The relationship between dioptric power and magnification in progressive addition lenses

Non-uniform magnification (distortion) and dioptric blur are two major undesired optical defects affecting vision when looking through progressive addition lenses (PALs) and studying them is potentially very valuable for PAL design. The major purpose of this paper is to analyse the relationship between dioptric power and magnification and, additionally, to evaluate the expected values of distortion and dioptric blur typically present in PALs. This has not been carefully and rigorously analysed to date.

We computed the local dioptric and magnification matrices (using a two-ray differential method) for different gaze directions in an archetypical model of a PAL. We used four different maps: scalar magnification and anamorphic distortion, to describe magnification, and mean power and astigmatism, to describe dioptric power.

There is a good correlation between scalar magnification and mean power on the one hand, and anamorphic distortion and astigmatism on the other hand. Changes of 1 D in mean power are associated with variations in scalar magnification of around 3%. Also, 3% of anamorphic distortion is associated with increasing astigmatism up to 1 D. The directions of maximal power and maximal magnification are quite similar, though not equal (differences up to ± 1.5°). These directions strongly change from close to isotropic at the intermediate corridor to around 45° of oblique inclination for a few degrees of horizontal eye rotation. In typical PALs the level of distortion, which is unavoidably present when dioptric blurring appears, is small for usable vision zones (below 1 D of astigmatism).

The combined analysis of dioptric power and magnification in PALs helps to understand their limitations as a visual aid. On the one hand, the potentials of including distortion magnitude as a target in the metric function being optimised in the PAL design are reduced; on the other hand, it seems worthwhile to explore adding the degradation orientation as an additional target.