Ray tracing approach to refractive index measurement of prism samples in a vacuum cell

Research experiments and advanced applications often require the knowledge of the refractive index of vitreous materials under specific environmental conditions. Measurements are carried out by placing the glass sample in a cell where the required conditions are established; the probe beam enters and exits the cell through a pair of windows. A typical case is the measurement in vacuum, as it occurs when thermal cycles down to cryogenic temperatures have to be performed. In such a case, data processing has to take into account the specific geometry of the cell and the windows. Here we present closed formulas for a symmetrical configuration, and a ray tracing approach for general cases where symmetry is not guaranteed. In particular, the experimental configuration is conveniently modeled, and ray tracing is used to find out the conditions of minimum deviation, starting from a tentative value of the refractive index. The latter is successively modified until the data actually obtained from experiments are matched. Specific software is developed, accomplishing the computation task automatically by recursive iterations. The ray-tracing model is also used to numerically estimate the sensitivity of the results to the influence variables, and to work out the uncertainty balance.