.15

⫾2.87 D (range -9.25 to +1.25 D.

Repeatability and validity of

refractive error measurements

The distribution of between-session differ-

ences in spherical equivalent are shown in

Figure 1 and the repeatability of refractive

error measurements is summarised in

Table 1. As expected, none of the mean

differences was signiﬁcantly different from

zero. For the spherical equivalent (M), the

repeatability of the Zywave was better than

that of the autorefractor under both mani-

fest and cycloplegic conditions. The 95%

LoA were narrowest for the default and

three millimetre pupils under cycloplegia.

The repeatability of astigmatism showed

similar trends.

The validity of refractive error measure-

ments is summarised in Table 2. All values

are in comparison with the cycloplegic

subjective refraction. For the spherical

equivalent (M), the mean values for the

autorefractor are closest to zero. The 95%

LoA are narrowest for the autorefractor

under cycloplegia, closely followed by the

Zywave under cycloplegia for the default

and three millimetre pupil. For astig-

matism, the validity is similar for all

measurements.

For the Zywave, the spherical equivalent

showed a systematic shift in the myopic

direction as the pupil size is increased

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00

Mean spherical equivalent (D)

Difference in mean spherical equivalent (D)

Zywave 3 mm Zywave 5 mm Zywave 7 mm Zywave default Nidek

Figure 1. Summary mean versus difference plot comparing the Zywave at all pupil sizes

and the Nidek autorefractor under cycloplegic conditions

Measurement M J0J45

Mean SD 95% LoA Mean SD 95% LoA Mean SD 95% LoA

Nidek ARK–700A—Manifest -0.03 0.28 -0.57 to +0.52 +0.01 0.10 -0.19 to +0.22 -0.02 0.12 -0.26 to +0.22

Nidek ARK–700A—Cycloplegic +0.01 0.23 -0.45 to +0.47 +0.01 0.12 -0.22 to +0.24 +0.01 0.08 -0.15 to +0.17

Zywave—Manifest (default) +0.04 0.22 -0.39 to +0.48 +0.01 0.08 -0.15 to +0.18 -0.00 0.06 -0.13 to +0.12

Zywave—Cycloplegic (default) +0.04 0.17 -0.29 to +0.37 +0.00 0.07 -0.14 to +0.14 +0.00 0.07 -0.13 to +0.13

Zywave—Cycloplegic (3 mm) +0.04 0.14 -0.23 to +0.32 -0.01 0.11 -0.23 to +0.21 -0.01 0.09 -0.18 to +0.16

Zywave—Cycloplegic (5 mm) +0.03 0.21 -0.37 to +0.43 -0.03 0.16 -0.33 to +0.28 -0.03 0.11 -0.25 to +0.19

Zywave—Cycloplegic (7 mm) -0.02 0.16 -0.34 to +0.30 +0.01 0.09 -0.16 to +0.19 +0.00 0.06 -0.11 to +0.12

Table 1. The repeatability of refractive error measurement for the Nidek ARK–700A autorefractor and the Bausch & Lomb Zywave. All

values are in dioptres.

TheB&LZywave aberrometer Dobos, Twa and Bullimore

from three to seven millimetres. This

trend is shown in Figure 2, which illus-

trates that the mean is -1.91 D for the three

millimetre pupil but -2.60 D for the seven

millimetre pupil. It was hypothesised that

this shift was due to spherical aberration

so the myopic shift was plotted as a func-

tion of the C40coefﬁcient obtained for a

seven millimetre pupil (Figure 3). As can

be seen, those eyes with higher levels of

spherical aberration show the greatest

myopic shift associated with increasing

pupil size (r2=0.35).

Repeatability of higher-order

aberrations

Table 3 shows the repeatability of the

Zernike terms for the three, ﬁve and seven

millimetre pupils. For the three millime-

tre pupil, the Zywave only generates

Zernike terms through the third order.

