Higher Order Monochromatic Aberrations of the Human Infant Eye

Journal of Vision (2005) 5, 543-555 http://journalofvision.org/5/6/6/ 543

Higher order monochromatic aberrations of the human infant eye

Indiana University School of Optometry, Jingyun Wang Bloomington, IN, USA Indiana University School of Optometry, T. Rowan Candy Bloomington, IN, USA

The monochromatic optical aberrations of the eye degrade retinal image quality. Any significant aberrations during postnatal development could contribute to infants’ immature visual performance and provide signals for the control of eye growth. Aberrations of human infant eyes from 5 to 7 weeks old were compared with those of adult subjects using a model of an adultlike infant eye that accounted for differences in both eye and pupil size. Data were collected using the COAS Shack-Hartmann wavefront sensor. The results demonstrate that the higher order aberrations of the 5-to-7-week-old eye are less than a factor of 2 greater than predicted for an adultlike infant eye of this age. The data are discussed in the context of infants’ visual performance and the signals available for controlling growth of the eye.

Keywords: visual development, optical aberrations, human infant Introduction acuity is only 1-2 cpd (Teller, Regal, Videen, & Pulos, 1978). The visual performance of human infants improves The higher order optical aberrations, beyond defocus dramatically after birth. The spatial contrast sensitivity and astigmatism, are unlikely to dramatically limit human function matures over a number of months so that both infants’ visual performance. Fundus details are easily re- the resolution limit and peak sensitivity to contrast increase solved during an infant eye examination (Cook & Glass- by approximately a factor of 10 during the first postnatal cock, 1951) and a recent study demonstrated almost adult- year (reviewed by Teller, 1997). like resolution of stages of the infant visual system preced- A number of studies have sought to determine the ing the first major nonlinearity (Candy & Banks, 1999). structural immaturities that limit performance in the neo- However, given the structural differences between infant natal visual system (in humans, see Brown, Dobson, & and adult eyes, optical quality of the infant eye may differ Maier, 1987; Banks & Bennett, 1988; Wilson, 1988; significantly from that of the adult. The length of the hu- Candy, Crowell, & Banks, 1998; in macaque, see Boothe, man newborn eye is approximately two-thirds of the adult 1982; Jacobs & Blakemore, 1988; Kiorpes, Tang, Hawken, length (e.g., Larsen, 1971; Fledelius, 1992; Denis et al., & Movshon, 2003). These analyses incorporated immaturi- 1993), the cornea has greater curvature than in the adult ties in dimensions of the eye, the photoreceptors, and the (Mandell, 1967; Inagaki, 1986; Insler, Cooper, May, & receptive field properties of neurons. The studies of human Donzis, 1987), and the lens undergoes significant postnatal reconfiguration (Gordon & Donzis, 1985; Wood, Mutti, & development were unable to fully address the role of the Zadnik, 1996). In fact, coordinated growth of the eye over eye’s optical quality because the available data were limited the first two postnatal years leads to a loss of 20-30 D of to the lower order aberrations of defocus and astigmatism total optical power while approximate emmetropia is main- (reviewed by Saunders, 1995). One previous study had tained (Bennett & Francis, 1962). noted the presence of spherical aberration in human infant At a more detailed level, the distribution of individual eyes but had not measured it (Molteno & Sanderson, higher order aberrations in the infant eye is of particular 1984). The studies of infant macaques, however, were able interest (e.g., coma or spherical aberration). In the presence to incorporate data from a study conducted by Williams of defocus alone, the retinal image is the same for equal and Boothe (1981). They used a double-pass technique to amounts of myopic and hyperopic defocus. The visual sys- measure the optical transfer function (OTF) of the infant tem therefore requires an additional signal to determine monkey eye. These data demonstrated a small maturation the sign or direction of any defocus. Higher order mono- of the OTF over the first 13 weeks after birth, but clearly chromatic aberrations have been proposed to provide reti- showed that the optical quality of the newborn monkey eye nal image cues that guide the control of defocus through was superior to the resolution of their visual system as a accommodation and emmetropization (Wilson, Decker, & whole. In those experimental viewing conditions, the ma- Roorda, 2002; Wallman & Winawer, 2004). The types and caque OTF extended out to 32 cpd at an age when visual amount of aberrations present in the infant eye need to be

