Analytical determination of the complex refractive index and the incident angle of an optically isotropic substrate by ellipsometric parameters and reflectance.

An analytical solution for the determination of both angle of incidence (AOI) and the complex refractive index from combined ellipsometric and reflectometric measurements at optically isotropic substrates is presented. Conventional ellipsometers usually measure flat surfaces because the curvatures of the surface alter the reflected or transmitted light, which causes experimental errors due to the deviation of the incident angle. However, in real industrial applications, the shapes of samples are usually curved or even free-form. In this case, the knowledge of the AOI is essential. The proposed method provides a simple way to measure the AOI and the complex refractive index of nonplanar samples without extra or complicated hardware.