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Vision Research 46 (2006) 1633–1645

Accommodation stimulus–response functionand retinal image quality

Tobias Buehren *, Michael J. Collins

Contact Lens and Visual Optics Laboratory, School of Optometry, Victoria Park Road, Kelvin Grove, Queensland University of Technology,

Brisbane, Qld 4059, Australia

Received 20 April 2005; received in revised form 7 June 2005

Abstract

Accommodation stimulus–response function (ASRF) and its relationship to retinal image quality were investigated using a mod-ified wavefront sensor. Ten subjects were presented with six vergence stimuli between 0.17 D and 5 D. For each vergence distance,ocular wavefronts and subjective visual acuity were measured. Wavefronts were analysed for a fixed 3-mm pupil diameter and fornatural pupil sizes. Visual Strehl ratio computed in the frequency domain (VSOTF) and retinal images were calculated for each con-dition tested. Subjective visual acuity was significantly improved at intermediate vergence distances (1 D and 2 D; p < 0.01), andonly decreased significantly at 5 D compared with 0.17 D (p < 0.05). VSOTF magnitude was associated with subjective visual acuityand VSOTF peak location correlated with accommodation error. Apparent accommodation errors due to spherical aberration werehighly correlated with accommodation lead and lag for natural pupils (R2 = 0.80) but not for fixed 3-mm pupils (R2 < 0.00). Thecombination of higher-order aberrations and accommodation errors improved retinal image quality compared with accommodationerrors or higher order aberrations alone. Pupil size and higher order aberrations play an important role in the ASRF.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Accommodation stimulus–response; Higher-order aberrations; Pupil size; Retinal image quality

1. Introduction

The classical accommodation stimulus–responsecurve is S-shaped (Morgan, 1944). It shows a lead ofaccommodation at distance, a cross-over point close tothe tonic level or resting point of accommodation, alinear portion with a slope of less than one and abreak-off-point at the clinical amplitude of accommoda-tion (Charman, 1982, 1999).

Most studies that have measured accommodationstimulus–response have used auto-refractometers (seeChen, Schmid, & Brown, 2003, for a review). More re-cent studies have used PowerRefractor based on pho-to-retinoscopy (Schaeffel, Weiss, & Seidel, 1999;Seidemann & Schaeffel, 2003) or wavefront sensors

0042-6989/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.visres.2005.06.009

* Corresponding author. Tel.: +617 3864 5717; fax: +617 3864 5665.E-mail address: [email protected] (T. Buehren).

(Hazel, Cox, & Strang, 2003; Plainis, Ginis, & Pallikaris,2005). The methods used to correct individual refractiveerrors prior to accommodation measurement includesubjective distance refraction (Abbott, Schmid, &Strang, 1998; Bullimore, Gilmartin, & Royston, 1992;McBrien & Millodot, 1986), retinoscopy (Gwiazda,Bauer, Thorn, & Held, 1995; Gwiazda, Thorn, Bauer,& Held, 1993), auto-refraction (Rosenfield, Desai, &Portello, 2002) and a calibration procedure using aPowerRefractor combined with retinoscopy (Schaeffelet al., 1999; Seidemann & Schaeffel, 2003). Correctionof refractive errors can either be done with spectacles(Chen & O�Leary, 2000; Gwiazda et al., 1995, 1993),contact lenses (Bullimore et al., 1992; Rosenfield et al.,2002; Rosenfield & Gilmartin, 1987, 1988) or both(Jiang & White, 1999). When spectacles are used, lenseffectivity formulas are needed to calculate effectivestimulus and response values (Abbott et al., 1998;

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1634 T. Buehren, M.J. Collins / Vision Research 46 (2006) 1633–1645

Gwiazda et al., 1993; Mutti, Jones, Moeschberger, &Zadnik, 2000). Techniques to stimulate accommodationinclude Badal lens systems (e.g., Plainis et al., 2005; Sei-del, Gray, & Heron, 2003), distance induced (e.g., McB-rien & Millodot, 1986) or lens-induced stimulation (e.g.,Gwiazda et al., 1993). Accommodation stimulus–re-sponse has also been measured under binocular (e.g.,Bullimore et al., 1992; McBrien & Millodot, 1986), mon-ocular (e.g., Gwiazda et al., 1993; Jiang & White, 1999;Rosenfield et al., 2002) or both viewing conditions (e.g.,Ramsdale, 1979; Seidemann & Schaeffel, 2003).

While there has been a large range of methodologiesemployed, as well as a striking variability of measuredlags as noted by Seidemann and Schaeffel (2003) reducedaccommodation response in myopes has been reportedby many studies (see Chen et al., 2003, for a review).The associated increase in retinal blur during near workin myopes has been suggested to provide a cue to eyegrowth and ultimately to lead to myopia development(Gwiazda et al., 1993). One important aspect of accom-modation lag at near is the associated retinal imagequality, which often is described as the retinal blur-circlein various models of myopia development (Flitcroft,1998; Hung & Ciuffreda, 2000). While retinal blur isan essential part of the hypothesis and is thought to re-sult from accommodation errors, little is known aboutthe quality of the retinal image at various levels ofaccommodation. Seidemann and Schaeffel (2003) havesimulated retinal image quality for various levels ofaccommodation lag for a diffraction-limited eye andfound surprisingly poor letter contrast on the retina.However for real eyes, there are several other factorsthat can influence retinal image quality including thenatural variation in pupil size (Hazel et al., 2003; Plainiset al., 2005; Ward & Charman, 1985) and higher orderaberrations (Hazel et al., 2003; Plainis et al., 2005).