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understood to assess their potential role in these processes. Alignment The growth of the cornea and lens has also been proposed The adult subjects were asked to fixate the center of the to be coordinated with each other, so that their combined instrument’s fixation target while their head was placed in aberrations become lower than those of either the cornea the chin-rest. The instrument was then aligned with their or the lens alone (Kelly, Mihashi, & Howland, 2004; Artal, entrance pupil such that the exiting beam from the pupil Giurao, Berrio, & Williams, 2001). What is the pattern of was centered on the instrument’s measurement axis and the combined aberrations at birth? Does this pattern lenslet array. change with further growth of the cornea and lens? The infants could not be asked to fixate the fixation The goal of this study was to measure the higher order target in the instrument and therefore their alignment had monochromatic aberrations of the human infant eye and to to be performed objectively. The chin-rest was removed and compare them with those of the adult. The impact of these the infant’s chin gently rested in an experimenter’s hand aberrations on retinal image quality was assessed, as was while the experimenter aligned the infant using real-time their potential for signaling defocus to the developing vis- video. The video contained an image of the eye and a series ual system. of 1st Purkinje images generated by LEDs adjacent to the instrument’s viewing aperture (see Figure B1). Aberration Methods data were collected only when the experimenter holding the infant and another observer operating the COAS were in agreement that the image of the eye was in focus and all Aberrometer Purkinje images fell within the infant’s entrance pupil (as Monochromatic aberrations were measured using a demonstrated in Figure B1). This criterion led to an esti- Complete Ophthalmic Analysis System Aberrometer mate of the deviation between the measurement and pupil- (COAS) manufactured in 2000 (Wavefront Sciences lary axes of less than 10 deg (see Appendix B). Assuming that the neonatal line of sight sits an average of 8 deg na- Inc., Albuquerque, NM). The COAS incorporates a Shark- sally from the pupillary axis, this limit would define an ex- Hartmann wavefront sensor that samples the wavefront treme range for the measurement axis from 2 deg nasally to emanating from a point object generated on the retina. The 18 deg temporally from the line of sight (Slater & Findlay, sensor takes up to 44 x 33 simultaneous, evenly distributed 1972; Riddell, Hainline, & Abramov, 1994; Wick & Lon- samples of the local slope of the wavefront using a lenslet don, 1980). array. The lenslets have a separation of 288 μm in the entrance pupil plane. The shape of the wavefront leaving the Data analysis eye can then be interpolated, reconstructed, and described using Zernike polynomials. The design, validation, and Aberration estimates and image quality both vary with pupil size, so comparisons of optical quality between eyes reliability of the COAS aberrometer at Indiana University are typically made after equating pupil size (e.g., Thibos, have been described previously (Cheng, Himebaugh, Koll- Hong, Bradley, & Cheng, 2002). This is appropriate for baum, Thibos, & Bradley, 2003, 2004). comparing eyes of the same axial length but will result in unequal numerical apertures in eyes of different sizes, such Subjects as infant and adult eyes. Twenty-two full-term infants from 5-to-7-weeks old and We therefore developed predictions for an adultlike one parent of each infant were recruited from the public eye scaled to the size of an infant eye (see Appendix C). The birth records and the local community. None of the sub- adultlike eye was a three–dimensionally (3D) scaled version jects had any clinically significant ocular abnormalities. The of the adult eye with adultlike refractive indices. This adult- parents provided informed consent after the study had like eye therefore included a pupil size scaled down by the been fully explained to them. The protocol had been re- ratio of eye sizes. With such a model, the wavefront root viewed and approved by the local Indiana University Insti- mean square (RMS) error of the scaled adultlike eye will tutional Review Board (See Appendix A for a discussion of differ from that of the adult eye by the scaling factor (see retinal light exposure). also Howland, 2005), whereas the adult and adultlike point spread functions (PSFs) will be approximately matched in Procedure angular units (although the effect of diffraction on the PSFs One Shack-Hartmann image was collected from the will scale with pupil size). right eye of each subject in dim room illumination. The The axial length of the human newborn eye is ap- luminance of the instrument case around the viewing aper- proximately two-thirds of the adult axial length (e.g., Lar- ture was 20 cd/m2. The illumination was made bright sen, 1971; newborn mean axial length of 16.6 mm and enough to provide a clear image of the eye for alignment adult mean axial length of 24.0 mm). This scaling factor purposes, but kept at the minimum usable value to maxi- was used to estimate the difference in eye size between mize the subject’s pupil size. The subjects wore no optical adults and infants and to generate the scaled adultlike pre- correction. dictions. The pupil sizes used for the aberrometry analysis

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were scaled by this ratio (pupil diameters of 3 mm were used for infants and 4.5 mm for adults). Zernike coefficients up to the 6th order and the combined RMS wavefront error were then calculated for each individual subject according to the Optical Society of America (OSA) recom- mended standards (Thibos, Applegate, Schwiegerling, & Webb, 2002). Thus the infant RMS data would be considered adultlike if they equaled two-thirds of the real adult values, and the infant PSFs would be considered adultlike if they had approximately the same angular size as the real adult data. Results Data were successfully collected from all of the adults and 17 of the 22 infant subjects. The remaining five infants were either too sleepy or fussy.

Shack-Hartmann images Shack-Hartmann images from infant subjects were included in the analysis if the natural pupil size was greater than 3 mm, and there were no missing centroids in the analyzed pupil area. These criteria permitted inclusion of data from 12 of the infant subjects, whose pupil sizes ranged from 3.06 mm to 4.65 mm. Data from these infants’ parents were used for the adult analysis. In this adult group, the pupil size ranged from 4.52 mm to 6.58 mm (all 12 adults therefore had pupil sizes greater than the re- quired 4.5 mm). The Shack-Hartmann images from the 12 included infant eyes are shown in Figure 1, panel A, and from the adults in Figure 1, panel B. The adult images include a bright spot caused by the reflection of the colli- mated super-luminescent diode beam. The infant images typically do not include this spot, indicating that the subjects were displaced laterally from exact alignment with the Figure 1. Shack-Hartmann images collected from subjects wear- instrument (this has been shown to have little impact on ing no optical correction. A. Twelve infants between 5 and 7 the measurements; Cheng, Himebaugh et al., 2003). weeks old. B. Adults. Each adult is a parent of the infant in the The data in Table 1 illustrate that, in the viewing con- corresponding location in A. ditions used, the ratio of actual infant to adult pupil sizes closely approximated the 2:3 ratio used in the analysis. Therefore, the theoretically motivated use of a common 6 numerical aperture actually closely reflects the physiological infant pupil size ratio for these subjects. 4 adult

