The mean (±1 SEM) distance logMAR acuity without astigmatism in experiment 1 was −0.06 ± 0.08, and it decreased monotonically with increasing magnitudes of induced myopic and hyperopic astigmatism for all four axes tested (Fig. 2A). Two-factor analysis of variance (ANOVA) showed that the magnitude of astigmatism had significant effects on distance acuity (F595, 9 = 172.6; p < 0.001), whereas the axis (F595, 3 = 0.75; p = 0.52) and the interaction between magnitude and axis (F595, 27 = 0.54; p = 0.97) were not significant. Post hoc Games-Howell test showed that the distance acuity without astigmatism was significantly different from those obtained with all magnitudes of induced astigmatism (p < 0.001), except with 0.5 D of induced hyperopic astigmatism (p = 0.93).
The deterioration in distance acuity was greater with induced myopic than with induced hyperopic astigmatism, with the rate of change in acuity being 0.31 logMAR per diopter of astigmatism in the former and 0.23 logMAR per diopter of astigmatism in the latter (r2 ≥ 0.97 for both; p < 0.001) (Fig. 2A). The y intercept for both regression equations was −0.13 logMAR, and it corresponded well to the distance acuity obtained without astigmatism (Fig. 2A).
The mean (±1 SEM) near logMAR acuity in experiment 1 was 0.6 ± 0.15 without astigmatism. Two-factor ANOVA showed that astigmatic magnitude had a significant effect on near acuity (F595, 9 = 57.5; p < 0.001), whereas axis (F595, 3 = 0.53; p = 0.66) and the interaction between magnitude and axis were not significant (F595, 27 = 0.18; p > 0.9). Post hoc test showed that near acuity with all magnitudes of induced myopic astigmatism (except 0.5 D) was significantly better than the acuity without astigmatism (p < 0.001). Near acuities with 0.5 and 1.0 D of induced myopic astigmatism were significantly different from each other (p = 0.01), beyond which they were not statistically significant (p > 0.9). Near acuity deteriorated slightly with induced hyperopic astigmatism, and this deterioration was significant only for 2 D of hyperopic astigmatism (p < 0.001).
Figure 2C plots histograms of the mean (± 1 SEM) near logMAR acuity obtained for the word reading and optotype recognition tasks. Data from all axes were pooled together in this analysis. Two-factor ANOVA (astigmatism magnitude × reading task) showed a statistically significant main effect of astigmatism magnitude on the near acuity (F75, 2 = 67.9; p < 0.001), with post hoc Games-Howell test showing near acuity with +1 D (words, 0.25 ± 0.01; optotypes, 0.26 ± 0.02) and +2 D (words, 0.16 ± 0.01; optotypes, 0.14 ± 0.01) induced astigmatism to be statistically significantly different from each other (p < 0.001) and from the habitual viewing condition (words, 0.38 ± 0.02; optotypes, 0.40 ± 0.03) (p < 0.001 for both). The main effect of reading task and the interaction between astigmatism magnitude and reading task were not statistically significant (p > 0.9). The nature of near task therefore did not play a crucial role in determining the near acuity of pseudophakes with induced astigmatism (Fig. 2C).
The changes in distance and near acuities with induced astigmatism were also qualitatively similar and well correlated with the corresponding changes in blur strength (r = 0.93) (Fig. 2D).
To determine the relation between the loss of distance acuity and the gain in near acuity with induced myopic astigmatism, the change in near acuity with 1 and 2 D of myopic astigmatism at all axes tested (relative to the no astigmatism condition) was plotted against the corresponding change in distance acuity for each subject (Fig. 4). Positive values of x and y axes in this figure indicated an improvement in acuity with induced astigmatism. Distance acuity deteriorated, and the corresponding near acuity improved with induced myopic astigmatism relative to no astigmatism (Fig. 4). Most data points with 2 D of induced myopic astigmatism were more negative than the 1-D data points, indicating that the former resulted in greater loss of distance acuity than the latter, with no further improvement in near acuity (Fig. 4). The change in distance and near acuities with induced myopic astigmatism was poorly correlated to each other, suggesting that the loss in distance acuity cannot be easily predicted from the gain in near acuity (r ≤ ± 0.25; p ≥ 0.66).
