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Vision Research 46 (2006) 3707–3722 www.elsevier.com/locate/visres

Neural and optical limits to visual performance in

David A. Atchison *, Katrina L. Schmid, Nicola Pritchard

School of , Queensland University of Technology, Victoria Park Road, Kelvin Grove, Qld., 4059, Australia

Received 13 February 2006; received in revised form 27 April 2006

Abstract

We investigated the relative importance of neural and optical limitations to visual performance in myopia. A number of visual per- formance measures were made on all or subsets of 121 eyes of emmetropic and myopic volunteers aged 17–35 years. These tests included visual measures that are mainly neurally limited (spatial summation out to ±30 in the horizontal visual field and resolution acuity out to ±10 in the horizontal visual field) and central ocular aberrations. We found that myopia affected the neurally limited tests, but had little effect on central higher order aberration. The critical area for spatial summation increased in the temporal visual field at 0.03 log units/ dioptre of myopia. Resolution acuity decreased at approximately 0.012 log units/dioptre of myopia. Losses of visual function were slight- ly greater in the temporal than in the nasal visual field. The observed visual deficit in myopia can be explained by either global retinal expansion with some post-receptor loss (e.g. ganglion cell death) or a posterior polar expansion in which the point about which expan- sion occurs is near the centre of the previously emmetropic globe. 2006 Elsevier Ltd. All rights reserved.

Keywords: Aberrations; Myopia; Neural limits; of the human eye; ; Spatial summation; Visual performance

1. Introduction dominant ocular (and optical) feature is the increasing vitreous chamber depth (Bullimore, Gilmartin, & Royston, 1.1. Visual performance 1992; Grosvenor & Scott, 1991, 1993, 1994; McBrien & Millodot, 1987; Stenstrom, 1948). Myopia occurs because of a mismatch between the When myopic eyes are fully corrected by ophthalmic length of an eye and its power, such that either the length and spectacle magnifications (Atchison, 1996) are can be considered to be too long for the power, or the taken into account (negative spectacle lenses to correct power can be considered to be too high for the length. myopia reduce retinal image size), some studies but not Although population studies have found some changes in others, have found reductions in visual performance. For the other ocular parameters with increase in myopia, resolution acuity, Chui, Yap, Chan, and Thibos (2005) including anterior corneal radius of curvature (Atchison, found reductions with myopia in central and peripheral 2006; Budak, Khater, Friedman, Holladay, & Koch, vision (although not significant for the former), while Col- 1999; Carney, Mainstone, & Henderson, 1997; Goh & etta and Watson (2006) found non-significant reductions in Lam, 1994; Goss, Van Veen, Rainey, & Feng, 1997; Grosv- resolution acuity out to 10 in the nasal visual field. For enor & Scott, 1991, 1994; Sheridan & Douthwaite, 1989; high contrast , Strang, Winn, and Bradley Stenstrom, 1948), anterior corneal asphericity (Carney (1998) found decreases at a rate of 0.011 logMAR/dioptre et al., 1997), and anterior chamber depth (Carney et al., of myopia, but Bradley, Hook, and Haeseker (1991) found 1997; Grosvenor & Scott, 1991; Stenstrom, 1948), the no effects. For the contrast sensitivity function, Thorn, Corwin, and Comerford (1986) and Collins and Carney * Corresponding author. Fax: +61 7 3864 5665. (1990) found no effect of myopia while Liou and Chiu E-mail address: [email protected] (D.A. Atchison). (2001) found losses for a highly myopic group (>12 D)

0042-6989/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2006.05.005 3708 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 for which pathological processes might be expected to be For other visual performance measures other than visual manifest. acuity and contrast sensitivity, Jaworski et al. (2006) found Although it might seem reasonable to directly compare reduced contrast sensitivity at the critical spot size in a spa- visual performances of emmetropes and corrected myopes tial summation experiment for their highly myopic group as long as compensation is made for ophthalmic magnifica- as compared with an emmetropic group. Ito, Kawabata, tion, the assumption of an increase in axial length without Fujimoto, and Adachi-Usami (2001) found that frequency any other changes to the ocular optics or to the retinal doubling perimetry was not different between groups con- anatomy (e.g. no retinal stretching affecting the foveal sisting of emmetropes and low myopes (1.16 D ± region) means that corrected myopes should then have bet- 0.23 D), intermediate myopes (4.05 ± 0.17 D), and high ter resolutions than emmetropes. This is because a particu- myopes (8.12 ± 0.36 D) (correction modality not speci- lar spacing on the retina should correspond to smaller fied). In terms of retinal responses, Kawabata and angles in object (visual) space as myopia increases. This Adachi-Usami (1997) reported reduced and delayed can be taken into account by calculating retinal resolution responses in the multifocal electroretinograms (mfERGs) in cycles/mm based on refraction and ocular parameters. of myopes and Chen, Brown, and Schmid (2006) found a However, if the ocular parameters are not known, Knapp’s delayed response in the mfERGs of myopes. law can be invoked. This law is that an axially ametropic eye with a spectacle placed at its anterior focal point 1.2. Models of myopia elongation has the same retinal image size as that of a standard emme- tropic eye. Most spectacle lenses are placed near this point, Myopia may be classified in terms of where the myopic 16–17 mm in front of the eye’s anterior principal plane elongation occurs: equatorial (peripheral) expansion (Van (about 1.5 mm inside the eye). Accordingly, the raw spatial Alphen, 1986), posterior pole (central) elongation (Sorsby, visual performance results can be used (e.g. resolution in Sheridan, & Leary, 1961), or global expansion (both cen- cycles/degree) when myopic subjects wear spectacles, leav- tral and peripheral) (Cheng et al., 1992). The equatorial ing the data uncorrected for spectacle magnification expansion model was invoked above when we argued that because the retinal image minification from spectacles will it might be expected that vision should improve as myopia be compensated perfectly by increased axial length. Results increases. obtained with correction will need to be In relation to eye dimensional changes in myopia, a adjusted to higher spatial frequencies to simulate the opti- recent magnetic resonance imaging study of 87 emmetro- cal minification that would have occurred if spectacles had pic and myopic eyes up to 12 D has found a variety of been worn. We refer to this as ‘‘spectacle corrected visual different eye shapes (Atchison et al., 2004). Within con- space.’’ siderable inter-individual variation, with increase in When either retinal resolution or spectacle corrected myopia eyes increased in size both horizontally and ver- visual space results are used, the changes in visual perfor- tically as well as axially in the approximate ratios of mance with myopia mentioned above become more 1:2:3. Vertically, similar numbers of myopic eyes fitted marked and where changes were not found with contact an equatorial expansion model (combining both equato- lenses they sometimes became significant with spectacle rial expansion and posterior pole elongation models) lenses. Concerning resolution acuity and referencing this and a global expansion model, while horizontally many to the retina, in Chui et al.’s study (2005) the foveal as well more eyes fitted the equatorial expansion model than as the peripheral losses in visual acuity became significant the global expansion model (Atchison et al., 2004). A with changes between 0.009 and 0.019 log unit/D of myo- qualitative analysis of retinal shape showed no obvious pia, while Coletta and Watson (2006) found significant evidence of posterior polar elongation for any subjects effects at fixation and 10 in the nasal visual field, with rates (Atchison et al., 2005). of change of 0.013 and 0.015 log unit/D of myopia (but no Williams (1985) calculated that the resolution limit effect at 4 in the nasal visual field). Concerning high con- imposed by the retina of emmetropic eyes at their foveolas trast visual acuity, Bradley et al. (1991) did not distinguish was 56 cycles/deg. He based his approximation on a centre- between contact lens and spectacle corrections in their sub- to-centre foveal cone spacing of 3 lm and on 0.29 mm of jects, so it is not known whether this would have mattered. the retina corresponding to 1 of visual space. Strang For the contrast sensitivity function, Collins and Carney et al. (1998) predicted how the ‘‘neural’’ resolution limit (1990) and Liou and Chiu (2001) found losses in moderate might change in myopic eye models, based on Emsley’s myopes wearing spectacle lenses that had not been there in reduced schematic eye. Assuming a fixed optical perfor- a contact lens wearing group, Fiorentini and Maffei (1976) mance cut-off of 50 cycles/deg, the posterior polar expan- found considerable contrast sensitivity losses in spectacle sion and global stretching models predicted that central corrected subjects, and Jaworski, Gentle, Zele, Vingrys, resolution will be neurally rather than optically limited and McBrien (2006) found losses in a highly myopic group for myopic refractive errors above 3 D and 7 D of myopia, (mean correction 10 ± 1 D) compared with an emmetro- respectively. This should manifest as aliasing, in which the pic group, when spatial frequency results were referenced presence of a stimulus pattern can be detected but it cannot to the retina, beyond 18 cycles/mm. be resolved correctly (e.g. Thibos, Still, & Bradley, 1996). D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3709