Compared with most autorefractors, the PowerRe-fractor has the advantage of using the entire pupil areato derive its measurement, thereby taking into accountpupil size and pupil constriction during accommodation(Choi et al., 2000). However, it does not give insight intothe eye�s wavefront aberrations. A wavefront sensor cando both and was used by Hazel et al. (2003) who foundsignificant differences between fixed 2.9-mm pupil dataversus natural pupil data, particularly for their myopicsubjects. They concluded that accommodation accuracyis largely influenced by higher-order aberration levels.Plainis et al. (2005) recently supported this conclusionby showing that the one-to-one stimulus/response slopeshould not be considered as ideal since higher-orderaberrations, especially spherical aberration, can influ-ence the actual accommodation demand.

A number of studies have investigated changes inhigher-order aberrations with accommodation (Atchi-son, Collins, Wildsoet, Christensen, & Waterworth,1995; Cheng et al., 2004a; Hazel et al., 2003; He, Burns,

& Marcos, 2000; Ninomiya et al., 2003). The most con-sistent finding of these studies is the change of sphericalaberration in the negative power direction with accom-modation. Several studies concerning visual perfor-mance have noted a relationship between sphericalaberration and defocus (Applegate, Marsack, Ramos,& Sarver, 2003; Cheng, Bradley, & Thibos, 2004b;Jansonius & Kooijman, 1998; Wilson, Decker, & Roor-da, 2002). In the presence of spherical aberration, a cer-tain amount of defocus is beneficial in order to optimiseretinal image quality. It is therefore likely that sphericalaberration plays a role in the accommodation (defocus)response of the eye when measuring the accommodationstimulus–response curve.

In this study, we analyse some of the previously em-ployed methods to measure accommodation stimulus–response. We then use a wavefront sensor to investigatethe effects of pupil size, higher order aberrations, mon-ocular and binocular fixation on retinal image qualityduring accommodation stimulus–response. We predictvisual performance based on wavefront aberrationsand compare this with subjectively measured visual acu-ity at a range of accommodation levels.

2. Methods

2.1. Subjects

Ten subjects, five females and five males, participatedin the experiment. The participants� mean age was 27years, ranging from 22 to 36 years. Subjects were select-ed to have no significant ocular disease, normal binocu-lar vision (i.e., heterophoria within normal limits),anisometropia less than 0.50 D (best sphere) and similarvisual acuity in each eye (i.e., <1 line difference). Fivesubjects were emmetropes and five were myopes. Meanrefractive error (best sphere) of the myopes and emme-tropes was �2.25 D ± 0.85 and +0.05 D ± 0.19, respec-tively. Mean refractive astigmatism for the group was�0.30 D ± 0.45. All subjects had greater than 5 D ofaccommodation and achieved clear vision of the lettercharts for all accommodation levels.

2.2. Distance refraction

Correction of refractive errors prior the measurementof accommodation response is important, especiallywhen subjects with different refractive errors are tested.For each of the subjects, we performed a slit lamp exam-ination and subjective refraction of both right and lefteyes followed by a binocular balance test. Chart lumi-nance during both subjective refraction and accommo-dation measurements was set to approximately 140 cd/m2 to ensure similar pupil sizes. Subjective refractionswere performed at a distance of 4 m and then �0.25 D

T. Buehren, M.J. Collins / Vision Research 46 (2006) 1633–1645 1635

was added to the result so as to correct the eyes for a farpoint at infinity. The on-campus ophthalmic dispensinglaboratory enabled us to provide all subjects (both myo-pes and emmetropes) with the appropriate spectacle cor-rection determined this way within less than 20 min.Subjects with any refractive error wore their spectaclecorrection during the accommodation measurements.

The standard clinical procedure of subjective refrac-tion determines the best spherical lens to be the lowestnegative power lens or highest plus power lens toachieve optimal visual acuity. This clinical procedureof subjective refraction will potentially lead to slightlymore plus power than required, within the range ofthe depth-of-focus of the eye. The far point of the eyecorrected in this manner is known as the hyperfocal dis-tance (Thibos, Hong, Bradley, & Applegate, 2004).Based on subsequent estimates of depth-of-focus forour subject group we estimate the resultant error fromthe hyperfocal distance to be close to the clinical accura-cy of ±0.125 D for subjective refraction, when 0.25 Dpower increments are utilized.

2.3. Spectacle lens effectivity

For spectacle lens corrected subjects, effectivity for-mulas must be used to correct for apparent stimulusand response values. Mutti et al. (2000) presented thethin lens formula for correcting the accommodation re-sponse. To correct the apparent stimulus and responsevalues, Mutti et al.�s (2000) thin lens formula can beused for both conditions. The instrument output andthe inverse of target distance have to be replaced withinthe formula to calculate corrected response and correct-ed stimulus respectively. Thereby the instrument output(RawAR) and the refractive error (RX) have to be cali-brated for the corneal plane. The thin lens formulas thatcorrect for spectacle lens effectivity are

AS ¼ 11

1DLE�DTE

þ LENS� DLE

� RX cornea; ð1Þ

AR ¼ 11

11

RawARcorneaþ DLE

þ LENS� DLE

� RX cornea; ð2Þ

where AS and AR are the corrected accommodationstimulus and response respectively, RXcornea is therefractive error at the corneal plane (as correction),DLE is the vertex distance in meters, DTE is the distancefrom the target to the cornea in meters (both DTE andDLE are positive), LENS is the signed dioptric power ofthe lens in front of the eye and RawARcornea is the spher-ical equivalent of the instrument reading calibrated forthe corneal plane.

We useMutti et al.�s (2000) thin lens formula because itcan be applied to all types of induced accommodation de-

mands (i.e., negative-lens induced, distance induced andpositive-lens induced). This is not the case for all formulasthat have been presented in the past (Abbott et al., 1998;Chen & O�Leary, 2000; Gwiazda et al., 1995, 1993; He,Gwiazda, Thorn, Held, & Vera-Diaz, 2005). Responseformulas, which do not take into account changes intarget distance, will overestimate accommodationresponses for distance and positive-lens induced accom-modation demands. For example, the calculated (i.e.,corrected) accommodation response for the most myopicsubject of our study (spherical equivalent = �3.125 D)and a 5 D accommodation demand would be 0.34 Dhigher using Gwiazda et al.�s (1993) formula comparedwith Mutti et al.�s (2000) formula, whereas the correctedaccommodation stimulus of both the Gwiazda et al.(1993) and Mutti et al. (2000) formulas is the same.

