Optometry (2011) 82, 231-240

Comparison of refractive error measurements in adultswith Z-View aberrometer, Humphrey autorefractor, andsubjective refraction

Jeffrey Cooper, O.D.,a Karl Citek, O.D., Ph.D.,b and Jerome M. Feldman, Ph.D.a

aState University of New York State College of Optometry, New York, New York; and bPacific University College ofOptometry, Forest Grove, Oregon.

KEYWORDS Abstract

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152

doi

Aberrometer;Autorefractor;Subjective refraction;Sphere;Cylinder;Axis;Higher-order

aberrations;

Visual acuity

BACKGROUND: The aim of this study was to evaluate whether measurements obtained with theOphthonix Z-View aberrometer (Vista, California) and a Humphrey autorefractor (Zeiss Humphrey,Dublin, California) correlate with standard subjective refraction measurements, based on visual acuityresults.METHODS: A retrospective data analysis was completed for 97 patients, age range 18 to 66 years, withoutevidence of systemic or ocular disease. All datawere collected without dilation or cycloplegia. Refractivecorrection measurements (sphere, cylinder, axis) were converted to power vectors for analysis.RESULTS: Differences-versus-means plots show generally excellent agreement between the results ofeach instrument and subjective refraction, all r2. 0.77, with the Z-View consistently exhibiting less var-iability than the autorefractor (AR). Nonetheless, the Z-View tends to undercorrect myopia, whereas theAR tends to overcorrect myopia, with statistically significant mean differences (6SD) in spherical equiv-alents with respect to subjective refraction of 0.118 (60.311) and20.193 (60.474) diopters (D), respec-tively. Both instruments tend to overcorrect astigmatism of less than21.25 and20.75 D, respectively, insome cases by asmuch as20.87D. Both instruments also tend to err in cylinder axismeasurement for lowastigmatism, often by more than 10�.CONCLUSIONS: The Ophthonix Z-View aberrometer is a useful objective clinical instrument that pro-vides better accuracy than an AR, and its results can be used as a good starting point for a subjective re-fraction for most patients. It also measures higher-order aberrations not identified by other techniques.However, as with AR results, a spectacle prescription based solely on its measurements may not be ap-propriate for all patients.Optometry 2011;82:231-240

Most clinicians begin a subjective refraction with apatient-objective measure, such as retinoscopy, autorefrac-tion, or lensometry. In many busy practices, either of the

Disclosure: The authors have no financial or other relationships that

ght lead to a conflict of interest.

Corresponding author: Jeffrey Cooper, O.D., State University of

w York State College of Optometry, 33 W. 42nd Street, New York,

10036.

E-mail: Cooperjsc1@gmail.com

9-1839/$ - see front matter � 2011 American Optometric Association. All r

:10.1016/j.optm.2010.09.013

latter 2 procedures often is not performed by the clinicianbut by a technician. Previous studies have found that resultsfrom most commercially available infrared autorefractors(AR) provide a good starting point for the subjectivemanifest refraction (SR), but for many patientsmeasurements are not accurate enough to prescribe fromdirectly.1-4

Until recently, measurement and correction of refractiveerror has been limited to sphere and cylinder powers, also

ights reserved.

232 Optometry, Vol 82, No 4, April 2011

known as lower-order aberrations. With the advent ofwavefront technology, both lower- and higher-order aber-rations (HOAs) can be measured.5,6 Early assumptions hadbeen that HOAs are difficult to measure and correct andthat they have little effect on vision.7 However, several ab-errometers have been developed for clinical use, and resultsfrom wavefront-guided laser in situ keratomileusis(LASIK) demonstrate that reducing HOAs can result in im-proved visual acuity (VA) and contrast sensitivity comparedwith conventional LASIK.8,9 Similar to AR, an aberrometercan be used by a technician to provide objective data to theclinician.

Previous studies have compared measurements fromvarious aberrometers with those of AR and SR.7,10-15 Mostof these studies demonstrate good repeatability for individ-ual instruments and high correlations between methods fortheir study populations. However, many of these studiesalso show significant deviations for individual subjects, in-cluding instrument myopia and cylinder axis variability.

Ophthonix, Inc. (Vista, California) developed theZ-View� aberrometer to measure HOAs of the humaneye16 and likewise published studies favorably comparingits results with those of SR17 and other aberrometers.18

The Z-View specifically is designed to take measurementson nondilated, noncyclopleged eyes. However, Lai et al.17

assessed only the root-mean-square of the Z-View resultsagainst the SR spherical equivalent for only 10 eyes.

