Visual acuity under combined astigmatism and coma: Optical and neural adaptation effects

Abstract

Previous studies suggest that certain combinations of coma and astigmatism improve optical quality over astigmatism alone. We tested these theoretical predictions on 20 patients. Visual acuity (VA) was measured under best spherical correction for different conditions: low- and higher order aberrations corrected, in the presence of 0.5 D of induced astigmatism, and adding different amounts of coma to 0.5 D of astigmatism. Measurements were performed for different relative angles between coma and astigmatism and for selected conditions, also through-focus. Adding coma (0.23 μm for 6-mm pupil) to astigmatism resulted in a clear increase of VA in 6 subjects, consistently with theoretical optical predictions, while VA decreased when coma was added to astigmatism in 7 subjects. In addition, in the presence of astigmatism only, VA decreased more than 10% with respect to all aberrations corrected in 13 subjects, while VA was practically insensitive to the addition of astigmatism in 4 subjects. The effects were related to the presence of natural astigmatism and whether this was habitually corrected or uncorrected. The fact that the expected performance occurs mainly in eyes with no natural astigmatism suggests relevant neural adaptation effects in eyes normally exposed to astigmatic blur.

Introduction

The availability of aberrometers and the improvement in the refractive correction techniques (from conventional glasses and contact and intraocular lenses to laser refractive surgery) have opened the possibility to consider the correction of some of the higher order aberrations (HOAs) of the eye or even produce a customized correction of not only defocus and astigmatism but also of HOA, with the aim of improving retinal image quality and subsequently vision. For example, aspheric intraocular lenses have been introduced in cataract surgery and have been shown to produce a compensation of the average natural spherical aberration of the cornea (Marcos, Barbero, & Jiménez-Alfaro, 2005). Custom contact lenses are being designed to correct the large amounts of astigmatism and coma present in keratoconic eyes (Sabesan et al., 2007). Custom refractive surgery has shown controversial results on normal eyes but seems to be able to compensate abnormal high amounts of HOA, generally induced by a previous surgery (Mrochen, Kaemmerer, & Seiler, 2001). On the other hand, standard refractive surgery has been shown to induce HOA, particularly spherical aberration in post-operative eyes (Applegate & Howland, 1997; Moreno-Barriuso et al., 2001; Porter et al., 2006; Yoon, MacRae, Williams, & Cox, 2005). Conventional techniques also leave HOA uncorrected and, in some cases, also induce small amounts of astigmatism and HOA, i.e., ophthalmic lenses may induce astigmatism and coma (Villegas & Artal, 2006). Correcting or inducing aberrations change the natural aberration pattern of the eye. It has been shown that inducing aberrations, in general, produce a decrease on visual function (Marcos, 2001) as well as of the accommodative response (Fernandez & Artal, 2005; Gambra, Sawides, Dorronsoro, & Marcos, 2009), and full correction of HOA results in an increase in visual acuity (VA) over a large range of luminance and polarities (Marcos, Sawides, Gambra, & Dorronsoro, 2008), in contrast sensitivity (Liang & Williams, 1997; Yoon & Williams, 2002), and in functional visual tasks (Dalimier, Dainty, & Barbur, 2008; Sawides, Gambra, Pascual, Dorronsoro & Marcos, 2010). However, in most cases, aberrations are selectively induced or corrected, and the interactions across different aberrations are therefore altered. Interactions between aberrations have been shown to critically affect retinal image quality. McLellan, Marcos, Prieto, and Burns (2002) showed that the presence of natural monochromatic aberrations minimizes the negative effects of longitudinal chromatic aberration on retinal image quality. This may explain why the visual benefits of correcting chromatic aberrations have been relatively modest in experimental studies (Marcos, Burns, Moreno-Barriuso, & Navarro, 1999; Zhang, Thibos, & Bradley, 1997). Interactions between symmetric low and HOAs have been studied computationally and experimentally (Applegate, Ballentine, Gross, Sarver, & Sarver, 2003; Thibos, Hong, Bradley, & Applegate, 2004). Previous studies have shown that spherical aberration and defocus can interact favorably to achieve better image quality than either one alone (Applegate, Marsack, Ramos, & Sarver, 2003). Favorable interactions between HOAs seem to occur in the human eye, as artificial combinations of similar amounts of Zernike but random signs produce lower MTFs than the actual Zernike set (McLellan, Prieto, Marcos, & Burns, 2006). In a previous study, we also showed possible favorable interactions of astigmatism and coma (de Gracia et al., 2010). We found that optical quality in the presence of astigmatism can be very significantly improved by adding coma. For example, Strehl ratio (SR) increased by a factor of 1.7 by adding 0.23 μm of coma to 0.5 D of astigmatism, over Strehl ratio for 0.5 D of astigmatism alone for a pupil of 6 mm. Improved VA when astigmatism and coma were combined was demonstrated on two subjects who did not have significant amounts of natural astigmatism. 