A reduction in pupil diameter had an overall beneficial effect on distance and near logMAR acuity with and without induced astigmatism (Fig. 3). The distance acuity loss with induced astigmatism was least with the 1.5-mm pupil diameter, followed by the 3.0- and 6.0-mm pupil diameters (Fig. 3A). Two-factor ANOVA showed a statistically significant main effect of pupil diameter (F135, 2 = 47.6; p < 0.001) and astigmatism magnitude (F135, 4 = 55.2; p < 0.001) on distance acuity of pseudophakes (Fig. 3A). Post hoc Games-Howell test showed that distance acuities for all three pupil diameters were significantly different from each other (p < 0.01). The distance acuities for all magnitudes of astigmatism were also significantly different from each other (p < 0.01). The interaction between pupil diameter and astigmatism magnitude was statistically significant (F135, 8 = 1.32; p = 0.009), indicating that the changes in distance acuity with induced astigmatism depended on the pupil diameter.
Near acuity also changed significantly with pupil diameter (F135, 2 = 44.1; p < 0.001) and astigmatism magnitude (F135, 4 = 57.2; p < 0.001) (Fig. 3B). Post hoc Games-Howell test showed that near acuities with all three pupil diameters were significantly different from each other (p < 0.01). The near acuities for all magnitudes of astigmatism (except between 1 and 2 D of myopic astigmatism) were significantly different from each other (p < 0.01). The interaction between pupil diameter and astigmatism was not statistically significant (F135, 8 = 0.32; p = 0.23), indicating that the magnitude of near acuity change with induced astigmatism was independent of pupil diameter.
This study determined the impact of uncorrected astigmatism on monocular distance and near logMAR acuity of pseudophakes with monofocal IOL implants. This was achieved by inducing astigmatic errors of various magnitudes and axes before one eye of otherwise emmetropic pseudophakes. The key findings of this study are as follows:
1) Distance acuity deteriorated significantly with increasing magnitudes of induced astigmatism for all axes tested (Fig. 2A). The loss in distance acuity was greater for induced myopic astigmatism than for induced hyperopic astigmatism (Figs. 2A).
2) Near acuity was relatively poor without astigmatism, and it improved with up to 1 D of induced myopic astigmatism before saturating for all axes tested (Fig. 2B). Near acuity deteriorated with induced hyperopic astigmatism for all axes tested (Fig. 2B).
3) The deterioration in distance acuity with induced astigmatism was lesser for smaller pupils (Fig. 3A). The corresponding improvement in near acuity with induced myopic astigmatism was similar for all pupil diameters (Fig. 3A).
4) The empirical trends in acuity were qualitatively similar and well correlated to the changes in magnitude of blur experienced by the pseudophakic eye (Figs. 1C, D; 2D).
These results have important implications for the management of astigmatism in pseudophakic eyes. It is apparent that uncorrected myopic astigmatism has a beneficial effect on monocular near acuity of pseudophakes implanted with monofocal IOL (Figs. 2–4). Near acuity improves from about 0.6 logMAR units without astigmatism to about 0.4 logMAR units with 1 D of induced myopic astigmatism, beyond which near acuity leveled off (Fig. 2B). The latter acuity roughly corresponds to the size of a newspaper print, suggesting that pseudophakes may be able to perform their routine near tasks with this magnitude of uncorrected myopic astigmatism. The restoration of near vision with induced myopic astigmatism is however only partial, as indicated by the fact that the best-corrected near acuity of all participants was better than or equal to 0 logMAR units. Tasks requiring very fine near acuity may therefore require additional near-vision correction.