2.4. Accommodation stimulus

Since spectacle lens effectivity changes the uncorrect-ed accommodation stimulus, subjects with differentrefractive errors would each be provided with differenteffective accommodation stimuli depending on the mag-nitude of their refractive errors. For example the effec-tive accommodation stimulus of an emmetrope and aspectacle corrected �6.00 D myope, differs by as muchas 0.54 D for a +4 D apparent accommodation stimulusand a vertex distance of the spectacle lens of 13 mm. Onemethod of compensation is to calculate the uncorrectedaccommodation stimuli for each spectacle-lens and tar-get-distance combination for each subject. In this waythe effective accommodation stimuli for all subjectscan be the same. We have calculated our apparentaccommodation stimuli so that the corrected accommo-dation stimuli were +1 D, +2 D, +3 D, +4 D, and +5 Dfor every subject. For example, target distances rangedbetween 94 and 100 cm to induce 1 D of accommoda-tion stimulus for this group of subjects.

2.5. Data collection procedure

A Complete Ophthalmic Analysis System (COAS,WaveFront Sciences) was used for accommodationand wavefront aberration measurements. The COASwavefront sensor was modified to present external fixa-tion targets at various distances from the eye via a beamsplitter between the eye and wavefront sensor. The nor-mal fixation target inside the wavefront sensor wasswitched off. A beam splitter allowed both monocularand binocular fixation of targets, which were presentedto induce accommodation stimuli of 0.17 D (i.e., 6 mtarget distance), 1 D, 2 D, 3 D, 4 D, and 5 D. Thefixation target at the 6 m stimulus distances was a 0.4logMAR letter in the centre of a high contrast Baily-Lovie logMAR chart. For the near conditions (i.e.,1 D to 5 D) the fixation targets were high contrast


Baily-Lovie logMAR charts on slide films with diffusebackground illumination. For each condition the beamsplitter could be adjusted to enable the alignment ofthe letter in the centre of the chart with the measurementaxis of the instrument (i.e., the instrument�s fixationspot). A different logMAR chart, appropriately scaledfor the size of the letters, was used at each of the stimu-lus distances. The setup allowed the subjects� head to bepositioned normally in the headrest. The subject wasinstructed to focus on the letter at the centre of the 0.4logMAR line and keep it ‘‘as clear as possible’’ duringthe wavefront measurements. All subjects reportedachieving ‘‘clear vision’’ of the letter charts for allaccommodation levels up to 5 D. All subjects� responseswere measured for both monocular and binocular fixa-tion conditions. The order of the testing (i.e., monocu-lar/binocular) was randomized between subjects toavoid systematic bias. For each of the six stimulus con-ditions, 6 · 25 frames (i.e., 150 measurements) of ocularwavefront measurements were acquired. The right eyewas used for all monocular measurements while the lefteye was covered using an eye patch during this testcondition.

2.6. Subjective visual acuity during accommodation

Following the monocular accommodation measure-ments, subjective visual acuity was determined at eachstimulus distance. Subjects were instructed to read upto the smallest visible line on the Baily-Lovie chartand then continue guessing until a full line was incor-rectly read. The measured visual acuity in logMAR(0.02 logMAR steps) at the six stimulus distances wasnoted for every target distance. Each Baily-Lovie log-MAR chart contained a different configuration of opto-types so as to avoid learning effects. Letter size at each ofthe stimulus distances was not affected by differences inspectacle lens minification between emmetropic andmyopic subjects because the corrected stimulus distancesalso ensured equivalent target sizes for each of the spec-tacle-lens and target-distance combinations.

2.7. Data analysis

The wavefront data was fitted with a 7th order Zer-nike expansion and exported for further analysis. Wave-fronts were fitted with Zernike polynomials for both afixed 3 mm entrance pupil size as well as for each sub-ject�s natural pupil sizes during the various accommoda-tion conditions. The 3-mm fixed entrance pupil waschosen because it was close to the minimum diameterof natural pupil sizes of all subjects at the variousaccommodation levels. This diameter also approximatesthe measurement region used by many autorefractors.The wavefronts of both monocular and binocularaccommodation were corrected for spectacle lens

effectivity and the stimulus–response curves, based onthe Zernike Z0

2 defocus term, were plotted for the fixed3 mm entrance pupil size as well as the natural pupil siz-es. For both fixed 3-mm pupil and natural pupil sizes thebest spherical lens was calculated from each of the Z0

2

defocus terms of the 150 wavefront measurements andthen averaged.

After the defocus terms of the wavefronts were cor-rected for spectacle lens effectivity, the corrected accom-modation stimuli were subtracted from the correctedaccommodation (defocus) responses to derive the leadsand lags of accommodation. To average Zernike poly-nomials from 150 measurements of natural pupil sizes,the average pupil size based on the COAS measurementsof pupil size for each accommodation stimulus condi-tion was calculated. Then the 150 wavefronts were re-scaled according to the average pupil size of thesample using the method described by Schwiegerling(2002) and the Zernike coefficients were averaged.