In the current study, we tested whether the theoretical optical improvement achieved with certain combinations of coma and astigmatism results in a systematic increase of visual performance. Experimental measurements were performed in a group of 20 young normal patients, with various amounts of spherical and cylindrical refractions, with no a priori selection of their refractive profiles. We found that astigmatic subjects, particularly subjects where astigmatism was not habitually corrected, did not improve visual acuity when astigmatism was added, in contrast to the optical predictions. The fact that subjects with identical optical properties exhibit very different relative responses is suggestive of adaptation effects, to astigmatic blur in particular. Adaptation to the blur induced by low and HOAs has been suggested before. Several studies report improved visual performance in myopes after periods of adaptation to defocus (Collins, Ricci, & Burkett, 1981; Pesudovs & Brennan, 1993). This phenomenon has also been reported in emmetropic subjects after periods of induced defocus (George & Rosenfield, 2004). Changes in the perception of blur after brief periods of adaptation to blurred or artificially sharpened images have also been demonstrated (Webster, Georgeson, & Webster, 2002). In a recent study, we have shown angular selective adaptation to astigmatic blur after brief periods of adaptation to images blurred by horizontal or vertical astigmatism (Sawides, Marcos et al., 2010). Artal et al. (2004) showed better visual performance in patients with their natural aberrations than with an artificial pattern of aberrations that would generate identical but rotated Point Spread Function (PSF), suggesting that the eye would be adapted to the orientation of the natural PSF. 

On the other hand, numerous works have shown that a prolonged exposure to astigmatism at early stages of development produces meridional amblyopia (Dobson, Miller, Harvey, & Mohan, 2003; Freeman, Mitchell, & Millodot, 1972; Mitchell & Wilkinson, 1974), although this astigmatism-related amblyopia seems to be minimized with spectacle correction, if provided sufficiently early (Dobson, Clifford-Donaldson, Green, Miller, & Harvey, 2009). Non-corrected astigmatic patients might experience a double-faced phenomenon; on the one hand, visual deprivation in some orientations results in reduced acuity, even after full correction of astigmatism (known as “meridional amblyopia”), and on the other hand, neural adaptation mechanisms might appear to compensate some of the deleterious effects of astigmatism on non-corrected astigmatic subjects; therefore, non-adapted observers degraded with similar amounts of astigmatism might show significantly visual worse performance. Similar effects have been found in keratoconic patients versus normal subjects with simulated keratoconus (Sabesan & Yoon, 2010). 

In this study, we tested the interactions of astigmatism, coma, and defocus in a group of 20 subjects. The subjects included three refractive profiles (non-astigmatic emmetropes, astigmatic patients that were habitually corrected by spectacles, and non-corrected astigmatic subjects). A post-hoc analysis of the data showed that the differences in the response were associated to the presence/absence of astigmatism and whether this was habitually corrected. We hypothesized that prior adaptation to astigmatism is responsible for the discrepancy from the optical predictions of the benefits of adding coma to astigmatism. 