Inspection of Table 3 suggests that repeat-

ability, as indicated by the size of the 95%

LoA, is best for the higher-order terms

and poorest for the lower-order aberra-

tions. For example, the largest standard

deviation and 95% LoA belongs to the C20

coefﬁcient, which corresponds to the

spherical defocus. This is misleading

because for a given subject, the low order

terms are relatively large and vary consid-

erably across the subjects. In contrast,

the higher-order terms tend to be very

small in magnitude and vary little between

subjects. To compensate for this, the

within-subject, between-session standard

deviations for the seven millimetre pupil

Measurement M J0J45

Mean SD 95% LoA Mean SD 95% LoA Mean SD 95% LoA

Nidek ARK–700A—Manifest +0.06 0.40 -0.73 to +0.84 +0.06 0.16 -0.25 to +0.36 +0.00 0.12 -0.24 to +0.23

Nidek ARK–700A—Cycloplegic -0.06 0.28 -0.62 to +0.49 -0.07 0.15 -0.36 to +0.22 -0.03 0.11 -0.23 to +0.18

Zywave—Manifest (default) +0.11 0.46 -0.80 to +1.02 +0.10 0.13 -0.16 to +0.37 +0.02 0.13 -0.23 to +0.28

Zywave—Cycloplegic (default) +0.21 0.35 -0.47 to +0.90 +0.11 0.13 -0.15 to +0.37 +0.01 0.10 -0.19 to +0.20

Zywave—Cycloplegic (3 mm) +0.23 0.35 -0.46 to +0.92 +0.10 0.14 -0.16 to +0.37 +0.00 0.09 -0.18 to +0.18

Zywave—Cycloplegic (5 mm) -0.26 0.51 -1.26 to +0.75 -0.26 0.13 -0.50 to +0.01 -0.04 0.10 -0.24 to +0.16

Zywave—Cycloplegic (7 mm) -0.45 0.54 -1.51 to +0.61 +0.11 0.15 -0.19 to +0.41 -0.08 0.11 -0.29 to +0.14

Table 2. The validity of refractive error measurements compared to the subjective refractions. All values are in dioptres.

Zywave

3 mm

pupil

Zywave

default

pupil Nidek ARK-700A

Pupil diameter (mm)

2345678

Zywave

5 mm pupil

Subjective

refraction

Zywave

7 mm pupil

Mean spherical equivalent (D)

-1.00

-1.50

-2.00

-2.50

-3.00

Figure 2. Mean spherical equivalent determined by the Zywave as a function of pupil

size. The values for subjective refraction and the Nidek autorefractor are plotted as lines

for comparison.

Spherical aberration for 7 mm pupil (µm)

Difference in M (D)

7 mm minus 3 mm pupil

-2.00

-1.50

-1.00

-0.50

0.00

0.50

-0.50 0.00 0.50 1.00 1.50

Figure 3. Change in spherical equivalent refraction when pupil size is increased from

3 mm to 7 mm as a function of spherical aberration (C40) for a 7 mm pupil

TheB&LZywave aberrometer Dobos, Twa and Bullimore

from Table 3 are shown again in Table 4

along with the between-subject, within-

session standard deviations. The latter

values represent the distribution of

Zernike terms across our subject popula-

tion. The ratios of these two standard

deviations were calculated and are shown

in Table 4 and plotted in Figure 4. A low

ratio indicates good repeatability relative

to the variation within the subject popula-

tion. As would be expected, the second

order Zernike terms representing sphere

and cylinder have very low ratios indicat-

ing that the between-session variability

within a subject is very low compared to

the variability across subjects. In contrast,

some of the higher-order aberrations have

ratios of around one, indicating that a

repeated measure on a single subject will

differ by a similar amount to a new

measure on a completely different subject.

Of the higher-order aberrations, the coma

coefﬁcient (C3

+1and C3-1) and spherical

aberration coefﬁcient (C40) have the

lowest ratios. Analysis of the ﬁve millime-

tre pupil data shows very similar trends but

neither the data nor the analysis are

shown in the interest of space.

