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Optik 124 (2013) 13201323

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Optik

journal homepage: www.elsevier .de/ i j leo

An objective inspection method ofvisual acuity basedon wave front aberrations ofhuman eye

Wei Quan a, Guicai Song b, Zhao-Qi Wangc,

a Schoolof Science, Shenyang LigongUniversity, Shenyang 110159, PR Chinab Schoolof Science, ChangchunUniversity of Science andTechnology, Changchun130022, PR Chinac Institute ofModernOptics, Nankai University, Tianjin 300071, PR China

a r t i c l e i n f o

Article history:

Received 1 November 2011Accepted 15 March 2012

Keywords:

Visual acuityWavefront aberrationHartmannShack sensorModulation transfer functions

a b s t r a c t

Visual acuity is an important vision evaluation index. Visual acuity examination has great practical andclinical significance. Objective visual acuity detection method based on the wave front aberrations ofhuman eyes is explored in this paper. The wavefront aberrations ofhuman eyes were measured withthe HartmannShack wavefront sensor and modulation transfer function was computed from the wavefront aberrations. The maximum spatial resolution ofhuman eye was obtained from modulation transferfunction and the retinal aerial image modulation. Visual acuity can be derived from the maximum spatialresolution ofhuman eye. Visual acuity ofrandomly selected 15 eyes was examined with the objectivemethod based on wavefront aberrations ofhuman eyes and with the subjective visual chart method aswell. The test results show that the visual acuity values are basically the same when visual acuity is testedwith the two methods. The inspection method ofvisual acuity based on wavefront aberrations ofhumaneyes possesses advantages ofobjectivity, rapidity and accuracy, without the shortcomings ofthe visualchart method ofslowness and subjectivity relying much on subject cognition and statement.

2012 Published by Elsevier GmbH.

1. Introduction

The human eye is the most important organ to obtain informa-tion of outside world. 95% of the information comes from visualsense when human beings perceive the world around them. Visualacuity is the main parameter for the ophthalmologist to evaluatethe performance of visual system. Visual acuity is widely used tocharacterize the global quality of vision of a subject. Visual acuityis extremely helpful in detecting the presence of visual problems,especially in performing subjective refraction [1]. Accurate mea-surement of visual acuity is required not only for the selectionof optical correction in everyday practice, but also in the courseof medical exams to evaluate the degree of fitness in professionalscreening, as well as to evaluate the dynamics of the visual func-

tions. Visual acuity is the most important parameter of the organof vision and a necessary criterion for estimating visual capability[2].

The most common method to test visual acuity is to use thestandard Snellen chart. Snellen visual acuity is obtained by ask-ing the subject to perform a pattern-recognition task, typicallyunder maximum contrast conditions. The minimum size of the

Corresponding author. Tel.: +86 431 85582527; fax: +86 431 85582527.E-mail addresses: songcust@163.com (G. Song), wangzq@nankai.edu.cn

(Z.-Q. Wang).

targets (optotypes) for which the number of correct answers isabove threshold determines the value of visual acuity. One of thereasons for the great success of Snellen visual acuity among clini-cians is itshigh sensitivity to optical imperfections, such as defocus.Indeed, visual acuity can easily detect defocus values equal to orless than 1/4diopter (D). However, there are some difficulties toovercome when visual acuity is detected with Snellen chart: (1)the method to test visual acuity with Snellen chart is slowand sub-

jective, which requires subjects cooperation and depends much onsubjects cognition and answer. Repeated use of the same Snellenchartcanleadtomemorizationoftheletters.Inoccupationalhealthexamination, the eye chartmay be memorizedbeforehand by somesubjects so that the test results are false information. (2) For earlyagechildren, it is difficult to have their eyes tested. Sometimestheir

eyes cannot even be examined because they cannot be in cooper-ation. The visual acuity children graph vision inspection is used insome hospitals, but children still need to be trained before test. (3)There is often not enough distance in the laboratory for the sub-

ject to stand 20 ft (or 6 m) from the Snellen chart. However, thetest distance is 20ft (or 6m) with Snellen chart. And the attend-ing investigator has to stand next to the subject to adequately hearsubject reading the letters. This becomes more critical in the caseof thepoor sound transmission through the respirator and the loudbackground noise generated by a treadmill [3,4].

A significant development in the visual optics and ophthalmol-ogyattheendof20thcenturyistheprogressinmeasurementofthe

0030-4026/$ see front matter 2012 Published by Elsevier GmbH.

http://dx.doi.org/10.1016/j.ijleo.2012.03.038

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W. Quan et al. / Optik 124 (2013) 13201323 1321

Table 1

The maximum spatial resolution of 15 human eyes.

