Effect of Positive and Negative Defocus on Contrast Sensitivity in Myopes

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Vision Research 44 (2004) 1869–1878 www.elsevier.com/locate/visres

Eﬀect of positive and negative defocus on contrast sensitivity in myopes and non-myopes

Hema Radhakrishnan *, Shahina Pardhan, Richard I. Calver, Daniel J. O’Leary Department of Optometry and Ophthalmic Dispensing, Anglia Polytechnic University, East Road, Cambridge CB1 1PT, UK Received 22 October 2003; received in revised form 8 March 2004

Abstract This study investigated the effect of lens induced defocus on the contrast sensitivity function in myopes and non-myopes. Contrast sensitivity for up to 20 spatialfrequencies ranging from 1 to 20 c/deg was measured with verticalsine wave gratings under cycloplegia at different levels of positive and negative defocus in myopes and non-myopes. In non-myopes the reduction in contrast sensitivity increased in a systematic fashion as the amount of defocus increased. This reduction was similar for positive and negative lenses of the same power (p ¼ 0:474). Myopes showed a contrast sensitivity loss that was significantly greater with positive defocus compared to negative defocus (p ¼ 0:001). The magnitude of the contrast sensitivity loss was also dependent on the spatial frequency tested for both positive and negative defocus. There was significantly greater contrast sensitivity loss in non-myopes than in myopes at low-medium spatial frequencies (1–8 c/deg) with negative defocus. Latent accommodation was ruled out as a contributor to this difference in myopes and non-myopes. In another experiment, ocular aberrations were measured under cycloplegia using a Shack– Hartmann aberrometer. Modulation transfer functions were calculated using the second order term for defocus as well as the fourth order Zernike term for sphericalaberration. The theoreticalmaximalcontrast sensitivity based on aberration data predicted the measured asymmetry in contrast sensitivity to positive and negative defocus that was observed in myopic subjects. The observed asymmetry in contrast sensitivity with positive and negative defocus in myopes may be linked to the altered accommodative response observed in this group. Ó 2004 Elsevier Ltd. All rights reserved.

Keywords: Myopia; Contrast sensitivity; Defocus; Aberration; Accommodation

1. Introduction 1988). Recent reports also suggest that the accommodative response mechanism plays an important role in It is known that opticaldefocus guides severalvisual myopia development/emmetropization (Wildsoet & processes including accommodation and emmetropiza- Schmid, 2001). tion (Diether & Schaeffel, 1997; Kruger & Pola, 1987; It is well known that reduced accommodative re- Schmid & Wildsoet, 1997). The human eye constantly sponse to negative lenses occurs in myopes (Gwiazda, encounters opticaldefocus in the normalvisualenvi- Thorn, Bauer, & Held, 1993; O’Leary & Allen, 2001; ronment as a result of various factors including refrac- Seidel, Gray, & Heron, 2003). A possible explanation tive error and microfluctuations in accommodation. for the reduced accommodative response in myopes was Variation in the retinalimage quality with changing given by Jiang (1997). He proposed a modelof static levels of defocus is of considerable interest as the defo- accommodation and evaluated it by substituting mea- cused image is thought to provide feedback for emme- sured accommodative response values from a group of tropization. In emmetropes the feedback mechanism is late-onset myopes and emmetropes. This model pre- considered to act normally and guide the growth of the dicted that the lowered accommodative response in eye such that there is minimalrefractive error (Hung, myopes is due to a reduction in blur sensitivity. Since Crawford, & Smith, 1995; Shaeffel, Glasser, & Howland, then, some researchers have investigated blur sensitivity in myopes directly. * Corresponding author. Tel.: +44-1223-363271x2237; fax: +44- Rosenfield and Abraham-Cohen (1999) measured 1223-417712. defocus thresholds in myopes and emmetropes with the E-mail address: [email protected] (H. Radhakrishnan). BadalOptometer system. Adultsubjects were asked to

