An Analytical Model Describing Aberrations in the Progression Corridor of Progressive Addition Lenses

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Abstract
Purpose.: In the progression corridor of a typical progressive addition lens (PAL) with an addition of 2.5 D, the power changes by roughly 1/8 D/mm. This renders a power difference of some 0.5 D across a typical pupil diameter of 4 mm. Contrary to this fact, PALs do work well in the progression zone. To explain why, we apply a simple model to derive wavefront characteristics in the progression zone and compare it with recent experimental data. Methods.: We consider a simple analytic function to describe the progression zone of a PAL, which has been introduced by Alvarez and other authors. They considered the power change and astigmatism, which are second‐order wavefront aberrations. We include third‐order aberrations and compare them with spatially resolved wavefront data from Hartmann‐Shack‐sensor measurements. Results.: The higher‐order aberrations coma and trefoil are the dominant aberrations besides astigmatism as given by experimental data. According to our model, the third‐order aberrations in the transition zone are strongly coupled to the power change and the cubic power of the pupil radius. Their overall contribution according to experimental data is nicely reproduced by our model. The numeric contribution of higher‐order aberrations is small and, for practical purposes, the wavefront can be described locally by the second‐order components of sphere and astigmatism only. Conclusions.: We propose a simple analytical model to understand the optics in the progression corridor and nearby zones of a PAL. Our model confirms that for typical pupil sizes, all higher‐order aberrations, including the dominant modes of coma and trefoil, are small enough to render an undisturbed vision in the progression zone. Therefore, higher‐order aberrations have a minimal impact on the optical performance of these lenses.

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