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From the Department of Biology, City College, City University of New York, New York, New York.
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METHODS. Chicks were fitted with mixed astigmatic (toric) lenses with +5 D on one meridian and -5 D on the orthogonal meridian (Jackson crossed cylinders), thus producing massive blur while having no spherical equivalent power. Chicks wore these lenses either alone or in combination with +6 D, +3 D, -3 D, or -6 D spherical lenses. To produce a similar degree of image degradation in a different way, other chicks were fitted with weak diffusers, with or without spherical lenses.
RESULTS. Eyes fitted with astigmatic lenses alone became mildly hyperopic, whereas those fitted with weak diffusers became mildly myopic. Eyes wearing both the astigmatic and spherical lenses compensated as completely for the spherical lenses as did the eyes wearing spherical lenses alone—the compensation being caused by changes in both choroidal thickness and ocular length. Eyes wearing weak diffusers and spherical lenses also compensated but did so without a change in choroidal thickness.
CONCLUSIONS. Severe astigmatic blur does not interfere with spectacle lens compensation. From this it can be inferred that the average amount of blur is not an important error signal for spectacle lens compensation and therefore probably not for emmetropization either. These results strengthen the case that the sign of defocus is used to direct eye growth.
However, it can also be argued that the eye need not distinguish the sign of its refractive error to accomplish compensatory growth responses to positive and negative spectacle lenses. Instead, these could occur as a consequence of the eye’s growing in the direction of myopia if vision were blurred and growing in the direction of hyperopia if vision were sharp. Put differently, the amount of ocular elongation may simply reflect the average amount of blur or image degradation: If the eye sees more blur, the eye elongates more; if the eye sees less blur, it elongates less.8 This argument, which we refer to as the quantity-of-blur hypothesis depends on two premises: that young animals generally view nearby objects and that accommodation is imperfect, so that some blur remains. As a consequence, even emmetropic eyes would experience some blur, which would contribute to maintaining a normal rate of ocular elongation. Eyes with hyperopia (including that imposed by the wearing of negative lenses) would experience even more blur, which would speed ocular elongation even more, resulting in compensation for the hyperopia. Only eyes with myopia (including that imposed by positive lenses) would see sharp images, and this would halt elongation, resulting in growth toward hyperopia as the focal length of the eye continued to increase with age. Such a control mechanism would maintain emmetropia by negative feedback because errors in the direction of hyperopia would increase blur and hence elongation, thereby reducing the hyperopia, whereas errors in the direction of myopia would decrease blur and elongation, thereby reducing the myopia, thus in both cases tending to drive the eye back toward emmetropia.
If this quantity-of-blur hypothesis is correct, any device that increases blur, even without creating a net spherical refractive error, would have several consequences. First, it would drive an emmetropic eye toward myopia. Second, it would increase the response to negative spectacle lenses by adding to the blur-driven compensatory ocular elongation. Third, it would reduce the effect of positive spectacle lenses by reducing the sharp vision, thus reducing the predicted slowing of ocular elongation that would lead to compensatory hyperopia. We tested whether the average amount of blur guides eye growth, by raising chicks with mixed astigmatic (toric) lenses without spherical equivalent power (Jackson crossed-cylinder lenses, +5 D along one axis, -5 D along the orthogonal axis; called here, +5/-5-D lenses or simply astigmatic lenses). By having chicks wear these lenses, we tested whether the greatly increased blur would drive the eye toward myopia. By having them worn together with spherical lenses, we tested whether the additional average blur would augment the effect of negative lenses and subtract from the effect of positive lenses. For comparison, to increase the overall level of image degradation in a manner different from the astigmatic lenses, we superimposed weak diffusers on the spectacle lenses. Unlike strong diffusers, which prevent form vision and therefore result in form-deprivation myopia, weak diffusers permit impaired form vision and cause only mild myopia in both chicks and monkeys.9 10
To clarify the way in which spherical lenses and our astigmatic lenses add, Figure 1 shows how several lenses affect the size of the blur circle of a point source at different image planes. Note that the crossed astigmatic lenses that we used (Jackson crossed cylinders), although they have no spherical power, cause the blur circle to be the same size on the retina as in an eye wearing a +5-D or a -5-D lens. This arises because, in one meridian, the crossed astigmatic lens would focus light exactly like a +5-D lens, whereas in the orthogonal meridian it would focus light like a -5-D lens.11 12 As the image plane is moved either in front of or behind the retina (by changing the state of accommodation or by adding a spherical lens), the blur circle of a point source in an eye wearing the astigmatic lens becomes an increasingly elongated ellipse until one orientation is correctly focused, whereas the orthogonal orientation is 10 D out of focus—all other orientations being substantially blurred in any plane. As a consequence, if the image of an object were moved back and forth within this interval (the interval of Sturm), the image would not be brought in and out of focus, but instead the focus along one astigmatic meridian would improve at the expense of the quality of focus along the orthogonal meridian. Therefore, the average quality of focus (or the average blur) would change much less than normal as the object was moved back and forth. One could say that the depth of focus of the eye has been greatly increased by adding the astigmatic lens, because it now requires a larger defocus to cause a detectable change in the average defocus.
