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本文提出了使用一组正交多项式推导出波前多项式的方法,而正交多项式在光学设计和评价中与扇形光束有着特殊的联系。本方法剔除了一般曲线拟合法中不能令人满意的方面,一般曲线拟合法是用排列、相切或最小二乘方来建立一个光瞳径向坐标和光瞳方位角余弦的升幂多项式。
In this paper, we propose a method to derive wavefront polynomials using a set of orthogonal polynomials. Orthogonal polynomials have a special relationship with fan-shaped beams in optical design and evaluation. This method eliminates unsatisfactory aspects of the general curve fitting method. Generally, the curve fitting method uses an arrangement, a tangent or a least squares method to establish an ascending polynomial of the pupil radial coordinate and the pupil azimuth cosine.