Pupil diameter (mm) Infant Adult 2 Minimum 3.06 4.52

Maximum 4.65 6.58 ZC Value (micron) 0 Mean 3.89 5.65 -2 Table 1. Infant and adult measured pupil sizes. − + Z 2 Z 0 Z 2 2 2 2 nd 2 -order aberrations Figure 2. Second-order Zernike coefficient values. The variance nd 0 The distribution of 2 -order Zernike coefficients for in the adult Z2 data occurred because some of the subjects are individual infant and adult subjects is shown in Figure 2. myopic (positive coefficients correspond to myopic focus). t tests indicated that there were no significant differences

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between the infant and adult means for either of the astig- df2 = 1, p=.546, and the components that reached a p value –2 +2 matic terms (Z2 : p = .429; Z2 : p = .718). Overall, there of < .05 in t tests of the difference between groups for indi- +4 –1 was also no significant difference in the defocus term at vidual components were Z4 (p=.014), Z3 (p = .047), and 0 0 this sample size (Z2 , p =.152), even though some of the Z4 (p = .021). adults were myopic and we could not instruct the infants to accommodate accurately to the target. Infants in this age range are typically hyperopic (Cook & Glasscock, 1951; A. Mayer, Hansen, Moore, Kim, & Fulton, 2001), but overac- commodate for distant targets such as the one presented in 0 the COAS (Banks, 1980). The Z2 coefficients were converted to equivalent diopters giving a mean absolute magnitude of defocus of 1.79 D, SD ± 2.35, for the adults, and B. 1.62D, SD ± 0.71, for the infants (see Appendix C, Equation 2).

3rd-, 4th-, and 5th-order aberrations The distribution of 3rd-to-5th-order Zernike coefficient values is shown for the infant and adult groups in Figure 3, –3 –1 +1 +3 –4 –2 0 +2 +4 –5 –3 –1 +1 +3 +5 Z 3 Z 3 Z 3 Z 3 Z Z Z Z Z Z 5 Z 5 Z 5 Z 5 Z 5 Z 5 panel A. The mean values are all comparable and close to 4 4 4 4 4 zero in the two groups. A Hotelling T2 test suggested that Figure 3. Infant and adult 3rd-to-5th-order Zernike coefficients. the vector of mean coefficients was not significantly differ- A. Mean and standard deviation of the individual values. B. Mean ent between groups, F = 0.699, df1 = 22, df2 = 1, p = .756. and standard deviation of the absolute magnitudes. The difference between the groups for each individual Zernike component was also analyzed in a two-sample t test (with no correction for multiple tests). The only compo- RMS wavefront error nent to reach a t test p value of < .05 for the difference be- rd th tween the groups was Z +4 (p = .014). This was not consid- The Zernike coefficients from the 3 to 6 order were 4 combined to form RMS errors in Figure 4. The RMS wave- ered highly significant given the large number of t tests be- front error is shown for each subject and individual order, ing performed. The Z 0 spherical aberration term had a 4 and then for each subject for the combined 3rd to 6th or- p value of .091. One-sample t tests were also performed to rd th ders. The lowest p value resulting from t tests of the differ- determine whether the individual 3 -to-5 -order compo- ence between infants and adults for each of these variables nents differed significantly from a mean of zero. In the was p = .337, which was considered insignificant. adult data, the components that reached a t test p value of –1 –3 0 < .05 were Z5 (p = .015) and Z5 (p=.031). The Z4 term 0.3 had a p value of .051. In the infant data, the components +2 infant that reached a t test p value of < .05 were Z4 (p=.019) and +4 0 0.2 adult Z4 (p=.026). The Z4 term for that group had a p value of .93. These values < .05, again, were not considered highly significant due to the large number of tests being per- 0.1

formed, although the adult data are consistent with the RMS Value (micron) 0 literature finding positive values of Z4 (e.g., Thibos, Hong 0 et al., 2002). Overall, these data suggest that there is no 3rd 4th 5th 6th 3rd-6th consistent trend in the sign of the coefficients within the populations, and that the infant distribution is not dra- Figure 4. RMS wavefront error for individual subjects. The data matically different from that of the adult. rd th The distributions of absolute magnitude of each are presented for each of the 3 to 6 orders separately and Zernike coefficient are shown in Figure 3, panel B. Both then as a combined higher order value. the adult and infant data in this figure are consistent with the previous adult literature in that they show a decrease in The model of an adultlike infant eye developed in the mean magnitude with increasing order (Liang & Wil- Appendix C predicts that the real infant RMS values liams, 1997; Porter, Guirao, Cox, & Williams, 2001; Thi- should equal two-thirds of the real adult values. To test bos, Hong et al., 2002; Castejon-Mochon, Lopez-Gil, this prediction, two-sample t tests were performed as a Benito, & Artal, 2002). A Hotelling T2 test suggested no function of scale factor applied to the adult data. The re- significant difference between the distribution of infant sults indicated that the infant and adult combined RMS and adult absolute coefficient values, F = 1.720, df1 = 22, (3rd to 6th order) were most similar when the adult data