0042-6989/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2004.03.007 1870 H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 report when they first noticed a difference in clarity be- an overestimation of the aberrations in myopes in this tween two parts of a bipartite target when the movable study. If indeed myopes have higher magnitudes of half of the target was oscillated. Their results showed ocular spherical aberrations, this should result in a significantly higher defocus detection thresholds in more negative focus for peak contrast at low-medium myopes (±0.19D) when compared to non-myopes spatialfrequencies in this group (Charman & Jennings, (±0.11D). However, they did not differentiate between 1976). blur thresholds for target moved towards and away So far, no study has compared contrast sensitivity from the subject, which would simulate positive and with positive and negative defocus in myopes and non- negative defocus, respectively. myopes. We investigated the effect of lens-induced de- Schmid, Iskander, Li, Edwards, and Lew (2002) focus on contrast sensitivity in myopes and non-myopes. measured blur thresholds in children with simulated blur The study was conducted in three parts. In the first part targets obtained by Fourier transformation of the we examined the effect of sign of defocus on contrast opticaltransfer function. They found no significant sensitivity; in the second part we studied the effect of difference in thresholds between myopes and non-myo- different magnitudes of defocus on contrast sensitivity, pes for simulated positive and negative defocused tar- and thirdly we predicted the contrast sensitivity of the gets. This study does not provide information on the subjects based on the aberration data. Our results re- interaction between defocus and the eye’s opticalprop- vealed significant differences in contrast sensitivity in the erties, but shows that myopic children do not have an presence of positive and negative lens-induced defocus advantage over emmetropes in interpreting details in a between myopes and non-myopes. picture that have been blurred by external factors. The spatialfrequency content of the target is an important characteristic affecting accommodation 2. Methods (Charman & Heron, 1979; Owens, 1980) and emmetropization (Schmid & Wildsoet, 1997). Studies on 2.1. Part 1: Effect of type of defocus on contrast contrast sensitivity with defocus show that the optimum sensitivity focus is dependent on spatialfrequency (Green & Campbell, 1965). The optimum focus is more myopic for 2.1.1. Subjects low and medium spatial frequencies relative to the high Eight myopic and eight non-myopic subjects took spatialfrequencies, a resultthat is attributed to ocular part in the study. The relevant information about the aberrations (Green & Campbell, 1965). Equal magni- subjects is given in Table 1. All subjects had visual tudes of positive and negative defocus can therefore acuity of at least 6/5. Subjects with )1.00D myopia or result in different thresholds in the presence of spherical more following cycloplegia were included in the myopic aberration. Charman and Jennings (1976) and Jansonius group, and those with cycloplegic spherical equivalent and Kooijman (1998) calculated the effect of spherical refractive error ranging between )0.25D and +1.25D aberration on the modulation transfer function and were considered non-myopic. The subjects included in found that in the presence of sphericalaberration the the non-myopic group had non-cycloplegic refractive modulation transfer function for intermediate spatial error ranging between Plano to +0.50D. All subjects frequencies is much higher with negative defocus when were screened to exclude astigmatism greater than compared to positive defocus. 1.25D, myopic retinaldegeneration, amblyopia or any Some previous studies which have measured aber- ocular disease. rations have shown that the ocular aberrations are The measurements were carried out on the left eye higher in myopes when compared to emmetropes (He only. Two drops of cyclopentolate hydrochloride 1%, et al., 2000, 2002). On the other hand, Cheng, Bradley, were instilled with a 3 min interval in the left eye. One Hong, and Thibos (2003) found that myopic eyes do drop of cyclopentolate hydrochloride 0.5% was instilled not have significantly different amounts of monochro- every 2 h during the experimentaltrial.Thirty minutes matic aberrations compared with emmetropes. Al- after the instillation of the first drop of cycloplegic the though Collins, Wildsoet, and Atchison (1995) showed pupildiameter had increased to 7 mm or more. The that fourth order aberrations were lower in some refractive error was initially determined with a cyclo- myopic subjects compared to emmetropes, in a signifi- plegic AutoRefractor (Nidek AR600-A) reading fol- cant number of myopic subjects aberrations were so lowed by a full subjective refraction (to an accuracy of great that measurement was not possible. Applegate ±0.12D) with an artificialpupil(6 mm diameter). The (1991) using a subjective single-pass aberroscope had refraction was determined for both 1 and 6 m test dis- also found dramatically increased coma and spherical tance. The end point of refraction was duochrome bal- aberration in some myopic eyes. However, the failure to ance at 1 m and a reduction in vision by at least four take into account the differences in size of grid spacing lines with +1.0DS blur test at a test distance of 6 m. and its projection on the entrance pupilmay have ledto During the experiment the refractive error of all the H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 1871

