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Optometry & Vision Science:
doi: 10.1097/OPX.0000000000000192
Original Articles

Image Quality Analysis of Pseudophakic Eyes with Uncorrected Astigmatism

Pesala, Veerendranath*; Garg, Prashant; Bharadwaj, Shrikant R.

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Author Information

*BS

MS

BS, PhD

Prof. Brien Holden Eye Research Centre, Hyderabad Eye Research Foundation, Hyderabad, Andhra Pradesh, India (VP, SRB); Cornea and Anterior Segment Services, Hyderabad Andhra Pradesh, India (PG); and Bausch and Lomb School of Optometry, L. V. Prasad Eye Institute, Hyderabad, Andhra Pradesh, India (SRB).

Shrikant R. Bharadwaj Prof. Brien Holden Eye Research Centre Hyderabad Eye Research Foundation L. V. Prasad Eye Institute Road No. 2 Banjara Hills Hyderabad 500034 Andhra Pradesh India e-mail: bharadwaj@lvpei.org

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Abstract

Purpose: To determine the combined impact of uncorrected astigmatism, pupil diameter, and wavefront aberrations on the distance and near visual performance of pseudophakic eyes with monofocal intraocular lens (IOL) implants using objective image quality (IQ) metrics.

Methods: Monocular distance (4 m) and near (40 cm) logMAR acuities of 15 emmetropic pseudophakic eyes were obtained without astigmatism and with 2.5 diopters myopic to 2.5 diopters hyperopic astigmatism induced along a 90-degree axis. The IQ metrics were calculated from the participant’s wavefront aberrations and habitual pupil diameter for all values of astigmatism and correlated with logMAR acuity. The analysis was repeated without higher-order aberrations (HOAs) and with the entire wavefront data for 6-, 3-, and 1.5-mm pupil diameters.

Results: Distance acuity deteriorated with uncorrected astigmatism (p < 0.01), whereas near acuity improved with uncorrected myopic astigmatism and deteriorated with uncorrected hyperopic astigmatism (both p < 0.01). The logEW IQ metric showed the best correlation with logMAR acuity (r = 0.86). Distance logEW values deteriorated whereas near logEW values improved in the presence of HOAs for all values of uncorrected astigmatism (p < 0.01). Distance logEW values for 6- and 3-mm pupil diameters were worse than that of the 1.5-mm pupil diameter for all values of uncorrected astigmatism and for both viewing distances (p < 0.01).

Conclusions: Image quality metrics analysis can be used successfully to determine the impact of uncorrected astigmatism, pupil diameter, and HOAs on the distance and near logMAR acuities of pseudophakic eyes with monofocal IOL implants. The improvement in near IQ with uncorrected myopic astigmatism and HOAs suggests that these two factors supplement each other to improve near visual performance of pseudophakic eyes. Such an improvement in near vision is however associated with a loss of distance vision in these eyes.

Clear vision is restored after cataract surgery using an intraocular lens (IOL) that matches the overall optical power to the axial length of the eye (pseudophakia).1,2 For eyes implanted with monofocal IOLs, the distance vision is typically maximized by full correction of the residual spherocylindrical refractive error, whereas near vision is restored using near-addition lenses. Specifically, significant effort has been expended in the recent past to correct any preexisting astigmatism or those induced after cataract surgery to maximize the patient’s distance vision (e.g., the Alpins method for analyzing astigmatism3,4 and toric IOL technology5–7). Although zero astigmatism has been the preferred end point of refraction of pseudophakic eyes, alternate strategies involving uncorrected myopic astigmatism have been suggested for improving the unaided near acuity of pseudophakes implanted with monofocal IOLs, but with a small cost to distance vision.8–13 The improvement in near vision may be greater for uncorrected against-the-rule myopic astigmatism than for uncorrected with-the-rule myopic astigmatism,9,10,12,13 although a previous study from our laboratory found no influence of astigmatic axis on the near acuity improvement.11 These results offer an attractive alternative to conventional spherocylindrical bifocals in that the residual myopic astigmatism encountered in pseudophakic eyes may be left uncorrected after cataract surgery to improve near vision, whereas their distance vision may be largely (although not perfectly) restored using low-cost, ready-made, spherical lenses.

