高阶衍射积分ENZ理论中级数表达式的截断策略
Truncation strategy for the series expressions in the advanced ENZ-theory of diffraction integrals
摘要：
最近发表在J. Europ. Opt. Soc. Rap.公众8，13044（2013），以双无穷级数的形式给出了每个Zernike项的衍射积分。除了总方位角因子之外，这些双级数还涉及用于径向依赖性的Jinc函数与结构量$c_t$的乘积，该结构量取决于光学系统的光学参数（诸如NA和折射率）和散焦值。二重级数中的乘积具有与Clebsch-Gordan系数相关的系数，该系数取决于Jinc函数的阶数和结构量的指数$t$，以及所涉及的Zernike项的方位角阶数和度。此外，结构量本身也以双无穷级数的形式给出。在本文中，我们给出了截断规则的各种无穷级数取决于指定的所需的精度。
英文摘要：
The advanced ENZ-theory of diffraction integrals, as published recently in J. Europ. Opt. Soc. Rap. Public. 8, 13044 (2013), presents the diffraction integrals per Zernike term in the form of doubly infinite series. These double series involve, aside from an overall azimuthal factor, the products of Jinc functions for the radial dependence and structural quantities $c_t$ that depend on the optical parameters of the optical system (such as NA and refractive indices) and the defocus value. The products in the double series have coefficients that are related to Clebsch-Gordan coefficients and that depend on the order of the Jinc function and the index $t$ of the structural quantity, as well as on the azimuthal order and degree of the involved Zernike term. In addition, the structural quantities themselves are also given in the form of doubly infinite series. In this paper, we give truncation rules for the various infinite series depending on specified required accuracy.
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