Table 1 For the first five myopes and five non-myopes, con- Biometrics of the subjects included in Experiments 1 and 2 trast sensitivity was measured for spatialfrequencies Subject Age Experiment Age of Sphericalequivalent ranging between 1 and 20 c/deg in 1 c/deg steps. For the onset refractive error remaining three myopes and three non-myopes contrast Non-myopes sensitivity was measured for spatialfrequencies 1, 2, 3, 1 23 1 & 2 NA +1.25D 4, 6, 8, 10, 13, 16 and 20 c/deg. The test distance was 2 24 1 & 2 NA +0.12D 3 21 1 & 2 NA +0.25D altered to account for individual spectacle magnification 4 20 1 & 2 NA +0.87D for each myopic subject as appropriate. 5 22 1 & 2 NA +1.00D A random double staircase procedure (Cornsweet, 6 21 1 NA +0.37D 1962) was used to determine the contrast sensitivity 7 22 1 NA +0.75D function. The initialcontrast levelwasdetermined using 8 20 1 NA +0.50D 17 20 2 NA )0.25D the ‘method of limits’. Two contrast staircases of the 18 20 2 NA +0.87D same spatialfrequency were presented in a randomised 19 22 2 NA +1.12D order. Ten blank trials were randomly included in the Myopes staircases to check for any false positive responses. Each 9211&29)5.00D trialwas started by a computer mouse clickand an 10 20 1 & 2 9 )6.00D auditory cue was given 50 ms prior to stimulus presen- 11 38 1 & 2 19 )1.25D tation. The trialconsisted of a 250 ms exposure and the ) 12 20 1 & 2 10 8.25D subject responded indicating whether they could see the 13 21 1 5 )6.00D 14 21 1 16 )1.12D target using the computer mouse. The subject was not 15 21 1 17 )1.25D given any feedback regarding the response. Stimulus 16 20 1 6 )9.00D contrast was changed in steps of 9% of the previous 20 20 2 18 )1.87D contrast level during each trial. The program terminated ) 21 20 2 14 2.50D after 12 reversals in each staircase. The first four rever- 22 21 2 8 )11.00D 23 21 2 7 )3.12D sals in both staircases were excluded in calculating the The refractive error was determined for 6 m distance, to an accuracy of threshold. The program also terminated if there were ±0.12D. more than two false positive responses in a run. A second set of data was generated (at spatialfrequencies 1, 3, 6, 12 and 24 c/deg) for the first 10 subjects to determine subjects was corrected using trial lenses placed at a the repeatability of the data. vertex distance of 13 mm. All measurements were carried out with a 6 mm The tenets of the Declaration of Helsinki were fol- diameter artificial pupil placed in a trial frame as close to lowed. Informed consent was obtained from every sub- the subject’s eye as possible. The subject’s head was ject after verbaland written explanationof the nature stabilised using a chin rest and a brow bar. The subject and possible consequences of the study. The Anglia was asked to fixate at the centre of the stimulus and the Polytechnic University Research Ethics Committee ap- artificialpupilwas centred on the fovealachromatic proved this research project. axis. A fixation point was presented at the centre of the screen in the intervalbetween two target presentations. 2.1.2. The effect of lens induced defocus on the contrast Measurements were made for changes in focus levels sensitivity function 1 relative to the screen distance. A change in focus of ei- Sine wave gratings were displayed with a NIH im- ther )2.00D (hypermetropic ocular defocus) or +2.00D age macros program on a Power Mac G4. The non- (myopic ocular defocus) was induced by placing linear luminance response of the display was linearised appropriate trial lenses next to the artificial pupil. The by digitalgamma correction using a CRS Opticalpho- spectacle defocus required to produce ±2.00D ocular tometer. The average luminance of the screen was 42 cd/ defocus was calculated for each subject and the appro- 2 m . The experiments were performed under laboratory priate lens was used to induce defocus. For example, in conditions with the computer screen being the only case of a subject requiring )10.00D correction at the test source of light. All subjects were adapted to the condi- distance, to produce )2.00D ocular defocus the effective tions for about 10 min before commencement of the defocusing lens placed in front of the eye was )2.62D; to experiment. The stimuli used were vertical sine wave produce +2.00D ocular defocus a +2.50D lens was used. gratings filtered through a Gabor function. Each Gabor patch subtended an angular size of 6° at the testing 2.1.3. Cycloplegia stability distance of 1 m. The phase of the gratings with respect The range of accommodation and amplitude of to fixation was changed randomly at each presentation. accommodation was checked using the ‘push up’ and ‘push down’ method (Chen, O’Leary, & Howell, 2000). 1 Available at http://rsb.info.nih.gov/nih-image/ The amplitude of accommodation was measured every 1872 H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878