The strategy of leaving myopic astigmatism uncorrected for restoring near vision of pseudophakes must be considered in the context of the associated loss in distance acuity. Indeed, distance acuity deteriorated monotonically with increasing myopic astigmatism even while near acuity leveled off beyond 1 D of myopic astigmatism (Figs. 2–4). Therefore, while uncorrected myopic astigmatism may be considered as a strategy for optimizing distance and near vision of pseudophakes, only up to 1 D of myopic astigmatism may be left uncorrected to partially restore near vision, without introducing a large compromise in distance vision. Beyond this magnitude, the visual experience of pseudophakic eyes may be suboptimal because of a large loss in distance acuity, at no additional benefit to near acuity. Residual hyperopic astigmatism must be fully corrected in pseudophakic eyes to avoid deterioration of distance and near vision (Figs. 2, 3).
The changes in distance and near acuity with induced astigmatism can be readily explained from the underlying changes in the magnitude of blur strength (Fig. 1). Notably, the improvement in near acuity with induced myopic astigmatism (or plus cylindrical lenses) is caused by the overall reduction in the magnitude of hyperopic blur induced by the shift in the location of one of the focal planes toward the retina and may not necessarily be caused by the meridional blur induced by uncorrected myopic astigmatism. Conversely, the worsening of near acuity with induced hyperopic astigmatism (or negative cylindrical lenses) is caused by an increase in the magnitude of hyperopic blur induced by the shift in one of the focal planes away from the retina. Similar logic can be applied to explain the loss in distance acuity with both induced myopic and hyperopic astigmatisms.
Changes in distance and near acuity were similar for all four axes of induced astigmatism, suggesting that the axis of uncorrected astigmatism has no bearing on the visual experience as long as the magnitude of astigmatism is optimized (Fig. 2). This result is similar to that observed by Remon et al.22 for five different axes of induced myopic astigmatism in young phakic eyes. However, this result differs from those of studies that report better near acuity in pseudophakes with uncorrected against-the-rule myopic astigmatism than with uncorrected with-the-rule myopic astigmatism.8,11–13 The difference in results may arise from the fact that earlier studies determined near acuity with habitual uncorrected astigmatism, whereas the current study determined near acuity with induced astigmatism. Adaptation to astigmatic blur is orientation dependent,16,23 and, perhaps, pseudophakes in the former group adapted to against-the-rule astigmatic blur more than to with-the-rule astigmatic blur. Although short-term adaptation to astigmatic blur has been reported previously,16,24 it seems unlikely in this study because the magnitude, axis, and polarity of astigmatic blur varied continuously and randomly during the experimental period.
A reduction in pupil diameter had a significant beneficial impact on the distance and near acuity of pseudophakes without astigmatism (Fig. 3). Although not measured, reduced pupil diameter may also have resulted in better habitual near acuity for subjects who participated in the control experiment (∼0.4 logMAR units) than those of the entire cohort (∼0.6 logMAR units) (compare Fig. 2B, C). The magnitude of deterioration in distance acuity with induced astigmatism was lesser for smaller pupil diameters, whereas the corresponding improvement in near acuity was about the same for all pupil diameters (Fig. 3). These results suggest that pupillary miosis would supplement the beneficial impact of uncorrected myopic astigmatism in improving near vision of pseudophakic eyes. Overall, these results are completely predicted from the reduction in size of the blur patch and widening of depth of focus that occurs with a reduction in pupil diameter.25,26
Induced myopic astigmatism resulted in greater loss of distance acuity than induced hyperopic astigmatism (Fig. 2A). This is similar to the observations of Ravikumar et al.,27 Ohlendorf et al.,28,29 and Atchison and Mathur18 on young phakic eyes. This difference may be caused by variations in the accommodative state of the eye with induced astigmatism—eyes with hyperopic astigmatism could accommodate to place the circle of least confusion on the retina, thereby experiencing slightly better acuity than eyes with myopic astigmatism.28,30 The current study in pseudophakes however suggests only a minimal role of accommodation in causing this difference. The typical anterior movement of a monofocal IOL to increase optical power during attempted accommodation (∼0.05 mm31) seems too small to account for the observed differences in acuity (1.0 mm anterior movement of a 20-D IOL in an eye with 24-mm axial length generates a power change of about 1.3 D).32 Alternately, the observed difference in distance acuity could arise from the way myopic and hyperopic astigmatisms interact with the eye’s higher order optical abberrations33,34 or be caused by differences in phase shifts induced in the retinal image with astigmatic blur.27 Further experiments are required to address these possibilities in detail.