Chui et al. (2005) did in fact find that many of their subjects the greatest changes and is the only one that changes sys- exhibited foveal aliasing. tematically, moving in the negative direction (Atchison, Strang et al. (1998) found that the posterior polar elon- Collins, Wildsoet, Christensen, & Waterworth, 1995; Berny gation model most accurately predicted reduction in visual & Slansky, 1970; Cheng et al., 2004; Collins et al., 1995; resolution with increased myopia. Chui et al. (2005) con- Hazel, Cox, & Strang, 2003; He, Burns, & Marcos, 2000; cluded that the global stretching model could not explain Ivanoff, 1956; Jenkins, 1963; Katsanevaki, Panagopoulou, their losses in resolution in the near peripheral field with Plainsis, Ginis, & Pallikaris, 2004; Koomen, Tousey, & increase in myopia, and that either the posterior polar Scholnik, 1949; Ninomiya et al., 2002; Panagopoulou, Pla- model was correct or that global expansion is accompanied insis, MacRae, & Pallikaris, 2004; Plainsis, Ginis, & Pallik- by loss of retinal ganglion cells. Coletta and Watson (2006) aris, 2005; Schober, Munker, & Zolleis, 1968) and also supported the posterior polar expansion model. The becoming negative in most people at about 1–3 D of Atchison et al. (2004) study showed that the global expan- accommodative response (Atchison et al., 1995; Cheng sion model would need to be modified to take into account et al., 2004; He et al., 2000). The degree of myopia a person the different rates of increases in axially, vertical and hori- has does not seem to affect this trend (Collins et al., 1995), zontal dimensions with increase in myopia. but Buehren et al. (2005) found that myopes had greater changes in some aberrations than emmetropes after sus- 1.3. Optical aberrations tained reading. As well as the monochromatic aberrations, eyes suffer The assumption in Strang’s modelling in central vision from longitudinal and transverse . that (corrected) optical performance is unaffected by myo- Longitudinal chromatic aberration of about 2.1 D chro- pia level might be incorrect. An increase in higher order matic difference of refraction occurs for wavelengths aberrations with increased levels of myopia would result between 400 nm and 700 nm (see Atchison & Smith, in poorer image quality, making the transition from opti- 2000). On theoretical grounds there should be only slight cally limited to retinally limited resolution occur at higher increases in longitudinal chromatic aberration due to axial levels of myopia than for their posterior expansion and length increases (0.6%/D of axial myopia) or power global stretching models; it may even prevent the transition increases of the ocular components (2.4%/D of refractive from occurring in some eyes. However, myopia appears to myopia) (Atchison, Smith, & Waterworth, 1993), and so be accompanied by only moderate (Buehren, Collins, & it is not surprising that an experimental study was unable Carney, 2005; He et al., 2002; Marcos, Moreno-Barriuso, to find any influence of myopia on longitudinal chromatic Llorente, Navarro, & Barbero, 2000; Paquin, Hamam, & aberration (Wildsoet, Atchison, & Collins, 1993). We are Simonet, 2002) or no increases in higher order aberrations not aware of any studies relating myopia and transverse (Carkeet, Luo, Tong, Saw, & Tan, 2002; Cheng, Bradley, chromatic aberration. Hong, & Thibos, 2003; Netto, Ambro´sio, Shen, & Wilson, The peripheral optics is poor, overwhelmingly so 2005; Porter, Guirao, Cox, & Williams, 2001; Zadok et al., because of focusing errors in the form of field curvature 2005), and one study reported greater aberrations in hyper- and astigmatism. When the periphery is corrected follow- metropes than in myopes (Llorente, Barbero, Cano, Dor- ing refraction, the image quality improves considerably ronsoro, & Marcos, 2004). There are two older studies (Williams, Artal, Navarro, McMahon, & Brainard, 1996) using the Howland crossed-cylinder aberroscope that and marked improvement in detection ability occurs found some aberration differences between emmetropes (Wang, Thibos, & Bradley, 1997). Several studies have and myopes (Applegate, 1991; Collins, Wildsoet, & Atchi- investigated peripheral refraction in emmetropic and myo- son, 1995), but they were affected by technical issues such pic eyes (Atchison, Pritchard, & Schmid, 2006; Logan, Gil- as much lower sampling rates across the pupil compared martin, Wildsoet, & Dunne, 2004; Love, Gilmartin, & with those with more recent instruments. On theoretical Dunne, 2000; Millodot, 1981; Mutti, Sholtz, Friedman, & grounds, increasing myopia caused by greater eye length Zadnik, 2000; Rempt, Hoogerheide, & Hoogenboom, will be accompanied by increases in any existing positive 1971; Schmid, 2003; Seidemann, Schaeffel, Guirao, spherical aberration (Atchison & Charman, 2005; Cheng Lopez-Gil, & Artal, 2002). Along the horizontal meridian, et al., 2003), but this has not been supported experimental- most emmetropes show myopic shifts into the periphery. ly (Carkeet et al., 2002; Cheng et al., 2003; Porter et al., However in low myopia these shifts reduce and relative 2001; Zadok et al., 2005). hypermetropic shifts occurs for subjects with 2–4 D myo- Myopes’ responses to accommodative stimulation are pia. Along the vertical meridian, most emmetropes show poorer than those of emmetropes (Abbott, Schmid, & a myopic shift into the periphery, but this does not change Strang, 1998; Gwiazda, Thorn, Bauer, & Held, 1993; He, into a relative hypermetropic shift with increase in myopia Gwiazda, Thorn, Held, & Vera-Diaz, 2005; McBrien & (Atchison et al., 2006). Peripheral astigmatism is similar in Millodot, 1986; O’Leary & Allen, 2001). As accommoda- both emmetropes and myopes along both horizontal and tion response increases, aberrations change (Cheng et al., vertical visual fields (Atchison et al., 2006), but with a 2004). Although many higher order aberration coefficients small, significant decrease with increase in myopia along change with , spherical aberration shows the horizontal visual field. Atchison (2006) developed 3710 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 schematic eyes based on parameter measurements. These Sony Trinitron Multiscan G520 monitor under the control of a Visual Stimulus Generator VSG 2/5 system (Cambridge Research Instruments). were successful in demonstrating the trends in the experi- p mental results, except that in the schematic eye models The 13 stimuli sizes varied in 2 (or 0.1505 log) steps between 5 and 320 min arc diameter against a background luminance of 30 cd/m2. The there was a predicted relative hypermetropic shift into the participant’s task was to indicate whether a stimulus was visible or not vis- vertical periphery as myopia increased, albeit at a much ible by pressing the appropriate key on a response box. Testing was con- slower rate than along the horizontal meridian. A few stud- ducted monocularly (the contralateral eye being patched) at 4 m test ies have measured higher order aberrations across the hor- distance for testing at fixation and at 1 m for testing the peripheral visual izontal visual field in small numbers of subjects (Atchison field. The two largest sizes (226,320 min arc) were not used for measures at fixation and the two smallest sizes (5,7.07 min arc) were not used for test- & Scott, 2002; Guirao & Artal, 1999; Navarro, Moreno, ing the peripheral visual field. Illuminance on the walls of the laboratory & Dorronsoro, 1998) but the influence of myopia on these was approximately 40 lux. A LED fixation device was positioned to place aberrations has not been investigated. the stimulus at the appropriate angle relative to fixation. The subjects aligned their heads with the stimulus and turned their eyes to look at the fixation device. 1.4. Summary and scope The initial Weber contrast for each stimulus size was 0.0 log unit. Each stimulus was presented for 200 ms in the form of a temporal ‘‘top hat’’ Reduction in vision performance in corrected myopia (square wave) function. The presentation was accompanied by an auditory could occur because of the neural and/or optical changes tone. The participant pressed one of two buttons depending upon whether that occur with myopia development. From the above dis- or not the stimulus was visible. The button press triggered the next presen- tation. The contrast increased in 0.4 log steps until that stimulus size was cussion, the evidence would seem to favour the former, not visible, and then its contrast varied in 0.2 log steps. When visible but there is conflicting evidence about whether aberrations again, its contrast varied in 0.1 log steps. The contrast threshold was taken might increase with myopia. The purpose of this paper is to as the mean of five subsequent reversals. Presentations of the varied sized describe visual performance and optical performance in a stimulus were randomly interleaved. group of emmetropic and myopic eyes whose ocular optical The foveal region was tested first (as this was the easiest to perform), followed by either the nasal or temporal field (randomly assigned). Each and associated anatomical properties have been described angle was tested in a single run and each run took approximately 5– already (Atchison, 2006; Atchison et al., 2004, 2005, 10 min. Head alignment was monitored intermittently by the investigator 2006). We will attempt to relate the findings of this paper during the runs. with earlier studies to explain any changes in visual perfor- Contrast sensitivity (inverse of contrast threshold) of each stimulus was defined as L/DL where L is the background luminance and DL is mance found as myopia increases and determine the relative 2 the stimulus luminance. Critical area Ac (min arc ) was determined using importance of neural and optical limits to vision. the following equations:

log contrast sensitivity ¼ log area þ K area 6 Ac ð1Þ 2. Methods 0 log contrast sensitivity ¼ 0:25 log area þ K area > Ac ð2Þ