30 min after the instillation of the first drop of cyclo- The modulation transfer function of the eye was plegic for the first 2 h, and then once in every 60 min. calculated from the fourth order Zernike term for The change in refractive error on introduction of sphericalaberration and the defocus coefficient with the defocusing lenses was tested using the PowerRefractor Simusofte (Spot-Optics srl, Italy) program. The pro- (Allen, Radhakrishnan, & O’Leary, 2003). Dynamic gram calculated modulation transfer functions for a measurements of refraction were obtained with the pupildiameter of 6 mm; the totalocularaberrations ±2.00D defocusing lenses sampling at a rate of 25 Hz for were also analysed over a 6 mm pupil diameter. A 2 min to ensure that no accommodative changes could wavelength of 644 nm was used for the modulation be induced under our experimentalconditions. transfer function calculations. Modulation transfer functions for +2.00D and )2.00D defocus were calcu- 2.2. Part 2: Effect of defocus magnitude on contrast lated for each subject. The defocus coefficient was con- sensitivity sidered to be zero at the subjectively chosen ‘in-focus’ condition. Contrast sensitivity was measured for different levels Contrast sensitivity (CS) with defocus was predicted of defocus at spatialfrequencies 3, 6, 10, 13 and 16 c/ from the calculated modulation transfer function data deg, in eight myopes and eight non-myopes. The bio- (MT) using a formula similar to that used by Strang, metric information of the subjects is given in Table 1. Atchison, and Woods (1999): The exclusion criteria were the same as in part 1. Two MT ðdefocusÞ drops of 1% cyclopentolate hydrochloride were instilled CS ðdefocusÞ¼CS ðinfocusÞ : MT infocus in the subject’s left eye allowing a 3 min interval between ð Þ the drops. The experimental data was collected 30 min after the instillation of the second drop. One drop of 2.3.1. Analysis of fits 0.5% cyclopentolate hydrochloride was instilled every 2 To assess the accuracy of contrast sensitivity predic- h during the experiment. Contrast sensitivity was mea- tions with the above mentioned formula, the root mean sured as described previously. As explained before, the square error (RMSE) was calculated (Atchison, Woods, range of accommodation was checked using the ‘push & Bradley, 1998; Strang et al., 1999) for each subject up’ and ‘push down’ method every 30 min after the using the equation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi instillation of the first drop for the first 2 h, then once in P every 60 min. ðCS CS Þ2 ) RMSE ¼ meas pred ; The induced defocus ranged from 3.00DS to n 1 +3.00DS in 1.00DS steps for spatialfrequency of 3 c/ deg. For all the remaining spatial frequencies, contrast where CSmeas is measured log contrast sensitivity, CSpred sensitivity was measured at defocus levels of ±0.50DS, is predicted log contrast sensitivity and n is the number ±1.00DS and ±2.00DS. A more detailed analysis of of spatialfrequencies tested. Atchison et al.(1998) re- contrast sensitivity loss was carried out at smaller de- ported the RMSEs of two repeated contrast sensitivity focus steps of 0.25DS for all the above spatial frequen- measurements with )2.00D defocus of two subjects to cies in two myopes and two non-myopes. be 0.14 and 0.15 log units. Strang et al. (1999) compared measured and predicted contrast sensitivity with ±2.00D 2.3. Part 3: Predicted contrast sensitivity based on defocus in three subjects and reported RMSEs ranging aberration data between 0.12 and 0.44 log units.

All the 23 subjects included in part 1 and 2 took part in the study. Ocular aberrations were measured using 3. Results the Shack–Hartmann aberrometer. The Hartmann– Shack plate in the instrument samples at 0.6 mm inter- 3.1. Part 1: Effect of the type of defocus on contrast vals across the pupil. The wavelength of the light source sensitivity used in the instrument was 644 nm. Dilation of the pupil and cycloplegia was achieved Repeatability of the random double staircase proce- through instillation of 1–2 drops of 1% cyclopentolate dure was tested and the coefficients of repeatability hydrochloride in the left eye. Following pupil centra- (Bland & Altman, 1986) were found to be 0.0082, tion, 25 images of the Shack–Hartmann grid were taken 0.0114, 0.0091, 0.0104 and 0.0123 for spatialfrequencies for each subject. The image was then analysed using the 1, 3, 6, 12 and 24, respectively. The low values of coef- Sensofte software (Spot-Optics srl, Italy). A minimum ficients of repeatability show the results to be very of 10 images were analysed, and an average of the repeatable for all the spatial frequencies tested. readings of the fourth order sphericalaberration in The residual amplitude of accommodation following Zernike terms was calculated for each subject. cycloplegia was found to be constant throughout the H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 1873 test. The mean amplitude of accommodation, including tically significant differences were found in contrast depth of focus, was found to be 0.21D ± 0.06D sensitivity determined with positive and negative de- throughout the duration of the contrast sensitivity focus in myopes (ANOVA; F1;143 ¼ 191:9; p ¼ 0:001). measurements. The mean AutoRefractor reading chan- The difference in contrast sensitivity between the posi- ged from +0.08D (with 0D defocus) to )1.95D with a tive and negative defocus was dependent on the spatial +2.00D lens and to +2.17D with a )2.00D lens. frequency tested (interaction between sign of defocus The mean in-focus contrast sensitivity function of and spatialfrequency; ANOVA; F8;143 ¼ 5:21; myopes was slightly lower than in non-myopes, espe- p ¼ 0:001). Post-hoc test (Scheffe) showed significant cially at high spatial frequencies. Analysis of variance, differences at all spatial frequencies between 1 and 8 c/ with in-focus contrast sensitivity as the dependent vari- deg (p < 0:05). No significant differences existed be- able, and refractive group and spatial frequency as tween spatialfrequencies 9–20 c/deg ( p > 0:05). independent variables, showed a significant difference Fig. 1(B) shows the results averaged for eight non- between in-focus contrast sensitivity in myopes and non- myopes. No significant difference was found between myopes (F1;158 ¼ 35:42; p ¼ 0:001). The difference in contrast sensitivity with positive and negative defocus in contrast sensitivity between the two groups was depen- non-myopes (ANOVA; F1;142 ¼ 0:516; p ¼ 0:474). Con- dent on the spatialfrequency tested (interaction between trast sensitivity is reduced by equalmagnitudes with prescription group and spatialfrequency; ANOVA; equalamounts of positive and negative defocus in non- F9;147 ¼ 2:001; p ¼ 0:043). Post-hoc test (Scheffe) showed myopes. significant differences (p < 0:05) at spatialfrequencies 8, Fig. 2(A) and (B) shows contrast sensitivity with 10, 13, 16 and 20 c/deg. positive and negative defocus in two myopic subjects for Fig. 1(A) shows the results averaged for eight myo- spatialfrequencies of 1–20 c/deg. The resultsare un- pes. Analysis of variance was performed with contrast likely to be a result of over-plussed refraction since sensitivity as dependent variable, and the sign of defocus contrast sensitivity with positive and negative defocus is and spatialfrequency as independent variables.Statis- reduced by similar amounts at high spatial frequencies (16 c/deg and higher) and the best contrast sensitivity at

