Wavefront expansion basis functions and their relationships

Wavefront expansion basis functions are important in representing ocular aberrations and phase perturbations due to atmospheric turbulence. A general discussion is presented for the conversions of the coefficients between any two sets of basis functions. Several popular sets of basis functions, namely, Zernike polynomials, Fourier series, and Taylor monomials, are discussed and the conversion matrices between any two of these basis functions are derived. Some analytical and numerical examples are given to demonstrate conversion of coefficients of different basis function sets.