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were scaled by 0.87 (the p value for the adult data scaled by the equivalent width metric (Thibos, Hong, Bradley, & the adultlike model of 0.67 was 0.076, for the adult data Applegate, 2004), which gives the width of a uniform circu- scaled by 0.8 was 0.580, scaled by 0.87 was 0.977, and lar PSF with the same intensity as the peak of the actual scaled by 0.9 was 0.793). That is, when employing the same PSF. The mean adult value was 1.57 arcmin (SD ± 0.49) numerical aperture, infant eyes have an RMS that is 0.87 and the mean infant value was 2.07 arcmin (SD ± 0.48). that of adult eyes, not the 0.67 predicted by the simple These distributions were significantly different (p = .016), scaled eye model. Thus, the data suggest that the mean implying again that the effect of higher order aberrations is higher order aberrations of the infant eye are somewhat somewhat more disruptive to retinal image quality in in- larger (by 20% of the mean adult value) than predicted by fants than in adults. An adultlike infant eye was predicted the adultlike model. This mean difference is small when to have the same angular PSF width as the real adults compared with immaturities in infants’ visual performance (Appendix C). at this age and the range of higher order aberrations seen in both adult and infant eyes. Correlation between infants and parents The fact that the adult data were collected from the in- Radial modulation transfer functions fants’ parents (9 mothers and 3 fathers) allowed us to de- Adult and infant mean optical modulation transfer termine whether an infant’s higher order aberrations were functions (MTFs) are shown in Figure 5. These functions more correlated with their parent than any of the other were calculated from the wavefront error maps. Each MTF adult subjects. The first analysis is shown in Figure 6, panel function is averaged over meridia and includes the effects A. The x-axis represents infant subject number, and the y- of aberrations from the 3rd to 6th order. These data again axis represents the correlation between that infant’s set of suggest that the infants’ higher order optical quality is 3rd-to-6th-order coefficients and an adult’s. The black sym- slightly worse than that of adults at 5 to 7 weeks after birth. bols show each infant’s correlation with their own parent, For example, at 10 c/deg, the infant optics transfer a mean and the small gray symbols show the correlation with each of 20% of the object contrast to the image, whereas adult of the other adults. The horizontal line shows the level at optics transfer a mean of 33%. Interestingly, if we compare which the correlation becomes significant at the .01 level the contrast transferred at spatial frequencies scaled to the (one-tailed test, alpha level = 0.01, df = 10, r = 0.658, with a acuity limit, we find the reverse is true. For example, at null hypothesis of zero correlation and an alternative hy- 50% of the adult resolution limit (~25 c/deg), only 11% is pothesis that the correlation is positive, with no compensa- transferred, but at 50% of the infant resolution limit tion for multiple tests). The graph demonstrates that the (~1 c/deg), 93% is transferred. Thus, although the infant correlation between individual infants and their parents is optics are inferior to those in the adult eye, they are more inconsistent across infants, and also that the range of corre- efficient at transferring a neurally detectable signal to the lations with parents across the group approximates the retinal image. range of correlations between each infant and any other adult. These correlations are typically insignificant, with only 4 (2 with parent and 2 with another adult) of the total 1 adult 144 correlations reaching significance at the 0.01 level. infant An alternative analysis is shown in Figure 6, panel B. In 0.1 this graph the x-axis represents individual Zernike coefficients, and the y-axis represents the correlation of that coefficient in the infant group with the adult group. The black

Modulation 0.01 symbols show the correlations when the infants are all aligned with their parents, and the small gray symbols show the correlations when the infants are compared with the 0.001 other possible arrangements of the adult group (each infant 0.1 1 10 100 1000 Spatial Frequency (cpd) matched with each adult only once). The horizontal line again shows the level at which the correlation becomes Figure 5. Mean and standard deviation of the infant and adult significant (one-tailed test, alpha level = 0.01, df = 20, radial-average MTF data. Aberrations from 3rd to 6th order were r = 0.492, with a null hypothesis of zero correlation and an included. Pupil sizes were set to 3 mm and 4.5 mm for infants alternative hypothesis that the correlation is positive, with and adults, respectively. no compensation for multiple tests). The aligned infant and parent correlations are very variable. The cases where the parent correlation is clearly greater than the correlation -3 -2 0 Point spread functions with other adults are Z3 , Z4 , and Z4 . The parent correla- rd th -3 0 The PSFs for the 3 -to-6 -order aberrations were calcu- tions for Z3 and Z4 are also greater than the 0.01 signifi- lated using Fourier optics. PSF width was quantified using cance level for the one-tailed test, although given the num-

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-3 -1 1 3 -4 -2 0 2 4 -5 -3 -1 1 3 5 -6 -4 -2 0 24 6

Z Z Z Z 3 4 5 6

Figure 6. A. Correlation between infant and adult 3rd-to-6th-order Zernike coefficient values. Black symbols represent the correlation between an infant and their parent across the set of coefficients. Gray symbols represent the correlation between the infant and the other adults. The line represents threshold for a significant positive correlation at the 0.01 level. B. Correlation between infant and adult distributions of each Zernike coefficient. Black symbols represent the correlation between infants aligned with their parents. Gray symbols represent the correlation between the infants and adults in a different alignment. The line represents threshold for a significant positive correlation at the 0.01 level.

