... Optical Science Laboratory, Department of Physics and Astronomy, University College London, London, WC1E 6BT, U.K. љ The simplex method, a data fitting method to any type of function, is refined by eliminating a redundant process. The refined method is applied to Zernike polynomials in Cartesian coordinates, which describe an optical surface or wavefront in terms of aberrations. ... Data fitting to Zernike polynomials has mainly been done by the least-squares method (Malacara et al. ...