Zernike

coeff.

Within-

subject SD

(from Table 3)

Between-

subject SD

Ratio

C200.233 4.985 0.047

C2-2 0.064 0.787 0.081

+20.102 1.467 0.070

C3-1 0.113 0.333 0.338

+10.059 0.240 0.246

C3-3 0.053 0.197 0.268

+30.051 0.193 0.263

C400.043 0.304 0.143

+20.046 0.114 0.402

C4-2 0.034 0.065 0.524

+40.051 0.093 0.546

C4-4 0.054 0.060 0.893

+10.025 0.029 0.850

C5-1 0.029 0.047 0.606

+30.028 0.036 0.774

C5-3 0.031 0.031 0.988

+50.034 0.050 0.684

C5-5 0.038 0.031 1.221

Table 4. Comparison of the repeatability (within subject SD,

in mm) with the between-subject variability (SD, in mm) for

higher-order aberrations measured with the Zywave for 7 mm

pupil. The ﬁnal column shows the ratio of these values, a

smaller value representing better repeatability.

Zernike

coeff.

3 mm pupil 5 mm pupil 7 mm pupil

Mean SD 95% LoA Mean SD 95% LoA Mean SD 95% LoA

C20+0.075 0.282 -0.478 to +0.628 +0.033 0.127 -0.216 to +0.282 +0.024 0.233 -0.433 to +0.481

C2-2 +0.011 0.037 -0.062 to +0.084 +0.009 0.050 -0.089 to +0.108 +0.016 0.064 -0.106 to +0.141

+2+0.006 0.047 -0.086 to +0.098 +0.010 0.071 -0.130 to +0.150 +0.006 0.102 -0.194 to +0.206

C3-1 -0.006 0.024 -0.053 to +0.042 -0.022 0.042 -0.104 to +0.061 -0.017 0.113 -0.237 to +0.204

+1+0.003 0.018 -0.031 to +0.037 +0.009 0.045 -0.080 to +0.098 +0.013 0.059 -0.103 to +0.129

C3-3 -0.005 0.023 -0.050 to +0.040 +0.008 0.035 -0.061 to +0.076 +0.005 0.053 -0.099 to +0.108

+3-0.004 0.015 -0.034 to +0.025 +0.006 0.026 -0.044 to +0.056 +0.018 0.051 -0.081 to +0.117

C40-0.004 0.015 -0.035 to +0.026 -0.010 0.043 -0.095 to +0.075

+2+0.001 0.013 -0.024 to +0.027 +0.008 0.046 -0.083 to +0.098

C4-2 -0.002 0.014 -0.030 to +0.026 -0.001 0.034 -0.067 to +0.066

+4+0.001 0.014 -0.026 to +0.028 -0.002 0.051 -0.102 to +0.097

C4-4 -0.002 0.022 -0.044 to +0.041 -0.005 0.054 -0.111 to +0.100

+1-0.000 0.010 -0.021 to +0.020 -0.003 0.025 -0.051 to +0.046

C5-1 +0.002 0.013 -0.023 to +0.027 +0.009 0.029 -0.048 to +0.065

+3+0.001 0.007 -0.013 to +0.016 -0.011 0.028 -0.065 to +0.043

C5-3 -0.001 0.012 -0.025 to +0.023 -0.003 0.031 -0.064 to +0.057

+5-0.002 0.010 -0.021 to +0.017 -0.009 0.034 -0.077 to +0.058

C5-5 -0.002 0.009 -0.020 to +0.016 +0.005 0.038 -0.070 to +0.080

Table 3. Repeatability of higher-order aberrations measured with the Zywave. All values are in mm.