ber of correlations calculated (264), this is not strong evi- adultlike refractive indices. That model predicts smaller dence of significance at least for this sample size. RMS in the infant eyes than the adult eyes by a factor of two-thirds (see Appendix C). Howland (2005) has recently Discussion developed the same prediction for equivalent optical quality in eyes of different sizes, and extended the analysis to Higher order monochromatic aberrations were meas- include relative pupil size changes in the eyes being com- ured in human infant and adult eyes. The wavefront errors pared. (defined as individual Zernike coefficients or overall wave- The infant and adult RMS data were most similar front RMS) of 5-to-7-week-old eyes differed little from adult when the adult data were scaled by a factor of 0.87, suggest- eyes when the pupil size was scaled to maintain a constant ing that the infant aberrations are somewhat greater than numerical aperture. The ratio of infant to adult natural the adultlike prediction. There are a number of possible pupil sizes in these experimental conditions was consistent explanations for this result. with the constant numerical aperture scaling, and therefore We were unable to direct the infants’ accommodative suggests that the adult and infant wavefront errors were response to the instrument’s fogged distant target. Infants also comparable in natural viewing. aged 5-7 weeks tend to be hyperopic and to overaccommo- The RMS data are not consistent with a hypothesis that date to distant targets (Banks, 1980). Thus the infants are the infant eye is a 3D-scaled version of the adult eye with likely to have been exerting accommodative effort when the

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measurements were made. The adults could be instructed Appendix C was based on adultlike refractive indices) to fixate the target and had a range of refractive errors. The (Wood et al., 1996). adults were therefore unlikely to be matched with the infants for accommodative effort during data collection. He, Effect of higher order monochromatic Burns, and Marcos (2000) (first 35 terms with defocus ex- aberrations on visual performance nd th cluded) and Cheng, Barnett et al. (2004) (2 to 6 order The poorer MTFs (Figure 5) and larger equivalent excluding defocus) have both noted minimal change in width of the 5-to-7-week-old higher order PSFs both suggest adult higher order RMS for accommodative efforts from a slightly inferior image quality relative to adults. This dif- 0-3 D, but an increase in RMS of almost a factor of 2 be- ference may be due to the accommodative or fixation fac- tween 3 D and 6 D of effort. If the infant eyes also exhibit tors mentioned above or be fully attributable to fundamen- this behavior, the relatively greater RMS in the infant eyes tal differences in optical quality. This likely upper bound could result from their increased accommodative effort. If estimate of the difference between infants and adults can this were the case, the infant RMS may actually be closer to be approximated in diopters of defocus using the concept the adult prediction for a matched accommodative re- of “equivalent defocus” (Thibos, Hong et al., 2002; see sponse (although any increase in aberrations associated Equation 2 in Appendix C). This conversion provides the with the myopic refractive errors of the adults could negate diopters of defocus necessary to generate the same level of the increase due to the accommodation in the infants wavefront RMS. The 3rd-to-6th-order RMS of adult and in- (Collins, Wildsoet, & Atchison,1995; Carkeet, Luo, Tong, fant eyes are equivalent to 0.22 D (SD ± 0.09) and 0.43D Saw, & Tan, 2002; Llorente, Barbero, Cano, Dorronsoro, (SD ± 0.13), respectively, and thus the difference between & Marcos, 2004; but see Cheng, Bradley, Hong, & Thibos, them is equivalent to 0.21 D of defocus. 2003). The cutoff of the preferential-looking contrast sensitiv- The studies of aberrations as a function of accommoda- ity function at 5-7 weeks old is approximately 2 cycles/deg tion in adults have also demonstrated that spherical aberra- (Atkinson, Braddick, & Moar, 1977; Banks & Salapatek, 0 tion (Z4 ) becomes less positive with increasing accommoda- 1978). A visual system with this acuity is not sensitive to tion (He et al., 2000; Cheng, Barnett et al., 2004). If this is subtle changes in focus, as quantified by Green, Powers, also true in infants, the spherical aberration data (Figure 3) and Banks (1980), who predicted a depth of focus of ap- are also consistent with the infants exerting a greater ac- proximately ± 1 D at this age (based on infants’ acuity and 0 commodative effort than the adults. The mean Z4 coeffi- pupil size). Thus the 0.43 D of absolute equivalent defocus cient is less positive in the infants than in the adults. An is unlikely to have a large impact on infants’ visual per- alternative interpretation of these data is that the positive formance, and the 0.21 D increase relative to adults would 0 increase in mean Z4 with age is consistent with the same have even less effect. trend seen across the adult age range (McLellan, Marcos, & It is also interesting to note that the Nyquist limit of Burns, 2001; Glasser & Campbell, 1998). the foveal infant photoreceptor array falls well within the Poor fixation control in the infant group might provide bandwidth of their OTF. Based on inner segment spacing, another explanation for the relatively larger RMS aberra- Candy et al. (1998) calculated a newborn foveal Nyquist tions in the infant eyes. The adult aberrations were meas- limit of approximately 15 cpd. Based on the MTF data in ured along the line of sight, but this may not be the case for Figure 5, the 5-to-7-week-old infant eye would pass more the infant eyes. Our observation of pupil and Purkinje im- than 10% of the contrast in a stimulus at that spatial fre- ages indicates that the infant data were collected within ± quency. These data support the potential for aliasing of 10 deg of the pupillary axis. Optical aberrations tend to periodic patterns in the young infant eye, although the ef- increase with increasing eccentricity in adults (Jennings & fect of any aliasing on perception will depend on the spatial Charman, 1981; Navarro, Moreno, & Dorronsoro, 1998; frequency and contrast of the alias itself, plus the amounts Cheng, Himebaugh et al., 2004), and if infant eyes demon- of lower order aberrations—defocus and astigmatism—in the strate the same characteristic, it is possible that the infant image. Foveal vision in the adult eye is protected from alias- aberrations would have been slightly lower if we were able ing because the optics of the eye do not transmit sufficient to measure them closer to the line of sight. If correct, this contrast at spatial frequencies higher than the Nyquist limit explanation also implies that foveal retinal image quality in of the photoreceptor sampling array (Campbell & Green, the infant eye may actually be even more similar to that of 1965; Williams, 1985). adults than we have observed. Alternatively, if the relative increase in infant RMS is a true indication that the infant aberrations are greater than The role of monochromatic aberrations in the adult eye, this increase may result from the immature in the development of the visual system steeper and more powerful dimensions of the ocular struc- It has been shown that adult observers can distinguish tures (e.g., Mandell, 1967; Inagaki, 1986; Insler et al., hyperopic from myopic defocus using higher order mono- 1987) or the infant eye having a higher refractive index chromatic aberrations in defocused PSFs (Wilson et al., than found in adults (the adultlike prediction generated in 2002). It has also been suggested that these differences in

