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Geometrical description of quasi-hemispherical and calotte-like surfaces using discretised argument-transformed Chebyshev-polynomials

The even Chebyshev-polynomials of the second kind - modified with appropriate argument-transforms - were used to describe quasi-hemispherical and calotte-like natural surfaces over a set of discrete points - and via interpolation - between these points. The point-set used was selected in a manner that promotes the proper approximation of such surfaces and the numerical implementation of the surface representation algorithm. The representations of such optical surfaces (e.g., the outer surface of the human cornea) in the basis formed by these Chebyshev-polynomials - and by their transformed versions - provide computational alternatives to the Zernike-based description of the optical aberrations caused by such surfaces.