Vector polynomials for direct analysis of circular wavefront slope data

In the aberration analysis of a circular wavefront, Zernike circle polynomials are used to obtain its wave aberration coefficients. To obtain these coefficients from the wavefront slope data, we need vector functions that are orthogonal to the gradients of the Zernike polynomials, and are irrotational so as to propagate minimum uncorrelated random noise from the data to the coefficients. In this paper, we derive such vector functions, which happen to be polynomials.