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the PSFs may play a role in the control of both infant ac- eyes of infants and their parents. For this sample size, there commodation and emmetropization processes (reviewed by was no consistent correlation between the set of coefficients Wallman & Winawer, 2004). We have examined the na- in an infant and their parent, and the range of correlations ture of this cue derived from our aberration data. Using for related individuals approximated that between infants Fourier optics, we computed PSFs for three representative and unrelated adults. It is possible, however, that the corre- infant eyes for a range of defocus levels (a through-focus lations would have been higher if the parent and infant analysis of the PSF). These PSFs are shown in Figure 7. It is aberrations could be compared at the same age. The par- clear that positive and negative defocus generate dis- ent’s aberrations may have more closely correlated with criminable PSFs in two of the three infants (A and C) and their infant’s during their own infancy, but then have thus that the cue could be used to control the direction of changed as their eye grew or their refractive error changed accommodation and emmetropization in these individuals. (Artal et al., 2001). However, for this cue to be employed, it must be detect- The coefficient showing the most significant positive 0 able. Its visibility will therefore once more depend on pho- correlation between infants and their parents was Z4 toreceptor sampling and neural processing of the image, as spherical aberration (even though it had one of the larger in the case of spatial aliases. differences between adult and infant mean amplitudes in The variability of the Zernike coefficients across indi- Figure 3). There is some evidence of a correlation between viduals also implies that the PSF can be dramatically differ- the amount of spherical aberration and refractive error in ent for any two infants (as shown in Figure 7). This variabil- adults (Collins et al., 1995; Carkeet et al., 2002; Llorente et ity suggests that any mechanism responsible for interpreting al., 2004; but see Cheng, Bradley et al., 2003), and so it defocus in the PSF using higher order aberrations would could be interesting to explore more closely this coefficient need to be calibrated for the individual’s optics. The accu- and its relationship with current and future refractive error racy of the interpretation might also be strongly influenced in infants. Overall, these correlations might obviously be by changes in an individual’s ocular aberrations with increased if the infant alignment were controlled. growth of the eye (Kelly et al., 2004; Artal et al., 2001). The low levels of monochromatic aberrations and the Given the hereditary component of myopia develop- population means of approximately zero for almost every ment in humans (Hammond, Snieder, Gilbert, & Spector, aberration in adults (Liang & Williams, 1997; Porter et al., 2001; Rose, Morgan, Smith, & Mitchell, 2002; Mutti, 2001; Thibos, Hong et al., 2002; Castejon-Mochon et al., Mitchell, Moeschberger, Jones, & Zadnik, 2002), one might 2002) combined with the elegant compensatory relation- ask whether there is a correlation between the optics of the ship between the corneal and lenticular aberrations (Artal

Figure 7. Through-focus PSFs for three infants. In each case defined amounts of defocus were added to the higher order (3rd to 6th) aberrations of the infant eye. These three individuals demonstrate the variability in PSFs across infants and the differing effects of defocus. Positive and negative defocus have different effects for infants A and C, but equal effects on the PSF of infant B (this difference between infants is the result of individual differences in the ratio of even- and odd-order aberrations).

