Department of Electrical Engineering, University of Malaya, Kuala Lumpur, Malaysia.
Opt Lett. 2013 Jul 15;38(14):2487-9. doi: 10.1364/OL.38.002487.
In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.
在光学中，泽尼克多项式被广泛应用于测试、波前传感和像差理论。这组独特的径向多项式在单位圆上是正交的，在其边界上是有限的。本文提出了一种使用径向多项式和第二类切比雪夫多项式之间的关系来计算泽尼克径向多项式的递归公式。与以前的算法不同，推导出的递归关系既不依赖于径向多项式的阶数，也不依赖于其方位角阶数。这导致了计算复杂度的降低。
