Geometrical interpretation of dioptric blurring and magnification in ophthalmic lenses

Blur and non-uniform magnification are two related undesired effects affecting vision when looking through eyeglasses. We propose a geometrical framework to study the relationship between both effects. Magnification and blur are locally characterized by dioptric and magnification matrices, respectively, which we compute here by using a novel two-ray numerical method. We propose a set of geometrical entities associated with the dioptric and magnification local matrices, which are analyzed in several examples. We prove that there is a strong correlation between such entities (e.g., astigmatism and anamorphic distortion), which, to a certain extent, is maintained even in highly asymmetric lenses. We also show the somewhat anti-intuitive result that the axis of maximal blurring is sometimes close to orthogonal to the axis of maximal distortion. The results provide useful clues for ophthalmic lens design.