Monocular near logMAR acuity of pseudophakes improves with up to 1 D of uncorrected myopic astigmatism but only with a proportional loss in distance acuity. The visual experience may be suboptimal beyond this magnitude because of a large loss of distance acuity at no additional benefit to near vision. Leaving myopic astigmatism uncorrected for optimizing near vision of pseudophakic eyes must therefore be considered in the context of the associated loss in distance vision. The beneficial effect of uncorrected myopic astigmatism may be further supplemented in pseudophakes with smaller pupil diameters. Both distance and near acuity deteriorate with uncorrected hyperopic astigmatism, and it should be fully corrected after cataract surgery.
Shrikant R. Bharadwaj
Prof. Brien Holden Centre for Eye Research
Hyderabad Eye Research Foundation
L. V. Prasad Eye Institute
Road no. 2 Banjara Hills
Hyderabad—500034 Andhra Pradesh
This work was supported by the Ramalingaswami Fellowship from the Government of India Department of Biotechnology to Dr. S. R. Bharadwaj.
The authors have no proprietary or commercial interest in any materials discussed in this article.
Received October 1, 2012; accepted December 30, 2012.
1. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg 1993; 19: 524–33.
2. Aristodemou P, Knox Cartwright NE, Sparrow JM, Johnston RL. Formula choice: Hoffer Q, Holladay 1, or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J Cataract Refract Surg 2011; 37: 63–71.
3. Lee AC, Qazi MA, Pepose JS. Biometry and intraocular lens power calculation. Curr Opin Ophthalmol 2008; 19: 13–7.
4. Bourne RR, Dineen BP, Huq DM, Ali SM, Johnson GJ. Correction of refractive error in the adult population of Bangladesh: meeting the unmet need. Invest Ophthalmol Vis Sci 2004; 45: 410–7.
5. Keay L, Gandhi M, Brady C, Ali FS, Mathur U, Munoz B, Friedman DS. A randomized clinical trial to evaluate ready-made spectacles in an adult population in India. Int J Epidemiol 2010; 39: 877–88.
6. Zeng Y, Keay L, He M, Mai J, Munoz B, Brady C, Friedman DS. A randomized, clinical trial evaluating ready-made and custom spectacles delivered via a school-based screening program in China. Ophthalmology 2009; 116: 1839–45.
7. Huber C. Planned myopic astigmatism as a substitute for accommodation in pseudophakia. J Am Intraocul Implant Soc 1981; 7: 244–9.
8. Nanavaty MA, Vasavada AR, Patel AS, Raj SM, Desai TH. Analysis of patients with good uncorrected distance and near vision after monofocal intraocular lens implantation. J Cataract Refract Surg 2006; 32: 1091–7.
9. Savage H, Rothstein M, Davuluri G, El Ghormli L, Zaetta DM. Myopic astigmatism and presbyopia trial. Am J Ophthalmol 2003; 135: 628–32.
10. Bradbury JA, Hillman JS, Cassells-Brown A. Optimal postoperative refraction for good unaided near and distance vision with monofocal intraocular lenses. Br J Ophthalmol 1992; 76: 300–2.
11. Verzella F, Calossi A. Multifocal effect of against-the-rule myopic astigmatism in pseudophakic eyes. Refract Corneal Surg 1993; 9: 58–61.
12. Nagpal KM, Desai C, Trivedi RH, Vasavada AR. Is pseudophakic astigmatism a desirable goal? Indian J Ophthalmol 2000; 48: 213–6.