Eye no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f0cycle/ 10.56 14.17 19.32 20.84 23.61 25.55 27.78 28.77 29.83 31.11 32.51 36.11 35.44 37.17 39.39

wave front aberrations of human eye and the advanced vision cor-rection using adaptive optics [5]. In the middle of 1990s, Liang and

Josef F. Bille demonstrated a new technique to measure the eyeswavefrontaberration,basedontheHartmannShackprinciple,andprovided a more complete description of all the wave front aber-rations of the eye with the Zernike terms up to 65, correspondingto tenth-order or Zernike modes [6]. With the wave front technol-ogy, the measurement of the wave front aberrations of human eyecanbe completed rapidly within 1 s. The accuracy of the wave frontsensor is /400 (=0.633m) and the repeatable standard devia-tion of the wave front aberration measurement is/14 in average.More importantly, the measurement of wave front aberrations ofhuman eye based on HartmannShack technology is objective andrapid.

Thegoalofthispaperistoexploreanobjectiveandrapidmethodto test visual acuity. This paper proposes an objective detectionmethod of visual acuity based on wave front aberrations of humaneye.Withthistestmethodthevisualacuitycanbemeasuredobjec-tively, rapidly and accurately, which avoids the shortcomings ofthe visual chart method such as slowness and subjectivity in theinspection.

Firstly, thewave front aberrations of human eyewere measuredwiththeHartmannShackwavefrontsensorandmodulationtrans-fer function (MTF) was computed from the wave front aberrationsof human eye. Then the maximum spatial resolution of human eyewas obtained from modulation transfer function and the retinalaerial image modulation (AIM). Visual acuity was derived from themaximum spatial resolution of human eye. The visual acuity mea-surement method based on wave front aberrations of human eyeis objective, rapid and accurate. The inspection results can be givenwithin several seconds.

2. Method

2.1. Measurements of the wave front aberrations of human eyes

The wave front aberrations of 50 human eyes were measuredwithHartmannShack wavefront sensor, andexpressedby Zernikepolynomials. Therange of thesubjectsages wasfrom20to46withdiopters from 0 D to5.0D, and the measurements were repeatedfor 20 times for each eye. The tested wave front aberrationsW(x,y)were assumed to be expressed by

W(x, y) =

kmaxk

CkZk(x, y) (1)

whereZk(x,y)isthe kth Zernike polynomial function,Ckis the coef-ficient of the Zernike polynomial,kmaxis the maximum truncationitem andkmax =65.

Fig.1 showsthecoefficientdiscretedistributionsofthirdto65thZernike terms obtained by an average of 20 measurements for 50human eyes. Since the coefficientsC1and C2are not important tothe optical performance they are ignored here and after.

2.2. Modulation transfer function calculation

Modulation transfer function of optical system of human eye

can be calculated from the wave front aberrations acquired by the

HartmannShacksensor[7]. Firstthe wavefront aberrationsW(x,y)are used to construct the generalized pupil functionP(x,y):

P(x, y) =p(x, y) exp[iw(x, y)] (2)

wherep(x,y) denotes a pupil aperture of radius r, defined as

p(x, y) =

1r2

, x2 +y2 r2

0, otherwise(3)

Optical transfer function (OTF) is obtained as the complex autocor-relation ofP(x,y)

OTF(x, y) =

P(x, y)P(x x, y y)dxdy (4)

where P*(x,y) is the conjugate ofP(x,y). MTF is defined as the mod-

ulus of OTF:(5)MTF = |OTF|According to the wave front aberrations of human eyes given

by Fig. 1, the modulation transfer functions of 50 human eyes werecalculated from Eqs. (1)(5). Fig. 2 shows the modulation transferfunctionsof 15humaneyesselectedrandomlyandthe retinal aerialimage modulation curve expressed by dotted line.

2.3. The maximum spatial resolution of human eyes

The retinal aerial image modulation curve shown with dottedline in Fig. 2 is based on date found in Ref. [8]. Retinal aerial imagemodulationcurveindicatestheimagemodulationrequiredinorderforthat image to be resolved by the visualsystem. The retinal aerialimage modulation curve is a function of the frequency as well, and

on the dimensions and structure of the sensor elements (cones) ofthe retina, at the region of maximum resolution, fovea. The hori-zontal ordinate of the intersection of modulation transfer functionand retinal aerial image modulation curve is the maximum spa-tial resolution of human eye. Table 1 shows the maximum spatialresolution of 15 human eyes provided by the abscissa of the cross-ing point of modulation transfer function and retinal aerial imagemodulation curve in Fig. 2.

Fig. 1. 3-65 Zernike terms coefficient discrete distribution of 20 measurements for

50 eyes.

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1322 W.Quan etal./ Optik 124 (2013) 13201323

Fig.2. Modulationtransferfunctionof15humaneyesselectedrandomlyandretinalaerial image modulation curve expressed by dotted line.

2.4. Visual acuity

Visual acuity, visualperformance evaluation parameters, can becomputed from the maximum spatial resolution of human eye.

Visual size perception excited by the outside object depends onthe size of its image on the retina. According to the principle ofgeometry optics, we have

size of image on the retina

=size of object distance from retina to image nodal point

distance from object to object nodal point(6)

Because theangle of optotype E is small in commonvisual chart,the tangent of the angle can be approximated by radians. The radi-

ans value of the intersection angle of optotype E is defined as visualangle. Therefore, the object size perceived by human eye dependson visual angle, shown in Fig. 3.

