Application of Tikhonov Regularization Method in Zernike Polynomials Fitting

To acquire coefficients of Zernike polynomials is a discrete ill-posedness problem.Common methods,such as Least Squares Error method,Cram-Schmidt orthogonalization method and Householder transformation method,can not obtain a stable numerical solution.The instability of ill-posedness problem is analyzed and a Tikhonov regularization method is introduced to solve ill-posed problem.The L curve criterion is used to determine regularization parameter.Simulation result shows that Tikhonov regularization method is stable and effective for solving ill-posedness problem.