This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field behavior of Zernike polynomials are derived from the fourth-order wavefront aberration function for this class of optical systems. Then, such expressions are combined to retrieve the full field dependence of primary coma, primary astigmatism, and field curvature. They are described by an elliptical conic-shaped surface with a variable apex location over the field of view, by a binodal surface with two nodes over the field of view, and by a general elliptical surface with one node. The proposed analytical expressions provide a better understanding of the primary aberration behavior for these systems and can be of great use in their optical design and aberration correction. An optical system constituted by a pair of tilted and decentered biconic lenses is studied to validate the proposed expressions.

中文翻译：

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具有圆形光瞳的摄动双平面对称系统中主像差的全场依赖性

本文研究了由倾斜和偏心表面以及圆形光瞳组成的扰动双平面对称光学系统的基本像差理论。首先，从此类光学系统的四阶波前像差函数中得出描述Zernike多项式的全场特性的解析表达式。然后，将这些表达式组合起来以检索原发性昏迷，原发性散光和场曲的全场依赖性。它们由在视场上具有可变顶点位置的椭圆形圆锥形表面，在视场上具有两个节点的二面体表面以及具有一个节点的普通椭圆形表面来描述。所提出的解析表达式可以更好地理解这些系统的主要像差行为，并且可以在其光学设计和像差校正中大量使用。研究了由一对倾斜和偏心的双锥形透镜构成的光学系统，以验证所提出的表达式。