Degeneracy in freeform surfaces described with orthogonal polynomials

Abstract

Orthogonal polynomials offer useful mathematical properties for describing freeform optical surfaces. Their advantages are best leveraged by understanding the interactions between variables such as tip and tilt, base sphere and conic variables, and packaging variables that define the problem of design for manufacture. These interactions can cause degeneracy, which can complicate the interpretation of design specifications in manufacturing and, consequently, negatively impact the cost of fabrication and assembly. Optimization constraints to break degeneracy during design are also discussed.