The pseudophakic eye corrected using this strategy experiences simple myopic astigmatism for distance and compound hyperopic astigmatism for near. The effect of combined defocus and astigmatism on image quality (IQ) and visual acuity, as experienced by these pseudophakes, has been examined previously.11,14–16 Sawusch and Guyton16 and Naeser and Hjortdal14 computed the cumulative area of the Sturm conoid over a range of viewing distances (0.5 to 6 m) to determine IQ with uncorrected astigmatism. Raasch15 and Singh et al.11 modeled the combination of defocus and astigmatism as a vector with length equivalent to the square root of the sum of squares of the individual power vector terms. All studies (except that of Naeser and Hjortdal14) noted an increase in blur magnitude for distance and a reduction in blur magnitude for near with increasing magnitudes of myopic astigmatism. The changes in visual acuity correlated well with the blur magnitude, overall supporting the strategy of leaving myopic astigmatism uncorrected for improving the unaided near vision of pseudophakic eyes but with a small loss in distance vision.10,14

Although the impact of spherocylindrical refractive error on blur magnitude and IQ of pseudophakic eyes have been modeled successfully, these studies have all ignored the role of higher-order aberrations (HOAs) and pupil diameter in determining the IQ. These parameters have been shown to exert a significant influence on the eye’s IQ and visual performance.17–19 Higher-order aberrations, for instance, expand the optical depth of focus, thereby improving the out-of-focus visual acuity of the eye.20–23 The magnitude of HOA is dependent on pupil diameter, and thus, its effects will be reduced with pupil miosis.24 A comprehensive analysis of the pseudophakic eye’s optics and its correlation with visual performance (e.g., logMAR acuity) is therefore necessary to determine the realistic extent of improvement in near vision and loss in distance vision associated with the uncorrected astigmatism strategy. This knowledge can be obtained using objective IQ metrics analysis,25 similar to previous studies on simple refractive errors,26 keratoconus,27 and post–refractive surgery.28 The main aims of this study were therefore to (1) identify an IQ metric that correlated well with the logMAR acuity of pseudophakic eyes and (2) use this metric to determine the impact of pupil diameter and HOAs on the distance and near IQ of these eyes with uncorrected astigmatism.

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METHODS

Data were collected from a total of 15 unilateral pseudophakes (mean ± SEM age, 51.33 ± 2.44 years) recruited from the L. V. Prasad Eye Institute, Hyderabad, India. The study adhered to the tenets of the Declaration of Helsinki, and it commenced after subjects provided written informed consent that was duly approved by the local institutional review board. Subjects had no reported history of ocular or systemic ailments, and they all underwent uncomplicated cataract surgery with acrylic foldable monofocal IOL implantation (Acrysof, Alcon). The study was conducted at least 5 weeks after surgery, and it was ensured that the eye had no complications, with the IOL positioned appropriately in the lens bag at the time of data collection. All subjects were deemed to be emmetropic through standard refraction procedures, with best corrected acuity better than 20/40 for distance (4 m) and near (40 cm) viewing distances.

Data collection and analyses proceeded along the following six steps.

Step 1: Monocular distance and near logMAR acuities were measured in each subject without astigmatism and with 2.5 diopters (D) myopic to 2.5 D hyperopic astigmatism, induced in 0.5-D steps, along a 90-degree axis. No other axes were tested, as the previous study from our laboratory indicated no significant impact of astigmatic axis on distance and near acuities.11 Astigmatic lenses were placed on a trial frame at 14-mm vertex distance while the fellow eye was occluded (the effective powers of the largest cylindrical lenses used here differed from their expected value by only 0.2 D, which was considered insignificant). Distance acuity was determined for each lens power on a letter-by-letter basis (0.02 logMAR units allotted per letter) using English optotype charts.29 Near acuity was recorded using English word charts as the smallest line that was read correctly at least halfway through. Subjects did not wear any near-addition lenses while measuring near acuity. Five acuity charts with different combinations of optotypes were used to avoid memorization of the letter sequence. The order of lenses was also randomized such that the smallest acuity line read was different each time. All acuity measurements were made with the subject’s habitual pupil diameter (Table 1). The induced astigmatism paradigm ensured that the impact of astigmatic blur on acuity and IQ was determined systematically without the influence of confounding factors that may be present in subjects with habitual astigmatism (e.g., adaptation to astigmatic blur30).