This study followed the tenets of the Declaration of Helsinki and where K is a constant and K0 is the log contrast sensitivity corresponding 0 received ethical clearance from the Queensland University of Technology’s to Ac, with the limit K = K + 0.75*log(Ac) for continuity (Felius, Swan- Human Research Ethics Committee. Informed consent was obtained from son, Fellman, Lynn, & Starita, 1997). The first equation describes com- each participant after explanation of the nature of the study. plete summation (slope 1) for stimuli with areas smaller than Ac, and the second equation describes probability summation (slope 0.25) for stim- 2.1. Subjects 1.5 The study cohort comprised 121 participants within the age range Log contrast sensitivity 17–35 years of which 74 (64%) were female. The best subjective mean = 0.25 log area + K' spherical correction of participants ranged from +0.75 D to 1.0 K' 12.38 D; the emmetropic range was defined as 0.50 D to +0.75 D. The myopic refraction range was restricted to reduce the likelihood of secondary ocular pathologies. The majority (108) of subjects had <0.5 D astigmatism. Participants were also excluded if in either eye they 0.5 had any ocular disease, previous ocular surgery, or had ocular tension itivity (log units) >21 mm Hg. Right eyes were measured in 94% of cases. The left eye was used where it met the inclusion criteria and the refraction of the 0.0 Log contrast sensitivity right eye was outside spherical or astigmatic limits (nine cases). Pupil = log area + K sizes were greater than 5 mm with the exception of one participant, who was dilated where appropriate. Best-spherical contact lens or spec- sens Contrast -0.5 tacle correction was used where appropriate (indicated in following sec- tions). Tests investigating visual field spatial summation, resolution Log Ac acuity, and ocular and corneal aberrations were conducted on subsets -1.0 of individuals, as described in Sections 2.2; 2.3; 2.4; 2.5. 01234 Area (log min arc2) 2.2. Spatial summation Fig. 1. Log contrast sensitivity as a function of log area for one run in the Spatial summation data were determined for a subset of 114 eyes (91% spatial summation experiment. The fitted functions given by Eqs. (1) and right eyes) along the horizontal visual field to 30 nasal and temporal from (2) are shown, together with the critical log area (log Ac) and its the fixation in 10 steps. Achromatic circular stimuli were presented on a corresponding log contrast sensitivity (K0). D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3711 uli larger than the critical area. Fig. 1 gives an example of the results of a is 210 lm. The lens of the relay system nearer the eye moves along a slider run. The critical area was converted to a diameter in both min arc in visual and in the usual mode of use moves to maximise image quality. The position space and mm on the retina. Refractive errors were corrected with specta- of the slider then corresponds approximately to a spherical equivalent (at cles (37% of group) or contact lenses (33% of group). 842 nm), with a correction of approximately 0.7 D applied for a visible To investigate the effect of spectacle versus contact lens correction, for wavelength of 550 nm (Ma, Atchison, & Charman, 2005). five subjects with corrections ranging between +0.75 D and 5.25 D, we Measurements were taken with a natural pupil in all but one case where conducted measurements at 30 temporal, fixation and 30 nasal both with the natural pupil was small (3 mm), here the pupil was dilated to slightly a correcting contact lens and then with a contact lens with an excess power above 5 mm with 0.5% tropicamide. For each eye, up to three images were of approximately +5.00 D. The latter condition required correction by tri- taken. Aberrations were determined with the OSA/ANSI Z80.28 -2004 stan- al lenses of powers 2.50 D to 11.50 D. The vertex distances were care- dard (American National Standards Institute, 2004; Thibos, Applegate, fully measured for the calculation of retinal image sizes. For the group, the Schwiegerling, Webb, & Members, 2002) up to the 6th radial order for difference between critical retinal image size wearing contact lenses and the 5 mm pupils. These were referenced to the anterior and a wavelength trial lens/contact lens combinations was not significantly correlated with of 550 nm. The averages of the individual aberration coefficients were deter- refractive correction at 30 temporal (p = 0.85), fixation (p = 0.11) or mined. To account for the expected nasal-temporal asymmetry, signs of 30 nasal (p = 0.81). Futhermore, measurement of critical retinal image some of the left eye coefficients were changed to make left and right eye data size was repeatable; test and retest with contact lens correction (as well comparable (American National Standards Institute, 2004). as results with spectacles) were not significantly different (paired t-tests, Corneal aberrations were determined using the Medmont E-300 com- p > 0.05). puterized video-keratoscope and the computer package VOL-CT V6.3 (Sarver & Associates) which performs a raytrace into the anterior cornea 2.3. Interferometry from infinity to determine aberrations. Again, images were made with the natural pupil. As for the wave aberration data, signs of some left eye coef- Resolution interferometry was performed on a subset of 29 right eyes ficients were changed. One corneal image was used for each participant. using both horizontal and vertical gratings on-axis and at 10 in the nasal The Medmont E-300 software gives the position of the pupil centre rela- and temporal visual fields. A Lotmar Visometer (Lotmar, 1980) imaged tive to the corneal vertex, and VOL-CT permits aberrations to be deter- two point sources at the entrance pupil of the eye (3 mm inside the anterior mined with reference to both of these locations. cornea). Motors were mounted to the interferometer to enable spatial fre- As is standard practice (Atchison, 2004), the contributions of internal quency, grating orientation, and shutter changes under computer control. ocular components to ocular aberrations were estimated by subtracting cor- A gimbal mount rotated the presentation arm of the instrument around neal aberration coefficients from total aberration coefficients. As well as the two point sources. The sources interfered to produce a 1.5 field of determining individual aberration terms, the root-mean-squared aberra- 100% contrast fringes on the retina. A narrow band interference filter tions (RMS) were determined for the 2nd radial order (disregarding defo- (550 nm) gave a mean luminance of 50 cd/m2. cus), the higher radial orders and for the combined higher radial orders. Participants were positioned using a dental-impression bite bar. They were trained and adapted to the room lighting for approximately 10 min 2.5. Retinal image sizes and spatial frequencies before commencement of the experiment. As the sound of the motor con- trolling the grating orientation may have provided a cue to orientation, For spatial summation and interferometry experiments, visual angles in participants wore headsets providing white noise to mask the sound. As object space were converted into retinal image distances or cycles/distance interference fringes are formed directly on the retina, their resolution using a method developed by Bennett (1988). This requires anterior chamber should not be affected by uncorrected refractive errors. In the presence depth, lens thickness, and vitreous chamber depth (all obtained with ultra- of ametropia, fringes are formed in the region of partial overlap for the sound, Quantel medical Axis II, France), vertex distance (taken as 0 mm patches of light illuminating the retina, and this may provide an orienta- with contact lenses and estimated as 14 mm with spectacle lenses), the power tion cue (Thibos, 1990). Accordingly, contact lenses were used to correct of the contact lens or spectacle lens correction, and mean anterior corneal myopias greater than approximately 2 D. curvature (Medmont E-300 keratometer). The Gullstrand–Emsley three Resolution was determined using a staircase procedure with inter- refracting surfaces model eye (Atchison & Smith, 2000) was used to estimate leaved horizontal and vertical gratings. The initial spatial frequency was several quantities, and it was assumed that the distances between the lens 3 cycles/deg. The gratings were presented for 1.0 s, preceded by an audito- vertices and principal planes were in the same proportion to the lens thick- ry tone. The participant indicated the orientation of the grating using a ness as they are in the Gullstrand–Emsley model eye. This procedure pro- forced-choice push-button response box; this response determined the sub- vides an estimation of lens power. The results provide less accurate sequent presentation. If the response was correct, the spatial frequency estimates at the higher angles (e.g. 30) when the image sizes will be influ- increased in 0.3 log unit steps until an incorrect response was made, and enced also by the peripheral optics and cannot be easily modelled. then a first reversal occurred so that its spatial frequency decreased in 0.15 log unit steps. Once the next correct response was made, the staircase 2.6. Statistical analysis operated in a 3:1 pattern in which three correct responses were needed to increase spatial frequency and one incorrect response led to a decrease in Linear regression was used to determine the relationship between each spatial frequency. After the second reversal, the step size became 0.05 log ocular parameter and best spherical refractive correction. Summary units. Testing continued until a further six reversals occurred. Disregard- descriptive statistics are reported for ocular parameters and are expressed ing the first reversal, the threshold was taken as the average of the mid- as mean ± standard deviations (SD) unless stated otherwise. In all tests, p- points of successive reversals. An average of two runs was calculated for values less than 0.05 were considered significant. For spatial summation each participant. This procedure estimates the 79% threshold. and interferometry, significance was also considered using Bonferroni corrections. 2.4. Ocular and corneal aberrations

Ocular and corneal aberrations were determined for a subset of 63 eyes 3. Results (58 right eyes). Wavefront aberration data were obtained using a COAS Hartmann-Shack wavefront analyser (Wavefront Sciences, USA). This 3.1. Spatial summation instrument uses a superluminescent diode source with a central wavelength of approximately 840 nm. The cornea is imaged onto an array of square ele- 2 ments of dimension 144 lm. A relay system between the eye and the array Fig. 2 shows the critical retinal areas (log mm ) and the has a magnification of 0.685· so that the sampling interval across the pupil contrast sensitivities corresponding to the critical areas for 3712 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

a -1.4 The mean contrast sensitivities corresponding to the critical areas were greatest at fixation and at other positions -1.6 were approximately half that observed at fixation with no ) 2 -1.8 effect of myopia (Fig. 2b, see also Table 1). It should be noted that there was a significant positive correlation -2.0 between critical area and its corresponding contrast sensi- -2.2 tivity at all positions.

-2.4 3.2. Interferometry -2.6

-2.8 Fig. 4 shows resolutions for horizontal and vertical grat- Critical retinal area (log mm ings as a function of refraction for 10 temporal field, fixa- -3.0 tion, and 10 nasal field, with resolution expressed in log Temporal Field Nasal Field -3.2 cycles/degree in the left column and in log cycles/mm on the retina in the right column. Table 1 shows the regression b 1.4 equations. For the study population, resolution acuities at fixation were about 0.6 log (four times) higher than in the 1.2 periphery, with little difference between horizontal and ver- tical gratings. When the resolutions were expressed in log 1.0 cycles/degree, resolution changed significantly with refrac- tion only for the temporal field with vertical orientation.

itivity (log units) 0.8 When the resolutions were expressed in log cycles/mm, these decreased with increase in myopia for all field posi-

0.6 tions, but only significantly for the vertical orientation. Across all field positions and both orientations, the mean

Contrast sens Contrast loss in resolution was 0.012 log cycles/mm per dioptre of 0.4 myopia, with a multivariate analysis failing to show signif- Temporal Field Nasal Field icant differences between grating orientations or between 0.2 visual field positions. -40-30-20-100 10203040 Eccentricity (degrees) 3.3. Aberrations Emmetropes 8 D myopic group