Methods

Experimental setup

A custom-developed Adaptive Optics System was used in the study to induce the desired patterns of astigmatism and coma, while the natural low- and higher order aberrations were corrected. The system has been described in detail in previous publications (de Gracia et al., 2010; Marcos et al., 2008). In brief, the main components of the system are a Hartmann–Shack wavefront sensor (composed by 32 × 32 microlenses, with 15-mm effective diameter and a CCD camera; HASO 32 OEM, Imagine Eyes, France) and an electromagnetic deformable mirror (MIRAO, Imagine Eyes, France). The desired mirror states were achieved by a closed-loop operation. Dedicated routines have been developed specifically for this study, allowing a full automatization of the process, so that after the mirror state is created, no further interaction from the experimenter is required. 

Visual stimuli were presented on a minidisplay (12 mm × 9 mm SVGA OLED minidisplay, LiteEye 400), viewed through the AO mirror, and a Badal system. VA was measured using a 4-alternative forced-choice procedure with tumbling E letters and a QUEST procedure programmed in psychotoolbox (Brainard, 1997). 

Optical predictions

We have shown previously that, under certain conditions, adding coma to astigmatism improves optical quality over astigmatism alone. We calculated the SR values for amounts of coma ranging from 0 to 1 μm, astigmatism from 0 to 1.5 D, and defocus from −1 to 1 D, respectively, for 2 different pupil diameters (4 and 6 mm). We predicted a peak improvement in SR by a factor of 1.7 when adding 0.23 μm of coma to 0.5 D of astigmatism, in an otherwise fully corrected eye (for 6-mm pupils). Improvement of SR by adding coma to 0.5 D of astigmatism was found for a range of 0.85 D of defocus, for coma values ranging from 0.15 to 0.35 μm of coma, and a range of 60° of relative angle (from 0 to 60; de Gracia et al., 2010). 

Experimental protocols

To further explore possible interactions between coma, astigmatism, and defocus, VA was measured under a total of 18 conditions in 20 subjects. The conditions were selected according to the predictions from computer simulations, which identified the amounts and orientations of coma that interacted favorably with 0.5 D of astigmatism at 45° (de Gracia et al., 2010). A set of conditions varying the amount of coma, relative angle of coma, and astigmatism and defocus was tested. In all cases, natural astigmatism and HOA of the subject were corrected, and the desired combinations of astigmatism and coma were induced. In particular, we tested VA for the following conditions: (1) Across defocus experiment: 0.5 D of astigmatism at 45°, 0.23 μm coma, a relative angle of 0°, and defocus varying from −0.6 D to 0.6 D (amount of defocus tested: −0.6, −0.2, 0, 0.2, 0.6); (2) Across coma experiment: 0.5 D of astigmatism at 45°, variable coma (from 0.11 to 0.41 μm in 0.06-μm steps), and a relative angle of 0°; (3) Across relative angle experiment: 0.5 D of astigmatism, coma (0.11, 0.23, and 0.35 μm), and relative angles of 0°, 45°, and 90°. In addition, VA was measured also for 2 control conditions, with all low and HOAs corrected and with all low and HOAs corrected and 0.5 D of astigmatism at 45°. The order in which the different conditions were tested was randomized. The series of measurements of conditions 1, 2, and 3 represent the experiments labeled as 1, 2, and 3, respectively. 

All the experiments were performed under dilated pupils (by tropicamide 1%), with an artificial pupil of 6 mm placed in a plane conjugate to the pupil in the psychophysical channel. Wave aberrations were fitted by 7th-order Zernike polynomials. We used the OSA convention for ordering and normalization of Zernike coefficients. 

Each VA measurement consisted on 50 trials, each one presented during 0.5 s. Subjects had to determine the orientation of the letter E (pointing up, down, left, or right). The introduction of astigmatism at 45° in most of the VA measurements, along with the fact that Z ₋₂ ² is introduced by the mirror at the circle of least confusion, (equivalent spectacle prescription: +0.25 −0.50 × 45°) helps minimize differences between the four possible letter orientations. There was no feedback to the subjects. As a control parameter to decide the validity of the VA measurement, at least 8 of the last 25 trials must have a standard deviation under 0.06 arcmin. If the measurement did not meet this criterion, it was discarded and repeated. Taking into account the light losses in the system, the effective luminance of the minidisplay at the pupil plane was 25 cd/m². 