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et al., 2001; Kelly et al., 2004) are possibly indicative of a adults (greatest density in the macula region and least in postnatal emmetropization-like process that refines higher the periphery) was reversed in their fetal and neonatal eyes. order aberrations (Kelly et al., 2004). However, the observa- Streeten (1969, p. 393) also notes a delay in RPE pigmenta- tions from our infant eyes, that they also have low levels of tion in the macula until well into infancy. Her data docu- aberrations and that their population means are also almost ment a reduced RPE cell density in the posterior pole in zero, seem to suggest that if present any active feedback the neonatal period with a later cell migration into the process does not change the overall aberrations of the eye macular area. An adultlike or higher RPE cell density was dramatically. found in the neonate only at eccentricities in the mid- periphery or beyond. Robb (1985) also notes a postnatal Appendix A migration of RPE cells toward the macular area during the first 6 postnatal months. These data suggest that the infant After performing routine calculations to confirm that RPE in the posterior pole does not contain a higher pig- the retinal exposure generated by the COAS falls within ment density than found at the same location in the adult. ANSI standards established for adult eyes (ANSI Z136.1, If anything, these lines of evidence suggest that the 2000), the question that remains is whether the biological 850-nm image formed on the retina in the posterior pole tissue in the developing infant eye is more susceptible to should result in less temperature elevation in the infant eye damage than in the adult eye. Is the human threshold for than in the adult. light damage lower in the developing eye than in the ma- ture eye? This question cannot be answered definitively in animal models because of potential species differences. A Appendix B theoretical analysis of relevant immaturities in the human The optical quality of the adult eye varies as a function infant eye was therefore undertaken before conducting this of retinal eccentricity (e.g., Navarro, Artal, & Williams, study. 1993). It is likely that this is also the case for the infant eye. The super-luminescent diode in the COAS system gen- We, therefore, wanted to estimate the eccentricity at which erates an image of a point source on the retina at a wave- the aberration measurements were recorded from infants to length of 850 nm. This wavelength presents a potential help determine how closely the data represented foveal op- photothermal hazard to the posterior segment of the eye, tical quality. The data were collected only when the 1st Pur- through heat generation and temperature elevation in kinje images generated by the LEDs around the instru- structures containing pigments that absorb near infrared ment’s viewing aperture all fell within the entrance pupil (IR) (Sliney & Wolbarsht, 1980, p. 126). (a typical situation is shown in Figure B1). This inclusion The risk to photoreceptors in adults is small because criterion limited the angular deviation of the pupillary axis the photopigments absorb very little at this wavelength. Human infants have immature photoreceptors with even less photopigment than those of the adult. Yuodelis and Hendrickson (1986) found neonatal human outer segments to be shorter than those of an adult by a factor of approximately 10. Thus, infant photoreceptors would absorb even fewer photons than adult photoreceptors. After passing through the photoreceptor layer, near IR will be absorbed by the melanin pigment in the retinal pigment epithelium (RPE) or by hemoglobin in the chor- oid. The chief concern is absorption in the RPE (see Sliney & Wolbarsht, 1980, Figure 4.16). The proportion of photons absorbed by the RPE depends on the density of melanin granules in its cells, and unfortunately there is little developmental human data available on this topic. Studies have noted that the RPE has become an adultlike single layer of cells with some pigment by 2 months of gestation Figure B1. An example of the image used to align subjects dur- (Mund, Rodrigues, & Fine, 1972; Hollenberg & Spira, ing data collection. The six 1st Purkinje images have been out- 1973), and that pigment melanosomes are formed from the lined and connected with the dashed circle. The pupil has been th th 7 to 27 week of gestation (Mund et al, 1972), but the outlined using the dotted circle. Infant data were collected only absolute density of pigment has not been plotted as a func- when all Purkinje images fell inside the pupil. The misalignment tion of age. However, of relevance to the current study, of the instrument axis with the pupillary axis was estimated Friedman and Ts’o’s (1968) study of donor tissue notes using the locations of the centers of the Purkinje image and pupil that the gradient of pigment density typically found in circles.

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from the instrument axis, and thus the deviation of the line A. Constant pupil size of sight from the instrument axis. For example, if the Pur- kinje image ring had the same radius as the pupil, this criterion would force the data to be collected on the pupillary axis. The radii of the pupil and the Purkinje image ring (which depends on the individual’s corneal curvature) were not equal, however, and were not constant across observers. The fixation error tolerance therefore varied across observers. The range of pupil diameters recorded from the included infants was 3.06–4.65 mm and the Purkinje image B. 3D scaling with pupil ring, which was smaller than the pupil, was noted to have a radius greater than one-third of the pupil radius. The most extreme deviation possible, therefore, where the Purkinje image ring would be decentered the most from the pupil center, would be when the Purkinje image ring is abutting the pupil margin and has a radius of one-third of the pupil radius. In this case the ring would have a center 1–1.5 mm from the center of the pupil for this range of pupil sizes. Using a standard Hirschberg ratio of 12 deg/mm (Wick & C. Constant numerical aperture London, 1980; Riddell et al., 1994), we therefore estimate that aberration data could be collected no more than 12–18 deg from the pupillary axis. As previously stated, however, the Purkinje image ring radius was noted to be more than one-third of the pupil radius, and the ring was generally well centered on the pupil when data were collected. For the mean infant pupil size of 3.8 mm and a more typical case such as shown in Figure B1, where the ring might be decentered from the pupillary axis by one quarter of the pupil radius, the devia- Figure C1. Derivation of the adultlike infant eye model. A. The tion would equate to 0.5 mm or 6 deg. We therefore con- implications of maintaining a constant analysis pupil size, in sider it is reasonable to estimate that our infant aberration terms of numerical aperture. B. The implications of scaling a data were collected within 10 deg of the pupillary axis. pupil function in three dimensions. C. Demonstration of scaling pupil size to maintain a constant numerical aperture (defined as pupil radius divided by the distance from the center of the exit Appendix C pupil to the retina). Zernike coefficients are a representation of the summed wavefront modulation across the pupil area. pression in the axial 3rd dimension will reduce the ampli- Changing pupil size will therefore change the Zernike coef- tude of the optical path difference (OPD) by the scaling ficients that describe an otherwise identical eye (e.g., Thi- factor at all points (Figure C1B). Thus a 3D-scaled version bos, Hong et al., 2002). It might be logical to compare of the adult eye is predicted to have a total RMS that is re- adult and infant eyes for a matched pupil size to control duced from the true adult value by the scaling factor. Be- for this effect. However, the infant eye is considerably yond its simplicity, this compression model is attractive in smaller than the adult eye and so a matched pupil size cor- that it results in the same numerical aperture for the adult responds to a relatively larger aperture in the infant eye and scaled eyes and therefore light being collected over the (Figure C1A). To determine whether the higher order aber- same angle at the retina (Figure C1C). rations of the infant eye are adultlike, it was necessary to What would the prediction be for the point spread generate a prediction for an adultlike infant eye that ad- function of the adultlike scaled eye? The size of the blur dressed the fundamental difference in both eye and pupil circle on the retina in radians subtended at the exit pupil, size between infant and adult eyes. b, can be approximated using the following equation: The simplest model to test is to propose that the infant b = P * D (1) eye is merely a compressed version of the adult eye— it is smaller in all three dimensions by a constant factor (with where P is the pupil diameter in meters, and D is defocus adultlike refractive indices). Compressing the adult pupil in diopters (Smith, 1982). and wavefront by the constant factor across the 2D pupil Using Equation 1, the smaller pupil size in the scaled plane has no effect on the RMS wavefront error, but com- eye, with no change in defocus, would result in a reduction