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Finally, this experiment also permitted us to test the claim that the chick eye can compensate for imposed astigmatism.2 15 We investigated whether eyes wearing our +5/-5-D astigmatic lenses would develop a compensatory astigmatism dependent on the lens orientation.
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Lenses
Lenses were attached to rigid plastic rings mounted on Velcro support rings. Mated Velcro rings were attached with collodion to the feathers around one eye of each bird. Astigmatic lenses with +5 D along one axis and -5 D along the orthogonal axis, 12 mm in diameter, were made from CR39 plastic (Tri-Supreme Optical, Farmingdale, NY). Spherical lenses (plano [no optical power], +3 D, +6 D, -3 D, and -6 D) were made from PMMA with a base curve of 7 mm and an optic zone diameter of 10 mm (Conforma Contact Lens Co., Norfolk, VA). To combine astigmatic lenses with spherical ones, the spherical lenses were placed on top of the astigmatic lenses, and both were fitted into a clear plastic tube. The resultant lenses had the following powers along their two orthogonal axes: +8/-2 D, +11/+1 D, +2/-8 D, and -1/-11 D, respectively.
Lenses were fitted over one eye at 6 days of age. To align the lenses in relation to the normal head angle, chicks were photographed from the side in their cages and an estimate made of the average angle between the horizontal and the line formed by the auditory meatus and the beak tip—an angle of 18° (beak down). Consequently, we marked the Velcro rings that the birds wore at that angle, and we fitted the astigmatic lenses either in the WTR or ATR orientation or at 45°. When combined with spherical lenses, the astigmatic lenses were always oriented at 45°. This orientation produced maximum image distortion, because it blurred the vertical and horizontal bars of the chicks’ cage. It also caused maximum image motion during horizontal or vertical head movements.
Diffusers
To obtain different degrees in reduction of image sharpness, Bangerter occlusion foils (Ryser Optik, St. Gallen, Switzerland) were used. These lightly frosted flexible diffusers are manufactured for use with human spectacle lenses. The diffusers were cut into 8-mm circles and applied wet to the posterior surface of the lenses worn by the chicks. Because of the steep curvature of the lenses, it was not possible to cover the inside of the lens completely with the diffusers, and so a white cloth ring covered the gap between the diffuser and the outer rim of the lens. This reduction in aperture size has been reported not to impair lens compensation.15 Diffusers of two different degrees (0.4 [more dense] and 0.8 [less dense]) were placed inside plano, +6-D, and -6-D lenses. As a control, +6-D, and -6-D lenses were used alone.
Optical Effects of Astigmatic Lenses and Diffusers
To characterize very approximately the optical effect on the chicken eye of the astigmatic lenses and diffusers, we photographed a scene at 25 cm with a video camera somewhat similar to the chick eye (focal length, 8 mm; pupil diameter, 4 mm). The resultant images (Fig. 2) were transformed into the spatial frequency domain and the power spectra were summed radially (Fig. 3 , calculations by NIH Image program; produced by W. Rasband, National Institutes of Health; available by ftp from zippy.nimh.nih.gov). This computation confirms the visual impression that the astigmatic lenses degrade the image more than the diffusers do. The effects of these diffusers on the human contrast sensitivity function has been described.16
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A-scan ultrasonography with a 30-MHz polymer transducer sampled at 100 MHz was used to measure internal axial dimensions (for detailed methods, see Ref. 17 ). We calculated the thickness of each axial structure from the cornea to the external scleral surface, using the appropriate velocity of sound for each structure.18 To obtain the ocular length, we summed all these distances. This measure differs from the common clinical convention of regarding axial length as the distance from cornea to retina. Because our ocular length is the length of the eye globe, it would not be affected by expansion of the choroid, which would reduce the conventional (clinical) axial length, just as it would reduce the vitreous chamber depth. Thus, we have independent measures of the two principal components of lens compensation, length of the eye and thickness of the choroid.
