A-POSTERIORI ERROR OF THE TRANSMISSION INTERFERENCE METHOD OF THIN-FILM REFRACTIVE-INDEX CALCULATION

The method of a posteriori error calculation has been applied to the c alculation of the refractive index and thickness of optical thin films from spectrophotometric transmission interference measurements. The r efractive index and thickness of transparent or semitransparent thin f ilm deposited on a transparent substrate can be calculated using both Edser-Butler and Swanepoel equations. A least-squares method and smoot hing have been used to refine the Swanepoel's estimate and a correlati on analysis has been applied to the differences between the two refrac tive index estimates. The refractive index covariance function is appr oximated by an exponential function and is then used in the statistica l modelling process. The method has been applied to the calculation of the refractive index of a Sc2O3 thin film deposited on a quartz subst rate. In practice the method is especially useful in view of its abili ty to detect the deterioration of data caused by instrumental drift.