Fig. 2. (a) Critical retinal area (log mm2) and (b) the contrast sensitivities The 2nd order RMS and a small number of aberra- (log units) corresponding to the critical areas, for emmetropic and 8 D tion coefficients were significantly correlated with refrac- myopic subgroups as a function of visual field position. The emmetropic tion for each of total ocular aberration, corneal group had a mean (±SD) refraction of +0.02 ± 0.31, range +0.75 D– aberration and internal aberration (Table 2). Apart from 0.50 D and consisted of 29 subjects. The 8 D myopic subgroup had a three cases (corneal aberration, 6th order; internal aber- mean (±SD) refraction of 8.33 ± 1.53 D, range 6.51 to 12.00 D, and consisted of 11 subjects. Error bars indicate standard deviations. ration, 5th and 6th orders), higher order RMS and the total higher order RMS were not significantly correlated emmetropic and 8 D myopic subgroups as a function of with refraction (Table 2). The 5th and 6th order aberra- visual field position. For emmetropes, the critical area tions were small compared with the 3rd and 4th order increased in size from fixation by 0.7 and 0.9 log units at aberrations. In general, the corneal higher order RMS 30 temporal and 30 nasal, respectively (Fig. 2a). The high was greater than ocular higher order RMS, indicating a myopes had similar critical areas as the emmetropes in the degree of balance between corneal and internal aberra- nasal visual field, but greater critical areas than the emme- tions (Fig. 5). tropes in the temporal field by more than 0.3 log units (>2 For total ocular aberration, the mean higher order RMS times) at 30 temporal. This figure represents the trend with of the total group was 0.18 ± 0.07 lm. Excluding defocus, increase in myopia: increasing critical areas in the temporal only two individual aberration coefficients were correlated 2 but not the nasal visual field. Regression equations for crit- significantly with refraction: 90–180 astigmatism c2 and 3 ical areas as a function of refractive correction, with the horizontal trefoil c3 (the former is significant because the critical areas expressed as both angular and retinal areas, subject inclusion criterion regarding astigmatism was are shown in Table 1,andFig. 3 shows the regressions at relaxed slightly for the higher refractions). Coefficients that 20 temporal, fixation and 20 nasal for critical retinal were significantly different from zero and with absolute 2 1 areas. The critical areas were influenced significantly by means >0.01 were c2 (0.11 ± 0.34 lm), c3 (+0.04 ± 3 0 refraction at all temporal angles, and, in the case of retinal 0.07 lm), c3 (+0.02 ± 0.06 lm), and c4 (+0.04 ± 0.06 lm area, at the fovea. However, there were no significant for total group, +0.06 ± 0.05 lm for emmetropes, see effects at nasal angles. Fig. 6a). D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3713

Table 1 Linear regression analysis (y = slope Æ x + intercept) results for visual performance parameters as a function of refractive correction Test/parameter Position in visual field Intercept (0 D) Slope (parameter/D) Adj. R2 p-value Slope sig.# Spatial summation (n = 114) Critical area (log min arc2)30 T 2.454 0.0230 0.053 0.008 * 20 T 2.379 0.0251 0.048 0.011 * 10 T 2.104 0.0205 0.034 0.027 * 0 1.737 0.0127 0.014 0.112 10 N 2.254 0.0056 0.004 0.444 20 N 2.465 0.0067 0.001 0.357 30 N 2.741 0.0043 0.006 0.556 Critical retinal area (log mm2)30 T 2.207 0.0285 0.085 0.001 ** 20 T 2.273 0.0288 0.063 0.005 ** 10 T 2.566 0.0274 0.068 0.003 ** 0 2.920 0.0185 0.036 0.027 * 10 N 2.408 0.0001 0.009 0.994 20 N 2.204 0.0134 0.023 0.061 30 N 1.924 0.0104 0.008 0.171 Contrast sensitivity corresponding 30 T 2.092 0.009 0.005 0.220 to critical area (log unit) 20 T 1.931 0.006 0.005 0.504 10 T 1.983 0.002 0.008 0.760 0 2.264 0.000 0.009 0.978 10 N 2.081 0.007 0.001 0.301 20 N 2.026 0.008 0.005 0.219 30 N 1.925 0.009 0.012 0.133 Interferometry (n = 29) Resolution (log cycles/degree) 10 T horiz. 1.076 0.006 0.003 0.310 10 T vert. 1.028 0.009 0.116 0.043 * 0 horiz. 1.595 0.001 0.035 0.912 0 vert. 1.607 0.007 0.019 0.221 10N horiz. 1.054 0.007 0.003 0.346 10 N vert. 1.027 0.011 0.050 0.136 Resolution at retina (log cycles/mm) 10 T horiz. 1.621 0.011 0.094 0.062 10 T vert. 1.573 0.015 0.261 0.003 ** 0 horiz. 2.141 0.006 0.002 0.314 0 vert. 2.153 0.013 0.120 0.034 * 10 N horiz. 1.600 0.012 0.061 0.114 10 N vert. 1.573 0.016 0.132 0.035 * # *p < 0.05; ** significant with Bonferroni.

1 3 For corneal aberration referenced to the pupil centre, the (+0.40 ± 0.27 lm), c3 (+0.08 ± 0.08 lm), c3 (+0.02 ± 0 mean higher order RMS of the total group was 0.06 lm), and c4 (0.10 ± 0.05 lm, see Fig. 6a). 0.23 ± 0.08 lm. Excluding defocus, some aberration coeffi- cients were correlated significantly with refraction, including 4. Discussion 2 2 1 3 c2 , c2, c3, c3 and some 5th and 6th order coefficients. The 2 greatest dependency occurred for c2, whose slope was nearly In our young adult group, the magnitude of myopia twice that of both the ocular aberration coefficients affected spatial summation at fixation and in the temporal 2 3 c2 (Fig. 6b), and c3. Coefficients that were significantly differ- field, it had a small effect on grating resolution in the tem- ent from zero and with absolute means >0.01 lm were poral and nasal visual fields and at fixation, and had hardly 2 1 0 c2 (0.50 ± 0.42 lm), c3 (0.05 ± 0.08 lm), c4 (+0.14 ± any affect on foveal aberrations. The data are discussed in 2 0.04 lm, see Fig. 6a), and c4 (0.02 ± 0.03 lm). When the more detail in the following sections. corneal aberrations were referenced to the corneal vertex, 1 c3 lost its significant dependence on refraction (Fig. 7). 4.1. Spatial summation For internal aberrations, the mean higher order RMS of the total group was 0.20 ± 0.07 lm when referenced to the We found that myopia influenced spatial summation as pupil centre. Excluding defocus, only four aberration coef- measured by the size of critical area, but not by the con- 2 3 ficients were correlated significantly with refraction: c2, c3 , trast sensitivity corresponding to the critical area. This 3 1 c5 and c5. Coefficients that were significantly different influence occurred in the temporal visual field and at fixa- 2 from zero and with absolute means >0.01 lm were c2 tion, but not in the nasal visual field. The effect was 0.02 3714 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

a the critical area increasing by 0.16 log units (achromatic) and 0.19 log units (blue cone) and the contrast sensitivity reducing by 0.12 and 0.18 log units. The differences were significant, except for critical area with achromatic targets. Thus there is some discrepancy between our results and Jaworski et al.’s results at the fovea.

4.2. Interferometry

Interferometry images sinusoidal patterns directly onto the retina, thus bypassing the optics of the eye, and giving a measure of the resolution capabilities of the neural pro- cessing system (i.e. retina–brain). We found a reduction in resolution performance in the temporal visual field, at b fixation and in the nasal visual field with increasing myo- pia, but this was significant for only vertical gratings. Refractive effects were more marked when results were in cycles/mm at the retina rather than in cycles/degree in visu- al space. Across all field positions and both orientations, the loss in resolution was 0.012 log cycles/mm per dioptre of myopia. Our results can be compared with the studies of Coletta and Watson (2006) and Chui et al. (2005). Coletta and Wat- son measured resolution with a laser interferometric tech- nique for both vertical and horizontal gratings at fixation and at locations 4 and 10 in the nasal visual field. The study combined horizontal and vertical grating stimuli and covered a wide range of refractions (17 subjects, +2 D to c 15 D). Using a procedure similar to that used here, resolu- tion was converted from cycles/degree to cycles/mm at the retina. The reported loss in resolution with increase in myo- pia across the three field positions was 0.012 log cycles/mm per dioptre, the same as our measured reduction. Chui et al. (2005) measured resolution for high contrast gratings generated on a computer and so the results could have been influenced by the eye optics. However, they found that detection was better than resolution at all posi- tions tested, and thus reported that resolution was sam- pling (neurally) limited. The study combined horizontal and vertical grating results and considered a large number of participants and refractions (60 subjects, 0.5 to 14 D) and angles between 10 temporal and 15 nasal visual field. They corrected their participants with spectacle lenses and Fig. 3. Critical retinal area (log mm2) as a function of refraction for (a) 20 temporal visual field, (b) fixation and (c) 20 nasal visual field. Linear converted their results to cycles/mm on the retina on the regression fits are shown in Table 1. Critical retinal area is significantly basis of eyes being purely axially myopic. The loss in reso- correlated with refraction for 20 temporal visual field and fixation, but lution with increase in myopia was significant at all posi- not for 20 nasal visual field. tions, being 0.009 log cycles/mm per dioptre at the fovea and 0.014 to 0.019 log cycles/mm per dioptre at the periph- to 0.03 log units per dioptres of myopia when the retinal eral locations. The previous studies and our study give sim- critical area was estimated. ilar effects of myopia on resolution, except that the Chui Jaworski et al. (2006) measured spatial summation for et al. study gave greater effects than the other studies in achromatic and S-cone isolating targets in emmetropes the periphery. and a highly myopic group (mean refraction 10 ± 1 D). These measurements were done at fixation only. They 4.3. Aberrations found that both the critical areas on the retina (calculated similarly to that done here) and the contrast sensitivity cor- Overall only small effects of myopia on the magnitude of responding to the critical areas changed with myopia, with the eye’s ocular aberrations were observed. The higher D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3715

a 2.4 1.8 (i) (ii) 2.2 1.6

1.4 2.0 cles/mm) y

1.8 c 1.2 g

1.0 1.6

0.8 1.4

(a) (lo Resolution Resolution (log cycles/degree) (log Resolution 0.6 10˚ Temporal Field1 0˚ Temporal Field 1.2

b 2.4 1.8 2.2 1.6

2.0 1.4 es/mm)

1.2 1.8

1.0 1.6

0.8 1.4 Resolution (logcycl Resolution (log cycles/degree) (log Resolution 0.6 Foveal Foveal 1.2

2.4 c 1.8

1.6 2.2

1.4 2.0

1.2 1.8

1.0 1.6

0.8 1.4 Resolution (log cycles/mm) (log Resolution Resolutioncycles/degree) (log 0.6 10˚ Nasal Field 10˚ Nasal Field 1.2