3 (A) Plano 3 With +2.00D lens Plano 2.5 With -2.00D lens (A) With +2.00D Lens 2.5 With -2.00D Lens 2 2 1.5 1.5 1 1 Log Contrast sensitivity 0.5

Log Contrast Sensitivity 0.5 0 0 5 10 15 20 25 0 Spatial Frequency (c/deg) 0 5 10 15 20 25 Spatial Frequency (c/deg)

3 (B) Plano 3 With +2.00D lens (B) Plano 2.5 With -2.00D lens With +2.00D Lens 2.5 With -2.00D Lens 2 2 1.5 1.5 1 1 Log Contrast Sensitivity 0.5 Log Contrast Sensitivity 0.5 0 0 5 10 15 20 25 0 Spatial Frequency (c/deg) 0 5 10 15 20 25 Spatial Frequency (c/deg) Fig. 1. Average (n ¼ 8) contrast sensitivity (A) in myopes and (B) in non-myopes with and without ±2.00D defocus. Error bars show ±1 Fig. 2. Contrast sensitivity in two myopic subjects: (A) Subject 2 and standard error of mean. The data has been corrected for the spectacle (B) Subject 3. The data has been corrected for the spectacle magnifi- magnification (of ±2.00D lens) induced spatial frequency shift. cation (of ±2.00D lens) induced spatial frequency shift. 1874 H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 these spatialfrequencies is at the subjectivelychosen ‘in- The non-myopic group was divided into a hyperme- focus’ condition. The subject whose results are shown in tropic and an emmetropic group, in order to determine Fig. 2(A) had a high magnitude of ocular spherical the presence of any possible differences within this aberration. The line through the data is not smoothed, group. The refractive error in the hypermetropic group since irregularities are expected due to notching (Strang ranged from +0.62D to +1.25D, and in the emmetropic et al., 1999). Fig. 3(A) and (B) shows contrast sensitivity group between )0.25D and +0.50D. No significant dif- with positive and negative defocus in two non-myopic ference in contrast sensitivity was found with positive subjects for spatialfrequencies of 1–20 c/deg. (two-tailed t-test; p ¼ 0:241) and negative defocus (two- We compared the contrast sensitivity with negative tailed t-test; p ¼ 0:746) between these two groups. defocus in myopes and non-myopes. Analysis of variance with contrast sensitivity in the presence of negative 3.2. Part 2: Effect of defocus magnitude on contrast defocus as the dependent variable, and refractive group sensitivity and spatialfrequency as independent variablesshowed a significant effect on refractive group (ANOVA; Fig. 4(A) and (B) show the average contrast sensi- F1;142 ¼ 73:5; p ¼ 0:001) and spatialfrequency (ANO- tivity as a function of defocus in myopes and non- VA; F9;142 ¼ 95:76; p ¼ 0:001). The differentialeffect of myopes, respectively. Fig. 5 shows contrast sensitivity negative defocus on contrast sensitivity between the two with different levels of defocus measured at different groups was clearly dependent on spatial frequency spatialfrequencies in myopes (Fig. 5(A) and (B)) and (interaction between refractive group and spatialfre- non-myopes (Fig. 5(C) and (D)). The results shown in quency: ANOVA; F8;135 ¼ 2:347; p ¼ 0:004). Post-hoc Fig. 5(A) are from the same subject as in Fig. 2(A) and test (Scheffe) showed significant differences at spatial this subject had a high magnitude of ocular spherical frequencies between 1 and 10 c/deg (p < 0:05). Analysis aberration. was also carried out on contrast sensitivity with positive A regression line was computed between adjacent defocus in myopes and non-myopes. No significant defocus levels for each subject at each spatial frequency. difference was found in the effect of positive defocus on The slope of the regression line was then plotted as a contrast sensitivity in myopes and non-myopes (ANO- function of the mean defocus (the average of the two VA; F1;142 ¼ 0:998; p ¼ 0:319).