Ophthonix claims that a spectacle lens manufacturedbased on data derived directly from Z-View measurementsresults in improved vision.19,20 When we first used this sys-tem, we noted some discrepancies between findings on theZ-View and SR, in that some patients did not achieve thesame visual success or comfort with their aberrometer-based prescriptions as with ‘‘traditional’’ prescriptions.This study compares patients’ refractive corrections, as de-termined by their VAs, based on SR with those based onmeasurements made with the Z-View and a common ARused in our clinic.

We recognize that there is no perfect ‘‘gold standard’’ forrefraction because many factors in addition to VA can beconsidered, including the patient’s accommodative ability(especially for young patients and low hyperopes), blurinterpretation, contrast sensitivity, cognitive ability, ambientand task lighting, and visual demands, among others.Clinically, though, subjective visual comfort is tantamountfor most adult patients, as some may even relinquish a bitof VA for an improvement of overall ‘‘comfort.’’ Conse-quently, SR, verified by trial framing, still is the best methodof achieving this clinical goal for most typical patients.

Methods

Data from 100 consecutive patients examined in a privatepractice were considered for evaluation. This study wasexempt from review by an institutional review boardaccording to guidelines for retrospective clinical studiesbecause all data were collected for the purpose of rendering

clinical care. No identifying subject information is beingreported, and all patients were provided written noticebefore examination that their data may be used in a futurepublished research study.

Patient requirements for inclusion in the analysis wereminimum age of 18 years, clear ocular media, no knownocular or systemic disease, no rigid contact lens wear for atleast 1 year, and no prior refractive surgery. Soft contactlens wearers removed their lenses at least 30 minutes beforetesting. Patients were not cyclopleged or dilated for thispart of the examination. Ninety-seven patients (56 women,41 men) qualified for the study, ranging in age from 18 to66 years. Results of the Student t test show that there is nosignificant difference in ages based on gender (t[95] 50.072, P 5 0.943). Overall mean (6SD) age was 36.7(612.7) years: 10 patients were 18 to 24 years of age, 50were 25 to 34 years of age, 17 were 35 to 49 years ofage, and 20 were 50 to 66 years of age. Only the measure-ments for the right eye of each patient were analyzed.

Each eye was measured once with a Humphrey 599autorefractor keratometer (Zeiss Humphrey, Dublin, Cal-ifornia) and automatically up to 3 times with the Z-Viewaberrometer, per the manufacturer’s recommendations.21

The Z-View measures were averaged by its software to pro-vide a single set of results. The Z-View also measures thepatient’s actual pupil diameter and reports the pupil diam-eter used for HOA calculations. The Z-View software esti-mates the blur induced by trefoil, coma, sphericalaberration, and all HOAs for the eye, but it does not reportthe individual Zernike coefficients. However, using a pro-prietary algorithm, it does determine whether the patientwould be a good candidate for the Ophthonix iZon� (Oph-thonix) custom prescription lens. We did not prescribe ororder such custom lenses for our patients because thatwas not part of their clinical care. Thus, this retrospectivestudy cannot assess such lenses or how our patients wouldhave performed with them; this could be the goal of a futureprospective study.

AR and Z-View measurements were conducted in ran-dom order by various trained technicians under normalroom lighting, as is customary for each instrument. SR thenwas performed by a single experienced optometrist undermesopic lighting using a plus-cylinder phoropter and cross-cylinder lenses. VA was measured with a standard Snellenprojected chart at 20 feet (6 m), using different lines of let-ters for the different corrections resulting from each refrac-tion method to avoid memorization by the patient. Guessingby the patient was encouraged, but no extra or additionaleffort was used to elicit, coax, or coach the patient forany method.

The starting point for SR was the refractive correctionrecommended by Z-View. The endpoint was the lens powerthat resulted in the best VA and/or visual comfort. Allmeasurements assumed a spectacle lens vertex distance of14 mm.