-12 -10 -8 -6 -4 -2 0 2 -12 -10 -8 -6 -4 -2 0 2

Best sphere correction (D) Best sphere correction (D) Horizontal Vertical

Fig. 4. Horizontal and vertical resolution in (i) log cycles/degree and (ii) log cycles/mm as a function of refractive correction for (a) 10 temporal visual field, (b) fixation, and (c) 10 nasal visual field. Linear regression fits are shown in Table 1. Resolution in log cycles/degree was not significantly correlated with refractive correction, but resolution in log cycles/mm was significantly correlated with refractive correction at all positions for vertically orientated gratings. order RMS did not change significantly with myopia, myopia as found by Cheng et al. (2003) and Marcos which is consistent with data of Cheng et al. (2003) and et al. (2004). Artal, Benito, and Tabernero (2006) found Zadok et al. (2005) but not with that of other studies that that the absolute magnitudes of lateral coma coefficient 1 found moderate increases in aberrations with myopia c3 were smaller in a myopic than a hypermetropic group, (Buehren et al., 2005; He et al., 2002; Marcos, Barbero, but we found no trend in coma with refraction. & Llorente, 2004; Marcos et al., 2000; Paquin et al., In general, as has been found for young participants by 2002). Ocular spherical aberration was found to have a Artal et al. (Artal et al., 2006; Artal, Guirao, Berrio, & Wil- mean positive value that was significantly different from liams, 2001), corneal and internal higher order RMS were zero, as reported for unaccommodated eyes in other studies higher than ocular higher order RMS (Fig. 5), indicating (e.g. Cheng et al., 2004; Porter et al., 2001; Thibos, Bradley, a degree of balance between corneal and internal aberra- & Hong, 2002) and was unaffected by the presence of tions. Referencing corneal aberrations to the corneal 3716 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

Table 2 Linear regression analysis (y = slope Æ x + intercept) results for RMS aberrations and some aberration co-efficients as a function of refractive correction (n = 63) Parameter Intercept (0 D) Slope (lm/D) Adj. R2 p-value Slope sig.# Ocular aberrations RMS (lm) 2nd Order 0.700 0.797 0.974 0.000 * 3rd Order 0.140 0.005 0.025 0.112 4th Order 0.079 0.000 0.016 0.983 5th Order 0.027 0.001 0.027 0.105 6th Order 0.020 0.000 0.011 0.198 3rd Order and above 0.169 0.005 0.021 0.134 2 * c2 0.027 0.032 0.065 0.024 0 c4 0.052 0.004 0.031 0.091 Corneal aberrations RMS (lm)—pupil referenced 2nd Order 0.764 0.041 0.101 0.007 * 3rd Order 0.160 0.003 0.007 0.465 4th Order 0.151 0.000 0.016 0.902 5th Order 0.016 0.001 0.027 0.105 6th Order 0.006 0.001 0.111 0.004 * 3rd Order and above 0.230 0.002 0.012 0.617 2 * c2 0.366 0.055 0.142 0.001 1 * c3 0.063 0.007 0.058 0.031 0 c4 0.140 0.000 0.016 0.896 1 Corneal aberrations RMS (lm)—corneal vertex referenced c3 0.012 0.001 0.015 0.740 Internal aberrations RMS (lm)—pupil referenced 2nd Order 0.495 0.754 0.960 0.000 * 3rd Order 0.147 0.002 0.009 0.499 4th Order 0.100 0.003 0.019 0.144 5th Order 0.029 0.002 0.068 0.022 * 6th Order 0.021 0.001 0.077 0.016 * 3rd Order and above 0.192 0.004 0.012 0.193 2 * c2 0.338 0.023 0.051 0.041 0 c4 0.088 0.004 0.031 0.091 # *p < 0.05.

0.6 adjusted R2 = 0.072, p = 0.019), as also found by previous Ocular Corneal Internal authors (Artal et al., 2006; Bansal, Coletta, Moskowitz, & 0.5 Han, 2004). In most previous studies, either the difference in the 0.4 positions of the pupil centre and corneal vertex has been ignored or the corneal reference position has been chan- 0.3 ged to minimize corneal aberrations (Barbero, Marcos, & Merayo-Lloves, 2002; Buehren et al., 2005). We believe 0.2 that it is better to use the pupil centre so that the ocular and corneal aberrations have a common reference. The natural pupils were smaller for corneal topography than Higher Order RMS (micrometres) 0.1 for aberrometry, and even this correction is not ideal because the location of the pupil centre alters with 0.0 -12 -10 -8 -6 -4 -2 0 2 change in pupil size (Donnenfeld, 2004; Walsh & Char- Best sphere correction (D) man, 1988; Wilson, Campbell, & Simonet, 1992; Wyatt, 1995; Yang, Thompson, & Burns, 2002). Usually there Fig. 5. Higher order (3rd and above) ocular, corneal (pupil referenced) is a small shift to the temporal side as pupil size increas- and internal (pupil referenced) RMS as a function of refractive correction. Linear fits, shown in Table 2, revealed no significant correlations. Corneal es (e.g. in Yang et al.’s study the mean shift was and internal RMS were higher than the ocular RMS, indicating a degree 0.133 mm for an increase in mean pupil diameter from of balance between corneal and internal aberrations. 4.1 mm to 6.3 mm). This would not be an issue for stud- ies using dilation for both techniques (e.g. Atchison, vertex, rather than the pupil centre, affected which aberra- 2004). In future studies it would be preferable to have tions were significantly correlated to refraction. In particu- a common reference position, which might involve iden- 1 lar, c3 was no longer influenced by refraction, and this was tifying the corneal limbus in images using both wave- probably a consequence of the pupil centre being less tem- front sensing and corneal topographer instruments, or porally displaced from the corneal vertex as refraction using an instrument that measures aberrations and increases (regression equation y = 0.015x 0.205, topography simultaneously. D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3717

a 0.4 In two of the studies reporting increases in the magni- tude of the eye’s aberrations with myopia (Buehren et al., 2005; Paquin et al., 2002), participants wore correcting neg- ative powered ophthalmic lenses in the spectacle plane. For 0.2 Hartmann-Shack sensors as used by us and these groups, correction should not alter aberration measurements pro- vided that it does not affect the reference plane for mea- 0.0 surements. However, in these two studies the images of

(micrometres) entrance pupils or in the lenses were used to specify 4 0

C pupil sizes, as it is these images, rather than the entrance -0.2 pupil or cornea themselves, which are then imaged on the plane of the lenslet array. Because the real (or effective) entrance pupils are bigger than their images in corrected -0.4 myopia, most aberrations in these studies would have been increasingly overestimated as myopia increased (Campbell, b 2 Bueno, Hunter, & Kisilak, 2003; Charman & Atchison, 2005). We estimated the influence of this pupil artefact using 1 our results. We calculated the spectacle magnification (SM) produced by thin lenses 14 mm from the cornea (as already mentioned, the COAS instrument uses the anterior 0 cornea as its reference position for aberrations), assuming that this was the vertex distance at which the subjects’ (micrometres) 2 2 refractions were determined. The spectacle magnification C -1 also gives the relative size of the image of the cornea in the ophthalmic lens, relative to the size of a particular region of the cornea, according to paraxial optics. If the (b) instrument images this image onto the lenslet array and -2 analyses a 5 mm diameter, the effective diameter D at -12 -10 -8 -6 -4 -2 0 2 e the cornea is given in millimetres by Best sphere correction (D) Ocular Corneal Internal De ¼ 5=SM ¼ 5ð1 vMÞð3Þ where v is the vertex distance and M is the mean spherical Fig. 6. Ocular, corneal (pupil referenced) and internal aberration coeffi- 0 2 refraction in the spectacle plane. We recalculated the aber- cients as a function of refractive correction for (a) c4 and (b) c2. The corneal higher order aberration was greater than the ocular higher order rations for all eyes by extrapolation based on these new siz- aberration for most participants. Linear fits showed significant correla- es (Atchison, Scott, & Charman, 2003). 2 0 tions for c2 but not for c4 (Table 2). All of the ocular 3rd order RMS, 4th order RMS, 5th order RMS, 6th order RMS and total RMS are now signif- icantly affected by myopia, and according to linear regres- 0.4 Corneal - Pupil Referenced Corneal - Vertex Referenced sion the ocular total RMS increases by 7% per dioptre of 0.3 myopia. The results are shown in Fig. 8 for 3rd order, 4th order and total RMS. In Buehren et al.’s study and 0.2 for 5 mm pupils, 4th, 5th and 6th order RMS aberrations were 38%, 36% and 47% greater, respectively, for a myopic 0.1 group (mean refraction 3.84 D) than for an emmetropic group (mean refraction 0.00 D) in baseline measurements 0.0 (micrometres)

3 before performing a reading task. The differences in 3rd 1

C order RMS aberrations between the two refraction groups -0.1 were not significant and were not given. Our predictions for -0.2 4th, 5th and 6th order increases for their myopic group are 25%, 67% and 80%, respectively. We can thus explain -0.3 about 2/3rds of the increase in 4th order aberrations with -12 -10 -8 -6 -4 -2 0 2 myopia in the Buehren et al. study [we will ignore the 5th Best sphere correction (D) and 6th orders, as the magnitudes of these aberrations

1 are much smaller than those of the 4th order]. Similarly Fig. 7. Corneal aberration coefficients c3, referenced to the centre of the pupil and to the corneal vertex, as a function of refractive correction. The we can explain about 3/4ths of the increase in total RMS reference position influences the intercept and slope of the regression fits. aberrations with myopia in Paquin et al.’s (2002) study. 3718 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

0.6 the possibility that high levels or signs of some aberrations 3rd order 4th order Total in emmetropic eyes may predispose them to develop myo- 0.5 pia (Charman, 2005).