The relative contribution of spherical aberration toaccommodation lead and lag was also investigated foreach stimulus distance and compared as a function ofaccommodation stimulus for both fixed and natural pu-pils. Using primary and secondary Zernike sphericalaberration terms (Z0

4; Z06), the dioptric equivalent of the

balancing defocus in those terms was calculated byextracting components related to r2. Note that this diop-tric value does not represent Seidel spherical aberration,which is normally defined as the difference betweendioptric powers of the pupil centre and pupil edge, butrepresents the apparent (i.e., measured) defocus shiftcaused by Seidel spherical aberration. In the context ofthis study we call these values the apparent accommoda-tion leads and lags due to spherical aberration becausethey are an artefact of the measurement method. The ef-fect of pupil size on apparent accommodation lead andlag due to spherical aberration during each series of6 · 25 measurements at each accommodation stimuluswas also investigated. Apparent accommodation leadand lag due to spherical aberration was plotted as afunction of changing accommodation stimulus andchanging pupil size. For each accommodation level,the slope of the regression line of pupil size versusapparent accommodation lead and lag due to sphericalaberration was calculated.

To investigate metrics of image quality, the visualStrehl ratio of the optical transfer function (VSOTF)(Cheng et al., 2004b; Thibos et al., 2004) was derivedfrom the averaged wavefronts for each of the six accom-modation levels for both 3-mm and natural pupils. Alsothe location of the peak of the VSOTF and the depth-of-focus, based on the 80% level of the peak (Marcos,Moreno, & Navarro, 1999), were calculated by adjustingthe defocus component of the wavefronts (Cheng et al.,2004b; Collins, Buehren, & Iskander, 2005). The changein dioptric range was simulated by adjusting the defocus


component (in 0.125 D steps) of the measured wavefronterror for a range of ±2 D. Data points then were fittedwith a spline function and the magnitude and location ofthe peak of the VSOTF was identified.

Retinal images of a letter E (0.4 logMAR) werereconstructed using the wavefronts for both fixed 3-mm and natural pupil sizes. Retinal images and theVSOTF were also reconstructed for the leads and lagsof accommodation alone (i.e., eliminating all higher-or-der aberrations), as well as with the higher-order aberra-tions alone (i.e., eliminating all leads and lags). Retinalimages and VSOTF then were compared for the fixed3-mm pupil and the natural pupil size data.

2.8. Statistical analysis

Two-way analysis of variance (ANOVA) and Bonfer-roni post hoc tests were performed to investigate differ-ences between the fixed versus natural pupil size analysesas well as monocular versus binocular accommodation.One-way repeated measures ANOVA�s and Bonferronipost hoc tests were performed for the slopes of apparentaccommodation error due to spherical aberration versuspupil size, subjective visual acuity, VSOTF and DOFresults.

Fig. 1. Accommodation stimulus–response functions (ASRF)(±SEM) for natural pupils (top panel) and fixed 3-mm pupils (bottompanel) are shown. Dashed and solid lines indicate monocular fixationand binocular fixation, respectively.

3. Results

The accommodation stimulus–response function wassignificantly influenced by pupil size and higher orderaberration levels. Subjective visual acuity was best atintermediate distances and became worse at 5 D stimu-lus level compared with 0.17 D. Comparisons betweensubjective visual acuity and retinal image metrics calcu-lated from natural pupils showed better agreement thanimage metrics calculated from fixed 3 mm pupils.Apparent accommodation errors due to spherical aber-ration accounted for most of the measured leads andlags when natural pupils were considered. Under binoc-ular conditions, the accommodation error was smallerthan with monocular fixation.

3.1. Accommodation stimulus–response function

The accommodation response showed a significantlyshallower stimulus–response curve (i.e., more lead andmore lag) for monocular fixation compared with binoc-ular fixation (two-way ANOVA interaction p < 0.001).This was the case for the natural pupil size analysis(Fig. 1, top) but not for the fixed 3-mm pupil size anal-ysis (two-way ANOVA interaction p = 0.53) (Fig. 1,bottom). We also found slightly, but significantly small-er pupil sizes for binocular accommodation comparedwith monocular accommodation (two-way ANOVApupil size p < 0.001).

A significantly shallower stimulus–response curvewas found with natural pupils compared with fixed 3-mm pupils for both monocular and binocular fixation(both had two-way ANOVA interaction p < 0.001).For example, the monocular 5 D accommodation stim-ulus produced a group mean lag of accommodation of+0.91 D ± 0.23 for the natural pupil analysis and+0.46 D ± 0.27 for the fixed 3-mm pupil analysis (seeTable 1 for all stimulus levels).

3.2. Apparent accommodation errors due to spherical

aberration

For both pupil size analyses, apparent accommoda-tion errors due to spherical aberration (Fig. 2) changedsignificantly from negative to positive (i.e., lead to lag)with accommodation stimulus level (both two-wayANOVAs p < 0.001). The slope of change was signifi-cantly larger for natural pupils (Fig. 2, top) comparedwith 3-mm fixed pupils (two-way ANOVA interactionp < 0.001) (Fig. 2, bottom). Leads and lags of accommo-dation (calculated from Zernike Z0

2 defocus) were highlycorrelated with apparent accommodation leads and lags

Table 1Group mean (±SD) pupil size, accommodation lead and lag based on Zernike Z0

2 defocus , apparent accommodation lead and lag based on Zernikespherical aberration (Z0

4 and Z06 terms), subjective visual acuity (obtained through natural pupil sizes), VSOTF, peak of VSOTF and depth-of-focus

(DOF calculated from the 80% level of the VSOTF peak) for the six accommodation stimuli are shown

Accommodationstimulus level (D)

Pupil (mm) Lead/Lag fromZ02 defocus (D)

Apparent lead/lagdue to spherical aberration (D)

Subjective VA(log MAR)

VSOTF Peak ofVSOTF

DOF (D)