For calculation purposes, Snellen acuities were con-verted to log minimum angle of resolution (logMAR)

Table 1 Ametropia types identified by each method of refraction and resulting visual acuities

Humphrey autorefractor Z-View aberrometer Subjective refraction

Total number of patients 97 97 97Emmetropia 1 0 2Myopia 22 9 25Hyperopia 2 1 0Myopic astigmatism 58 70 55Hyperopic astigmatism 7 10 10Mixed astigmatism 7 7 5Against-the-rule astigmatism 16 21 25With-the-rule astigmatism 23 26 19Oblique astigmatism 33 40 26

logMAR mean (SD) 0.013 (0.073) 20.001(0.070) 20.040(0.054)Snellen equivalent mean 20/20.6 20/19.9 20/18.2Snellen equivalent range 20/15–20/40 20/15–20/30 20/15–20/25

Cooper et al Clinical Research 233

values, with ‘‘1’’ and ‘‘2’’ designations estimated asnumerical decreases and increases, respectively, of 0.025log unit (one fourth of a line). Refractive corrections wereconverted to minus cylinder form, and sphere (S), cylinder(C), and axis (q) values were converted to power vector M(identical to the spherical equivalent) and cross-cylindervectors J0 and J45, as described by Thibos et al.22:

M5S1C=2 ð1Þ

J05ð2C=2Þ cosð2qÞ ð2Þ

J455ð2C=2Þ sinð2qÞ ð3Þ

Converting refractive components to vectors allows fordirect comparisons with other factors, such as age andvisual acuity, as well as proper application of statisticalanalyses. Use of these vectors also allows calculation of thetotal power vector (TPV),22 astigmatic difference vector(ADV),15 and total dioptric difference (TDD) vector23:

TPV5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiM21J201J245

qð4Þ

ADV5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDJ0Þ21ðDJ45Þ2

qð5Þ

TDD5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDMÞ21ðDJ0Þ21ðDJ45Þ2

qð6Þ

Data analysis includes calculation of correlation coeffi-cients for nonrefractive factors, such as age and gender, aswell as linear regressions and difference-versus-meanplots.24 As noted by Pesudovs et al.,15 TPV, ADV, andTDD, as well as actual cylinder power, are not normallydistributed. Thus, it is more appropriate to report medians

and 95th percentiles (95%ile) for these factors rather thanmeans and standard deviations.

Results

Table 1 shows the ametropia and VA results for each mea-surement method. We defined nonastigmatic refractive cor-rections within 60.25 D as emmetropia, .20.25 D asmyopia, and.10.25 D as hyperopia. For refractive correc-tions requiring any amount of (minus) cylinder, we defineda negative spherical equivalent as myopic astigmatism, pos-itive spherical equivalent as hyperopic astigmatism, andzero spherical equivalent as mixed astigmatism. In addition,we defined minus cylinder axis within 15� of 180� as with-the-rule (WTR) astigmatism, within 15� of 90� as against-the-rule (ATR) astigmatism, and all other axes as oblique(OBL) astigmatism. Based on the subjective refraction forall subjects, sphere power ranged from 27.25 to 15.25 D(median, 22.00 D) and cylinder power ranged from 0 to23.00 D (median, 20.50 D).

Student t test analysis on all measured and calculatedvalues shows that there are no significant differences basedon gender (all P. 0.05). Age has a low but statistically sig-nificant correlation with only power vector M (sphericalequivalent) based on each method: AR, r 5 0.357, r2 50.127, P 5 0.0005; Z-View, r 5 0.363, r2 5 0.132, P 50.0004; and SR, r 5 0.380, r2 5 0.144, P 5 0.0002. Agehas a weak but statistically significant correlation withlogMAR VA only for SR, r 5 0.246, r2 5 0.061, P 50.016. Age has no statistically significant correlation withany other measured value (all r2 , 0.037) except for pupilsize and HOAs measured with the Z-View (see below).

Almost all subjects were able to achieve a VA of at least20/20 with at least 1 refraction method, with 2 subjects onlyable to achieve at best 20/25 and 20/251 with any method.Mean (6SD) improvement in logMAR VA with SR withrespect to the Z-View is20.039 (60.058) log unit, or about2 letters, and with respect to AR, 20.053 (60.076) log

Figure 1 LogMAR VA for Z-View aberrometer (ZV, black squares) and

Humphrey auto-refractor (AR, blue x’s) with respect to SR. Data points

above the line of identity indicate improvement with SR.

Figure 2 Differences-versus-means plots for logMAR VA for Z-View

aberrometer (black squares) and Humphrey auto-refractor (blue x’s) with

respect to SR. Negative values indicate improvement in VA with SR. For

Z-View versus SR results: bias, solid black line; 95% limits of agreement,

light dashed black lines; regression line, heavy dashed black line. For au-

torefractor versus SR results: bias, solid blue line; 95% limits of agreement,

light dotted blue lines; regression line, heavy dotted blue line.