Myopes 3 3 (A) Plano 3 c/deg With +2.00D Lens (A) 2.5 6 c/deg With -2.00D Lens 2.5 10 c/deg 13 c/deg 2 2 16 c/deg

1.5 1.5

1 1

Log Contrast Sensitivity 0.5 Log Contrast Sensitivity 0.5

0 0 5 10 15 20 25 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Spatial Frequency (c/deg) Defocus in Diopters

3 (B) Plano Non-myopes 2.5 With +2.00D Lens 3 With -2.00D Lens (B) 3 c/deg 2.5 6 c/deg 2 10 c/deg 13 c/deg 2 16 c/deg 1.5 1.5

1 1 Log Contrast Sensitivity Log Contrast

0.5

Log Contrast sensitivity 0.5

0 0 0 5 10 15 20 25 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Spatial Frequency (c/deg) Defocus in Diopters

Fig. 3. Contrast sensitivity in two non-myopic subjects: (A) Subject 1 Fig. 4. Effect of defocus on contrast sensitivity for five spatialfre- and (B) Subject 5. The data has been corrected for the spectacle quencies: (A) average (n ¼ 8) in myopes, and (B) average (n ¼ 8) in magnification (of ±2.00D lens) induced spatial frequency shift. non-myopes. Error bars show ±1 standard error of mean. H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 1875

3 3 3 c/deg 3 c/deg (B) (A) 6 c/deg 6 c/deg 2.5 2.5 10 c/deg 10 c/deg 13 c/deg 13 c/deg 16 c/deg 2 16 c/deg 2

1.5 1.5

1 1

0.5 Log Contrast Sensitivity 0.5 Log Contrast Sensitivity

0 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Defocus in diopters Defocus in Diopters

3 3 3 c/deg (C) 3 c/deg 6 c/deg (D) 6 c/deg 2.5 10 c/deg 2.5 10 c/deg 13 c/deg 13 c/deg 16 c/deg 2 2 16 c/deg

1.5 1.5

1 1 Log Contrast Sensitivity 0.5 Log Contrast Sensitivity 0.5

0 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Defocus in Diopters Defocus in Diopters

Fig. 5. Log contrast sensitivity as a function of defocus in myopes and non-myopes: (A) Subject 2 (myope), (B) Subject 6 (myope), (C) Subject 1 (non-myope), (D) Subject 7 (non-myope).

0.5 focus was significantly different in the myopic group y = 0.0087x - 0.1745 R2 = 0.2475 than the non-myopic group (F1;79 ¼ 28:9; p ¼ 0:001). 0 The spatialfrequency of the target alsohad a significant effect on optimum focus (F4;79 ¼ 5:501; p ¼ 0:001). A -0.5 significant interaction was found between the refractive y = 0.052x - 0.9267 R2 = 0.9429 error group and spatialfrequency ( F4;79 ¼ 3:356; -1 p ¼ 0:014). The post-hoc test (Scheffe) showed a signif-

Myopes icant diﬀerence in optimum focus between the two

Optimum focus (Diopters) -1.5 Emmetropes refractive groups at 3 c/deg (p < 0:05). No significant Linear (Myopes) Linear (Emmetropes) difference was found at any other spatialfrequency. -2 0 2 4 6 8 10 12 14 16 18 The magnitude of refractive error and optimum focus Spatial frequency (c/deg) were compared for different spatialfrequencies. A statistically significant correlation was found between the Fig. 6. Optimum focus in myopes and non-myopes as a function of magnitude of refractive error and optimum focus at 3 c/ spatialfrequency. Each data point is an average of resultsobtained deg (Pearson’s correlation ¼ 0.713; p ¼ 0:002), 6 c/deg from eight subjects. Error bars show ±1 standard error of mean. (Pearson’s correlation ¼ 0.490; p ¼ 0:054) and 10 c/deg (Pearson’s correlation ¼ 0.505; p ¼ 0:046). No significant correlation was found at 13 and 16 c/deg. defocus levels for which the slope of the regression line was calculated). The defocus level at which the slope was 3.3. Part 3: Predicted contrast sensitivity based on found to be zero was considered to be the optimum aberration data focus, which is the image position at which the maxi- mum contrast sensitivity occurs. The mean fourth order sphericalaberration was The mean optimum focus for each spatialfrequency found to be higher in myopes (0.40 ± 0.58 lm) than in was calculated and plotted for the two groups (Fig. 6). non-myopes (0.06 ± 0.23 lm). However, this difference Analysis of variance with optimum focus as the depen- was not quite significant (two-tailed t-test; p ¼ 0:087). dent variable, and refractive group and spatial fre- The root mean square error did not show a significant quency as independent variables showed that optimum difference between the two refractive groups (two-tailed 1876 H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878