Fixed

0.17 3 +0.06 ± 0.16 �0.08 ± 0.47 �0.072 ± 0.06 0.486 ± 0.18 0.558 ± 0.16 0.40 ± 0.031.00 3 +0.18 ± 0.16 �0.10 ± 0.50 �0.152 ± 0.07 0.409 ± 0.15 0.534 ± 0.17 0.42 ± 0.072.00 3 +0.24 ± 0.16 �0.09 ± 0.47 �0.114 ± 0.04 0.338 ± 0.15 0.480 ± 0.20 0.45 ± 0.113.00 3 +0.28 ± 0.26 +0.02 ± 0.64 �0.066 ± 0.04 0.316 ± 0.17 0.443 ± 0.21 0.47 ± 0.104.00 3 +0.34 ± 0.21 +0.19 ± 0.68 �0.068 ± 0.05 0.261 ± 0.13 0.400 ± 0.18 0.48 ± 0.125.00 3 +0.46 ± 0.27 +0.20 ± 0.74 �0.040 ± 0.05 0.212 ± 0.13 0.393 ± 0.21 0.53 ± 0.21

Natural

0.17 6.04 ± 0.58 �0.07 ± 0.24 �0.13 ± 0.37 �0.072 ± 0.06 0.187 ± 0.08 0.232 ± 0.08 0.33 ± 0.091.00 5.78 ± 0.73 +0.17 ± 0.30 +0.01 ± 0.32 �0.152 ± 0.07 0.193 ± 0.10 0.258 ± 0.11 0.32 ± 0.092.00 5.83 ± 0.69 +0.36 ± 0.30 +0.24 ± 0.35 �0.114 ± 0.04 0.148 ± 0.07 0.234 ± 0.08 0.36 ± 0.143.00 5.66 ± 0.68 +0.55 ± 0.41 +0.44 ± 0.36 �0.066 ± 0.04 0.111 ± 0.08 0.196 ± 0.08 0.38 ± 0.124.00 5.30 ± 0.77 +0.69 ± 0.36 +0.62 ± 0.41 �0.068 ± 0.05 0.087 ± 0.06 0.177 ± 0.07 0.37 ± 0.085.00 5.09 ± 0.71 +0.91 ± 0.46 +0.78 ± 0.50 �0.040 ± 0.05 0.072 ± 0.05 0.172 ± 0.08 0.44 ± 0.23

Fig. 2. Group mean change (±SD) of apparent accommodation errordue to spherical aberration (D) with accommodation stimulus level fornatural pupil sizes (top panel) and fixed 3-mm pupils (bottom panel).Group mean natural pupil sizes (±SD) are shown at each accommo-dation stimulus level of the top panel.

Fig. 3. For all accommodation stimulus levels combined, the corre-lation between apparent accommodation error based on Zernikespherical aberration (Z0

4 and Z06 terms) and accommodation lead and

lag (based on the Zernike Z02 defocus term) is presented. Top panel

shows the results of the natural pupil analysis and bottom panel showsthe fixed 3-mm pupil analysis.


due to spherical aberration (R2 = 0.80) for natural pu-pils (Fig. 3, top) indicating that a large proportion ofaccommodation leads and lags was due to the effectsof spherical aberration. No correlation was found

(R2 < 0.00) for the fixed-3-mm pupil analysis (Fig. 3,bottom).

Fig. 4 shows a representative example (subject 10) ofthe interaction between pupil size, apparent accommo-

Fig. 4. A representative example (myopic subject 10) of the association between pupil size, apparent leads and lags due to spherical aberration andaccommodation stimulus level is presented. For each accommodation level, all 150 measurements of spherical aberration effects and pupil size areplotted. Note the increase in slope between apparent accommodation error and pupil size despite an overall pupil constriction with increasingaccommodation levels. Stimulus levels are shown alongside each data set.

Fig. 5. The group mean (±SD) VSOTF for both fixed 3-mm (top) andnatural pupil sizes (centre) are shown along with the group mean(±SD) subjective visual acuity (bottom). The change in VSOTF fornatural pupil data follows a similar pattern to changes in visual acuity(R = 0.56, p < 0.10). The VSOTF of fixed 3-mm pupils shows a poorercorrelation with visual acuity, particularly at the far stimulus level(0.17 D) (R = 0.43, p > 0.10).


dation error due to spherical aberration and accommo-dation stimulus level. As the accommodation stimuluslevel increased, the apparent accommodation leads andlags due to spherical aberration typically shifted fromnegative to positive while pupil size concurrently de-creased. The effect of pupil size variation on apparentaccommodation leads and lags due to spherical aberra-tion within a particular accommodation stimulus levelbecame more pronounced with increasing accommoda-tion stimulus level, as evidenced by the increased slopefitted to the data at the higher stimulus levels (Fig. 4).This is an unexpected result, since spherical aberrationeffects would normally be expected to be more sensitiveto pupil size changes in larger pupils. One-way repeatedmeasures ANOVA revealed a significantly increasingslope of the regression line of pupil size versus sphericalaberration effect with increasing accommodation level(one-way ANOVA p = 0.014). This increase in the slopeof apparent error due to spherical aberration versus pu-pil size occurred despite an overall decrease of the en-trance pupil size by about 1 mm from far to nearstimulus levels (i.e., pupil constriction withaccommodation).

3.3. Visual acuity and VSOTF

Subjective visual acuity (Figs. 5, top and bottom) wassignificantly better at intermediate stimulus levels (1 Dand 2 D) compared with the 0.17 D stimulus level (Bon-ferroni multiple comparisons; 0.17 D versus 1 Dp < 0.001; 0.17 D versus 2 D p < 0.01), and was also sig-nificantly worse at the 5 D stimulus level compared withthe 0.17 D stimulus level (Bonferroni multiple compari-sons; 0.17 D versus 5 D p < 0.05). A group mean differ-ence of about one line (0.112 logMAR) was found

between the highest and lowest acuity (1 D versus 5 Dstimulus levels). Visual acuity at the 3 D and 4 D stimu-lus levels was similar to that achieved at the far stimulus


level (0.17 D), while the visual acuity at the 5 D stimuluslevel was slightly worse (0.032 logMAR) (Table 1) thanthat at the 0.17 D stimulus level.