TheB&LZywave aberrometer Dobos, Twa and Bullimore

DISCUSSION

Repeatability and validity of

refractive error measurements

The Zywave gives valid and repeatable esti-

mates of refractive error as its measure-

ments compare favourably with the Nidek

ARK-700 autorefractor and the 95% LoA

are consistent with those found in previ-

ous studies of the repeatability of autore-

fractors.9,10 Estimates of repeatability and

validity can depend on the number of

measurements taken. Previous studies

have averaged between three and 10 mea-

surements. The Zywave also gives valid esti-

mates of a subject’s manifest refraction

and is comparable to other Shack-

Hartmann aberrometers.11–15

Two other studies have compared the

repeatability and validity of estimates of

refractive error using the Zywave. Hament,

Nabar and Nuijts11 compared Zywave mea-

surements to subjective refraction and

autorefraction in 20 myopic eyes. They

found that with a dilated pupil the Zywave

gave substantially more myopia than sub-

jective refraction (mean difference -1.10

⫾0.46 D). For a 3.5 mm pupil, the differ-

ence was smaller but still signiﬁcant (mean

difference -0.55 ⫾0.48 D). They also

report a repeatability coefﬁcient of -0.25 to

+0.25 D based on three repeat measure-

ments during a short period. Mirshahi and

co-workers16 determined repeatability (SD

of within-session measures) to be -0.15

to +0.15 D using a similar analytical

approach in 20 patients. They reported

negligible mean differences between the

spherical equivalent values from the

Zywave and for the studies from subjective

refraction but a large range (mean 0.09 D,

range -0.81 to +1.83 D). In summary, the

Zywave-derived estimates of refractive

error data in the current study agree more

closely with subjective refraction than in

the studies of Hament, Nabar and NJuijts11

and Mirshahi and co-workers.16

The exact method of determining the

Zywave’s or any clinical aberrometer’s

autorefraction may not be fully known.

In general, clinical aberrometers have

autorefractive repeatability that is similar

or better than those of clinical autorefrac-

tors. Although higher-order aberrations

are measured with clinical aberrometers,

their ﬂuctuating higher-order aberrations

may have minimal effects on the refractive

error data. Indeed, clinical aberrometers

have been shown to provide consistent

refractive error measurements despite

ﬂuctuations in high-order aberrations.16,17

Consistent with the ﬁndings of Hament,

Nabar and Nuijts,11 as pupil size is manipu-

lated from three, ﬁve and seven mil-

limetres on the Zywave, the refractive

error becomes more myopic (Table 2,

Figure 2). The values of C20change in a

corresponding manner (data not shown).

This reﬂects the spherical aberration of

the eye and is conﬁrmed by the correla-

tion between the myopic shift in refraction

and the C40coefﬁcient shown in Figure 3.

The higher the magnitude of the spherical

aberration term, a higher myopic shift is

seen in spherical equivalent. This relation-

ship among spherical aberration, pupil

size and refractive error has been de-

scribed and discussed previously.18,19 The

inﬂuence of pupil size on the estimate of

spherical equivalent refractive error will

depend ultimately on the algorithm used

by the instrument and some aberrometers

adjust for the eye’s spherical aberration

to give an estimate of refractive error

approaching that obtained with a smaller

pupil.19

Repeatability of higher-order

Zernike terms

Many of the higher-order Zernike terms

measured by the Zywave in this study are

small in quantity, as many are only one-

thousandth of a micron. Because of their

small magnitude, this can give the impres-

sion that these measurements are very

consistent. In contrast, measures of

second-order aberrations—corresponding

to sphere and cylinder—appear less re-

peatable, having larger between-session

standard deviations, however, these

lower-order aberrations vary considerably

among subjects. We attempted to take a

balanced approach by referencing the

between-session standard deviations to the

corresponding between-subject standard

deviations. We assert that the calculated

ratio of these standard deviations gives a

truer indication of the repeatability of the

Zywave’s ability to estimate each Zernike

term. Figure 4 emphasises that the repeat-

ability of the second-order terms is good

with ratios less than 0.1. The repeatability

of third-order aberrations and spherical

aberration coefﬁcients (C40) may be con-

sidered acceptable with ratios of around

0.2. In other words, the variation between

measurements on the same subject are

small compared to those between subjects.

