Smooth functions and their use in optical modeling and design

Analytical description of unknown smooth optical functions such as optical surface and wavefront phases will have profound importance in optical modeling and design. Polynomial models have been extensively used to describe smooth function. Various forms of polynomials for describing the smooth functions may be considered both in optical modeling and design. In optics, the Zernike polynomials are potential candidates to describe optical surface and wavefront phases. However, they are restrained to specific geometry and suffer from numerical instability, especially for describing complex functions. More recently, spline model functions were also investigated for describing the optical surface shape and wavefront phase.