The VSOTF for the natural pupil size analysisshowed better correlation with subjective visual acuity(R = 0.56, p < 0.10) than did the VSOTF for the fixed3 mm pupils (R = 0.43, p > 0.10). The most noticeabledifference between the pupil size analyses was shownat the 0.17 D stimulus level, with the 3-mm pupil analy-sis showing increased over-estimation of the VSOTFcompared with the natural pupil result (Fig. 5, top).Correlation between the peak of the VSOTF and visualacuity was R = 0.56 (p < 0.10) and R = 0.38 (p > 0.10)for natural and fixed 3-mm pupils respectively. Againthe change was largest for the 0.17 D stimulus level(Fig. 5, bottom). The group mean change of VSOTFand peak of VSOTF with stimulus level showed a steadydecrease with increasing accommodation level for thefixed 3-mm pupils (Bonferroni multiple comparisons;0.17 D versus 2 D and 3 D p < 0.01; 0.17 D versus 4 Dand 5 D p < 0.001) (Fig. 5). However the change inVSOTF for natural pupils with accommodation levelwas more consistent with changes in subjective visualacuity, showing a slight increase at the 1 D stimulus levelfollowed by a decrease thereafter (Bonferroni multiplecomparisons; 0.17 D versus 3 D p < 0.05; 0.17 D versus4 D and 5 D p < 0.001).

In Table 1 all VSOTF, peak of VSOTF, depth-of-fo-cus (DOF), visual acuity, apparent lead and lag due tospherical aberration, and lead/lag (i.e., based on Z0

2

defocus) results for each of the six accommodation levelsare summarized for both fixed 3-mm and natural pupilsizes. The calculated depth-of-focus of the eyes for bothpupil conditions (fixed 3-mm and natural) was slightlylarger at near, but the increase was not significant (allmultiple comparisons p > 0.05). The correlation betweenlead and lag of accommodation and the location of thepeak of the VSOTF is shown in Fig. 6. There was a

Fig. 6. Correlation between lead and lag of accommodation and thelocation of the peak of the VSOTF. The dashed line represents the oneto one relationship between accommodation error and peak locationof the VSOTF.

significant correlation (R = 0.75, p < 0.01) between thelocation of the VSOTF peak and lead/lag error ofaccommodation. Therefore 75% of the variance inaccommodation lead/lag error was associated with thepeak location of the VSOTF.

3.4. Retinal image reconstruction

The effect of accommodation lead and lag on retinalimage quality is shown for a representative subject (sub-ject 3) in Fig. 7. Not surprisingly, image reconstructionusing the fixed 3-mm pupil data shows a generally betterretinal image (Fig. 7, left column) compared with largernatural pupils (Fig. 7, centre left column). For the 3-mmpupil data, vision is best at distance and then continuesto worsen for closer target distances (also shown by theVSOTF; left column). For the natural pupil data howev-er (Fig. 7, centre left column), in agreement with thevisual acuity results, retinal image quality is best at the1 D stimulus level and then becomes slightly worse thanthe 0.17 D stimulus data for closer targets. It is worthnoting that the decrease in retinal image quality appearsto be mainly due to a loss in letter contrast rather than aloss in ‘‘clarity’’.

To examine the relative roles of defocus and higherorder aberrations we have also reconstructed retinalimages for the same accommodation lead and lag levelswithout higher-order aberrations (Fig. 7, centre rightcolumn) and defocus errors (Fig. 7, right column). Forthe 5 D stimulus level, VSOTF is three to ten times bet-ter when higher-order aberrations and defocus errors arecombined compared with the conditions where eithercomponent is excluded.

4. Discussion

We found that pupil size, binocular fixation and high-er-order aberration levels have a significant impact onaccommodation stimulus–response curves. Accommo-dation errors and spherical aberration effects with natu-ral pupils were significantly different to those calculatedfor the fixed pupil size. Subjective visual acuity was bestfor intermediate target distances. The VSOTF showedmoderate correlation with visual acuity while the loca-tion of the peak of the VSOTF showed good correlationwith accommodation error, suggesting that accommo-dation response ‘‘errors’’ serve to optimize the retinalimage quality.

4.1. Accommodation stimulus–response

Based on the natural pupil size analysis, the accom-modation lead and lag results in this study were withinthe range of values reported previously using autorefrac-tors. We found that the analysis of a fixed sub-aperture

Fig. 7. Retinal image reconstructions, accommodation errors, pupil sizes and VSOTFs� for a myopic subject (subject 3) are shown at variousaccommodation levels. Fixed 3-mm pupil data (left panel) shows best retinal image quality at 6-m distance. Retinal image quality for natural pupildata (other three panels) is generally best at 1-m distance and gets worse for both further and closer distances. With increasing accommodation levelsretinal image quality deteriorates substantially for only defocus (centre right panel) and only higher-order aberrations (right panel). Retinal imagequality for both defocus and higher-order aberrations combined maintains reasonably stable at a ratio in the area of 0.1.


of the natural pupil size can lead to significant differenc-es in the accommodation stimulus–response curve com-pared with natural pupil size data. These results are inagreement with Hazel et al. (2003) and Plainis et al.(2005) who also found that accommodation accuracyis influenced by pupil size and higher-order aberrationlevels. Hazel et al. (2003) also compared their wavefront

sensor results with the Shin-Nippon auto-refractometerand found significant differences between the two instru-ments for pupil size analyses and refractive error groups.However, variations with accommodation as measuredby the wavefront sensor were similar for the two refrac-tive error groups. Collins (2001) found that the CanonAutoref R-1 reading, which is not expected to account


for changes in pupil size or higher-order aberrations issignificantly affected by spherical aberration. The ques-tion then arises of how to interpret the results taken fromautorefractors. This is an important issue for the results ofstudies that have compared different refractive errorgroups. Is a sub-aperture of the natural pupil size appro-priate to investigate leads and lags and is the accommoda-tion responses calculated from paraxial optics orincluding higher-order aberrations more appropriate?

