Patent ID: 8504329
Filing Date: 2013-08-06
Classification: A61B,A61F,G06F

Abstract:
1. A method of determining a set of orthonormal polynomials F over a domain Σ corresponding to a noncircular pupil of an eye of a patient for use in determining a vision treatment for the patient, the method using a processor configured to perform the steps of: selecting a complete set of polynomials P as a basis for the orthonormal polynomials F; determining a set of sub-areas of the noncircular pupil; formulating a relationship between x and y within each of the sub-areas such that the set of polynomials P is integratable within each sub-area; calculating a conversion matrix M comprising an inner product of the complete set of polynomials P over the domain Σ; obtaining the set of orthonormal polynomials F based on the conversion matrix M and the complete set of polynomials P, wherein the set of orthonormal polynomials characterize ocular aberrations of the eye of the patient; and using a processing hardware having a non-transitory tangible medium embodying machine-readable code associated therewith to determine the vision treatment for the patient based on the set of orthonormal polynomials F, the vision treatment comprising a spectacle lens shape, an intraocular lens shape, a contact lens shape, a corneal ring implant shape, a corneal inlay shape, a corneal onlay shape, a corneal implant shape, or a laser treatment shape, wherein the domain Σ has a shape selected from the group consisting of a hexagon, an ellipse, an annulus, a rectangle, and a square, such that: when the domain Σ has the hexagon shape, the set of orthonormal polynomials F includes a polynomial term of 1, a polynomial term of  a polynomial term of  and polynomial term of when the domain Σ has the ellipse shape, the set of orthonormal polynomials F includes a polynomial term of 1, a polynomial term of 2 ρ cos θ, a polynomial term of  and polynomial term of when the domain Σ has the annulus shape, the set of orthonormal polynomials F includes a polynomial term of 1, a polynomial term of  a polynomial term of  and polynomial term of when the domain Σ has the rectangle shape, the set of orthonormal polynomials F includes a polynomial term of 1, a polynomial term of  a polynomial term of  and polynomial term of  and when the domain Σ has the square shape, the set of orthonormal polynomials F includes a polynomial term of 1, a polynomial term of √{square root over (6)}ρ cos θ, a polynomial term of √{square root over (6)}ρ sin θ, and polynomial term of wherein ρ and Θ are polar coordinates, wherein e and a are aspect ratios, and wherein ε is an obscuration ratio.