Table 1
Table 1
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Step 2: Monocular horizontal pupil diameter of each subject was subsequently measured for distance and near viewing while the subject read the optotype charts using an open-field autorefractor (Nvision-K 5001, Tokyo, Japan). The image of the pupil displayed in the video display of the autorefractor was calibrated by placing artificial apertures of known diameter (3 to 8 mm in 1-mm steps) at the same plane where the subjects are usually positioned for data collection. The horizontal pupil diameter was measured using a millimeter rule (with 0.5-mm resolution) for each aperture size, and they were linearly regressed against the known aperture diameters to obtain a slope of 10.43 and y intercept of 0.48 mm (r2 = 0.99). These coefficients were used to scale the pupil image on the video display into physical pupil diameter.

Step 3: The pupils were subsequently dilated with 1% tropicamide HCl, and monochromatic wavefront aberration data were obtained over the central 6-mm diameter of the pupil using the Zyoptik Zywave II aberrometer (Bausch & Lomb).31 Three measurements were obtained for each subject and averaged. Zernike polynomials starting with the defocus term (C20) and up to the oblique pentafoil term (C5+5) were collected from the aberrometer and scaled to the subject’s habitual pupil diameter using the technique described by Campbell.32

Step 4: Distance and near IQ was calculated using the IQ metrics proposed by Thibos and colleagues.17 All 31 metrics described in the group was calculated for the no-astigmatism condition and for all values of induced astigmatism using standard Fourier optics techniques.17 Because all participants in the study were emmetropic, the RMS value of the defocus term was set to zero for distance and to an equivalent of 2.5 D (∼1.16 μ) for near (40 cm) for the no-astigmatism condition. All other Zernike terms remained constant throughout the analysis. The defocus and astigmatism values in diopters were converted into power vector terms (M, J0, and J45) and then into their respective Zernike micron values of defocus (C20), horizontal astigmatism (C2+2), and oblique astigmatism (C2−2) using the equations proposed by Thibos et al.17,33 Thus, for each value of uncorrected astigmatism, both the defocus and astigmatism term varied in a manner that was optically similar to what happened experimentally in step 1 for both viewing distances. All Zernike terms used in the study were scaled to the subject’s habitual pupil diameter, as described in step 3, before the IQ metrics were calculated. Pearson correlation coefficient (r value) was then calculated between the log10 transformed IQ metric values and the corresponding distance and near logMAR acuities to identify the metric that correlated best with visual performance of these pseudophakic eyes. Rendering a subject “emmetropic” through standard refraction techniques does not guarantee that all residual defocus errors were fully corrected. Residual errors that are within the subject’s blur sensitivity range or the technique’s repeatability are difficult to quantify precisely; any may have remained uncorrected. Such defocus errors were considered to be small (e.g., ≤0.25 D or 0.3 μ [for 6-mm pupil diameter] for the repeatability of the refraction34), and they were not accounted for in the IQ analysis performed here.

Step 5: To determine the impact of HOAs on the distance and near IQ of pseudophakic eyes with uncorrected astigmatism, step 4 was repeated for each subject by setting all the HOA terms (C3−3 and higher) to zero. The lower-order aberration terms were not manipulated here, and they were changed in the same way with induced astigmatism as described in step 4. This analysis was conducted only for −1 D hyperopic astigmatism, no astigmatism, and +1 and +2 D of myopic astigmatism for ease of interpreting the results.

Step 6: To determine the impact of pupil diameter on the distance and near IQ of pseudophakic eyes with uncorrected astigmatism, step 4 was repeated in all subjects with 6-, 3-, and 1.5-mm pupil diameter. Both HOAs and lower-order aberrations were present in this analysis, and their values were scaled to the desired pupil diameter using the technique described by Campbell.32 As in step 5, the pupil size analysis was performed only for − 1 D hyperopic astigmatism, no astigmatism, and +1 and +2 D of myopic astigmatism for ease of interpreting the results.

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RESULTS

Data were successfully collected from all participants. The details of the participants, along with their age, sex, distance and near pupil diameter, total RMS deviation of HOAs for 6-mm pupil diameter, and the best-corrected distance and near logMAR acuities are shown in Table 1.