In contrast, the repeatability of other

higher-order Zernike terms should be

SD ratio

Zernike term

1.40

0C2

-2 C2

2C3

-1 C3

1C3

-3 C3

3C4

0C4

2C4

-2 C4

4C4

-4 C5

1C5

-1 C5

3C5

-3 C5

5C5

-5

1.20

1.00

0.80

0.60

0.40

0.20

0.00

Figure 4. The ratio of within-subject SD to between-subject SD for all Zernike aberration

terms measured with the Zywave for 7 mm pupil. A smaller ratio represents better

repeatability.

TheB&LZywave aberrometer Dobos, Twa and Bullimore

considered poor, with ratios closer

to 1.

A similar conclusion was drawn by Mir-

shahi and co-workers.16 Their approach

was slightly different—they calculated the

coefﬁcient of variation for each term (SD/

mean)—but the outcomes show trends

similar to our data, with unsatisfactory

repeatability for most fourth- and ﬁfth-

order Zernike terms. Inspection of their

Figure 2 shows that it has an appearance

very similar to our Figure 4.

With regards to higher-order aberra-

tions, there are many factors one must

examine as sources for differences in

repeatability data. For example, instru-

ment alignment,20 time between measure-

ments,20, 21 and biological variables (ocular

optics, tears, accommodation, pupil size)22

among others must be considered.

Aberrometry measurements and

wavefront-guided refractive

surgery

It is estimated that the higher-order aber-

rations of a normal and healthy eye

account for 0.25 D or less of dioptric

blur4,23,24 and yet, wavefront guided treat-

ments have increasingly become the

standard of care in corneal refractive sur-

gery.25 In part, this is because the visual

results of wavefront guided treatments are

somewhat better.26–28 Although higher-

order wavefront errors are only a small

fraction of the total optical aberrations of

the normal eye, when combined with the

additional aberrations induced by refrac-

tive surgical treatment, they can become

visually signiﬁcant.29,30 Applegate, Sarver

and Khemsara31 have demonstrated that

not all aberrations have an equal inﬂu-

ence on vision. Several third- and fourth-

order terms signiﬁcantly degrade vision in

the postoperative eye, suggesting that

accurate measurements to at least this

level are needed.31

When accurate preoperative measure-

ments of aberrations are combined with

information about the magnitude of

treatment-induced aberrations, it is pos-

sible to minimise the treatment-induced

aberrations and optimise vision. The

ability to achieve this goal depends on

several factors. These include:

1. the ability to correctly measure ocular

wavefront errors

2. translation of the measured error to an

appropriate treatment plan

3. successful execution of the treatment

plan

4. a predictable biological response to the

treatment.

Here we report on only the ﬁrst of these

factors that can inﬂuence visual results

after wavefront customised corneal refrac-

tive surgery.

Wavefront sensing has developed

rapidly in the ﬁeld of refractive surgery

due to the understanding of not only how

refractive surgery may induce higher-

order aberrations32 but also analysis of

higher-order aberrations pre-operatively

to design a customised correction that can

achieve excellent visual performance.33

Analysing the inconsistency of some

higher-order aberrations, potentially one

may relate the importance of speciﬁc

higher-order aberrations in complete

wavefront error, despite the overall sum

being less than 0.25 D or less of dioptric

blur. Cheng and colleagues21 also pro-

posed that certain higher-order aberra-

tions are more worthy of correction than

others. Trying to correct a small and ﬂuc-

tuating higher-order aberration may lead

to the generation of a further higher-

order aberration. Therefore, it is impor-

tant to identify the most relevant Zernike

terms, their role in determining the

overall wavefront and, ultimately, their

effect on vision when developing algo-

rithms for custom refractive surgery.

Caveats and limitations

Here we report on the performance of a

single commercially-available clinical aber-

rometer. The Zywave produces repeatable

and valid estimates of refractive error.