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Lens Compensation: Astigmatic Lenses Versus Diffusers
When the astigmatic lenses were combined with spherical lenses, the eyes compensated for the spherical error imposed as though the astigmatic lenses were not present (Fig. 5) . The change in the eye’s refractive error with either the +6-D or -6-D lenses was not significantly affected by the presence of the astigmatic lens (Fig. 5A ; change over 2 days: +6-D lens alone was +5.0 D vs. +6-D lens with astigmatic lens, which was +4.9 D; -6-D lens alone was -2.1 D vs. -6-D lens with astigmatic lens, which was -3.7 D; in both cases P > 0.05 by t-test; n = 7 to 12).
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The changes in the ocular components responsible for the refractive compensation were similar, whether or not astigmatic lenses were worn. In both cases, the change in refractive error was largely axial, as shown by the slope of 20 D/mm of the regression line between refraction and vitreous chamber depth, close to the 17 D/mm that would be predicted if only the axial length changed in birds of this age (for individual eyes, slope = 22 D/mm for spherical lenses with astigmatic lenses; 17 D/mm for spherical lenses alone; slopes not significantly different, t = 1.1, df = 20, P > 0.05; for group data, see Fig. 6A ). Furthermore, in both cases the compensation for negative lenses was accomplished principally by increased ocular elongation and secondarily by thinning of the choroid, and the compensation for positive lenses was accomplished by slowed ocular elongation and thickening of the choroid (Fig. 6B) . The eyes wearing astigmatic lenses alone showed an inhibition of ocular length without a change in choroidal thickness.
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The diffuser experiments, as well, indicate that sharp images are not required for spectacle lens compensation. The refractive compensation for spherical lenses worn together with either type of diffuser was similar to that with spherical lenses alone (Fig. 7) . Eyes wearing +6-D lenses with diffusers changed in the direction of hyperopia (mean change over 2 days with 0.8 diffuser = +3.1 D and with 0.4 diffuser = +3.0 D; in both cases P < 0.05 by t-test; n = 7–9). Eyes wearing -6-D lenses with diffusers induced eye growth in the myopic direction (mean change over 2 days with 0.8 diffuser = -2.5 D and with 0.4 diffuser = -3.5 D; in both cases P < 0.01 by t-test; n = 8–10). Thus, there was statistically significant compensation for both +6-D and -6-D lenses, despite the diffusers. Furthermore, there was no statistically significant effect of wearing either type of diffuser on the compensation for either the +6-D or -6-D lenses (P > 0.05 for all groups, n = 7–10), although there was a hint that the eyes wearing diffusers with lenses were slightly more myopic than those wearing the lenses alone, suggesting that the effects of the diffusers and the lenses are additive, but not significantly so.
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Other Effects of Imposed Astigmatism
If eyes used their intrinsic astigmatism to guide emmetropization, it would be expected that adding to or reversing this astigmatism by our imposed astigmatic lenses might cause the eye to change its refractive error in a direction that depended on the orientation of the astigmatic lens and the eye’s initial axis of astigmatism. Contrary to a published abstract,13 our results show no difference in the effect of our astigmatic lenses on spherical equivalent refraction related to the orientation of the lens (Fig. 4 ; ANOVA, F = 1.82, P > 0.05). Even restricting our analysis to 19 eyes showing WTR astigmatism, we found no evidence that the axis of astigmatism guides change in refractive status. Specifically, those wearing lenses in the WTR orientation changed by +2.8 ± 1.9 D, n = 9) over 2 days, and those wearing lenses in the ATR orientation changed by +2.2 ± 3.5 D, n = 10).
Furthermore, we did not find that eyes compensated for the imposed astigmatism. To show the changes in both the spherical refraction and astigmatism when the astigmatic lenses alone were worn, we present the refractions in relation to the first two terms of the Fourier decomposition (Fig. 8) . Clearly, most of the arrows are more horizontal than vertical, indicating that most eyes made larger spherical than astigmatic refractive changes. We found no significant differences between the eyes wearing astigmatic lenses in the WTR and ATR configurations, although there was a nonsignificant tendency for the eyes wearing astigmatic lenses in the WTR orientation to change more in spherical equivalent and in the J0 (cosine) component (P > 0.05, t-test, Fig. 8 , inset).