3 4. Discussion Predicted CS with +2.00D defocus (A) Predicted CS with -2.00D defocus 2.5 Contrast sensitivity in myopes is degraded relatively

2 less with negative defocus than with positive defocus for a range of intermediate spatialfrequencies (1–8 c/deg.). 1.5 In addition, optimum focus for intermediate spatial frequencies (3 c/deg) occurs at a more negative focus in 1 myopes compared to non-myopes. We ruled out 0.5 accommodation as contributing factor to these asym- metries because, due to the cycloplegia, no subject had 0 0 5 10 15 20 25 any signiﬁcant residualaccommodation during the Spatial frequency (c/deg) experiments. Raw data (Figs. 2 and 3) show local sensitivity min- 3 ima (which are possibly notches) in the contrast sensi- (B) Predicted CS with +2.00D defocus Predicted CS with -2.00D defocus 2.5 tivity function, although more points along the dips are needed to be more conclusive about these notches. The 2 existence of notches has been shown to provide information about the aberrations in the eye (Bour & Apk- 1.5 arin, 1996; Strang et al., 1999; Woods, Bradley, & 1 Atchison, 1996). As documented in the literature, we

Log contrast sensitivity Log contrast sensitivity also found large variations in the position and depth of 0.5 these notches between diﬀerent subjects which makes it

0 difficult to study any systematic differences between the 0 5 10 15 20 25 two refractive groups. These variations in the charac- Spatial frequency (c/deg) teristics of the notches between subjects are most likely Fig. 7. Predicted contrast sensitivity (A) in myopes and (B) in non- to be a result of large individual variations in the ocular myopes with +2.00D and )2.00D defocus. The error bars represent ±1 aberrations between subjects (Porter, Guirao, Cox, & standard error of mean. Williams, 2001). The results from Experiment 1 (part 1) showed significant difference between the in-focus contrast sensi- t-test; p ¼ 0:391). Fig. 7(A) and (B) show the predicted tivity function at spatialfrequencies between 8 and 20 c/ contrast sensitivity with positive and negative defocus in deg in myopes and non-myopes. These findings agree myopes and non-myopes, respectively. A significant with previous studies (Fiorentini & Maffei, 1976; Liou & difference was found in predicted contrast sensitivity Chu, 2001; Thorn, Corwin, & Comerford, 1986) where with positive and negative defocus in myopes (two-tailed no significant differences were found in contrast sensi- t-test; p ¼ 0:002). However, no significant difference was tivity of myopes and emmetropes except at high spatial found in non-myopes with positive and negative defocus frequencies. (two-tailed t-test; p ¼ 0:478). Although contrast sensitivity with positive defocus The predicted contrast sensitivity (Fig. 7) from the (especially at high spatial frequencies) was slightly better modulation transfer function overestimates the mea- in myopes in comparison to non-myopes in the present sured contrast sensitivity (Fig. 1), especially in the study, these differences were not statistically significant. myopic group. The average RMSE values in the non- This finding does not agree with the results from Thorn, myopic group were found to be 0.19 ± 0.07 with +2.00D Cameron, Arnel, and Thorn (1998) who found that the defocus and 0.17 ± 0.06 with )2.00D defocus. In the contrast sensitivity with positive defocus was signifi- myopic group the mean RMSE values were 0.23 ± 0.10 cantly higher in myopes than in emmetropes. They also and 0.26 ± 0.35 with +2.00D and )2.00D defocus, found that the effect of defocus on contrast sensitivity respectively. The agreement (RMSE) between the pre- varied for different spatialfrequencies. These differences dicted contrast sensitivity function and measured con- between the two studies might have an opticalcause. trast sensitivity function was found to be slightly higher Thorn et al.’s myopic subjects were corrected with con- in the non-myopic group than the myopic group. tact lenses that would have introduced negative spherical However, in both the refractive groups the RMSE val- aberration. If their myopes had positive sphericalaber- ues were similar to those determined by previous studies ration, as is normal, this would have been partially cor- (Atchison & Scott, 2002; Strang et al., 1999). One-way rected (perhaps over-corrected) by the contact lens intra-class correlation coefficient for predicted and induced sphericalaberration. However, the subjects in measured contrast sensitivity was found to be 0.6771 our study were corrected with spectacle lenses, hence less (F286;287 ¼ 3:0969; p ¼ 0:001). sphericalaberration was introduced in the present study. H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878 1877