The steps of an experimental session were, sequentially: (1) focus setting; (2) measurement of ocular aberrations with the Hartmann–Shack sensor; (3) closed loop for natural aberration correction; (4) set of mirror status (aberration correction + specific astigmatism/coma combination); (5) measurement of eye + mirror aberrations; (6) measurement of VA; (7) measurement of eye + mirror aberrations. The sequence was repeated for each condition tested. 

The focus setting was determined using a Maltese cross as a fixation target. The focus setting was determined for each subject under a mirror state that induced 0.5 D of astigmatism at 45° and 0.23 μm of coma at a relative angle of 0°, for all measurements except for the condition where all aberrations were corrected. For this condition, the focus setting was obtained for the state of the mirror producing best correction of astigmatism and HOA. 

Subjects

Twenty subjects participated in the study, with ages ranging from 23 to 42 years (29.1 ± 5.1). Spherical errors ranged from −5.75 D to +1.75 D (mean: −0.73 ± 1.72). Astigmatism ranged from 0 to 1.5 D. All patients followed an ophthalmological evaluation before performing the experiments. Subjects signed a consent form approved by the Institutional Review Boards after they had been informed on the nature of the study and possible consequences. All protocols met the tenets of the Declaration of Helsinki. Table 1 shows the profile of the patients, the subjective prescription, and whether they were habitually corrected. There were no significant differences in the wave aberration magnitude and distribution of the HOA across groups. 

Table 1

 

Profile of the subjects of the experiment. Group 1: No natural astigmatism, n = 10. Group 2: Habitually corrected natural astigmats (0.50–1.50 D), n = 5. Group 3: Habitually non-corrected natural astigmatism (0.25–0.50 D), n = 5.

Subject no.	Sph. (D)	Astig. (D)	Angle (degrees)	Eye	Age (years)	Habitual astigmatic correction	Group
1	0	0	–	Right	30	No	1
2	1.5	0	–	Right	37	No	1
3	−1.5	0	–	Right	25	No	1
4	0	0	–	Right	25	No	1
5	0	0	–	Left	26	No	1
6	0	0	–	Right	29	No	1
7	−5.75	0	–	Left	39	No	1
8	−1.25	0	–	Right	27	No	1
9	−0.75	0	–	Right	23	No	1
10	0.75	0	–	Left	31	No	1
11	−3	−0.5	180	Right	26	Yes	2
12	−4	−1	175	Right	27	Yes	2
13	−1.5	−1.5	150	Left	28	Yes	2
14	−1.75	−0.5	70	Right	25	Yes	2
15	−0.75	−0.75	75	Right	25	Yes	2
16	0.5	−0.25	110	Right	30	No	3
17	0.25	−0.5	50	Right	42	No	3
18	−0.5	−0.5	135	Right	33	No	3
19	1.75	−0.5	30	Right	28	No	3
20	0.5	−0.5	125	Right	25	No	3

The type of astigmatism differed across groups. Compound myopic astigmatism was predominant in the group of habitually corrected astigmats (5/5). Hyperopic astigmatism was predominant in habitually non-corrected astigmats (3/5). One subject showed compound mixed astigmatism (no. 17) and one subject showed compound myopic astigmatism (no. 18). None of the habitually non-corrected astigmats except for Subject 19 wore any prescription. Subject 19 is habitually corrected from 1.25 D of hyperopic defocus (residual prescription: +0.5 −0.5 × 30). Habitually corrected astigmats were habitually corrected for their sphero-cylindrical errors. It is commonly assumed that non-corrected hyperopic astigmats can shift their best focus by means of accommodation and, therefore, may experience images blurred along different orientations throughout the Sturm interval for distance vision. Figure 1 illustrates the range of PSFs (not taking into account HOA) available to the habitually non-corrected astigmats. For far vision, Subjects 17 and 18 may experience a more limited range of orientations in their PSFs than the hyperopic astigmats. 

Figure 1

 

PSFs for habitually non-corrected astigmatic subjects. The numbers under each PSF indicate the defocus required to place the image onto the retina. A schematic eye (not in scale) is included for reference in the background. PSFs available for distance vision are labeled in white. The vertical line represents the retinal plane for all subjects. The scale bar only applies to the size of the PSFs.

