泽尔尼克多项式拟合波面中采样点数目的研究

摘要

In order to study the effect of sampling point number on fitting precision when fitting wave front by Zernike polynomials, it was analyzed by means of the method of inadequate induction, and then the change law of sampling point number and fitting precision of dozens of different test functions was obtained.The results reveal that all test functions follow the same law that fitting precision has little change when sampling point number reach a certain number.In addition, the change law of sampling point number and Zernike polynomials term number was obtained by calculation.Thus, the experiential formula to determinate sampling point number are found, which is of great practical instructional significance in wave front fitting with Zernike polynomials.%为了研究采样点数目对由泽尔尼克多项式所拟合的波面的拟合精度的影响,采用不完全归纳法进行了理论分析,取得了数十个不同的测试函数的采样点与拟合精度之间的数据关系.结果表明,不同的测试函数遵循相同的规律,即采样点数目达到一定数目后,拟合精度随采样点的变化很小;并通过计算得到了在较高拟合精度时,采样点数目与泽尔尼克多项式的项数之间的变化规律,由此得到相关的采样点数目确定的经验公式.这对于泽尔尼克多项式拟合波面具有很好的指导意义.