Fast and robust computation of Cartesian derivatives of Zernike polynomials

This work deals with a problem of an effective and robust evaluation of Cartesian partial derivatives of Zernike polynomials. Calculations based on explicit relations suffer from high computational costs and are numerically instable for higher orders. Thus, fast and numerically stable methods for calculation of derivatives of Zernike polynomials are needed. Such methods employing recursive techniques based on the relation of Zernike radial polynomials to Jacobi polynomials are proposed. The performance of proposed algorithms is compared to the standard calculation using explicit relations.