We would argue that the accuracy of representationof the retinal image should determine the most appropri-ate description of the eye�s optics at different accommo-dation levels. Therefore, analysis of accommodationresponse should be based on natural pupil data becauseit takes into account the full optical information to esti-mate retinal image quality. Accommodation leads andlags alone appear not to be good estimators of visualperformance during accommodation. There can be littledoubt about the superiority of wavefront sensors in pro-viding more detailed information about the optics of theeye compared with auto-refractometers. Therefore manyof the conclusions from previous work based upon auto-refractors should be evaluated with this in mind.

With the wavefront sensor, we found nearly equalmonocular and binocular responses for the fixed 3-mmpupil analysis, but a significantly steeper binocular stim-ulus–response slope when natural pupil sizes were used.Ramsdale (1979) using a laser optometer, reported near-ly equal responses for binocular and monocular accom-modation fixation. Seidemann and Schaeffel (2003)found a small improvement with binocular comparedto monocular accommodation using the PowerRefrac-tor, that reached significance only for the 5 D stimuluslevel. While we investigated the effects of binocular ver-sus monocular fixation on the accommodation stimu-lus–response curve, we did not extend this analysis tothe interaction of higher-order aberrations and retinalimage quality. This is a complex issue when factors suchas binocular summation and ocular dominance duringbinocular accommodation are considered. Therefore,our results on binocular accommodation have to beevaluated with this in mind. As expected, we found sig-nificantly smaller pupil sizes for binocular, comparedwith monocular conditions and this is the likely explana-tion for reduced accommodation errors in binocularconditions because of the reduced effects of sphericalaberration and higher-order aberrations within thesmaller pupils.

4.2. Apparent accommodation errors due to spherical

aberration

While we have based the analysis of retinal imagemetrics and retinal image reconstruction on all lowerand higher-order aberrations, we have limited thedetailed investigation of higher-order aberrations to

spherical aberration. This was done because sphericalaberration is a major contributor to higher-order aber-rations, it shows the most systematic change withaccommodation (Atchison et al., 1995; Cheng et al.,2004a; Hazel et al., 2003; He et al., 2000; Ninomiyaet al., 2003) and it has been shown to affect the best focalplane (Applegate et al., 2003; Cheng et al., 2004b; Janso-nius & Kooijman, 1998; Plainis et al., 2005; Wilsonet al., 2002). We found a shift of spherical aberrationfrom positive to negative with increasing accommoda-tion levels as others have found previously (Atchisonet al., 1995; Cheng et al., 2004a; Hazel et al., 2003; Nin-omiya et al., 2003; Plainis et al., 2005). In agreementwith Plainis et al. (2005), we also found a clear associa-tion between spherical aberration and accommodationerrors under natural pupil conditions. He et al. (2005)recently reported no correlation between spherical aber-ration and accommodation lag. However, the wavefrontaberrations were measured only at the resting state ofaccommodation and not at the accommodation levelunder investigation.

Earlier studies using laser optometers showed signifi-cantly shallower stimulus–response functions under lowluminance conditions (Johnson, 1976; Tucker & Char-man, 1986) and this has been attributed to the inabilityof the visual system to use high spatial frequency com-ponents under low luminance conditions (Tucker &Charman, 1986). Therefore the best accommodation re-sponse would be expected for high luminance condi-tions. Some studies that have presented largeaccommodation errors (Gwiazda et al., 1993; He et al.,2005) have used luminance levels that were high enoughto allow good acuity, but low enough for pupil dilation(note that the distance-induced and positive lens-in-duced slopes of these studies should be shallower be-cause of the spectacle lens effectivity formulas applied).An explanation for the shallow slopes found in thesestudies is the increased effect of spherical aberrationassociated with larger pupils for both distance and nearfocus conditions. We have shown the effect of sphericalaberration on the apparent accommodation responseusing a wavefront sensor in this study and there is evi-dence that autorefractors are also affected by this factor(Collins, 2001).

The different pupil size analyses showed that theapparent accommodation lead and lag is an artefact ofthe measurement technique and is largely dependenton pupil size (i.e., central versus all pupil optics). In con-trast to the expected increase in accommodation re-sponse to negative spherical aberration, for the naturalpupil sizes the measured accommodation lag increasedwhen negative spherical aberration increased. This isrelated to the interaction between Zernike defocus andZernike spherical aberration. Negative spherical aberra-tion in Zernike terms has a balancing positive defocuscomponent to maintain orthogonality. The positive


defocus required to balance the negative spherical aber-ration leads to the Zernike defocus term becoming morenegative. This creates an apparent lag of accommoda-tion if Zernike defocus is considered in isolation. To fur-ther highlight the effect of this apparent accommodationlag we have also calculated accommodation lead and lagfor a 2-mm pupil diameter for the same subject (subject3 data in Fig. 7). The equivalent accommodation errorsin defocus for a 2 mm versus natural pupil for the0.17 D, 1 D, 2 D, 3 D, 4 D, and 5 D accommodationstimuli were (2 mm pupil = �0.17 D, +0.26 D,+0.11 D, �0.01 D, +0.03 D, and +0.02 D) and (naturalpupil = �0.34 D, +0.04 D, +0.45 D, +0.61 D, +0.80 D,and +1.02 D) respectively. This shows that the paraxialfocus (i.e., central pupil) is close to the retina, but as thepupil gets larger, the effects of higher order aberrationsalter the apparent leads and lags of accommodation.This factor affects the results of both wavefront sensorsand autorefractors, but in different ways. The ‘‘accom-modation’’ response in the wavefront error obtainedfrom a wavefront sensor is not the best sphere derivedfrom the second order terms of the Zernike polynomial,but is probably better represented by Seidel defocus.Autorefractors that sample in regions of the entrancepupil and not the whole pupil will also create errors inthe estimation of the accommodation response.

