Generalized Zernike polynomials: Integral representation and Cauchy transform

TL;DR

This paper derives an integral representation for generalized 2D Zernike polynomials and explicitly describes how the Cauchy transform acts on them, advancing mathematical tools for optical and image analysis.

Contribution

It provides a new integral representation for generalized Zernike polynomials and explicitly characterizes the Cauchy transform's action on these functions.

Findings

Integral representation of generalized Zernike polynomials derived

Explicit expression for the Cauchy transform on these polynomials obtained

Mathematical tools for optical and image processing enhanced

Abstract

The aim of this paper is two fold. We derive an integral representation for the generalized 2D Zernike polynomials which are of independent interest and give the explicit expression of the action of the Cauchy transform on them.