Zernike基到笛卡尔变换
Zernike Basis to Cartesian Transformations
摘要：
2D（圆形）和3D（球形）泽尼克函数的径向多项式被制成表作为径向距离的幂。还给出了一系列径向多项式中径向距离的幂的倒数列表，基于利用单位间隔上多项式的正交性的投影。它们可以在多项式的乘积展开为和的过程中发挥作用，并通过一些例子证明了这一点。多项式乘以角基（方位角、极角）定义了泽尼克函数，我们推导出该函数，并将其转换成以圆或球的中间为中心的笛卡尔坐标系，并将其转换成表格。
英文摘要：
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They may play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive and tabulate transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
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