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Distance and Near logMAR Acuities with Induced Astigmatism

The mean (±1 SEM) distance logMAR acuity without astigmatism was 0.00 ± 0.01, and it decreased monotonically with increasing magnitudes of myopic and hyperopic astigmatism (Fig. 1A). One-factor analysis of variance (ANOVA) showed that distance acuity varied significantly with the magnitude of induced astigmatism (F137,10 = 39.47; p < 0.001). Post hoc Games Howell test (with no assumption of equal variance) showed that the distance acuity without astigmatism was significantly different from all magnitudes of induced astigmatism (p < 0.001 for all), except with 0.5 D of hyperopic astigmatism (p = 0.21). The rate of loss in distance acuity was marginally greater for induced myopic astigmatism (0.24 logMAR units per diopter) than for induced hyperopic astigmatism (0.20 logMAR units per diopter) (r2 ≥ 0.98 for both; p < 0.001). The y intercepts of both linear regressions were close to the distance logMAR acuity without astigmatism (−0.004 logMAR for myopic astigmatism and −0.03 logMAR for hyperopic astigmatism).

Figure 1
Figure 1
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The mean (±1 SEM) near logMAR acuity was 0.68 ± 0.04 without astigmatism (Fig. 1B). Near acuity improved with increasing magnitudes of induced myopic astigmatism, whereas it deteriorated with increasing hyperopic astigmatism (Fig. 1B). One-factor ANOVA showed that near acuity changed significantly with the magnitude of induced astigmatism (F595,9 = 57.5; p < 0.001). Post hoc Games Howell 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 beyond 1.5 D of hyperopic astigmatism (p < 0.001).

The absolute value of Pearson correlation coefficient between the output of an IQ metric and logMAR acuity ranged from 0.16 to 0.86 for the 31 different metrics, with correlations of 0.8 or more seen for 11 metrics. The highest correlation coefficient was obtained for the logEW (equivalent width of centered PSF [arcmin]) metric (r = 0.86) (Fig. 2). The trends of distance and near IQ with all magnitudes of uncorrected myopic and hyperopic astigmatism were qualitatively similar to the empirical data, indicating that this metric could be used as a computational surrogate for determining the impact of HOAs and pupil diameter on the IQ of pseudophakic eyes with uncorrected astigmatism.

Figure 2
Figure 2
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Impact of HOAs on the IQ of Pseudophakic Eyes with Uncorrected Astigmatism

The mean (±1 SEM) total RMS deviations of HOAs (HORMS) of all pseudophakic eyes in this study were 0.72 ± 0.05 μ for a 6-mm pupil diameter (Table 1). The coefficients for primary spherical aberration and vertical coma were the largest in these eyes, as has been reported previously (C40 = 0.43 ± 0.06 μ and C3−1 = −0.36 ± 0.10 μ for 6-mm pupil diameters, respectively).35 For distance viewing, the IQ estimated using the logEW metric deteriorated with the magnitude of uncorrected astigmatism both in the presence and absence of HOAs (Fig. 3A). Image quality was worse in the presence of HOAs than in their absence for all values of uncorrected astigmatism, with this difference being greatest for the no-astigmatism condition (Fig. 3A). Two-factor ANOVA showed a statistically significant change in logEW metric with the magnitude of astigmatism (F112,3 = 109.9; p < 0.001) and wavefront aberrations (F112,1 = 45.8; p < 0.001]. Post hoc analysis for astigmatism magnitude indicated that the logEW output for each value of uncorrected astigmatism was statistically significantly different from all other values (p < 0.001). The interaction between astigmatism magnitude and wavefront aberrations was also statistically significant [F112,3 = 5.6; p = 0.001], indicating that the impact of HOAs on the IQ metric output was dependent on the magnitude of uncorrected astigmatism.

Figure 3
Figure 3
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For near viewing, the output of logEW metric improved in the presence of uncorrected myopic astigmatism, whereas it worsened in the presence of uncorrected hyperopic astigmatism, all relative to the no-astigmatism condition (Fig. 3A). Image quality was better in the presence of HOAs than in their absence for all values of uncorrected astigmatism—a trend that was opposite to the distance viewing trend (Fig. 3A). Two-factor ANOVA showed a statistically significant change in the logEW metric with astigmatism magnitude (F112,3 = 52.7; p < 0.001) and wavefront aberrations [F(112, 1) = 8.3; p = 0.005]. Post-hoc analysis for astigmatism magnitude indicated that the IQ metric output for each value of uncorrected astigmatism was statistically significantly different from all other values (p < 0.001). The interaction between astigmatism magnitude and wavefront aberrations was not statistically significant (p = 0.95), indicating that there was a uniform improvement in near IQ with HOAs for all values of induced astigmatism (Fig. 3A).

