双目瞳孔上的正交基函数集
Orthogonal Set of Basis Functions over the Binocular Pupil
摘要：
二维圆形区域上的正交基函数集-最常表示光学应用中的瞳孔-在文献中已知用于全圆（Zernike或Jacobi多项式）和环。本文提出了一个正交集，如果该地区是两个不重叠的圆形瞳孔相同的大小。主要的自由参数是瞳孔半径与两个圆之间的距离之比。越来越高阶的像差-定义为一个虚拟的更大的瞳孔，其中两个瞳孔嵌入-被送入一个Gram-Schmidt正交化，以实现一个独特的一组基函数。关键要素是计算出一整套原始基函数之间的重叠积分（两个瞳孔之间距离中点的幂与傅立叶型方位角函数的乘积）。
英文摘要：
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work proposes an orthogonal set if the area is two non-overlapping circular pupils of same size. The major free parameter is the ratio of the pupil radii over the distance between both circles. Increasingly higher order aberrations--as defined for a virtual larger pupil in which both pupils are embedded--are fed into a Gram-Schmidt orthogonalization to implement one unique set of basis functions. The key element is to work out the overlap integrals between a full set of primitive basis functions (products of powers of the distance from the mid-point between both pupils by azimuthal functions of the Fourier type).
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