234 Optometry, Vol 82, No 4, April 2011

unit, or about one half of a line. Within-subjects analysis ofvariance found a statistically significant difference betweenmethods, F(2,192) 5 29.58, P , 0.0005. A critical differ-ence of 0.014 log unit between any pair of means indicatesa significant effect at a level of 0.05. SR mean VA exceedsthis level with respect to both other methods, which (be-cause of rounding) are not significantly different fromeach other. Thus, subjects were able to achieve significantlybetter VAs with SR than with either of the other 2 methods.

Figure 1 shows the logMAR VA results for the Z-Viewand AR with respect to SR. Note that the total number ofdata points plotted for each method is less than the numberof subjects (N 5 97) because multiple subjects are repre-sented by many of the discrete pairs of values, especiallyfor data that fall on the line of identity. This also is truefor the remaining figures.

Statistical analysis of VA differences between methodsalso can be considered in a differences-versus-means plot,as described by Altman and Bland24 and shown in Figure 2.Differences are calculated such that negative values repre-sent improvements in VA with SR; as indicated above,only 2 data points, representing 1 patient each for theZ-View and AR, are positive, thereby showing improve-ments in VA with those methods over SR.

Differences of SR with respect to the Z-View showslightly less overall variability than with respect to AR,given by the narrower range of the 95% limits of agreement(LOAs), (20.152, 0.074) versus (20.202, 0.097), respec-tively. Also shown in Figure 2 are horizontal lines

representing the mean differences reported above, whichdenote the bias of each objective refraction method with re-spect to SR, as well as the linear regression, which indicatesthat the variation depends on the magnitude of the measure-ment if the slope is significantly different than zero. For theZ-View differences, the slope, m 5 20.315, is significantlydifferent than zero (t[96] 5 3.09, P 5 0.001). For AR dif-ferences, the slope, m 5 20.439, also is significantly dif-ferent than zero (t[96] 5 3.03, P 5 0.002). Thesenegative slopes indicate that VA with SR tends to improvemore for patients who had relatively poor VAs with theZ-View and AR than for those who had relatively goodVAs with those instruments.

Considering only the patients for whom VA improvedwith SR compared with the other methods, we find 44 suchpatients for Z-View and 54 such patients for AR. Theimprovement ranged from 0.025 log unit (about 1 letter) to0.222 log unit (over 2 lines) with respect to the Z-View,with a mean (6SD) improvement of 20.087 (60.054) logunit, or almost 1 line. With respect to AR, improvementranged from 0.025 log unit (about 1 letter) to 0.426 log unit(over 4 lines), with a mean (6SD) improvement of 20.096(60.077), or 1 line. Compared with the other 2 refractionmethods, SR resulted in poorer VA for 1 patient each(different patients), differing by 0.075 log unit (threefourths of a line) and 0.097 log unit (1 line), respectively.The remaining 52 and 42 patients, respectively, achievedthe same VA with each pair of refraction methods, albeitoften with different refractive corrections. Of these patients,all but 2 with the Z-View and 1 with AR achieved VA of20/20 or better.

Figure 3 shows the power vector M calculated from theZ-View and AR data with respect to that calculated fromthe SR data. For completeness, the regression line also isplotted for each comparison, with an overall almost perfectcorrelation: Z-View, r5 0.993, r2 5 0.986, P , 0.0005 and

Figure 3 Power vector M (spherical equivalent), in D, for Z-View aber-

rometer (ZV, black squares) and Humphrey AR (blue x’s) with respect to SR.

Line of identity, light black line. Regression lines: ZV with respect to SR,

heavy dashed black line; AR with respect to SR, heavy dotted blue line.

Figure 5 Cylinder power, in D, for Z-View aberrometer (ZV, black

squares) and Humphrey AR (blue x’s) with respect to SR. Line of identity,

light black line. Regression lines: ZV with respect to SR, heavy dashed

black line; AR with respect to SR, heavy dotted blue line.

