Lens design distortion management using orthogonal polynomial functions

We propose the use of slope orthogonal polynomials as a tool to manage distortion. The object-to-image mapping of the whole optical system is reduced to a single refracting surface, which reproduces the same lens mapping function (LMF) as the original optical system. Using slope orthogonal polynomials to describe this LMF equivalent surface, the orthogonal properties of the polynomial can be leveraged for efficient use of ray tracing by relating coordinates mapping to a surface gradient. We demonstrate that this distortion measurement can be linked to a physical surface aspherical departure in the case of a double Gauss objective. This relationship can be established for any surfaces, after a calibration step. We also show that this same relationship can be used to obtain a target LMF by setting a precomputed aspherical surface departure on a given surface. (c) 2023 Society of Photo-Optical Instrumentation Engineers (SPIE)