Abstract
Measurement and mathematical description of the corneal surface and the optical properties of the human eye is an active field in biomedical engineering and ophthalmology. One particular problem is to correct certain types of corneal shape measurement errors, e.g. ones that arise due to unintended eye-movements and spontaneous rotations of the eye-ball. In this paper we present the mathematical background of our recent approach, which is based on constructions of systems of orthonormal functions based on the well-known Zernike polynomials. For this, argument transformation by suitable Blaschke functions are used, as they correspond to the congruent transformations in the Poincaré disk model of the Bolyai–Lobachevsky hyperbolic geometry, making them a practical choice. The problem of discretization, and computation of the translated Zernike coefficients is also discussed.
The first author’s research was supported by the Hungarian Government and co-financed by the European Social Fund under project EFOP-3.6.3-VEKOP-16-2017-00001: Talent Management in Autonomous Vehicle Control Technologies. The second and the third authors’ research was supported by the Hungarian Scientific Research Funds (OTKA) No. K115804.
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Németh, Z., Schipp, F., Weisz, F. (2020). Hyperbolic Transformations of Zernike Functions and Coefficients. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12014. Springer, Cham. https://doi.org/10.1007/978-3-030-45096-0_47
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