Cooper et al Clinical Research 235

AR, r 5 0.979, r2 5 0.959, P , 0.0005. However, note thatfor the Z-View, most minus spherical equivalents are lessminus than those from SR (above the line of identity), con-firmed by the position of the regression line. On the otherhand, most minus spherical equivalents from AR aremore minus than those from SR (below the line of identity),again confirmed by the position of the regression line. Be-cause only 10 patients had hyperopia or hyperopic astigma-tism, the results do not allow for generalizations for thatpopulation, but inspection of Figure 3 shows that bothZ-View and AR tend to under-plus hyperopic refractive

Figure 4 Differences-versus-means plots for power vector M (spherical

equivalent), in D, for Z-View aberrometer (black squares) and Humphrey AR

(blue x’s) with respect to SR. Positive values indicate more plus power,

negative values more minus power, for each instrument versus SR. For

Z-View versus SR results: bias, solid black line; 95% limits of agreement,

light dashed black lines; regression line, heavy dashed black line. For

autorefractor versus SR results: bias, solid blue line; 95% limits of agree-

ment, light dotted blue lines; regression line, heavy dotted blue line.

corrections, as most of those data points lie below theline of identity.

Figure 4 shows the differences-versus-means plot forpower vector M. Differences are calculated such that posi-tive values indicate more plus power, and negative valuesindicate more minus power. Compared with SR, theZ-View tends to overplus (mean [6SD], 0.118 [60.311] D),whereas AR tends to overminus (20.193 [60.474] D); bothmeans are significantly different from zero (t[96] 5 3.72,P , 0.0005, and t[96] 5 4.00, P , 0.0005, respectively).The Z-View differences show less variability than thosefrom AR (95% LOAs of 20.493, 0.728 versus 21.123,0.737, respectively). However, for the Z-View differences,the slope of the linear regression of the difference scores,m 5 20.073, is significantly different than zero (t[96] 55.94, P , 0.0005), whereas for AR differences, the slope,m 5 0.006, is not significantly different than zero (P 50.383). This confirms that the Z-View tends to underminushigh myopic refractions more than low myopic refractions,whereas AR tends to overminus all refractions with no con-sistent error based on power.

Figure 5 shows cylinder power given by the Z-View andAR with respect to that given by SR. For completeness, theregression line also is plotted for each comparison, withoverall high correlation: Z-View, r 5 0.912, r2 5 0.831,P , 0.0005, and AR, r 5 0.879, r2 5 0.773, P , 0.0005.Note that this is a more clinically relevant presentationof the results than showing the cross-cylinder vectors, J0and J45, either individually or as the total astigmatic vector(calculated in the same manner as TPV [equation 4] butwithout the M2 term), as these terms are derived fromhalf the magnitude of the cylinder power (see equations 2and 3).

Figure 7 Power vector J45 differences versus J0 differences, in D. Astig-

matic difference vector of 0.125 D, heavy solid circle. (Note that J vectors

are each half the magnitude of the actual cylinder power, such that the

solid circle represents an absolute cylinder power difference of 0.25 D).

Figure 6 Differences-versus-means plots for power vectors A, J0 (hor-izontal/vertical cross-cylinder) and B, J45 (oblique cross-cylinder), in D,

for Z-View aberrometer (black squares) and Humphrey AR (blue x’s) with

respect to SR. Positive values indicate more absolute cylinder power, neg-

ative values less absolute cylinder power, for each instrument versus SR.

For Z-View versus SR results: bias, solid black line; 95% limits of agree-

ment, light dashed black lines; regression line, heavy dashed black line.

For AR versus SR results: bias, solid blue line; 95% limits of agreement,

light dotted blue lines; regression line, heavy dotted blue line.

236 Optometry, Vol 82, No 4, April 2011

Figure 5 demonstrates that compared with SR, theZ-View and AR tend to overcorrect cylinder powers ofless than about 21.25 and 20.75 D, respectively. Inaddition, each method can both miss a cylinder correctionidentified by SR (shown by points on the x-axis) and rec-ommend a cylinder correction not found by SR (shownby points on the y-axis), in some cases as large as 20.87 D.

Figure 6A shows the differences-versus-means plot forhorizontal/vertical cross-cylinder vector J0. Differencesare calculated such that positive values indicate more abso-lute cylinder power and negative values indicate less abso-lute cylinder power. Compared with SR, both the Z-Viewand AR tend to measure more cylinder power in the hori-zontal/vertical meridians (mean [6SD], 0.039 [60.128]D and 0.032 [60.146] D, respectively). Both means are sig-nificantly different from zero (t[96] 5 3.00, P 5 0.003, andt[96] 5 2.14, P 5 0.035, respectively). The Z-View differ-ences show less variability than those from AR, 95% LOAsof (20.211, 0.289) versus (20.254, 0.317), respectively.Nonetheless, neither of the slopes of the linear regressionof the difference scores are significantly different than

zero (m 5 0.044, P 5 0.123, and m 5 0.034, P 50.220, respectively).

