Ray and wave aberrations revisited: a Huygens-like construction yields exact relations.
Ray and wave aberrations revisited: a Huygens-like construction yields exact relations.
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DOI：
10.1364/josaa.33.000160
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
J. Restrepo;Pawel Stoerck;Ivo Ihrke
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文献类型：
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作者：
J. Restrepo;Pawel Stoerck;Ivo Ihrke
光学系统的像差可以用波像差来描述，波像差定义为与理想球面波前的偏离；或光线像差，其又是在像平面中测量的近轴光线交点的偏差。两种描述之间的经典联系是一种近似，据我们所知，其误差迄今为止尚未通过分析量化。我们推导出精确的解析方程，用于根据波像差 (OPD) 和参考球面计算波前表面、像差光线方向和横向光线像差。我们引入了函数成为 OPD 函数的精确条件，证明每个这样的函数都有一个相关的波前，并研究了经典近似产生的误差。我们设定严格的条件，使误差尽可能小。我们用数值模拟来说明我们的结果。我们的结果表明，大数值孔径和具有强梯度的 OPD 函数会产生更大的近似误差。
The aberrations of an optical system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersections measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, to our knowledge, so far not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and OPD functions with strong gradients yield larger approximation errors.