Visual acuity (VA) is the standard parameter by which the outcome of most clinical trials are judged. In particular, the relation between VA and refractive state is a matter of great interest to optometrists and ophthalmologists and especially clinical researchers. Several studies have described the effects on VA of spherocylindrical refractive errors. In 1961, Peters investigated the relation between VA and uncompensated ocular defocus. He developed charts of iso-oxyopia (lines of equal acuity) that gave expected VA in eyes of different uncompensated refractive states. In other studies relating VA and defocus, lenses were used to blur compensated eyes and VA tests of various types were used.
In most of these analyses, the traditional representation of astigmatic power in terms of sphere, cylinder, and axis was used and transformed to nearest equivalent sphere, ignoring the multivariate nature of refractive state. A three-dimensional power space for the representation of astigmatic powers as vectors and its relationship with VA gives interesting results. This space is uniform in the sense that an equal amount of defocus or a Jackson crosscylinder (JCC) lens produces blur circles of equal diameter. Using the empiric VA data compiled by Pincus, Raasch demonstrated that the single parameter that better correlates refractive errors with its associated VA is the strength (norm) of the vector that represents the refractive error in the three-dimensional power space. This theoretical model proposed by Thibos predicts that the cylinder axis has no influence on the expected VA. This result was later supported by Oechsner and Kusel using numeric simulations.
More recently, Rubin and Harris also explored the relation between VA and defocused refractive state in the context of a symmetric dioptric power space. For a single stimulus size (20/60 computer-generated letter O), they obtained the associated refractions simulated in healthy eyes by means of spheres and Jackson’s crosscylinders. They found that the experimental data represented in the dioptric power space can be fitted to surfaces of constant VA. These surfaces are in general ovoids, but it seems that when the effect of accommodation is minimized (elderly subjects), they become ellipsoids or spheres centered at the refractive compensation. They claimed that the elliptical cross-sections of these three-dimensional surfaces reveal the dependence of VA on cylinder axis. This assertion creates a discrepancy with previous results.
Discussion and Conclusions
Thibos and Raasch relate VA to a single parameter: the magnitude of the dioptric power vector u. In this approach, surfaces of constant VA in the three-dimensional power space are spheres of radius u. In this article, we confirmed this hypothesis for SMA. We found that astigmatic vectors corresponding to refractive states with the same magnitude of astigmatism, but different axis orientations have all nearly the same associated VA.
Only monocular measurements of VA have been included in this article. We designed an experimental protocol with 180 measurements of VA for each eye. To prevent the learning effect, two Internet-based VA test with random letter presentation were used. To prevent fatigue, the sessions for each eye were limited to 45 minutes per day.
It was found that when accommodation is not active, the influence of the cylinder axis is of less importance than other clinical variables such as the selected VA chart. Moreover, the same astigmatic error (same power and axis) induced in different eyes provides VA variations of higher amount than those provided by astigmatism of the same power and different axes induced in the same eye.
On the other hand, our results agree with those of Rubin and Harris to some extent. As they claimed, when there is a loss of ocular accommodation, surfaces of constant visual acuity take a nearly spheroidal form. Thus, the departure from the spherical surface in their study can be mainly attributed to accommodation, whose effect has been minimized in our study. It is interesting to note that although the experimental data of Rubin and Harris has been fitted to ellipses, many of the experimental data points lie in a circle; the authors did not comment on this particular result.
The fact that VA for an ametropic eye can be associated with a single refractive parameter could be very useful, especially in studies involving visual performance. However, additional research is needed to quantify the influence of accommodation on other types of astigmatism.
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