A statistically significant relationship was found be- tions in the population. Our results in this paper and in tween the magnitude of refractive error and the opti- investigating visualacuity with defocus (Radhakrish- mum focus at spatialfrequencies of 3, 6 and 10 c/deg. nan, Pardhan, Calver, & O’Leary, 2004) consistently Such a relationship did not exist for other spatial show that myopes respond differently from non-myopes frequencies. However the small number of subjects in- in the presence of defocus. A possible explanation is that cluded in the study makes it inappropriate to over- myopes have higher aberrations than non-myopes. generalise about a relationship between the amount of However, it is also evident that none of the existing refractive error and the shift in optimum focus. metrics of image quality seem to represent the visual Green and Campbell (1965) found a more negative quality accurately (Applegate, Thibos, & Williams, focus for low-medium spatial frequencies relative to high 2003; Cheng, Bradley, Thibos, & Ravikumar, 2003). spatialfrequencies as an effect of ocularsphericalaber- Aberration measurements are only estimates of optical ration. Charman and Jennings (1976) calculated the ef- properties of the eye and the data reported here shows fect of sphericalaberration on the modulation transfer the visualconsequences of these opticalproperties. Al- function and found that in the presence of spherical though the aberration data shows no significant differ- aberration, the modulation transfer function for inter- ence between myopes and non-myopes, the contrast mediate spatialfrequencies is much higher with negative sensitivity data shows that the existing differences have a defocus when compared to positive defocus. Also, myo- significant impact on visualperformance. pic subjects showed a more negative focus for interme- The asymmetry in contrast sensitivity with defocus at diate spatialfrequencies (e.g. 3 c/deg) when compared to intermediate spatialfrequencies may explain the high spatialfrequencies (e.g. 16 c/deg). Charman and abnormalaccommodative response to blurfound in Jennings (1976) and Jansonius and Kooijman (1998) also some myopes (Gwiazda et al., 1993; O’Leary & Allen, suggested that sphericalaberration wouldcause low 2001). Intermediate spatial frequencies play a major role spatialfrequencies to have a more negative optimum in determining the accommodative response (Charman focus. Furthermore, some of the differences in contrast & Heron, 1979; Hess, Pointer, & Watt, 1989; Owens, sensitivity found between myopes and non-myopes may 1980). In myopes, the optimum focus for intermediate be attributed to the presence of a higher magnitude of spatialfrequencies is more negative/myopic than for the sphericalaberration in myopes as previouslyshown by high spatialfrequencies. Therefore myopes need to Applegate (1991). The relatively lower loss of contrast accommodate less to bring the intermediate spatial fre- sensitivity with defocus found in the myopic subjects quencies in to focus when compared to non-myopes in could be predicted from the measured fourth order whom the optimum focus for high and intermediate Zernike term for sphericalaberration of the eye. spatial frequencies lie close together. The predicted contrast sensitivity calculated from the modulation transfer functions gave higher values when compared to measured contrast sensitivity in both the 5. Conclusion refractive groups. The prediction of relatively higher contrast sensitivity values is probably due to the modu- Myopes show lower contrast sensitivity loss with lation transfer function data used in the study being negative defocus when compared to positive defocus. generated from the fourth order sphericalaberration data The measured contrast sensitivity results seem to be only and the other ocular aberrations were not accounted consistent with the contrast sensitivity predicted from for in this model. Ocular aberrations reduce the image ocular spherical aberration in showing the asymmetry in quality of the eye. As the modulation transfer function sensitivity to positive and negative lenses in myopes. The calculations used in this study consider only defocus and results from this study also suggest that the intermediate fourth order sphericalaberration in Zernike terms, spatialfrequencies (3 c/deg) have a more myopic opti- omitting all other aberrations can result in under/over mum focus when compared to non-myopes. As it has prediction of contrast sensitivity. The purpose of the been shown that accommodation is driven by interme- present study however was to determine if the predicted diate spatialfrequencies, the reduced accommodative effect of fourth order sphericalaberration on contrast response reported in some myopes may be caused by the sensitivity can illustrate the differences in measured con- more negative optimum focus for this range of spatial trast sensitivity with positive and negative defocus in frequencies. myopes. Although the predicted contrast sensitivity was always found to be higher than the measured contrast sensitivity in this study, the results show reasonable References agreement (similar to those obtained in previous studies) Allen, P. M., Radhakrishnan, H., & O’Leary, D. J. (2003). Repeat- between predicted and measured contrast sensitivity. ability and validity of the PowerRefractor and the Nidek AR600-A Cheng, Bradley, Hong, and Thibos (2003) have in an adult population with healthy eyes. Optometry and Vision shown that there is a considerable variation of aberra- Science, 80, 245–251. 1878 H. Radhakrishnan et al. / Vision Research 44 (2004) 1869–1878

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