Visual acuity is defined as the ability of resolution of the min-imum distance between two objects and measured with visualangle. The smaller the visual angle resolved is, the better the visualacuity. So visual acuity is usually expressed by the reciprocal ofvisual angle. Visual acuityis the reciprocal of the visual angle of thesmallest test-object resolved by individual. Clinically, visual acuityhas different expressions on the basis of different eye charts, buttheirsignificance is synonymous. Here international universal frac-tions eye chart is used to express visual acuity. Fractions eye chartis represented by Snellen fraction. Visual acuity measurements

Fig. 3. Target and visual angle.

Fig.4. Visualacuitymeasurementswith theSnellenchart arebased uponthe abilityofaparticularindividualtoseeat20ftwhatanormalindividualcanseeatadifferentdistance,x. Bothletters subtend a visual arc of 5.

with the Snellen chart are based upon the ability of a particularindividual to see at 20ft (or 6m) from the chart to read the letters.Fig. 4 shows an individual can see at a different distancex. Bothletters subtend a visual arc of 5.

The Snellen chart expresses the visual angle with the test dis-tance and letter height. Namely,

visual acuity =test distance

distance corresponding to 5 min letter (7)

Therefore,inEq. (7) thenumeratortestdistanceis20ft(or6m)with Snellen chart, and the denominator distance correspondingto 5min letter is the distance which the minimum letter height,identified by individual as standing at 20ft (or 6 m)from the chart,forms a 5min angle. For example, a visual acuity score of 20/200indicates the distance, which the minimum size letter height iden-tified by individual forms a 5 min angle, is 200 ft when individualstands20 ft from the chart toreadthe letters. Thus, a score of 20/20indicates vision equal to normal, and a visual acuity score of 20/10indicates vision better than normal, a score of 20/40 worse thannormal.

Fig.5 is theSnellenchart,whichuseslettersEwithdifferentsizesand orientations. This Snellen chart is organized with a large E atthe top, and ten additional horizontal lines of letters of decreasing

Fig. 5. The Snellen chart.

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Table 2

Twosets of visual acuity values of15 human eyes.

Eye no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Visual acuity from wave-front aberrations 0.35 0.47 0.64 0.69 0.79 0.85 0.93 0.96 0.99 1.04 1.08 1.12 1.18 1.24 1.31Visual acuity from Snellen chart 0.3 0.4 0.6 0.6 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.2

Fig.6. Twosetsofvisualacuityvaluesof15humaneyesfromwavefrontaberrationsand Snellen chart.

size appears from top to bottom. Each line of letters E gives a visualacuity score that relates the ability of an individual standing 20ft(or 6m) from the chart to read the letters on that particular lineto the same ability of a normal individual to read the same letterswhile standing at a different distance from the chart (seeFig. 4).

If maximum spatial resolution of human eye isf0(cycle/), theminimum intersectionangle identifiedby human eyeis 1/f0. Corre-spondingly, the height of minimum size letter identified by humaneye is 2.520 (1/f0). Here number of 20 indicates the distance of20ft from the chart where the individual stands to read the letters,

and 2.5 is the cycle of letter E. The distance of the minimum sizeletter height of 2.520 (1/f0) forming a 5min angle (5/60) is L:

L =2.5 20

f0

5/60 (8)

According to Eqs. (7) and (8), visual acuity is

visual acuity =20L =

f030

(9)

The dimension off0is cycle/.From the above derivation modulation transfer function of

optical system of human eye is calculated from the wave frontaberrations measured with the HartmannShack sensor, and themaximum spatial resolution of human eye f0 can be given by

the intersection of modulation transfer function and retinal aerialimage modulation curve. Visual acuity can be obtained from Eq.(9). Thus visual acuity, main clinical index to evaluate the perfor-manceof visualsystem, canbe derived from wave front aberrationsof human eye.

3. Results

Table 2 lists two sets of visual acuity values of 15 human eyes,one of which is calculated from Eq. (9) according to the maximumspatialresolutionof15humaneyes(givenbyTable1), andtheotheris the measurement results with Snellen chart.

Fig. 6 shows two sets of visual acuity values of 15 human eyesfrom wave front aberrations and from Snellen chart (date fromTable 2), respectively. The white bars are the visual acuity valuescalculated from wave front aberrations andblack bars arethatmea-sured with Snellen chart. We can see from Fig. 6 that the two setsof visualacuity values are slightly different. The main reason is thatvisual acuity values from Snellen chart are discrete, which are 0.1,

0.15, 0.2, 0.3, 0.4, 0.6, 0.8, 1.0, 1.2, 1.5, 2.0(see Fig.5), butvisual acu-ity values calculated from wave front aberrations are continuous.Thus there is not a one-to-one correspondence between the twosets ofvisual acuitydata. However, thedifferencesbetweenthe twosets of visual acuity values are within the gradient of visual acuityexpressed by adjacent rows in Snellen chart. The visual acuity cal-culated from wave front aberrations is more accurate. Moreover,the vision inspection method based on wave front aberrations ofhuman eye is objective and rapid as compared with the methodof visual chart. The inspection can be completed within severalseconds.

Acknowledgment

This research is supportedby the National NatureScience Foun-dation of China (no. 60978068)

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