Unaided visual acuity and blur: a simple model

This article proposes a simple model that describes the quantitative relationship between unaided visual acuity and blur attributed to refractive errors.

The standard model for describing the relationship between visual acuity and blur, as published by Raasch, is used as a starting point to develop a simpler model based on heuristic arguments. The basis of Raasch's data is augmented by published findings in the range of low-level refractive errors. Sphero-cylindrical refractive errors are transformed into a single blur quantity b, also termed dioptric distance, which serves as an input in both models. The possible influence of the cylinder axis and the pupil size is not included.

The quite simple model for the unaided minimum angle of resolution, MAR ∝ 1+ b(2), nicely matches available data and improves the SE of the regression by a factor of 2 in comparison to Raasch's model.

Both models considered in this article describe measurement data equally well. They differ in terms of complexity and functional form. The simple model provides a valid description for low-level refractive errors, where Raasch's model fails. Actual uncertainties in experimental data on unaided visual acuity, especially the frequent lack of information on pupil diameter, prevent meaningful numerical comparison and the refinement of both models. However, theoretical arguments are provided in support of the simple model.