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Jim Schwiegerling; Basis Functions for Designing Progressive Addition Lenses. Invest. Ophthalmol. Vis. Sci. 2018;59(9):2976.
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To develop a set of functions that will aid in the design of customized Progressive Addition Lenses (PALs).
The progressive surface on PALs is a complex freeform shape that seeks to provide an increased add power through the progressive corridor, while at the same time limiting surface astigmatism in the lens periphery. This work examined creating an orthogonal set of functions that was defined over a sector of the unit circle and had the properties that the radial derivative is zero at the origin and the azimuthal derivative is zero at the boundary of the sector. These definitions effectively separate the progressive surface from an underlying base surface such as a spherical and rotationally symmetric aspheric surface. Given these requirements, known sets of orthogonal polynomials can be transformed into polar coordinates to create a novel and flexible set of basis functions for facilitating PAL design.
The figure below shows an example series of the basis functions. The sector has an angular subtense of 270 degrees which is consistent with many “soft” PAL designs. The first column shows functions that can define the add progression through the corridor. The second column shows asymmetric terms that can be used to shift the corridor towards the nasal side. The other columns represent additional terms that can be used to minimize surface aberrations in lens.
A useful set of functions has been developed that is applicable to common styles f PAL designs. These functions may provide benefit is customized design and reducing aberrations.
This is an abstract that was submitted for the 2018 ARVO Annual Meeting, held in Honolulu, Hawaii, April 29 - May 3, 2018.
PAL basis functions for 270 degree sector
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