Figure 6B shows the differences-versus-means plot foroblique cross-cylinder vector J45. Differences are calculatedsuch that positive values indicate more absolute cylinderpower, and negative values indicate less absolute cylinderpower. Compared with SR, both the Z-View and AR tendto measure less cylinder power in the oblique meridians(mean, 20.010 [60.095] D and 20.032 [60.129] D, re-spectively). The mean of the Z-View differences is not sig-nificantly different than zero (P 5 0.295) but that of ARdifferences is (t[96] 5 2.97, P 5 0.004). Likewise, theslope of the linear regression of the Z-View differences,m 5 0.023, is not significantly different than zero (P 50.278), whereas the slope for AR differences, m 520.039, is significantly different than zero (t[96] 5 1.91,P 5 0.030). The Z-View differences show less variabilitythan those from AR (95% LOAs of [20.197, 0.177] versus[20.293, 0.215], respectively).

Figure 7 plots the J45 differences against the J0 differ-ences. There is no correlation between the vectors fordifferences of either refraction method with respect to thesubjective refraction: for the Z-View, r 5 0.038, r2 50.001, P 5 0.709; and for AR, r 5 20.084, r2 5 0.007,P 5 0.411. However, the results show clinically relevantvariability of the cylinder vectors measured with theZ-View and AR compared with SR, especially when con-sidering the large number of data points that are morethan 0.125 D from the coordinate center in any direction,shown by the circle on the graph. (Note that the J vectorsand their combination are based on only half the magnitudeof the actual cylinder power and that many patients aresensitive to cylinder power changes of 0.25 D.)

Figure 8 Astigmatic difference vector versus minus cylinder power, in

D, for Z-View aberrometer (ZV, black squares) and Humphrey AR (blue x’s)

with respect to SR. Regression lines: ZV with respect to SR, heavy dashed

black line; AR with respect to SR, heavy dotted blue line.

Figure 9 Differences-versus-means plots for cylinder axis, in degrees,

for Z-View aberrometer (black squares) and Humphrey AR (blue x’s) with

respect to SR, for WTR, ATR, and OBL astigmatism. Positive values indicate

clockwise rotation, negative values indicate counterclockwise rotation, for

each instrument versus SR. For Z-View versus SR results: overall bias, solid

black line; overall 95% limits of agreement, light dashed black lines; indi-

vidual regression lines based on astigmatism type, heavy dashed black

line. For AR versus SR results: overall bias, solid blue line; overall 95%

limits of agreement, light dotted blue lines; individual regression lines

based on astigmatism type, heavy dotted blue line.

Cooper et al Clinical Research 237

Figure 8 shows the astigmatic difference vector (ADV,equation 5) with respect to the cylinder power determinedwith SR. ADV medians (95%ile) are 0.125 (0.355) D forthe Z-View and 0.126 (0.381) D for AR. Linear regressionshows that ADV increases with increasing cylinder powerfor both refraction methods because the slopes are signifi-cantly different than 0: for the Z-View, m 5 20.045,t(96) 5 2.85, P 5 0.003; and for AR, m 5 20.081,t(96) 5 4.11, P , 0.0005. Note that the slopes are negativebecause minus cylinder power increases to the right on thex axis.

SR identified 70 of the 97 patients as needing acorrection for astigmatism. The Z-View determined acylinder correction for 68 of these patients, missing 1 patienteach with WTR (C 5 20.25 D) and OBL (C 5 20.50 D)astigmatism. AR identified only 59 of the 70 patients,missing 5 with ATR (maximum C 5 20.50 D), 2 withWTR (maximum C 5 20.37 D), and 4 with OBL(maximum C 5 20.75 D) astigmatism. In addition, forpatients determined to not need an astigmatic correctionbased on SR, the Z-View identified 5 with ATR (maximumC 5 20.75 D), 10 with WTR (maximum C 5 20.87 D),and 7 with OBL (maximum C 5 20.37 D) astigmatism,whereas AR identified 5 with WTR (maximum C520.50 D)and 7 with OBL (maximum C 5 20.50 D) astigmatism.Because the number of patients in each of the foregoingcategories is quite low, any statistical analysis would havelimited meaning. We present the data merely to show thatthere is no obvious consistent bias in either the Z-View orAR to incorrectly identify astigmatism based on its type.

