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

To solve some problems in the determination of substance optical constants by spectral inversion, based on the traditional double thickness transmittance model, spectral transmittance equations with thicknesses of L and 2L are established. The eighth-order polynomial equation related to the attenuation coefficient is obtained through an algebraic operation. Real roots greater than 0 and less than 1 are solved to calculate the attenuation coefficient and extinction coefficient. Then, the quadratic equation with one unknown quantity about the interface reflectivity is solved, and the roots greater than 0 and less than 1 are selected to calculate the refractive index. In the process of determining the optical constants, the new method has no inversion error or iterative calculation time-consuming problems. The reliability of the new method is verified using the known optical constants of heptane from the literature, and the influence on the calculation results was analyzed when the double thickness does not satisfy the double relationship. In conclusion, when the relative error of the second thickness 2L was no more than 1%, the calculation error of the extinction coefficient was no more than 2.03%, and when three strong absorption points were not considered, the calculation error of the refractive index was no more than 1%.