A third‐order aberration analytical analysis method of soft X‐ray optical systems with orthogonal and coplanar arrangement of the main planes of elements is proposed. Firstly, the transfer equations of the aperture ray and the principle ray are derived; then, based on the third‐order aberration theory with the aperture‐ray coordinates on the reference exit wavefront of a plane‐symmetric optical system, the aberration expressions contributed by the wave aberration and defocus of this kind of optical system are studied in detail. Finally, the derived aberration calculation expressions are applied to calculate the aberration of two design examples of such types of optical systems; the images are compared with ray‐tracing results obtained using the Shadow software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory. The analytical analysis method of aberration is helpful in the design and optimization of the soft X‐ray optical systems with orthogonal and coplanar arrangement of the main planes of optical elements.

中文翻译：

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元素主平面正交和共面排列的软X射线光学系统的三阶像差

提出了一种软X射线光学系统的三阶像差分析方法，该方法在元素主平面正交和共面排列的情况下。首先，推导了孔径射线和主射线的传递方程。然后，基于三阶像差理论，在平面对称光学系统的参考出射波阵面具有孔径射线坐标，详细研究了这种光学系统的波像差和散焦所产生的像差表达式。最后，将导出的像差计算表达式用于计算这种类型的光学系统的两个设计示例的像差。将图像与使用“阴影”获得的光线跟踪结果进行比较验证像差表达式的软件。研究表明，像差表达的准确性令人满意。像差的分析分析方法有助于设计和优化具有正交且共面布置光学元件主平面的软X射线光学系统。