The advantage of using polynomials is that the wavefront aberration function is typically expanded in polynomials.
The choice of polynomials from the point of view of surface description can be challenged. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The majority of optical designs to date have relied on conic sections and polynomials as the functions of choice. Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. 36/3 (2012), 485-501.In this paper, we summarize our initial experiences in designing head-worn displays with free-form optical surfaces. Hickernell), Multivariate interpolation with increasingly flat radial basis functions of finite smoothness, Adv. Wozniakowski) On dimension-independent rates of convergence for function approximation with Gaussian kernels, SIAM J. McCourt) Stable evaluation of Gaussian radial basis function interpolants, SIAM J. Ye) Approximation of stochastic partial differential equations by a kernel-based collocation method, Int. Ye), Reproducing kernels of Sobolev spaces via a Green function approach with differential operators & boundary operators, Adv. Ye) Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, Appl. McCourt) An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels, Numerical Algorithms 86 (2015), 393-422. McCourt) The method of fundamental solutions in solving coupled boundary value problems for M/EEG, SIAM J. McCourt) Kernel-based Approximation Methods using MATLAB, Interdisciplinary Mathematical Sciences Vol.9, World Scientific Publishers, Singapore, 2015.
0 kommentar(er)