Data analysis

VA was compared across conditions and groups both in absolute and relative terms. The visual benefit of adding coma to astigmatism was expressed as the ratio between VA (for a given combination of astigmatism, coma, and defocus) and VA in the presence of astigmatism only: 

$\mathrm{V}\mathrm{i}\mathrm{s}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}=\frac{\mathrm{V}\mathrm{A}(\mathrm{A}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{m}+\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{a})}{\mathrm{V}\mathrm{A}(0.5\mathrm{D}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{m})}.$

(1)

 

The visual degradation produced by inducing astigmatism to fully corrected eye was defined as 

$\mathrm{V}\mathrm{i}\mathrm{s}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{D}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}=\frac{\mathrm{V}\mathrm{A}(\mathrm{A}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d})}{\mathrm{V}\mathrm{A}(0.5\mathrm{D}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{m})}.$

(2)

 

Statistical comparisons of the visual performance across groups were performed using a linear mixed model, with the VA as the dependent variable, group as a factor, and the different conditions as repeated measurements. Bonferroni definition of confidence intervals was used. 

Aberration correction and induction

Astigmatism and HOA were fully corrected and/or selectively induced (astigmatism and coma) by the mirror. The mirror states were measured just before and after each VA measurement. The achieved state was compared with the attempted state, and a maximum discrepancy of 0.10 μm in the astigmatism or coma terms was allowed. If the mirror state did not fulfill these requirements, the measurement was discarded and repeated. Figure 2 shows an example of correction and induction of aberration on one subject (no. 2). The top row shows the natural wave aberration pattern for the subject (excluding tilt and defocus (Figure 2A) and after AO correction (Figure 2B)). The bottom row shows the attempted wave aberration pattern, a combination of 0.5 D of astigmatism at 45° and 0.23 μm of coma at a relative angle of 0° (Figure 2C), the achieved pattern (after AO correction of the natural aberrations and induction of the desired pattern (Figure 2D)), and the error (Figure 2E). The examples show a high compliance in the correction and induction of aberrations. HOAs were successfully corrected in all subjects, with the residual RMS being lower than 0.11 μm (including errors in all HOAs and astigmatism). Figure 3 shows the residual RMS error for all subjects when inducing a wave aberration pattern of 0.5 D of astigmatism at 45° and 0.23 μm of coma at a relative angle of 0°. The difference between the attempted and achieved aberration patterns (for combinations of astigmatism and coma) did not vary significantly across groups. For example, for a combination of astigmatism of 0.5 D at 45° and coma of 0.23 μm, with a relative angle of 0° (as that shown in the example of Figure 3), the residual RMS error after correction of astigmatism and HOA was, on average, 0.082 for non-astigmats, 0.071 for habitually corrected, and 0.058 for habitually non-corrected astigmats. The residual RMS difference was found to be 0.024 μm larger in non-astigmats than in habitually non-corrected astigmats. Residual errors for the three groups are within a range from 10% to 15% of the ideal RMS attempted. 

Figure 2

 

Upper row: (A) Natural wave aberration of Subject 2 (excluding tilt and defocus RMS = 0.45 μm) and (B) wave aberration after AO correction (RMS = 0.020 μm). Bottom row: (C) Wave aberration for a mirror state attempting a combination of 0.23 μm of coma and 0.5 D of astigmatism both at 45°; (D) achieved wave aberration pattern; and (E) difference map between ideal and achieved (RMS = 0.030 μm). Pupil diameter: 6 mm.

Figure 3

 

RMS of the difference achieved–attempted map (for a combination of 0.5 D of astigmatism and 0.23 um of coma, at a relative angle of 0 deg) in all subjects. Green bars represent non-astigmats, blue bars represent habitually corrected subjects, and red bars represent habitually non-corrected ones. Pupil diameter = 6 mm.

