A posteriori error of the transmission interference method of thin film refractive index calculation

Abstract

The method of a posteriori error calculation has been applied to the calculation of the refractive index and thickness of optical thin films from spectrophotometric transmission interference measurements. The refractive index and thickness of transparent or semitransparent thin film deposited on a transparent substrate can be calculated using both Edser - Butler and Swanepoel equations. A least-squares method and smoothing have been used to refine the Swanepoel's estimate and a correlation analysis has been applied to the differences between the two refractive index estimates. The refractive index covariance function is approximated by an exponential function and is then used in the statistical modelling process. The method has been applied to the calculation of the refractive index of a thin film deposited on a quartz substrate. In practice the method is especially useful in view of its ability to detect the deterioration of data caused by instrumental drift.