A simplified expression for aspheric surface fitting

Compared to a conventional optical lens with spherical surfaces, an aspheric lens has many merits. However, due to the nonlinearity in its mathematical expression, its characterization is quite difficult. In this paper, we proposed a new method to construct discrete orthogonal polynomials by the binomial expansion of irrational part into even order terms. The proposed method utilizes last two polynomials to compute conic constant and subsequently applies it to separate desired coefficients. The least squares method is employed to retrieve coefficients of discrete orthogonal polynomials in fitting. Simulation and experiment were performed to test the method. The results indicate that the method is not only able to retrieve accurate parameters, but also has fast convergence speed.