Results

Visual acuity with combined astigmatism and coma

Figure 4 shows the visual benefit of adding coma to astigmatism over astigmatism alone (Equation 1) in all three experiments (across defocus, across coma, and across relative angle). Data are averaged across all subjects in each group. Optical predictions (in terms of Strehl ratio) anticipate a benefit across defocus for a range of 0.85 D, for amounts of coma between 0.15 and 0.35 μm, and for a range of relative angles between coma and astigmatism of 60° (0°–60°; de Gracia et al., 2010). Very consistently across experiments, the non-astigmatic group shows improved VA when coma and astigmatism are combined. The group with habitually corrected astigmatism does not show a clear benefit by adding coma to astigmatism, while for the habitually non-corrected astigmatic group, VA is decreased when adding coma. Altogether non-astigmatic subjects show a very similar trend to that expected from optical simulations. VA improved in a range of 0.7 D of defocus, in the tested range of coma (0.11 to 0.41 μm), and for a range of relative angle of 60°. However, in the other two groups the visual findings differ from optical predictions. While all experiments were performed under identical optical conditions for all subjects, the presence of natural astigmatism seems to be associated with the lack of correspondence between visual benefit and optical benefit. The disagreement is high in subjects that are habitually exposed to astigmatism (group 3). We explored the correlation between the predicted optical benefit (in terms of SR) and the measured visual benefit (in terms of VA), for all the tested optical conditions. We found significant correlations for non-astigmatic subjects (r = 0.67, p = 0.008) and habitually corrected astigmats (r = 0.59, p = 0.027). There was no correlation between optical predictions and visual measurements in habitually non-corrected astigmats (r = 0.44, p = 0.12). 

Figure 4

 

Averaged values of visual benefit of adding coma to astigmatism for the 3 groups (non-astigmatic, in green triangles; habitually corrected astigmatic subject in blue circles; habitually non-corrected astigmatic subject in red triangles). Experiment 1: Combined astigmatism (0.5 D) and coma (0.23 μm), as a function of defocus. Experiment 2: Combined astigmatism (0.5 D) with various amounts of coma. Experiment 3: Combined astigmatism and coma (average of various amounts) as a function of relative angle. Error bars stand for half standard deviations.

Figure 5 shows the visual benefit (averaged values across Experiments 1, 2, and 3 for each subject) as a function of the amount of natural astigmatism. Subjects from each group are identified by different colors. Most non-astigmatic subjects experience a visual benefit by adding coma and astigmatism (up to ×1.4). Visual benefit for habitually corrected astigmats is close to 1, whereas for habitually non-corrected astigmats it is less than 0.8. 

Figure 5

 

Visual benefit of adding coma to astigmatism over astigmatism alone averaged across Experiments 1, 2, and 3 for each subject, as a function of the amount of natural astigmatism. Non-astigmats are represented by green triangles, habitually corrected astigmats by blue circles, and habitually non-corrected astigmats by red triangles.

We found the difference across groups to be very robust, regardless of the axis of astigmatism of the eye. However, we explored potential relationships between the angle of the natural astigmatism of the subjects and the visual acuity for fully corrected optics, astigmatism alone (0.5 D at 45°), and combined astigmatism (0.5 D at 45°) and coma (0.23 μm at 45°). Figure 6 shows absolute decimal VA, under three different conditions: (1) Full correction of aberrations, (2) 0.5 D of astigmatism, and (3) combined coma and astigmatism (from Experiment 1: 0.23 μm of coma, 0.5 D of astigmatism at 45°, and a relative angle of 0°). Natural astigmatism is plotted in the range of 0° to 90° (as the habitually non-corrected astigmats experience retinal images in the two orientations). 

Figure 6

 

VA in all astigmatic subjects (habitually corrected and habitually non-corrected) as a function of the axis of their natural astigmatism (from 0 to 90°), for all aberrations corrected, yellow squares; combination of coma and astigmatism (average from Experiments 1 and 2), green squares; and/or 0.5 D of astigmatism, magenta squares.

We found that when the axis of natural astigmatism was aligned with the axis of the induced astigmatism, the effects are significantly stronger. Best performance in the presence of astigmatism only (0.5 D of astigmatism at 45°) is achieved by habitually non-corrected subjects with natural astigmatism axis close to 45° or 135° (astigmats 17, 18, 19, and 20). In those subjects, decimal VA in the presence of astigmatism is almost as high as their VA when all aberrations are corrected (ratio between VA with 0.5 D of astigmatism and with all aberrations corrected: 0.97). The lack of visual improvement when adding coma to astigmatism appears rather unaffected by the natural axis of astigmatism. 