0.4 4.4. Modelling

0.3 We have performed modelling of retinal stretching in an

0.2 endeavour to explain our results, and in particular the res- olution findings. Recently, based on magnetic resonance RMS (micrometres) 0.1 imaging data, we developed a non-rotationally symmetrical ellipsoid model of posterior retinas as a function of myopia 0.0 (Atchison et al., 2005). The retina has semi-diameters ðRx0 , Ry0 , Rz0 Þ such that:

-12 -10 -8 -6 -4 -2 0 2 Rx0 ¼ Rx 0:043M; Ry0 ¼ Ry 0:090M; Best sphere correction (D) Rz0 ¼ Rz 0:163M ð4Þ Fig. 8. Predicted ocular 3rd order, 4th order and total RMS coefficients if the eyes in the aberration experiments were corrected by thin lenses 14 mm where M is the spectacle refractive correction in dioptres in front of the corneas. Regression equations are: 3rd order, y = and the semi-diameters of the emmetropic ellipsoid (Rx, 2 0.0098x + 0.1420, adj. R = 0.094, t = 2.91, p = 0.005; 4th order, Ry,Rz) are (11.450 mm, 11.365 mm, and 10.118 mm). Dis- y = 0.0049x + 0.0763, adj. R2 = 0.109, t = 2.71, p = 0.009; total, regarding the small tilts and decentrations of the axis, the y = 0.1251x + 0.0169, adj. R2 = 0.176, t = 3.75, p = 0.0004. mapping of a position (xe,ye,ze) on an emmetropic retina onto the corresponding position (xm,ym,zm) on a myopic We do not know the exact vertex distances in these studies retina with the ellipsoid centre at (0,0,0) is: or for our subjects when corrected, so our explanation may have overemphasised the artefact magnitude if vertex dis- xm ¼ xeRx0 =Rx; ym ¼ yeRy0 =Ry; zm ¼ zeRz0 =Rz ð5Þ tance for most subjects were smaller than 14 mm (we In our modelling, the anterior vertex of the ellipsoid was repeated the procedure with a 12 mm vertex distance, and 3.1 mm behind the corneal vertex. Using the corneal vertex although the predicted increases were smaller, changes as as a reference point rather than the ellipsoidal centre, we a function of myopia remained significant). In addition to replace ze by ze Rz 3.1 and we replace zm by this point, recalculating aberrations at a larger pupil size zm Rz0 3:1 to give: than that for which data are available may not always give z ¼½ðz 3:1ÞR 0 þ 3:1R =R ð6Þ an accurate answer. Conversely we may have actually m e z z z underestimated the aberration artefact because our Substituting the values of (Rx,Ry,Rz) into the equations for approach may underestimate the effective pupil size. xm, ym,andzm, we have: Because of positive spherical aberration, the effective pupil xm ¼ xeð11:450 0:043MÞ=11:450 ð7aÞ diameter in most meridians for spectacle corrected myopic eyes would be greater than given by the Gaussian optics ym ¼ yeð11:365 0:090MÞ=11:365 ð7bÞ based Eq. (3) (Atchison & Charman, 2005). zm ¼½ðze 3:1Þð10:118 0:163MÞþ3:1 This pupil size artefact has probably affected other stud- 10:118=10:118 ð7cÞ ies that investigated the effect of magnitude of myopia on visual function. As an example, it would have affected the The expected ratio of myopic to emmetropic retinal resolu- results in the study of Radhakrishnan, Pardhan, Calver, tion is given for horizontal gratings by ye/ym and for verti- & O’Leary (2004), who found that the contrast sensitivity cal gratings by xe/xm. The expected ratio of myopic to function was affected more asymmetrically by defocus emmetropic increase in retinal area is given by xmym/(xe direction for myopes than for emmetropes. Asymmetry in ye). Using the slope of 0.012 log units/dioptre and 10 D response to positive and negative defocus occurs in the of myopia, we expected that retinal resolution should be presence of spherical aberration (e.g. Atchison, Joblin, & 76% of the emmetropic resolution, whereas the modelling Smith (1998)), and Radhakrishnan et al. attributed the predicts 93% and 96% of the emmetropic resolution for greater asymmetry for myopes to higher positive spherical horizontal and vertical gratings, respectively. As well as aberration in myopes than in emmetropes. At least part of the predicted changes being much smaller than the experi- this higher spherical aberration would have resulted mental changes, the magnitudes of changes for horizontal because artificial pupils to define the pupil size, along with and vertical gratings are contrary to that expected, as correcting/defocusing lenses, were placed in the spectacle greater reduction in experimental resolution occurs with in- lens plane (Atchison & Charman, 2005). crease in myopia for vertical than for horizontal gratings. Our results, combined with those of previous studies, This model is an example of a global expansion model in suggest that adult myopes do not have aberrations higher which the retina is stretched relative to its ‘‘anterior vertex’’ than those of adult emmetropes. This does not exclude due to the myopic elongation. Less sophisticated versions D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3719 of global expansion models have been presented previously relative hypermetropia along the horizontal visual field by Strang et al. (1998); Chui et al. (2005) and Coletta & (Atchison et al., 2006). Watson (2006), but like us these researchers found that As pointed out by Chui et al. (2005), the global expan- the models cannot explain the loss in resolution seen in sion model is not necessarily incorrect, but for it to be myopia. correct there must be some accompanying loss of post- Strang et al. (1998) developed a posterior expansion receptoral sensitivity, such as might occur with ganglion model in which the posterior retina expands about a point cell loss. between the ‘‘anterior vertex’’ of the retina and the emme- Gentle, Jaworski, Zele, Vingrys, & McBrien (2005) con- tropic retina. They selected a point half way between the sidered a set of myopic models in which retinal stretching centre of the posterior globe and the posterior vertex of increased the spacing between photoreceptor centres, as is their eye model, and found that this did a reasonable job implied in the models described above, and this could be of predicting losses in letter visual acuity with myopia. Col- accompanied by increase in size of the photoreceptors etta & Watson (2006) adapted this model for their data and and/or loss of post-receptor sensitivity due to stresses dur- estimated that the point about which posterior polar ing retinal stretching. They determined that their model 4 expansion might occur was 13 mm and 10 mm in front of (combination of all three factors) best explained their find- the emmetropic retina according to their fixation and 10 ings of reduced contrast sensitivity at the critical area nasal visual field results, respectively. We have done a sim- (although with no significant effect on the latter) in spatial ple, similar exercise as follows: summation experiments and reduced contrast sensitivity The point about which expansion occurs is a distance a function at higher spatial frequencies (>18 cycles/mm on in front of the retina, and the transverse retinal expansion retina). Our spatial summation experiment found an is given approximately by increase in critical area without change in the contrast sen- sitivity at this area for some of the visual field, while the x =x ðor y =y Þ¼ðAL AL þ aÞ=a ð8Þ m e m e m e resolution experiment found a loss in resolution with myo- where ALm and ALe are myopic and emmetropic axial pia. This matches the predictions for Gentle et al.’s (2005) lengths. From ultrasound measurements on 119 subjects model 1 (increased photoreceptor centre separations only) (Atchison, 2006), most of whom were used for this study, better than those of other models. Gentle et al. did not con- we obtained the linear regression sider the possibility of ganglion cell loss, but ganglion cell loss would exacerbate the increase in critical area and loss AL ¼ 23:70 0:298MðR2 ¼ 0:57Þð9Þ m of resolution. where ALm is in mm and myopic correction M is in diop- tres. Substituting the right hand expression for ALm in 4.5. Other comments Eq. (9) into Eq. (8) we get There is some evidence of greater myopic related loss in x =x ðor y =y Þ¼ða 0:298MÞ=a ð10Þ m e m e visual function in the temporal visual field than in the nasal The inverse of xm/xe(or ym/ye) gives the ratio of myopic visual field, with the increase in critical areas being signifi- and emmetropic resolutions. Because our resolution mea- cant for the former and not for the latter (Table 1). Also, surements and the corresponding regression fit were in the losses in spatial resolution were slightly greater in the log units, this tends to gives a variable solution to a temporal than in the nasal visual field (although not signif- depending upon refraction. Using the experiment fit of icantly so). This suggests that retinal stretching accompa- 0.012 log unit loss per dioptre of myopia, we get estimates nying myopia may be greater for the nasal than for the of a of 10.3 mm to 9.4 mm for the refraction range 3Dto temporal retina. However, we note similar loss on both 10 D, corresponding to positions slightly in front of to sides of the visual field in the Chui et al. (2005) study. slightly behind the centre of the emmetropic retinal ellip- soid model whose semi-diameter along the axial direction 5. Conclusion/summary is 10.12 mm. To explain resolution losses being greater for vertical than for horizontal gratings, the point of We have described optical and visual performance in a expansion could become a locus of points with the distance group of young adult emmetropes and myopes. Myopia a being smaller for expansion along the horizontal than has little effect on central higher order aberrations. Howev- along the vertical meridian.This means that the retina er, small levels of myopia related loss were found for other would be flatter in the region of the posterior pole along visual performance measures limited solely (interferome- the horizontal meridian than along the vertical meridian. try) or mainly (spatial summation) by neural consider- However this is inconsistent with MRI investigations find- ations. Loss appears to be slightly greater in the temporal ing that myopic posterior retinas are flatter along the ver- than in the nasal visual field. The loss can be explained tical meridian than along the horizontal meridian by global retinal expansion with some post-receptor loss (Atchison et al., 2004; Atchison et al., 2005). It is also (e.g. ganglion cell death) or a posterior polar expansion inconsistent with a study that found that myopes have rel- in which the point about which expansion occurs is near ative peripheral myopia along the vertical visual field and the centre of the emmetropic globe. 3720 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

