This paper demonstrates a multivariate approach to understanding the complicated relations of visual acuity to refractive state or ametropia. Other approaches, as previously used, included graphical representations of lines or profiles of iso-oxyopia (Peters, 1961). But one limitation of Peters' method is that cylinder axis was ignored. However, here the relationship between visual acuity and refractive power will be represented by estimated closed surfaces of constant visual acuity in symmetric dioptric power space. At or near the common center (of several closed surfaces, for example) is the refractive compensation. Coming outwards from such a center, the visual acuity drops in all directions in the space. The primary purpose of this paper was to present estimated closed surfaces of constant visual acuity for several eyes. Various procedures were performed on several subjects including measurement of iris aperture diameter, subjective refraction, and autorefraction. Thereafter, an automated phoropter and either Jackson cross-cylinders or spheres were used to influence dioptric blur or defocus in the subjects. The visual stimulus was a computer-generated nondirectional or meridionally independent letter O. Ovoidal surfaces fit the measurements obtained (with Jackson cross-cylinders and spheres) better than ellipsoidal surfaces. The cross-section, in symmetric dioptric power space, at powers with the same nearest equivalent sphere as the refractive compensation is elliptical in many cases and reflects a dependence of visual acuity on cylinder axis. The surfaces differ when powers are changed so that one is moving away from (decompensation surfaces) or toward (accompensation surfaces) the refractive compensation. The multivariate and graphical methods used in this paper probably have implications for the direction of future research in a number of areas involving measures of vision function such as autorefraction, retinoscopy, subjective refraction, and visual acuity.