Using ellipsometry for curved-surface characterization requires the knowledge of the surface normal vector in order to determine material-related surface parameters like refractive index, layer thickness, or birefringence of the surface material at the incidence point, because the recorded signal depends on both the (unknown) surface normal vector n → and material-related surface characteristics. It is convenient in ellipsometry to parametrize the surface normal vector by the angle of incidence θ and the azimuthal rotation angle ϕ. Depending on the design of the ellipsometer, there may be two angles, ϕ 1 and ϕ 2, necessary, which describe the azimuthal rotation before and after the light is reflected off the sample, respectively. The authors present analytic formulas to determine ϕ 1 and ϕ 2 for optically isotropic samples using generalized ellipsometry. The resulting measurement uncertainty is lower than that of previously known methods. Furthermore, the authors provide an analytic formula to calculate θ from the ellipsometric angles Ψ and Δ for bare substrates with known refractive index N 1 = n 1 − i k 1. The formulas have been evaluated with experimental data acquired with a conventional and an imaging retroreflection-based return-path ellipsometer.

中文翻译：

---

使用基于反射的广义椭偏法计算各向同性介质和裸基板的表面倾角的解析解

使用椭圆偏光法进行曲面表征需要了解表面法向量，​​以确定与材料相关的表面参数，例如入射点处表面材料的折射率、层厚度或双折射，因为记录的信号取决于（未知）表面法向量 n → 和材料相关的表面特征。在椭偏法中，通过入射角 θ 和方位角旋转角 ϕ 来参数化表面法向量是很方便的。根据椭偏仪的设计，可能需要两个角度 ϕ 1 和 ϕ 2 ，分别描述光从样品反射之前和之后的方位角旋转。作者提出了使用广义椭圆偏光法确定光学各向同性样品的 ϕ 1 和 ϕ 2 的解析公式。由此产生的测量不确定度低于以前已知的方法。此外，作者提供了一个解析公式，用于根据具有已知折射率 N 1 = n 1 − ik 1 的裸基板的椭偏角 Ψ 和 Δ 来计算 θ。这些公式已经用常规和成像逆向反射获得的实验数据进行了评估基于返回路径椭偏仪。