Acknowledgments Bansal, J., Coletta, N. J., Moskowitz, A., & Han, H. (2004). Pupil displacement in corneal topography images is related to the eye’s This work was supported by National Health and Med- refractive error. Investigative and Visual Science, 45, 2762, e-Abstract. ical Research Grant 199912. We thank Nancy Coletta and Barbero, S., Marcos, S., & Merayo-Lloves, J. (2002). Corneal and total Toco Chui for supplying us with data from studies of Col- optical aberrations in a unilateral aphakic patient. Journal of Cataract etta & Watson (2006) and Chui et al. (2005), respectively. and , 28, 1594–1600. We gratefully thank all our participants. Bennett, A. G. (1988). A method of determining the equivalent powers of the eye and its crystalline lens without resort to phakometry. Ophthalmic and Physiological Optics, 8, 53–59. References Berny, F., & Slansky, S. (1970). Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments. In J. Abbott, M. L., Schmid, K. L., & Strang, N. C. (1998). Differences in the H. Dickson (Ed.), Optical instruments and techniques (pp. 375–386). accommodation stimulus response curve of adult myopes and emme- England: Oriel Press. tropes. Ophthalmic and Physiological Optics, 18, 13–20. Bradley, A., Hook, J., & Haeseker, J. (1991). A comparison of clinical American National Standards Institute (2004). American National Stan- acuity and contrast sensitivity charts: effect of uncorrected myopia. dard for Ophthalmics—Methods for reporting optical aberrations of Ophthalmic and Physiological Optics, 11, 218–226. the eye. ANSI Z80.28-2004. Budak, K., Khater, T. T., Friedman, N. J., Holladay, J. T., & Koch, D. D. Applegate, R. (1991). Monochromatic wavefront aberrations in myopia. (1999). Evaluation of relationships among refractive and topographic Technical digest on noninvasive assessment of the visual system (1, parameters. Journal of Cataract and Refractive Surgery, 25, 814–820. pp. 234–237). Washington, DC: Optical Society of America. Buehren, T., Collins, M. J., & Carney, L. G. (2005). Near work induced Artal, P., Benito, A., & Tabernero, J. (2006). The human eye is an example wavefront aberrations in myopia. Vision Research, 45, 1297–1312. of robust optical design. Journal of Vision, 6, 1–7. Bullimore, M. A., Gilmartin, B., & Royston, J. M. (1992). Steady-state Artal, P., Guirao, A., Berrio, E., & Williams, D. (2001). Compensation of accommodation and ocular biometry in late-onset myopia. Documenta corneal aberrations by the internal optics in the human eye. Journal of Ophthalmologica, 80, 143–155. Vision, 1, 1–8. Campbell, M. C., Bueno, J. M., Hunter, J. J., & Kisilak, M. L. (2003). Atchison, D. A. (1996). Calculating relative retinal image sizes of eyes. Ophthalmic lens effects in Hartmann-Shack measurements. Journal of Ophthalmic and Physiological Optics, 16, 532–538. Vision, 3, 29a. Atchison, D. A. (2004). Recent advances in representation of monochro- Carkeet, A., Luo, H. D., Tong, L., Saw, S. M., & Tan, D. T. (2002). matic aberrations of human eyes. Clinical and Experimental Optom- Refractive error and monochromatic aberrations in Singaporean etry, 87, 138–148. children. Vision Research, 42, 1809–1824. Atchison, D. A. (2006). Optical models for human myopia. Vision Carney, L. G., Mainstone, J. C., & Henderson, B. A. (1997). Corneal Research, 46, 2236–2250. topography and myopia. A cross-sectional study. Investigative Oph- Atchison, D. A., & Charman, W. N. (2005). The influences of reference thalmology and Visual Science, 38, 311–320. plane and direction of measurement on eye aberration measurement. Charman, W. N. (2005). Aberrations and myopia. Ophthalmic and Journal of the Optical Society of America A. Optics and Image Science, Physiological Optics, 25, 285–301. 22, 2589–2597. Charman, W. N., & Atchison, D. (2005). Theoretical effect of changes in Atchison, D. A., Collins, M. J., Wildsoet, C. F., Christensen, J., & entrance pupil magnification on wavefront-guided laser refractive Waterworth, M. D. (1995). Measurement of monochromatic ocular corneal surgery. Journal of Refractive Surgery, 21, 386–391. aberrations of human eyes as a function of accommodation by the Chen, J. C., Brown, B., & Schmid, K. L. (2006). Delayed mfERG Howland aberroscope technique. Vision Research, 35, 313–323. responses in myopia. Vision Research, 46, 1221–1229. Atchison, D. A., Joblin, A., & Smith, G. (1998). Influence of Stiles– Cheng, H., Barnett, J. K., Vilupuru, A. S., Marsack, J. D., Kasthuriran- Crawford effect apodization on spatial visual performance. Journal of gan, S., Applegate, R. A., & Roorda, A. (2004). A population study on the Optical Society of America A. Optics and Image Science, 15, changes in wave aberrations with accommodation. Journal of Vision, 4, 2545–2551. 272–280. Atchison, D. A., Jones, C. E., Schmid, K. L., Pritchard, N., Pope, J. M., Cheng, H. M., Singh, O. S., Kwong, K. K., Xiong, J., Woods, B. T., & Strugnell, W. E., & Riley, R. A. (2004). Eye shape in and Brady, T. J. (1992). Shape of the myopic eye as seen with high- myopia. Investigative Ophthalmology and Visual Science, 45, resolution magnetic resonance imaging. Optometry and Vision Science, 3380–3386. 69, 698–701. Atchison, D. A., Pritchard, N., & Schmid, K. L. (2006). Peripheral Cheng, X., Bradley, A., Hong, X., & Thibos, L. N. (2003). Relationship refraction along the horizontal and vertical visual fields in myopia. between refractive error and monochromatic aberrations of the eye. Vision Research, 46, 1450–1458. Optometry and Vision Science, 80, 43–49. Atchison, D. A., Pritchard, N., Schmid, K. L., Scott, D. H., Jones, C. E., & Chui, T. Y. P., Yap, M., Chan, H. H. L., & Thibos, L. N. (2005). Retinal Pope, J. M. (2005). Shape of the retinal surface in emmetropia and stretching limits peripheral visual acuity in myopia. Vision Research, myopia. Investigative Ophthalmology and Visual Science, 46, 2698–2707. 45, 593–605. Atchison, D. A., & Scott, D. H. (2002). Monochromatic aberrations of Coletta, N. J., & Watson, T. A. (2006). Effect of myopia on visual acuity human eyes in the horizontal visual field. Journal of the Optical Society measured with laser interference fringes. Vision Research, 46, 636–651. of America A. Optics and Image Science, 19, 2180–2184. Collins, J. W., & Carney, L. G. (1990). Visual performance in high Atchison, D. A., Scott, D. H., & Charman, W. N. (2003). Hartmann- myopia. Current Eye Research, 9, 217–223. Shack technique and refraction across the horizontal visual field. Collins, M. J., Wildsoet, C. F., & Atchison, D. A. (1995). Monochromatic Journal of the Optical Society of America A. Optics and Image Science, aberrations and myopia. Vision Research, 35, 1157–1163. 20, 965–973. Donnenfeld, E. (2004). The pupil is a moving target: centration, Atchison, D. A., & Smith, G. (2000). Optics of the human eye. Oxford: repeatability, and registration. Journal of Refractive Surgery, 20, Butterworth-Heinemann. S593–S596. Atchison, D. A., Smith, G., & Waterworth, M. D. (1993). Theoretical Felius, J., Swanson, W. H., Fellman, R. L., Lynn, J. R., & Starita, R. J. effect of refractive error and accommodation on longitudinal chro- (1997). Spatial summation for selected ganglion cell mosaics in patients matic aberration of the eye. Optometry and Vision Science, 70, with glaucoma. Perimetry Update 1996/1997. Proceedings of the XII 716–722. International Perimetric Society Meeting (pp. 213–221). D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722 3721