13. Trindade F, Oliveira A, Frasson M. Benefit of against-the-rule astigmatism to uncorrected near acuity. J Cataract Refract Surg 1997; 23: 82–5.
14. Sawusch MR, Guyton DL. Optimal astigmatism to enhance depth of focus after cataract surgery. Ophthalmology 1991; 98: 1025–9.
15. Naeser K, Hjortdal J. Optimal refraction with monofocal intraocular lenses: no beneficial effect of astigmatism. Acta Ophthalmol 2011; 89: 111–5.
16. Sawides L, Marcos S, Ravikumar S, Thibos L, Bradley A, Webster M. Adaptation to astigmatic blur. J Vis 2010; 10: 22.
17. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci 1997; 74: 367–75.
18. Atchison DA, Mathur A. Visual acuity with astigmatic blur. Optom Vis Sci 2011; 88: 798–805.
19. Raasch TW. Spherocylindrical refractive errors and visual acuity. Optom Vis Sci 1995; 72: 272–5.
20. Bailey IL, Lovie JE. New design principles for visual acuity letter charts. Am J Optom Physiol Opt 1976; 53: 740–5.
21. Bailey IL, Lovie JE. The design and use of a new near-vision chart. Am J Optom Physiol Opt 1980; 57: 378–87.
22. Remon L, Tornel M, Furlan WD. Visual acuity in simple myopic astigmatism: influence of cylinder axis. Optom Vis Sci 2006; 83: 311–5.
23. Ohlendorf A, Tabernero J, Schaeffel F. Neuronal adaptation to simulated and optically-induced astigmatic defocus. Vision Res 2011; 51: 529–34.
24. Vinas M, Sawides L, de Gracia P, Marcos S. Perceptual adaptation to the correction of natural astigmatism. PLoS One 2012; 7: e46361.
25. Charman WN, Whitefoot H. Pupil diameter and the depth-of-field of the human eye as measured by laser speckle. Optica Acta 1977; 24: 1211–6.
26. Ogle KN, Schwartz JT. Depth of focus of the human eye. J Opt Soc Am 1959; 49: 273–80.
27. Ravikumar S, Bradley A, Thibos L. Phase changes induced by optical aberrations degrade letter and face acuity. J Vis 2010; 10: 18.
28. Ohlendorf A, Schaeffel F. Effects of astigmatic defocus on visual acuity, contrast sensitivity and contrast adaptation. Invest Ophthalmol Vis Sci 2011; 52;E-Abstract 1898.
29. Ohlendorf A, Tabernero J, Schaeffel F. Visual acuity with simulated and real astigmatic defocus. Optom Vis Sci 2011; 88: 562–9.
30. Stark LR, Strang NC, Atchison DA. Dynamic accommodation response in the presence of astigmatism. J Opt Soc Am (A) 2003; 20: 2228–36.
31. Nawa Y, Ueda T, Nakatsuka M, Tsuji H, Marutani H, Hara Y, Uozato H. Accommodation obtained per 1.0 mm forward movement of a posterior chamber intraocular lens. J Cataract Refract Surg 2003; 29: 2069–72.
32. Tsorbatzoglou A, Nemeth G, Math J, Berta A. Pseudophakic accommodation and pseudoaccommodation under physiological conditions measured with partial coherence interferometry. J Cataract Refract Surg 2006; 32: 1345–50.
33. Cheng X, Bradley A, Thibos LN. Predicting subjective judgment of best focus with objective image quality metrics. J Vis 2004; 4: 310–21.
34. de Gracia P, Dorronsoro C, Marin G, Hernandez M, Marcos S. Visual acuity under combined astigmatism and coma: optical and neural adaptation effects. J Vis 2011; 11: 5.
Keywords:© 2013 American Academy of Optometry
acuity; astigmatism; axis; blur; hyperopia; monocular; myopia; pupil