Discrete sampling points of non-circular aperture orthogonal polynomials wave-front fitting

The Zernike polynomial is a widely used analytical technique in optics. Because of the discrete sampled measurement data and widely used non-circle aperture system in modern optical engineering, Zernike polynomial fitting can not satisfy a requirement completely. A kind of non-circle aperture discrete sampled orthogonal polynomial based on Zernike polynomial was proposed. The orthogonal basis was obtained using matrix QR decomposition method for discrete samples. Zernike polynomial and orthogonal polynomial were used for fitting 150 mm90 mm rectangular grating wave-front. The differences of PV and RMS between two methods are 0.013 waves and less than 0.001 waves respectively for the residual wave-front. Comparison of different order fitting of the orthogonal polynomial and Zernike polynomial coefficients, indicate that the orthogonal polynomial coefficients are independent of each other. And the corresponding Seidel aberrations were calculated by the orthogonal polynomial coefficients. Orthogonal polynomial coefficients can be solved one by one. This method can significantly improve the solution speed.