Overall, the results of this analysis indicated that HOAs have a significant impact on the monocular IQ of pseudophakic eyes with varying amounts of astigmatism at the 90-degree axis—HOAs deteriorate IQ for distance viewing and improve IQ for near viewing for all values of uncorrected astigmatism tested.

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Impact of Pupil Diameter on the IQ of Pseudophakic Eyes with Uncorrected Astigmatism

For distance, the logEW metric was worse for the 6-mm pupil diameter than for the 3- and 1.5-mm pupil diameters for all magnitudes of uncorrected astigmatism (Fig. 3B). Two-factor ANOVA showed a statistically significant change in logEW metric with astigmatism magnitude (F168,3 ≥ 55.4; p < 0.001) and pupil diameter (F168,2 ≥ 84.5; p < 0.001). Post hoc analysis indicated that the IQ metric for each magnitude of uncorrected astigmatism was statistically significantly different from all other magnitudes across all pupil diameters (p < 0.001). The IQ metric output for each pupil diameter was statistically significantly different from the other two (p < 0.05). The interaction between astigmatism magnitude and pupil diameter was also statistically significant (F168,3 ≥ 5.0; p ≤ 0.003), indicating that the change in this metric with uncorrected astigmatism was not uniform for all pupil diameters.

For near, the logEW metric indicated the best IQ for the 1.5-mm pupil diameter (Fig. 3B). Near IQs with the 3- and 6-mm pupil diameters were similar to each other and poorer than the 1.5-mm values (Fig. 3B). Two-factor ANOVA indicated that the output of the logEW metric changed significantly with astigmatism magnitude and pupil diameter (F168,2 ≥ 41.8; p < 0.001 for both). Post hoc analysis indicated that the IQ metric for each magnitude of uncorrected astigmatism was overall significantly different from all other magnitudes across all pupil diameters (p < 0.001). Post hoc analysis for pupil diameter showed the general trend of the uncorrected near IQ quality to be best for 1.5-mm pupil diameter, followed by the 3- and 6-mm pupil diameters (Fig. 3B). Near IQ for the 3-mm pupil diameter was statistically significantly better than that of the 6-mm pupil diameter only for 1 D of uncorrected myopic astigmatism (p < 0.001). The interaction between astigmatism magnitude and pupil diameter was statistically significant for the logEW metric (F168,2 ≥ 3.2; p ≤ 0.005), indicating that the change in this metric with uncorrected astigmatism was not uniform for all pupil diameters.

Both the HOA and pupil diameter analyses were repeated for 45-, 135-, and 180-degree axes of astigmatism to determine if the results previously described varied with the axis of astigmatism. The results were identical to those obtained for the 90-degree axis (Fig. 3), indicating that the axis of uncorrected astigmatism did not have any impact on the observed changes in IQ.

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DISCUSSION

The IQ metrics described previously offer a comprehensive way of quantifying the image quality of an eye for a given combination of higher- and lower-order wavefront aberrations and pupil diameter. In this study, IQ metrics were calculated for distance and near viewing from the participant’s own wavefront aberrations and habitual pupil diameter for a range of uncorrected astigmatism, and these were correlated with the corresponding logMAR acuity values. Four key results were observed:

1. Distance logMAR acuity deteriorated with induced myopic and hyperopic astigmatism, whereas near logMAR acuity improved with induced myopic astigmatism and deteriorated with induced hyperopic astigmatism (Fig. 1).

2. Eleven IQ metrics had excellent correlation with logMAR acuity (absolute value of r ≥ 0.80), with the logEW metric correlating best with logMAR acuity (r = 0.86) (Fig. 2).

3. The presence of HOAs deteriorated distance IQ and improved near IQ of pseudophakic eyes with monofocal IOL implants for all values of uncorrected astigmatism (Fig. 3A).

