Related Experiment Video
Updated: May 18, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
Published on: August 13, 2019
Comparative assessment of freeform polynomials as optical surface descriptions
Ilhan Kaya1, Kevin P Thompson, Jannick P Rolland
1Department of Electrical Engineering and Computer Science, Univ. of Central Florida, 4000 Central Florida Blvd., Orlando, Florida 32816, USA. ilhan.b.kaya@gmail.com
Abstract:
Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication.
Related Concept Videos
Synthetic Disvision of Polynomials
Gauss's Law: Planar Symmetry
Theorems of Pappus and Guldinus: Problem Solving
Parseval's Theorem for Fourier transform
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
Polar Equations of Conics
Methods of Medium Optimization

