A C++ Incarnation of Zernike Circle Functions

TL;DR

This paper presents a C++ library for Zernike functions, enabling evaluation, conversion, and expansion of these functions for applications in optics and image analysis.

Contribution

It introduces a comprehensive C++ implementation with methods for evaluation, conversion between indices, and expansion of Zernike products, enhancing computational tools for optical analysis.

Findings

Provides efficient evaluation of Zernike functions inside the unit circle.

Enables conversion between radial/azimuthal parameters and Noll's index.

Supports expansion of Zernike products into sums of Zernike functions.

Abstract

An explicit C++ library is provided which deals with Zernike Functions over the unit circle as the main subject. The implementation includes basic means to evaluate the functions at points inside the unit circle and to convert the radial and azimuthal parameters to Noll's index and vice versa. Advanced methods allow to expand products of Zernike Functions into sums of Zernike Functions, and to convert Zernike Functions to polynomials over the two Cartesian coordinates and vice versa.