Given its level of sophistication compared

to traditional autorefractors, its superior

repeatability might have been anticipated.

The data were taken on the ﬁrst genera-

tion of the Zywave and it is possible

that subsequent hardware and software

upgrades may further improve the repeat-

ability of this instrument. We did not

evaluate other clinical aberrometers,

which are believed to produce similar val-

ues,15,34 although differences may exist.20

One important difference between the

Zywave and other clinical aberrometers is

the relatively low spatial resolution of its

Shack-Hartmann grid. The Zywave has 76

spots on its centroid pattern while others

such as the LADARWave (Alcon Labs, Inc,

Fort Worth, TX) has 204 to 213, the

Wavescan (VISX, Santa Clara, CA) has 240

and the COAS (AMO-Wavefront Sciences,

Albuquerque, NM) has 1,452 sampling

points.35 Work may be done to analyse

beneﬁts/limitations of the centroid pat-

terns and sampling points. It appears that

the Zywave will have a dynamic range that

is limited to calculating fewer Zernike

polynomial terms of lower frequency.15

Although this study was not speciﬁcally

designed to quantify the impact of Shack-

Hartmann spatial resolution on measure-

ment precision, we expect that this Zywave

design limitation explains some of the

poorer repeatability that we observed with

higher-order terms.

SUMMARY

The Zywave provides repeatable measures

of refractive error at the adjusted pupil

diameters under both cycloplegic and

manifest conditions over a range of refrac-

tive errors for normal eyes. The Zywave

refractive error estimates are comparable

to subjective refraction and another

autorefractor for small pupils but more

myopic when set to ﬁve or seven millime-

tres. The second-order Zernike terms

along with the spherical aberration and

coma terms derived from the Zywave show

good repeatability. Some of the higher-

order Zernike terms are small in magni-

tude and are variable between sessions.

GRANTS AND FINANCIAL SUPPORT

Supported by National Institutes of Health

grants NEI T35-07151 and K23-EY016225.

MAB has received research funding from

Bausch & Lomb that is unrelated to the

topic of this manuscript.

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Corresponding author:

Dr Michael J Dobos

The Ohio State University College of

Optometry

338 West 10th Avenue

Columbus, Ohio 43210-1280

USA

E-mail: dobos.10@osu.edu

TheB&LZywave aberrometer Dobos, Twa and Bullimore

Comparison of higher order wavefront aberrations with four aberrometers

Article

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Indian J Ophthalmol

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\dot{V}{\mathrm{O}}_2\mathrm{peak}

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\dot{V}{\mathrm{O}}_2\mathrm{peak}

= 45 ± 8.6 mL O2 kg⁻¹ min⁻¹) were recruited. Participants completed physical exertion on a stationary cycle ergometer for simultaneous pulmonary minute ventilation (V̇

\dot{V}

) measurements and EGAIC computations. Exercise protocols and subsequent conditions involved a 5‐min cycling warm‐up at 25 W min⁻¹, incremental exercise to exhaustion (V̇O2

\dot{V}{\mathrm{O}}_2

ramp test), then a steady‐state exercise bout induced by a constant Watt load equivalent to 80% ventilatory threshold (80% VT). A linear mixed model revealed that exercise intensity significantly affected V̇O2

\dot{V}{\mathrm{O}}_2

measurements (p < 0.0001), whereas airflow sensor method (p = 0.97) and its interaction with exercise intensity (p = 0.91) did not. Group analysis of precision yielded a V̇O2

\dot{V}{\mathrm{O}}_2

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\dot{V}

up to 150 L min⁻¹, indicating a decrease in precision and highlighting potential challenges in interpreting biological variability, training response heterogeneity, and test–retest comparisons. These findings suggest careful consideration of airflow sensor method variance across metabolic cart configurations.