4. Distance IQ of pseudophakic eyes deteriorated systematically with an increase in pupil diameter (Fig. 3B). Near IQ of pseudophakic eyes was best with the 1.5-mm pupil diameter (Fig. 3B). Near IQs with 3- and 6-mm pupil diameters were poorer than the 1.5-mm values, but they were not significantly different from each other, except for 1 D of uncorrected myopic astigmatism (Fig. 3B).

The changes in distance and near logMAR acuities with different magnitudes of induced astigmatism obtained in this study are very similar to our previous study on a different set of pseudophakes with monofocal IOL implants11 and by others on pseudophakes with habitual uncorrected astigmatism (Fig. 1).8–10,12,13 These results reinforce the notion that myopic astigmatism may be left uncorrected in pseudophakes with monofocal IOL implants to improve their monocular unaided near vision (Fig. 1B). This improvement comes, however, with an associated loss of distance vision (Fig. 1A). Induced hyperopic astigmatism results in a loss of both distance and near vision (Fig. 1). Both the axial and lateral characteristics of the retinal blur circle changed in this study for distance and near viewing. For near viewing, the circle of least confusion, an axial descriptor of blur circle size, shifts toward the retina in the presence of uncorrected myopic astigmatism, thereby reducing the magnitude of hyperopic blur, while it shifts away from the retina in the presence of uncorrected hyperopic astigmatism, thereby increasing the magnitude of hyperopic blur. For distance, the circle of least confusion moves away from the retina for both uncorrected myopic and hyperopic astigmatism. This change in axial blur circle size coupled with changes in the lateral characteristics of the blur circle induced by HOAs may explain the distance and near logMAR acuity results obtained in this study.

The near IQ trends support the belief of an improvement in near vision through an expansion in the optical depth of focus of the eye with HOAs.20–23 The results observed here indicate that the multifocality induced by HOAs and uncorrected myopic astigmatism supplement each other to improve the unaided near vision of pseudophakic eyes. The magnitude of HOAs is dependent on pupil diameter, and thus, its effects will reduce with pupil miosis.24 The additional benefit of HOAs will therefore be greater for large pupils, and the impact of HOAs will become inconsequential for very small pupils (e.g., <2 mm).36,37 The practical benefit of HOAs on the near vision of elderly pseudophakes with uncorrected astigmatism may therefore be apparent only for those with larger pupils or only under low light conditions where the pupils are relatively more dilated (∼5 to 6 mm) than under photopic conditions (∼3 to 4 mm).38 Any augmentation of near vision with HOAs, however, comes with a further compromise in distance IQ than what is already experienced by the pseudophakic eye with uncorrected astigmatism (Fig. 3A).

Taken together, the strategy of leaving myopic astigmatism uncorrected to improve near vision of pseudophakes with monofocal IOL implants must be reconciled with the fact that this improvement is partial and it is always associated with a loss in distance vision. From a public health standpoint, this trade-off may still be acceptable considering the high cost and longer time involved in dispensing custom-designed spherocylindrical bifocals or progressive lenses to optimize distance and near vision of the patient. In the uncorrected astigmatism strategy, the combination of residual myopic astigmatism, HOAs, and optimal pupil diameter improves the near vision of pseudophakic eyes while their distance vision may be largely (although not perfectly) restored using low-cost, ready-made, spherical lenses. The extent to which this strategy supports routine distance and near vision tasks of these pseudophakes needs further investigation. The balance between the augmentation of near vision and the loss of distance vision experienced in this strategy can, in theory, also be optimized to the visual needs of the patient by manipulating the magnitude of uncorrected astigmatism for a given pupil diameter and pattern of HOAs.