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in the angular size of the blur circle. Does defocus remain Atkinson, J., Braddick, O., & Moar, K. (1977). Develop- constant with scaling of eye size? As described above, the ment of contrast sensitivity over the first 3 months of RMS of the aberrations is predicted to be smaller in the life in the human infant. Vision Research, 17(9), 1037- scaled eye. The change in RMS can be converted into an 1044. [PubMed] equivalent defocus, D, using the following equation: Banks, M. S. (1980). The development of visual accommo- RMS dation during early infancy. Child Development, 51(3), D = k * (2) 646-666. [PubMed] r2 Banks, M. S., & Bennett, P. J. (1988). Optical and photore- where r is the pupil radius in mm, RMS is the root mean ceptor immaturities limit the spatial and chromatic vi- square wavefront error in microns and k is a constant (Thi- sion of human neonates. Journal of the Optical Society of bos, Hong et al., 2002). America A, 5(12), 2059-2079. [PubMed] With reference to Equation 2, the pupil radius and Banks, M. S., & Salapatek, P. (1978). Acuity and contrast RMS are both predicted to decrease by the scaling factor in sensitivity in 1-, 2-, and 3-month-old human infants. the scaled eye. The equivalent dioptric defocus, D, will 2 Investigative Ophthalmology and Visual Science, 17(4), therefore increase by the scaling factor, as a result of the r 361-365. [PubMed] term in the denominator. If the equivalent defocus increases and the pupil size Bennett, A. G., & Francis, J. L. (1962). Ametropia and its decreases by the scaling factor, Equation 1 predicts that the correction. In H. Davson (Ed.), The eye: Visual optics angular size of the blur circle will be the same for the scaled and the optical space sense (Vol. 4, pp. 145). New York: model and the true adult eye. Academic Press Inc. Thus to a first approximation, the scaled eye size Boothe, R. G. (1982). Optical and neural factors limiting model, including scaling of pupil size, would predict an acuity development: Evidence obtained from a mon- RMS that is reduced by the scaling factor from the true key model. Current Eye Research, 2(3), 211-215. adult value, and an angular blur circle size that is equal to [PubMed] the true adult value (also see Howland, 2005). Brown, A. M., Dobson, V., & Maier, J. (1987). Visual acuity of human infants at scotopic, mesopic and pho- Acknowledgments topic luminances. Vision Research, 27(10), 1845-1858. [PubMed] We would like to thank the following people for their help with the project: Francois Delori and Austin Roorda Campbell, F. W., & Green, D. G. (1965). Optical and reti- for discussion of the safety issues before we undertook the nal factors affecting visual resolution. Journal of Physiol- project; Diane Goss, Grazyna Tondel, and Heather McGill ogy, 181(3), 576-593. [PubMed] for assistance with data collection; The Borish Center for Candy, T. R., & Banks, M. S. (1999). Use of an early Ophthalmic Research at Indiana University, where the nonlinearity to measure optical and receptor resolu- COAS instrument is housed; and Larry Thibos, Arthur tion in the human infant. Vision Research, 39(20), Bradley, and the Visual Optics group at Indiana University 3386-3398. [PubMed] for use of their software and helpful discussion. This re- Candy, T. R., Crowell, J. A., & Banks, M. S. (1998). Opti- search was supported by National Institutes of Health cal, receptoral, and retinal constraints on foveal and Grant EY-014460 (TRC). peripheral vision in the human neonate. Vision Re- search, 38(24), 3857-3870. [PubMed] Commercial relationships: none. Corresponding author: T. Rowan Candy. Carkeet, A., Luo, H. D., Tong, L., Saw, S. M., & Tan, D. T. Email: [email protected]. (2002). Refractive error and monochromatic aberra- Address: Indiana University School of Optometry, 800 E. tions in Singaporean children. Vision Research, 42(14), Atwater Ave, Bloomington, IN 47405. 1809-1824. [PubMed] Castejon-Mochon, J. F., Lopez-Gil, N., Benito, A., & Artal, P. (2002). Ocular wave-front aberration statistics in a References normal young population. Vision Research, 42(13), 1611-1617. [PubMed] ANSI-Z136.1. (2000). American National Standard for Safe Use of Lasers. Orlando: Laser Institute of America. Cheng, H., Barnett, J. K., Vilupuru, A. S., Marsack, J. D., Kasthurirangan, S., Applegate, R. A., et al. (2004). A Artal, P., Guirao, A., Berrio, E., & Williams, D. R. (2001). population study on changes in wave aberrations with Compensation of corneal aberrations by the internal accommodation. Journal of Vision, 4(4), 272-280. optics in the human eye. Journal of Vision, 1(1), 1-8. http://journalofvision.org/4/4/3/, doi:10.1167/4.4.3. http://journalofvision.org/1/1/1/, doi:10.1167/1.1.1. [PubMed][Article] [Pubmed][Article]

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