Figures 7A and 7B show the visual benefit (Equation 1) of adding coma to astigmatism alone, averaged per group, for each experiment (across defocus, across coma, and across relative angles), and averaged across experiments, respectively. Non-astigmatic subjects experience an increase in VA when adding coma (visual benefit of 1.07, on average), habitually corrected astigmatic subjects do not experience an increase in VA (visual benefit of 0.99, on average), whereas habitually non-corrected astigmatic subjects show a decrease in VA when coma is added (visual benefit of 0.79, on average). Differences between non-astigmats and habitually non-corrected astigmats and between habitually corrected astigmats and habitually non-corrected astigmats are statistically significant in all cases. 

Figure 7

 

Visual benefit of combining astigmatism with coma for the three groups (A) for the three experiments and (B) averaged across experiments. Error bars stand for half standard deviations; **p < 0.001 and *p < 0.05.

Deleterious effect of astigmatism on visual acuity across groups

Differences across groups were also found in VA with astigmatism alone and VA with all aberrations corrected. Habitually non-corrected astigmatic subjects showed relatively higher VA when all aberrations are corrected and remarkably appeared to be insensitive to the addition of 0.5 D of astigmatism, as opposed to the non-astigmatic subjects, and the habitually corrected astigmatic subjects, who experienced a significant decrease in VA when astigmatism was induced. 

Figure 6 shows that the effect (little impact of induced astigmatism on VA) is larger when the axis of the natural astigmatism is parallel or perpendicular to that of the induced astigmatism (45° in this experiment), in habitually non-corrected astigmatism. We compared decimal VA across groups in the absence of low- and high-order aberrations (Figure 8A) and after induction of astigmatism (0.5 D at 45°, Figure 8B). Figure 8C shows the relative decrease (visual degradation) of inducing astigmatism. Fully corrected VA was not statistically significantly across groups. However, in the presence of astigmatism, VA was statistically significantly higher in habitually non-corrected astigmatic subjects than in non-astigmatic subjects (p < 0.01) and than in habitually corrected astigmatic subjects (p < 0.05). Inducing 0.5 D of astigmatism in non-astigmatic subjects produced a decrease in VA by 23% and in habitually corrected astigmatic subjects by 21%, whereas in habitually non-corrected astigmatic subjects, the decrease was only 5%. 

Figure 8

 

(A) Decimal VA when all aberrations are corrected. (B) Decimal VA, for 0.5 D of astigmatism only. (C) Visual degradation (ratio of data from (A) and (B)) when 0.5 D of astigmatism is added. Data are averaged across subjects in each group; **p < 0.001 and *p < 0.05.

Discussion

In a previous study, we had shown that optical interactions between astigmatism and coma can result in an improvement in optical quality (de Gracia et al., 2010). We predicted that adding amounts of coma between 0.15 and 0.35 μm to 0.5 D can lead to an increase in peak Strehl ratio values, in the absence of other HOAs, with a peak improvement of 27% for 0.23 μm of coma. The optical predictions were illustrated by improvements in VA in two subjects. In the present work, we extended the initial sample to 20 subjects and found that not all subjects improved as predicted by the optical simulations. In fact, we found that despite all subjects being measured under identical optical conditions, the visual improvement produced by adding coma to astigmatism seems to be highly dependent on the presence of natural astigmatism and whether this is habitually corrected or not. We have shown that non-astigmatic subjects generally improve VA (by a factor of 1.11) when coma (ranging from 0.11 to 0.35 μm, Experiment 2) is added to 0.5 D of astigmatism (data from Experiment 2), while naturally astigmatic subjects do not experience the predicted improvement. Habitually non-corrected astigmats actually experienced a decrease in VA when adding coma to astigmatism (by a factor of 0.79). In these experiments (as in the computer simulations), the natural aberrations of the eye were corrected, and identical aberration patterns were produced in all subjects; therefore, the different visual performance found across groups must arise from a neural component. The strong influence of the presence of natural astigmatism (and whether this is habitually corrected or not) on the response is suggestive of prior neural adaptation to astigmatism. The high tolerance to the induction of astigmatism in subjects with habitually non-corrected astigmatism may be indicative of an adaptation to astigmatism in these patients (and this being disrupted by the addition of coma). 

