基于环扇域正交多项式的波前重构仿真

以Zernike多项式为基函数,利用Gram-Schmidt正交化方法推导出在环扇区域内正交的一组多项式;通过对比发现,同阶的新多项式与Zernike多项式在各自正交的区域内具有相似的分布和物理意义;分别用Zernike多项式、环域正交多项式、外接圆多项式和环扇域正交多项式拟合环扇区域内一组给定的波面畸变采样数据,并仿真加入不同扰动时各组拟合系数的变化情况,得到环扇域正交多项式的拟合系数最为稳定,有最佳的抗扰动能力.

Simulation of Wavefront Reconstruction Based on Polynomials Orthogonalized in an Annulus Sector Domain

A series of polynomials orthogonalized in an annulus sector domain is derived from Zernike polynomials by using Gram-Schmidt orthogonalizing method. The same terms of the two polynomials are found to have similar distributions and physical meanings in their respective orthogonal domains. An aberrated wavefront on an annulus sector domain is expanded with Zernike polynomials, annular Zernike polynomials, circumcircle Zernike polynomials and annulus sector Zernike polynomials respectively. The 4 sets of coefficients are compared in cases where the aberrated wavefront is without and with additional perturbations. It is found that the coefficients of the annulus sector domain orthogonalized polynomials are the most stable ones and have the best anti-perturbation capability.