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May 2023
OPHTHAL PHYSL OPT

Purpose: To investigate the prevalence and repeatability of high-order aberrations (HOAs) from non-cyclopleged eyes in 1515 children and adolescents 2.5-18 years of age. Methods: The Leipzig Research Centre for Civilization Diseases (LIFE)-Child study is a population-based, prospective, observational single-centre study that investigates the development of children and adolescents in Germany. Wavefront measurements were repeated three times in each eye of 1515 healthy subjects. Results were described by 36 Zernike coefficients for a 5 mm reference pupil diameter. Short-term repeatability is given for each coefficient. The impact on vision is described by the root mean squared (RMS) value of the HOA Zernike coefficients. Results: High-order aberrations were dominated by five contributions. For 1004 right eyes: spherical aberration (c12 = 0.06 ± 0.07 μm), coma (c7 = 0.03 ± 0.09 μm, c8 = 0.03 ± 0.06 μm) and trefoil (c6 = -0.01 ± 0.07 μm, c9 = 0.008 ± 0.06 μm). The RMS value was 0.18 ± 0.06 μm. Modes higher than fourth order do not contribute clinically to the aberrations. HOAs show no clinically significant dependency with age. Instead, HOA values agree well with previous results on aberrations in adult eyes. Spherical aberration was highly correlated between the two eyes. Repeatability was worst for coma, 0.033 μm, due to variability in the alignment of the pupil centre. The left eye showed, on average, a 0.08 mm larger pupil diameter than the right eye (p < 0.02). Conclusions: Across the age span from 2.5 to 18 years, we see the same distribution of HOA as for adults. We established that only five Zernike coefficients, spherical aberration, coma and trefoil were of clinical significance in healthy eyes. A high correlation between the two eyes for spherical aberration suggests a common blueprint for each eye in any one subject.

Test-Retest Reliability of Clinical Shack-Hartmann Measurements

Article

Full-text available

Jan 2004
INVEST OPHTH VIS SCI

Xu Cheng

purpose. To evaluate the stability of clinical monochromatic aberrometry measurements over a wide range of time scales. methods. Monochromatic aberrations in four normal eyes were measured with a clinical Shack-Hartmann aberrometer. A chin rest or a supplemental bite bar attachment was used to stabilize head and eye position. Five repeated measurements were taken within one test (5 frames, t < 1 second) without realignment. With realignment between each measurement, aberration measurements were repeated five times (t < 1 hour) on each day, at the same time of day on five consecutive days, and again on 5 days at monthly intervals. A control experiment studied the effect of systematically misaligning the eye to determine whether fixation errors can account for the variation in the repeated measurements. results. Variability of wavefront root mean square (RMS) error (excluding defocus and astigmatism) was tracked across repeated measurements. Variances for different time scales were: 8.10 × 10⁻⁵ μm² (t < 1 second), 3.24 × 10⁻⁴ μm² (t < 1 hour), 4.41 × 10⁻⁴ μm² (t < 1 week), 9.73 × 10⁻⁴ μm² (t < 1 year). Bite bar and chin rest data were almost identical. Rotational fixation error up to 3° accounts for only part of the variability. conclusions. Increased variability in aberration maps between days and months indicates biological fluctuations that are large enough to prevent achievement of “perfect vision,” even in the unlikely event that spherical and astigmatic refractive errors are corrected perfectly. However, lack of stability does not justify withholding treatment. A lasting benefit of aberration correction is expected despite temporal variability.

Standards for Reporting the Optical Aberrations of Eyes

Conference Paper

Jan 2000

In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes. The following summary of the committee’s recommendations is available also in portable document format (PDF) on OSA Optics Net at http://www.osa.org/.