Very interestingly, habitually non-corrected astigmatic subjects show a high tolerance to astigmatism despite the fact that blur induced by astigmatism is troublesome (Atchison, Guo, Charman, & Fisher, 2009). This effect could result from neural adaptation to astigmatism, which would mitigate its deleterious effects on vision (Georgeson & Sullivan, 1975). Performance adaptation to defocus blur has been reported before resulting into an improvement of VA (Collins et al., 1981; Cufflin, Mankowska, & Mallen, 2007; George & Rosenfield, 2004). In addition, we have recently reported shifts in the perceived non-astigmatic defocused image after a brief period of adaptation to astigmatism, indicating that the perceptual adaptation to blur can be selective to the orientation of the blur. 

Habitually non-corrected astigmats can easily change the state of accommodation along the Sturm interval and are not necessarily adapted to blur in a particular orientation. Depending on the characteristics of the target and the availability of the different focal lines, a different value of accommodation may be chosen to provide the best visual performance (Freeman, 1975). The presence of astigmatic blur seems to provide blurred images in the two orientations (see Figure 1). 

We found larger effects in habitually non-corrected astigmats with the angle of natural astigmatism closer to 45 and 135°, but our experiments were not designed to match the angle of the induced astigmatism to the angle of astigmatism of the subject (in all cases, the astigmatism was induced at 45°). Ongoing experiments in our laboratory will try to further clarify this point by angle-specific tests that will take into account the angle of the natural astigmatism of the subject. 

In addition, in our sample, habitually non-corrected astigmats show high VA under full correction of all low- and higher order aberrations, indicating no sign of meridional amblyopia resulting from uncorrected astigmatism. This fact is not entirely surprising since amounts of astigmatism leading to meridional amblyopia are usually higher than 1 D, and amblyopia has a higher prevalence in subjects with both meridians myopic, rather than hyperopic astigmats (Dobson et al., 2003; Gwiazda, Mohindra, Brill, & Held, 1985). 

Our results show different responses between habitually corrected and habitually non-corrected astigmatic subjects. Habitually corrected astigmatic subjects tend to experience less benefits of adding coma to astigmatism than non-astigmatic subjects, but they definitely show lower tolerance to the induction of astigmatism than habitually non-corrected astigmatic subjects. An interesting question is whether a period of astigmatic correction would alter the response (both in terms of benefit of coma addition and tolerance to astigmatism) of the habitually non-corrected subjects. The question is relevant for a deeper understanding of the relationships between optical and visual performances (and in this particular study the implications of coma and astigmatism interactions), but also of important practical significance, as many contact lens wearers have their astigmatism typically left uncorrected (Tan et al., 2007). In fact, the adaptation to an astigmatic prescription has been largely debated in the clinical literature (Amos, 1987), and it has been reported that adaptation to changes from one astigmatic prescription to another may be limited and highly dependent of age (Guyton, 1977). An intriguing open question is whether these adaptation effects, in case they occur, require short periods of time, as shown in the shift of the perceived focused image by Sawides, Gambra et al. (2010), longer periods, up to 2 h of adaptation, as for the improvement in VA for defocus blur (George & Rosenfield, 2004), or even longer periods to become fully adapted to a new prescription. The study of the time course of adaptation mechanisms to astigmatism (or its correction) is an interesting open question, which we will address in a future work. 

Acknowledgments

The authors acknowledge funding from CSIC JAE-Pre to PdG, MICINN FIS2008-02065 to SM, EURYI-05-102-ES (EURHORCs-ESF) to SM, and a collaborative research project funded by Essilor International. 

Commercial relationships: Essilor. 

Corresponding author: Pablo de Gracia. 

Email: [e-mail]. 

Address: 121 Serrano, Madrid 28006, Spain.