获得了一组方形域内标准正交的矢量多项式集，可以用于方形域内图像畸变映射及波前梯度等矢量数据的拟合。这组矢量多项式是用Gram-Schmidt方法将泽尼克梯度多项式标准正交化后得到的。由该矢量函数拟合被测波前斜率，拟合系数经过简单的线性变换就可以直接得到用泽尼克多项式描述的波前，获得被测波前的相位信息。实验结果表明，该矢量集可以对夏克哈特曼传感器测得的方形孔径内的斜率进行很好的拟合。这种矢量拟合重构方法能获得很好的被测波前，具有与Southwell区域法相同的精度。

A new set of orthonormal vector polynomials in a square area, which can be used in image distortion mapping and wavefront gradient vector datum fitting, is derived. These vector polynomials are developed from the gradients of the circular Zernike polynomials orthonormalization by using Gram-Schmidt technique. When the slope is fitted by these vector polynomials, the fitting coefficients can be derived and transformed to the wavefront description of the Zernike polynomials mode by using a linear transform, and the phase information is then extracted. Experimental results show that the slope data from Shack-Hartmann wavefront sensor over a square area are well fitted by theses vector polynomials. The vector polynomial wavefront reconstruction method can reconstruct the tested wavefront quite well and achieve the same accuracy as Southwell zonal method does.