The present strategy of leaving myopic astigmatism uncorrected (combined with the eye’s native HOAs) to improve unaided near vision of pseudophakes may be compared with the performance of recently proposed multifocal lens designs that incorporate meridional variations in lens power to expand the eye’s depth of focus.39–41 These lens designs are different from the more conventional multifocal lenses in that they induce multifocality by incorporating angular (as opposed to radial) variations in optical power.39–41 The number of angular zones over which the optical power varies changes across lens designs, with some incorporating only two angular zones whereas others incorporate as many as 50 or more angular zones across the entire lens.39 Optical performance tends to be most optimal (i.e., large depth of focus with least loss of peak IQ) for lens designs with three to four angular zones, with the performance deteriorating progressively with an increase in the number of angular zones thereafter.39 The optics of the pseudophakic eye with uncorrected astigmatism are similar to these multifocal lenses with a large number of angular zones in that its optical power also varies continuously from the flattest to the steepest meridian across infinite angular optical zones. Light rays passing through such an optical system will be uniformly distributed across a range of focal distances (the Sturm conoid for astigmatism), resulting in nearly uniform IQ across the corresponding range of viewing distances. This was indeed the case for multifocal lenses containing 10 or more angular optical zones.39 This scenario is different from lenses containing smaller number of angular zones wherein the light rays tend to form a discrete number of focal points, resulting in IQ that is slightly better than the previous scenario but that tends to fluctuate significantly over this range. Whether this is a worthy trade-off or not requires further experimentation and analysis. The presence of HOAs in these multifocal lens designs further expands the optical depth of focus39,41 similar to what was observed in the present study with HOAs for the entire range of uncorrected astigmatism (Fig. 3A).

The EW metric that correlated best with logMAR acuity is one of the five IQ metrics that describe image quality in terms of the compactness of the point spread function (PSF).17,42 Smaller values of these metrics indicate greater compactness of the PSF and, therefore, better IQ.17 Specifically, the EW metric describes the diameter of the circular base of a right-angled cylinder that has the same volume and height as the entire PSF.17 Thus, as the height of the PSF falls with an increase in wavefront error—such as the case with increasing magnitudes of uncorrected astigmatism in this study—the diameter of the circular base increases to maintain constant volume under the PSF.17 The value of the EW metric therefore increases commensurately with an increase in the magnitude of uncorrected astigmatism. The EW metric values at near were overall larger than those at distance because of the uncorrected hyperopia at near in these pseudophakic eyes (Fig. 2). Overall, the EW metric captured several cardinal features of distance and near logMAR acuity with uncorrected astigmatism, suggesting that this metric could be used as a computational surrogate for describing acuity changes of the pseudophakic eye (Fig. 2). However, it did not capture the asymmetric loss in distance acuity with induced myopic and hyperopic astigmatism—the former resulted in greater loss of distance acuity than the latter for the same magnitude of induced astigmatism (Fig. 1A).11 The metric’s output was similar for both polarities of astigmatism, suggesting that the asymmetric loss of distance acuity may not arise from differences in the magnitude of focus error between myopic and hyperopic astigmatism. Recently, Ravikumar et al.43 found that phase shifts induced by the eye’s wavefront aberrations may be responsible for the asymmetrical loss of distance acuity with induced astigmatism. Because the EW metric is computed from the PSF, it should reflect changes in both the amplitude and phase of the image spectrum with different magnitudes of astigmatism. This suggests that the EW metric is either insensitive to the phase shifts that may exist with uncorrected astigmatism or that factors other than phase shifts may also be responsible for this result. The impact of phase shifts on other IQ metric output (e.g., SFcOTF [spatial frequency cutoff of the radially averaged OTF]) needs to be examined to determine if they reflect the asymmetric loss in IQ with the polarity of astigmatism.17 None of these metrics, however, featured in the top five correlation list here and hence were not considered for further analysis.

Shrikant R. Bharadwaj

Prof. Brien Holden Eye Research Centre

Hyderabad Eye Research Foundation

L. V. Prasad Eye Institute Road No. 2

Banjara Hills Hyderabad 500034

Andhra Pradesh

India

e-mail: bharadwaj@lvpei.org

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ACKNOWLEDGMENTS

The authors thank all the participants of this study and Prof. Larry Thibos of the Indiana University School of Optometry for help with analysis of image quality metrics. The authors also thank Prof. Clifton Schor, Dr. Sangeetha Metlapally, and the two anonymous reviewers for comments on the manuscript.

Funding for this project was received from the Government of India Department of Biotechnology Ramalingaswami fellowship to Dr. Shrikant Bharadwaj and a Champalimaud Foundation grant to the Prof. Brien Holden Eye Research Centre, L. V. Prasad Eye Institute.

The author(s) have no proprietary or commercial interest in any materials discussed in this article.

Received June 24, 2013; accepted December 16, 2013.

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Keywords:

acuity; astigmatism; blur; higher-order aberrations; image quality metrics; pupil

© 2014 American Academy of Optometry

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