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Other Studies
Three other studies have tested chicks with either astigmatic blur alone, or with a combination of cylindrical and spherical blur. Thibos et al.19 found that chick eyes wearing -10 D cylinders with +5 D spheres (optically equivalent to our +5/-5-D astigmatic lenses) become 2 D more hyperopic than eyes wearing plano lenses (similar to the +2.5 D that we found). When both spherical and cylindrical blur are presented, Irving et al.15 found that cylindrical lenses causes compensation that approximated the spherical equivalent of the lenses (that is, +10-D cylinders produce +4.25 D of compensation; -9-D cylinders produce -3.5 D of compensation), and Thibos et al.19 found that -10-D astigmatic lenses result in refractions 5 D more myopic than those produced by astigmatic lenses with zero spherical power. All these results are similar to our results.
In contrast, Schmid and Wildsoet20 found that wearing simple cylindrical lenses causes nearly complete compensation for +10-D lenses and little if any compensation for -10-D lenses. They infer that the eye compensates for the more myopic meridian. This interpretation does not fit with the present results nor with those of the studies cited in the prior paragraph. Differences that may contribute to this discrepancy are that Schmid and Wildsoet20 used much longer periods of treatment, and they fitted the lenses just after hatching, an age when chicks may compensate better for positive than negative lenses (see Fig. 2 of Ref. 21 ). Indeed, in the second week of lens wear, all their groups moved in the myopic direction.20 Without knowing the response to astigmatic lenses without spherical power, it is difficult to conclude whether the response to the combination of spherical and astigmatic defocus is stronger with positive lenses, as they suggest, or stronger with negative lenses, when expressed relative to the astigmatic baseline (that is, the refraction resulting from the astigmatic lenses with zero spherical power), as our results suggest.
Monkeys have also been fitted with lenses similar to (but weaker than) our astigmatic lenses with zero spherical power. Smith et al.22 found that emmetropization was interfered with, in that some eyes stayed more hyperopic than normal. Kee et al.23 found that when one eye had the lens fitted in the ATR orientation and the other eye in the WTR orientation, the former tend to be more myopic than the latter, similar to the (nonsignificant) trend we found in chicks and to the tendency found in children that those with ATR astigmatism are more likely to become myopic.14
Implications for Quantity-of-Blur Hypothesis
The quantity-of-blur hypothesis described in the introduction argues that the refractive status of the eye is determined by a balance between enhanced ocular elongation stimulated by degraded images and inhibited ocular elongation stimulated by sharp images. Our results argue against this hypothesis on two counts: First, substantially degrading the image quality by the astigmatic lenses without spherical power caused a modest change toward hyperopia, whereas a similar degree of image degradation by a weak diffuser causes a change toward myopia. Second, eyes showed good compensation for the defocus imposed by spherical lenses, even in the face of much greater astigmatic blur. This point was shown most convincingly by the differential compensation shown for +3- and -3-D lenses despite the presence of the astigmatic lenses. In these cases, the spherical lenses would account for only 18% of the 5.8 D of blur produced by the combination of spherical and astigmatic lenses, as calculated by the method of Thibos et al.12 Nevertheless, compensation occurs, arguing that the magnitude of blur is not a parameter crucial to the compensation.
Other Possible Cues
If the quantity of blur is not the essential cue guiding lens compensation and, presumably emmetropization, what cues might be used? One cue that may survive the image degradation imposed by our crossed astigmatic lenses is the chromatic signal arising from the longitudinal chromatic aberration of the eye. Because short-wavelength light is refracted more strongly than long-wavelength light, myopically defocused objects would have the long-wavelength light sharply focused and the short-wavelength light blurred, whereas hyperopically defocused objects would have the reverse. Thus, the blur circle would be more red in the center and more blue on the outside for myopic defocus (that is, more of the blur circle would be blue than red) and the reverse for hyperopic defocus. With our astigmatic lenses, each blur circle would consist of some radial segments more red on the outside and others more blue on the outside. Averaging around the blur circle could give a veridical measure of whether the eye were myopically or hyperopically defocused, but only if the red and blue were averaged by area, not by intensity. By such a criterion, the blur circles lying on the retina in the schematic illustration in Figure 1 would be easily identifiable as emmetropic, myopic, or hyperopic, regardless of their size, by whether they were mostly red, mostly blue, or equally red and blue. Thus, the chromatic cue to defocus may not be substantially degraded by our astigmatic lenses.