Figure 9 shows the differences-versus-means plot forcylinder axis. Differences are calculated such that positivevalues indicate a clockwise rotation, and negative values in-dicate a counterclockwise rotation with respect to SR axis.

Differences were considered only if astigmatism was iden-tified with both pairs of refraction methods. The mean(6SD) difference in axis for the Z-View with respect toSR is 21.18� (69.70), which is not significantly differentthan 0 (P 5 0.321); for AR, the mean (6SD) is 24.29�

(615.36), which is significantly different than 0 (t[58] 52.14, P 5 0.036). As with the other measures, theZ-View differences show less variability than those fromAR (95% LOAs of [220.2, 17.8] versus [234.4, 25.8], re-spectively). Note that the full range of differences for theZ-View is (227, 23), whereas for AR it is (274, 21).

Linear regression was calculated separately for eachtype of astigmatism, WTR, ATR, and OBL, because theangular scale for axis, from 1� to 180�, is continuous onitself. In addition, we wanted to assess whether eitherinstrument had more or less difficulty in determining aparticular type of astigmatism. With respect to SR, theslopes of the linear regressions of the Z-View differencesare not statistically different than zero for any type ofastigmatism (all P . 0.05); for AR differences, interest-ingly, only the slope for OBL astigmatism is significantlydifferent than zero (m 520.103, t[31] 5 2.25, P 5 0.016).

Figure 10 compares the cylinder axis differences withcylinder power, showing the same mean differences and95% LOAs as in Figure 9. Not surprisingly, both instru-ments tend to show greater variability in cylinder axiswith lower cylinder powers, with the Z-View and AR po-tentially exhibiting axis errors of more than 10� for powers,21.25 and21.50 D, respectively. The slopes of the linearregression lines are statistically different than zero for boththe Z-View (m 5 22.06, t[67] 5 1.75, P 5 0.042) and AR(m 524.32, t[58] 5 2.16, P 5 0.017). Note that the slopesare negative because minus cylinder power increases to theright on the x axis.

Figure 10 Cylinder axis differences, in degrees, versus minus cylinder

power, in D, for Z-View aberrometer (black squares) and Humphrey AR (blue

x’s) with respect to SR. Positive values indicate clockwise rotation, nega-

tive values counterclockwise rotation, for each instrument versus SR. For

Z-View versus SR results: bias, solid black line; 95% limits of agreement,

light dashed black lines; regression line, heavy dashed black line. For AR

versus SR results: bias, solid blue line; 95% limits of agreement, light dot-

ted blue lines; regression line, heavy dotted blue line.

Figure 11 Total dioptric difference vector versus total power vector, in

D, for Z-View aberrometer (ZV, black squares) and Humphrey AR (blue x’s)

with respect to SR. Regression lines: ZV with respect to SR, heavy dashed

black line; AR with respect to SR, heavy dotted blue line.

238 Optometry, Vol 82, No 4, April 2011

Figure 11 compares the total dioptric difference (TDD,equation 6), which is the absolute value of the differencein refractive corrections, with the total power vector(TPV, equation 4), which is the absolute value of the fullrefractive correction in Fourier form.22 Note that for theZ-View, TDD median (95%ile) is 0.275 (0.698) D anddoes not exceed 0.95 D, but the slope of the linear regres-sion, m 5 0.044, is significantly different than zero (t[96]5 4.43, P , 0.0005). AR shows more variability, with me-dian (95%ile) of 0.333 (0.973) D and maximum TDD of1.92 D, but with a linear regression slope, m 5 0.013,that is not significantly different than zero (P 5 0.244).

Even for patients who achieve the same VA withdifferent refraction methods, the refractive correction canvary. For the 52 and 42 patients who achieved the same VAwith the Z-View and AR, the ADV medians (95%ile) areless than for all subjects but not zero, (0.099 [0.262] and0.125 [0.261], respectively), as are the TDD medians (95%ile) (0.178 [0.531] and 0.251 [0.791], respectively). Linearregression shows that ADV still increases with increasingcylinder power for both refraction methods, in that theslopes are significantly different than zero: for the Z-View,m 5 20.069, t(51) 5 3.69, P , 0.0005; and for AR, m 520.058, t(41) 5 3.24, P 5 0.001. On the other hand,TDD does not vary significantly with increasing TPV(both P . 0.05).

