Determination of Optical Constants of Transparent Solids Based on Double Thickness Transmittance Model of Polynomial Root

In determining the optical constants of transparent solids using spectral inversion methods, certain problems such as inversion errors and computational time consumption, have to be solved. This study establishes two spectral transmittance equations with the thickness satisfying the integer ratio based on the traditional double-thickness transmittance model. A polynomial equation related to the extinction coefficient is obtained through an algebraic operation, and the extinction coefficient is calculated by solving and selecting a real root greater than 0 and less than 1. Subsequently, the unitary quadratic equation is solved for interface reflectivity, thereby selecting the roots that are greater than 0 and less than 1 to calculate the refractive index. In the process of determining the optical constants, the new method does not suffer from inversion errors, time-consuming iterative calculations, or multivalue problems. As an application example, the optical constants of CaF₂ and Si were calculated using the experimental data of double-thickness transmittance in the literature, and the results were compared with those in the literature. The results show that the new method is superior to traditional spectral inversion methods and provides a new option for high-precision determination of optical constants of transparent solids.