Another possible cue may be that the combined effect of various monocular aberrations causes images blurred in the hyperopic direction to appear different from those blurred in the myopic direction. This manifests itself as a difference in the modulation transfer functions and, consequently, in the contrast sensitivity functions, between the two directions of defocus.24 Because these differences occur at relatively high spatial frequencies, this cue seems to be compromised by the large amount of blur our astigmatic lenses create.
Accommodation may also be used as a cue to the sign of defocus. Because hyperopic eyes would, on average, accommodate more than myopic eyes, if the brain monitored the average amount of accommodation, this would yield a measure of whether the defocus was myopic or hyperopic. If, as has been suggested, the eye were to accommodate to the meridian requiring the least accommodation, our crossed astigmatic lenses would reduce the accommodative demand and thus the amount of accommodation, thereby simulating myopia. Perhaps this accounts for the modest shift toward hyperopia that we observed when the astigmatic lenses were worn alone. However, we also expected that accommodation would be impaired by our astigmatic lenses, because changes in accommodative output would cause a much smaller change in the amount of defocus than would normally be the case, thus impairing the normal feedback that guides accommodation.
Temporal Factors
Whatever error signals are used in lens compensation, the effect of an astigmatic lens differs from that of a spherical lens or weak diffuser, in that contours aligned with one of the axes of the crossed astigmatic lens are occasionally seen in sharp focus. Thus, any process that makes use of these moments of relatively sharp vision may escape the image-degrading effects of the astigmatic lenses. Furthermore, the astigmatic lenses used in the current study would also have the effect of causing any small region of retina to experience alternating episodes of myopic and hyperopic defocus, depending on the orientation of the contours viewed. To estimate the effect of these fraction-of-a-second episodes, we would have to know their temporal distribution. Recent work has shown that alternating the wearing of positive and negative lenses on a time scale of minutes causes compensation that greatly favors the effect of the positive lenses.25 Indeed, even a few minutes a day of positive lens wear can cancel the effects of wearing negative lenses the remainder of the day.26 However, as the frequency of alternation becomes faster (e.g., 2 Hz), the net effect becomes closer to being purely additive, but still with a bias toward the positive lens.27 If the same asymmetry were true for alternations of myopic and hyperopic defocus imposed by the astigmatic lenses used in this study, this may explain the small hyperopic shift observed in eyes wearing the astigmatic lenses alone.
Differential Effects of Diffusers and Astigmatic Lenses
Our results that diffusers and astigmatic lenses have differential effects on choroidal thickness and ocular elongation raise the possibility that different retinal signals may control each. Specifically, we find that weak diffusers prevent the normal choroidal changes when spherical lenses are worn. In a related report, we show that when weak diffusers are added to positive lenses, they not only reduce the choroidal thickening, but enhance the inhibition of ocular elongation (Park T, Winawer J, Wallman J, manuscript submitted). In contrast, when astigmatic lenses are added to spherical ones, the refractive compensation involves normal changes in both choroidal thickness and ocular elongation, although the astigmatic lenses alone inhibit ocular elongation.
Astigmatism as a Cue
Beyond the effects on spectacle lens compensation, we also do not find that the axis of imposed astigmatism significantly influences spherical lens compensation, as might be expected to occur if the eye used its astigmatism as a cue to the sign of defocus. Furthermore, we find no evidence that the eye compensates for the imposed astigmatism. However, neither of these conclusions is definitive, both because we found hints of both effects and because it could be that the 10 D of astigmatism imposed by our lenses was too great to be used as an error signal by the visual system. Thibos et al.19 and Schmid and Wildsoet20 also failed to find astigmatic compensation; the latter investigators pointed out that those who had found such compensation2 15 used a different strain of chickens (broilers). From our results we tentatively conclude that the eye’s astigmatism is not used as a directional error signal in emmetropization and that imposed astigmatism is not eliminated through visual feedback. The second of these conclusions is not surprising, because lens compensation occurs primarily by changes in the back of the eye. Compensation for imposed astigmatism would require the cornea or lens to become more curved along one meridian.
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Acknowledgements |
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Footnotes |
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Submitted for publication July 6, 2001; revised July 9, 2002; accepted July 31, 2002.
Commercial relationships policy: N.
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. 
1734 solely to indicate this fact.
Corresponding author: Josh Wallman, Department of Biology, City College, City University of New York, New York, NY 10031; wallman{at}sci.ccny.cuny.edu.
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