The Z-View also measures pupil size, 3 individual HOAs(trefoil, coma, and spherical aberration), and total HOAs.Pupil size ranged from 4.19 to 8.75 mm (mean [6SD], 6.61[60.98] mm), and as expected, shows a moderate, signif-icant negative correlation with age (r 5 20.514, r2 50.264, P , 0.0005). Pupil size also shows a weak butsignificant negative correlation with Z-View power vector

M (r 5 20.204, r2 5 0.042, P 5 0.046) but no statisticallysignificant correlation with any other factors measured bythe Z-View.

For 80 patients, the Z-View performed its calculationsusing a pupil size of 4.50 mm; for the remaining patients,the instrument used sizes of 3.26 to 4.40 mm. Pupil sizeused for calculations by Z-View shows a weak but statis-tically significant negative correlation with the total HOAmeasure (r 5 20.259, r2 5 0.067, P 5 0.011) but no otherstatistically significant correlation with any other factorsmeasured by the Z-View.

The Z-View estimates the blur induced by the presenceof uncorrected or undercorrected HOAs. As presented bythe Z-View as unsigned blur, these values are not normallydistributed. For all 97 patients, median (95%ile) blurinduced by trefoil is 0.100 (0.250) D; by coma, 0.110(0.266) D; by spherical aberration, 0.080 (0.170) D; and byall HOAs, 0.220 (0.362) D.

Total HOA shows moderate significant correlations totrefoil (r 5 0.636, r2 5 0.405, P , 0.0005); coma (r 50.767, r2 5 0.589, P , 0.0005); and spherical aberration(r 5 0.510, r2 5 0.260, P , 0.0005). However, theZ-View software’s assessment as to whether a patientwould be a good candidate for the iZon custom prescriptionlens shows a moderate but significant correlation only withthe spherical aberration measure (r 5 0.359, r2 5 0.129,P , 0.0005; all other r2 , 0.039).

Discussion

This retrospective clinical study was prompted by ourexperience that some prior patients did not achieve optimal

Cooper et al Clinical Research 239

VA with spectacle lens prescriptions recommended by theOphthonix Z-View aberrometer. Our results indicate thatwhen compared with SR, the Z-View has less variabilitythan a commercially available autorefractor that our officeroutinely uses. However, both instruments have a tendencyto incorrectly measure either or both cylinder power andaxis in some patients compared with SR. In addition, ARtends to overcorrect myopia, which is not an unusual orunexpected finding.3 On the other hand, the Z-View tendsto undercorrect myopia, which is contrary to the previouslyreported instrument myopia induced by most other aber-rometers7,10,11 but is consistent with the findings of Giessleret al.25 for dilated, noncycloplegic measurements.

In a cohort not evaluated in this study, and reported inseveral other studies, there are significant HOAs associatedwith conditions that interfere with the optics of the eye,specifically cataract and keratoconus.26-30 For these pa-tients, the wavefront analysis usually differs significantlyfrom SR because SR provides a best fit or average of allaberrations (lower and higher order) using only sphereand cylinder powers, whereas wavefront measurementscomprise the actual error contributed by each component,sphere, cylinder, or HOAs. Thus, one would expect SR re-sults to be different than the lower-order aberrations mea-sured by wavefront analysis. Interestingly, our resultssuggest that something similar occurred with some of ourphysiologically normal patients, given the often dramaticimprovements in VA (up to 2 lines or more) after subjectiverefraction.

The Ophthonix Z-View aberrometer is a useful objectiveclinical instrument that provides better accuracy than anautorefractor, and the results of which can be used as agood starting point for subjective refraction for mostpatients. It also identifies patients exhibiting HOAs, whichcan reduce visual acuity, not identified by other techniques.However, as with autorefractor results, a spectacle pre-scription based solely on its measurements may not beappropriate for all patients.

Acknowledgements

The authors thank Thomas O. Salmon, O.D., Ph.D., forproviding the Excel spreadsheets for data analysis;Raymond Applegate, O.D., Ph.D., for providing in-depthexplanations of characteristics of wavefront analysis; andJeremy Wilmer, Ph.D., and John R. Hayes, Ph.D., forreviewing the statistics. In addition, the authors thankAshley Fazzary, O.D., and Nadine Jamal, O.D., for datacollection.

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