Production and use of a lenticular Hartmann screen

Article

Jan 1971

Standards for reporting the optical aberrations of eyes

Conference Paper

Sep 2002

Accurasy, repeatability, and clinical application using timebased wavefront aberrometry measurements

Article

Jan 2006
OPHTHALMOLOGY

Wavefront-Guided LASIK for the Correction of Primary Myopia and Astigmatism: A Report by the American Academy of Ophthalmology

Article

Jan 2009
Year Bk Ophthalmol

Christopher J Rapuano

Wavefront-Guided LASIK for the Correction of Primary Myopia and Astigmatism

Article

Jul 2008

To describe wavefront-guided (WFG) LASIK for the primary treatment of low to moderate levels of myopia and astigmatism and to examine the evidence on the safety and effectiveness of the procedure in comparison with conventional LASIK. Literature searches conducted in 2004, 2005, 2006, and 2007 retrieved 209 unique references from the PubMed and Cochrane Library databases. The panel selected 65 articles to review, and of these, chose 45 articles that they considered to be of sufficient clinical relevance to submit to the panel methodologist for review. During the review and preparation of this assessment, an additional 2 articles were included. A level I rating was assigned to properly conducted, well-designed, randomized clinical trials; a level II rating was assigned to well-designed cohort and case-controlled studies; and a level III rating was assigned to case series, case reports, and poorly designed prospective and retrospective studies. In addition, studies that were conducted by laser manufacturers before device approval (premarket approval) were reviewed as a separate category of evidence. The assessment describes studies reporting results of WFG LASIK clinical trials, comparative trials, or both of WFG and conventional LASIK that were rated level II and level III. There were no studies rated as level I evidence. Four premarket approval studies conducted by 4 laser manufacturers were included in the assessment. The assessment did not compare study results or laser platforms because there were many variables, including the amount of follow-up, the use of different microkeratomes, and the level of preoperative myopia and astigmatism. There is substantial level II and level III evidence that WFG LASIK is safe and effective for the correction of primary myopia or primary myopia and astigmatism and that there is a high level of patient satisfaction. Microkeratome and flap-related complications are not common but can occur with WFG LASIK, just as with conventional LASIK. The WFG procedure seems to have similar or better refractive accuracy and uncorrected visual acuity outcomes compared with conventional LASIK. Likewise, there is evidence of improved contrast sensitivity and fewer visual symptoms, such as glare and halos at night, compared with conventional LASIK. Even though the procedure is designed to measure and treat both lower- and higher-order aberrations (HOAs), the latter are generally increased after WFG LASIK. The reasons for the increase in HOA are likely multifactorial, but the increase typically is less than that induced by conventional LASIK. No long-term assessment of WFG LASIK was possible because of the relatively short follow-up (12 months or fewer) of most of the studies reviewed.

Recent advances in representation of monochromatic aberrations of human eyes

Article

May 2004
CLIN EXP OPTOM

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. In this paper, I discuss the different ways of representing aberrations of the human eye, the terminology used, how wave aberrations are used to determine refractions, the influence of pupil size on aberrations, how to compare right and left eye aberrations, how aberrations can be manipulated into different forms, how to make corrections for changes in wavelength, the appropriate ocular axis, and corneal and lenticular components of the aberrations.

Clinical Applications of the Shack-Hartmann Aberrometer

Article

Dec 1999

The efficacy of the Shack-Hartmann technique for measuring the optical aberrations of the eye was evaluated for four classes of clinical conditions associated with optically abnormal eyes. These categories (with specific examples) are: anomalies of the tear film (dry eye), corneal disease (keratoconus), corneal refractive surgery [laser-assisted in situ keratomileusis (LASIK)], and lenticular cataract. We show that in each of these cases, it is possible to obtain at least a partial topographic map of the refractive aberrations of the patient's eyes, but severe losses of data integrity can occur. We further show that the Shack-Hartmann aberrometer provides additional information about the eye's imperfections on a very fine spatial scale (< 0.4 mm) which scatter light and further degrade the quality of the retinal image. Taken together, spatial maps of the variation of optical aberrations and scatter across the eye's entrance pupil represents an improved description of the optical imperfections of the abnormal eye.

Statistical-Methods For Assessing Agreement Between 2 Methods Of Clinical Measurement

Article

Apr 2010

In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analysed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.