4.3. Visual acuity and VSOTF

We found maximum visual acuity was achieved at the1-m stimulus distance and this coincided with the maxi-mum level of the VSOTF, the peak of the VSOTF aswell as the minimum level of apparent accommodationerror due to spherical aberration for the natural pupildata of this group of subjects. The fact that the VSOTFpeak showed better agreement with subjective visualacuity than did the VSOTF based on the mean accom-modation response (see Fig. 5), may be explained bymicrofluctuations that could temporarily bring the im-age to the best focus (Plainis et al., 2005) as well asthrough the depth of focus of the eye. This could allowthe visual system to reach acuity levels that correspondto the best achievable retinal image quality at a particu-lar accommodation level. Under-correction of the sub-jective refraction could have not been the reason forthe decrease of visual performance at the far distancein this study because all subjects were corrected within±0.12 D for infinity and the distance accommodationstimulus of 0.17 D was larger than the 0.12 D of poten-tial under correction due to clinical accuracy. Thechange in visual acuity with vergence distance has beenreported previously (Heron, Furby, Walker, Lane, &Judge, 1995; Johnson, 1976). Johnson (1976) found in-creased visual resolution for intermediate target distanc-es between 2 m and 50 cm and our data confirms thisfinding. Johnson (1976) attributed variations in visual

acuity with stimulus distance primarily to errors inaccommodation. Heron et al. (1995) also reported in-creased visual acuity in the range 1.2–1.6 m for someobservers but no relationship between individual stimu-lus–response characteristics and visual acuity was found.He speculated that aberrations are the most likely causefor the variation in visual acuity since studies haveshown decreased aberrations at intermediate distances(Denieul, 1982; van den Brink, 1962).

The variation in VSOTF derived for natural pupil siz-es in this study showed some correlation (p < 0.1) withvariations in subjective visual acuity. Given the limitedrange of visual acuity in this study (about 1 line), wewere surprised at how well the VSOTF predicted visualacuity. These results support previous findings that haveidentified the VSOTF as a good estimator of high con-trast visual acuity performance (Cheng et al., 2004b;Marsack, Thibos, & Applegate, 2004; Thibos et al.,2004). However we did not find a one to one relationshipbetween accommodation error and best retinal imagequality based on the location of the VSOTF peak (slope0.43). Several factors probably contribute to this find-ing. Depth-of-focus of the eye will probably allow theaccommodation error to reach a level which is just lessthan a perceptible or tolerable loss of visual perfor-mance. Our estimates of depth of focus based on 80%of the visual Strehl ratio can account for some, butnot all of this accommodation error. Other factors suchas chromatic aberration and the wavelength that is pref-erentially focussed during accommodation (Kruger,Nowbotsing, Aggarwala, & Mathews, 1995; Thiboset al., 2004) and the natural microfluctuations of theeye (Collins, Davis, & Wood, 1995; Plainis et al.,2005) will almost certainly contribute to the tolerable le-vel of accommodation error.

4.4. Retinal image reconstruction

The effect of the combination of higher-order aberra-tions and accommodation error on the retinal imagequality (reconstructed E targets) in this study was strik-ing. While there was some loss of image quality at farand near stimulus distances compared to intermediatedistances, the level of visual performance was not mark-edly worse at near. It is well known that the interactionbetween spherical aberration and defocus can improvevisual performance in contrast to the individual effectsof these aberrations (Applegate et al., 2003; Chenget al., 2004b; Jansonius & Kooijman, 1998; Wilsonet al., 2002; Woods, Bradley, & Atchison, 1996). Ourdata, in agreement with Plainis et al. (2005), suggeststhat this interaction plays an important role in the mea-sured errors of accommodation stimulus–responsecurves. The word error in this context is confusingthough, since this apparent accommodation ‘‘error’’in the presence of spherical aberration and other


higher-order aberrations does actually improve retinalimage quality compared with zero accommodationerror. It is clear that visual performance would be betterwithout spherical aberration and defocus. Yet if spheri-cal aberration is present, then defocus can improve visu-al performance and therefore the traditionally measuredlag of accommodation alone is not a good estimator ofthe performance of the visual system during accommoda-tion. Therefore studies that have used autorefractors tocompare accommodation stimulus–response as a func-tion of refractive error should be evaluated with this inmind. Although the VSOTF decreased slightly at nearstimulus distances, we did not find significant retinalimage degradation in terms of visual acuity. As shownin the example of Fig. 7, the loss in retinal image qualityappeared to be characterised primarily by a loss of lettercontrast rather than a loss in letter ‘‘clarity’’ and thischaracteristic was found consistently for most of our sub-jects. When binocular fixation is considered the imagedegradation at near is likely to be of lesser magnitude.

In summary, subjective visual acuity was best at inter-mediate accommodation levels and only became signifi-cantly worse at the nearest (5 D) accommodation levelcompared with the far (0.17 D) level. Changes in retinalimage quality metrics, such as the VSOTF with naturalpupil sizes showed general agreement with changes invisual acuity and the location of the peak VSOTF valuealso influenced the accommodation response. Autore-fractors which base their results on fixed pupil diameterswill not accurately represent the true optical characteris-tics of the eye during accommodation stimulus–responsemeasurements. The use of wavefront sensors with anal-ysis conducted using natural pupil sizes should providemore accurate estimates of the optical and visual perfor-mance of the eye across a range of accommodation lev-els. However the results of wavefront sensors can also bemisleading, if the interactions between lower and higherorder aberrations are not considered. Binocular accom-modation results with natural pupils are different tothose acquired under monocular conditions and withfixed pupils.

Acknowledgments

We wish to thank Sandra Gadamer, Cathleen Fedtke,Birgit Uebel, and Carina Schindler for their help duringdata collection. This work was funded by a grant fromthe Lee Foundation, Singapore.

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