Fiorentini, A., & Maffei, L. (1976). Spatial contrast sensitivity of myopic Lotmar, W. (1980). Apparatus for the measurement of retinal visual acuity subjects. Vision Research, 16, 437–438. by moire fringes. Investigative Ophthalmology and Visual Science, 19, Gentle, A., Jaworski, A., Zele, A. J., Vingrys, A. J., & McBrien, N. A. 393–400. (2005). Reduced visual sensitivity in axial high myopia: a receptoral or Love, J., Gilmartin, B., & Dunne, M. C. M. (2000). Relative peripheral post-receptoral phenomenon. Investigative Ophthalmology and Visual refractive error in adult myopia and emmetropia. Investigative Science, 46, e-Abstract 5606. Ophthalmology and Visual Science, 41, S302. Goh, W. S. H., & Lam, C. S. Y. (1994). Changes in refractive trends and Ma, L., Atchison, D. A., & Charman, W. N. (2005). Off-axis aberrations optical components of Hong Kong Chinese aged 19–39 years. following corneal refractive surgery. Journal Of Cataract and Refrac- Ophthalmic and Physiological Optics, 14, 378–382. tive Surgery, 489–498. Goss, D. A., Van Veen, H. G., Rainey, B. B., & Feng, B. (1997). Ocular Marcos, S., Barbero, S., & Llorente, L. (2004). The sources of optical components measured by keratometry, phakomemetry, and ultraso- aberrations in myopic eyes. Investigative Ophthalmology and Visual nography in emmetropic and myopic optometry students. Optometry Science, ARVO abstract # 1510. and Vision Science, 74, 489–495. Marcos, S., Moreno-Barriuso, E., Llorente, L., Navarro, R., & Barbero, Grosvenor, T., & Scott, R. (1991). A comparison of refractive components S. (2000). Do myopic eyes suffer from large amounts of aberration? in youth-onset and early-onset myopia. Optometry and Visual Science, VIII International Congress on Myopia, 118–121. 68, 204–209. McBrien, N. A., & Millodot, M. (1986). The effect of refractive error on Grosvenor, T., & Scott, R. (1993). Three-year changes in refraction and its the accommodative response gradient. Ophthalmic and Physiological components in youth-onset and early adult-onset myopia. Optometry Optics, 6, 145–149. and Vision Science, 70, 677–683. McBrien, N. A., & Millodot, M. (1987). A biometric investigation of late Grosvenor, T., & Scott, R. (1994). Role of the axial length/corneal radius onset myopic eyes. Acta Ophthalmologica, 65, 461–468. ratio in determining the refractive state of the eye. Optometry and Millodot, M. (1981). Effect of ametropia on peripheral refraction. Vision Science, 71, 573–579. American Journal of Optometry and Physiological Optics, 58, 691–695. Guirao, A., & Artal, P. (1999). Off-axis monochromatic aberrations Mutti, D. O., Sholtz, R. I., Friedman, N. E., & Zadnik, K. (2000). estimated from double pass measurements in the human eye. Vision Peripheral refraction and ocular shape in children. Investigative Research, 39, 207–217. Ophthalmology and Visual Science, 41, 1022–1030. Gwiazda, J., Thorn, F., Bauer, J., & Held, R. (1993). Myopic children Navarro, R., Moreno, E., & Dorronsoro, C. (1998). Monochromatic show insufficient accommodative response to blur. Investigative aberrations and point-spread functions of the human eye across the Ophthalmology and Visual Science, 34, 690–694. visual field. Journal of the Optical Society of America A. Optics and Hazel, C., Cox, M. J., & Strang, N. (2003). Wavefront aberration and its Image Science, 15, 2522–2529. relationship to the accommodative stimulus-response function in Netto, M. V., Ambro´sio, R., Shen, T. T., & Wilson, S. E. (2005). myopic subjects. Optometry and Vision Science, 80, 151–158. Wavefront analysis in normal refractive surgery candidates. Journal of He, J. C., Burns, S. A., & Marcos, S. (2000). Monochromatic aberrations Refractive Surgery, 21, 332–338. in the accommodated human eye. Vision Research, 40, 41–48. Ninomiya, S., Fujikado, T., Kuroda, T., Maeda, N., Tano, Y., Oshika, T., He, J. C., Gwiazda, J., Thorn, F., Held, R., & Vera-Diaz, F. A. (2005). Hirohara, Y., & Mihashi, T. (2002). Changes of ocular aberration with The association of wavefront aberration and accommodative lag in accommodation. American Journal of Ophthalmology, 134, 924–926. myopes. Vision Research, 45, 285–290. O’Leary, D. J., & Allen, P. M. (2001). Facility of accommodation in He, J. C., Sun, P., Held, R., Thorn, F., Sun, X., & Gwiazda, J. E. (2002). myopia. Ophthalmic and Physiological Optics, 21, 352–355. Wavefront aberrations in eyes of emmetropic and moderately myopic Panagopoulou, S. I., Plainsis, S., MacRae, S. M., & Pallikaris, I. G. school children and young adults. Vision Research, 42, 1063–1070. (2004). The implications of pupil size and accommodation dynamics Ito, A., Kawabata, H., Fujimoto, N., & Adachi-Usami, E. (2001). Effect on customized wavefront-guided refractive surgery. In R. R. Krueger, of myopia on frequency-doubling perimetry. Investigative Ophthalmol- R. A. Applegate, & S. M. MacRae (Eds.), Wavefront customized visual ogy and Visual Science, 42, 1107–1110. correction: the quest for super vision II (pp. 121–124). Thorofare: Slack Ivanoff, A. (1956). About the spherical aberration of the eye. Journal of the Incorporated. Optical Society of America, 46, 901–903. Paquin, M. P., Hamam, H., & Simonet, P. (2002). Objective measurement Jaworski, A., Gentle, A., Zele, A. J., Vingrys, A. J., & McBrien, N. A. of optical aberrations in myopic eyes. Optometry and Visual Science, (2006). Altered visual sensitivity in axial high myopia: a local post- 79, 285–291. receptoral phenomenon. Investigative Ophthalmology and Visual Plainsis, S., Ginis, H. S., & Pallikaris, A. (2005). The effect of ocular Science, 46, 3695–3702. aberrations on steady-state errors of accommodative response. Journal Jenkins, T. C. A. (1963). Aberrations of the eye and their effects on vision: of Vision, 5, 466–477. part 1. British Journal of Physiological Optics, 20, 59–91. Porter, J., Guirao, A., Cox, I. G., & Williams, D. R. (2001). Monochro- Katsanevaki, V. J., Panagopoulou, S. I., Plainsis, S., Ginis, H., & matic aberrations of the human eye in a large population. Journal of Pallikaris, I. (2004). Accommodation dynamics and its implication on the Optical Society of America A. Optics and Image Science, 18, customized corrections. In R. R. Krueger, R. A. Applegate, & S. M. 1793–1803. MacRae (Eds.), Wavefront customized visual correction: the quest for Radhakrishnan, H., Pardhan, S., Calver, R. I., & O’Leary, D. J. (2004). super vision II (pp. 115–119). Thorofare: Slack Incorporated. Effect of positive and negative defocus on contrast sensitivity in Kawabata, H., & Adachi-Usami, E. (1997). Multifocal electroretinogram myopes and non-myopes. Vision Research, 44, 1869–1878. in myopia. Investigative Ophthalmology and Visual Science, 38, Rempt, F., Hoogerheide, J., & Hoogenboom, W. P. H. (1971). Peripheral 2844–2851. and the skiagram. Ophthalmologica, 162, 1–10. Koomen, M., Tousey, R., & Scholnik, R. (1949). The spherical aberration Schmid, G. F. (2003). Variability of retinal steepness at the posterior pole of the eye. Journal of the Optical Society of America, 39, 370–376. in children 7–15 years of age. Current Eye Research, 27, 61–68. Liou, S. W., & Chiu, C. J. (2001). Myopia and contrast sensitivity Schober, H., Munker, H., & Zolleis, F. (1968). Die Aberration des function. Current Eye Research, 22, 81–84. menschlichen Auges und ihre Messung. Optica Acta, 15, 47–57. Llorente, L., Barbero, S., Cano, D., Dorronsoro, C., & Marcos, S. (2004). Seidemann, A., Schaeffel, F., Guirao, A., Lopez-Gil, N., & Artal, P. Myopic versus hyperopic eyes: axial length, corneal shape and optical (2002). Peripheral refractive errors in myopic, emmetropic, and aberrations. Journal of Vision, 4, 288–298. hyperopic young subjects. Journal of the Optical Society of America Logan, N. S., Gilmartin, B., Wildsoet, C. F., & Dunne, M. C. (2004). A. Optics and Image Science, 19, 2363–2373. Posterior retinal contour in adult human anisomyopia. Investigative Sheridan, M., & Douthwaite, W. A. (1989). Corneal asphericity and Ophthalmology and Visual Science, 45, 2152–2162. refractive error. Ophthalmic and Physiological Optics, 9, 235–238. 3722 D.A. Atchison et al. / Vision Research 46 (2006) 3707–3722

Sorsby, A., Sheridan, M., & Leary, G. A. (1961). Refraction and its Walsh, G., & Charman, W. N. (1988). The effect of pupil centration components during the growth of the eye from the age of three. and diameter on ocular performance. Vision Research, 28, Medical Research Council Special Report Series number 301. London: 659–665. Her Majesty’s Stationary Office. Wang, Y.-Z., Thibos, L. N., & Bradley, A. (1997). Effects of refractive Stenstrom, S. (1948). Investigation of the variation and the correlation of error on detection acuity and resolution acuity in peripheral vision. the optical elements of human eyes. Part V-Chapter III. Translated by Investigative Ophthalmology and Visual Science, 38, 2134–2143. D. Woolf. American Journal of Optometry and Archives of American Wildsoet, C. W., Atchison, D. A., & Collins, M. J. (1993). Longitudinal Academy of Optometry, 25, 438–449. chromatic aberration as a function of refractive error. Clinical and Strang, N. C., Winn, B., & Bradley, A. (1998). The role of neural and Experimental Optometry, 76, 119–122. optical factors in limiting visual resolution in myopia. Vision Research, Williams, D. R. (1985). Aliasing in human foveal vision. Vision Research, 38, 1713–1721. 25, 195–205. Thibos, L. N. (1990). Optical limitations of the Maxwellian view Williams, D. R., Artal, P., Navarro, R., McMahon, M. J., & Brainard, D. interferometer. Applied Optics, 29, 1411–1419. H. (1996). Off-axis optical quality and retinal sampling in the human Thibos, L. N., Applegate, R. A., Schwiegerling, J. T., Webb, R., & eye. Vision Research, 36, 1103–1114. Members, V. T. (2002). Standards for reporting the optical aberrations Wilson, M. A., Campbell, M. C., & Simonet, P. (1992). Change of pupil of eyes. Journal of Refractive Surgery, 18, S652–S660. centration with change of illumination and pupil size. Optometry and Thibos, L. N., Bradley, A., & Hong, X. (2002). A statistical model of the Vision Science, 69, 129–136. aberration structure of normal, well-corrected eyes. Ophthalmic and Wyatt, H. J. (1995). The form of the human pupil. Vision Research, 35, Physiological Optics, 22, 427–433. 2021–2036. Thibos, L. N., Still, D. L., & Bradley, A. (1996). Characterization of Yang, Y., Thompson, K., & Burns, S. A. (2002). Pupil location under spatial aliasing and contrast sensitivity in peripheral vision. Vision mesopic, photopic, and pharmacologically dilated conditions. Investi- Research, 36, 249–258. gative Ophthalmology and Visual Science, 43, 2508–2512. Thorn, F., Corwin, T. R., & Comerford, J. P. (1986). High myopia does Zadok, D., Levy, Y., Segal, O., Barkana, Y., Morad, Y., & Avni, I. (2005). not affect contrast sensitivity. Current Eye Research, 5, 635–639. Ocular higher-order aberrations in myopia and skiascopic wavefront Van Alphen, G. W. H. M. (1986). Choroidal stress and emmetropization. repeatability. Journal of Cataract and Refractive Surgery, 31, Vision Research, 26, 723–734. 1128–1132.