# Non-Destructive Ellipsometric Analysis of the Refractive Index of Historical Enamels

## TL;DR

This study uses non-destructive ellipsometry to measure the refractive index of historical enamels and compares mathematical models for lead glasses.

## Contribution

The paper evaluates and compares mathematical models for calculating the refractive index of historical enamels using non-destructive methods.

## Key findings

- Measured refractive indices of historical enamels (1.59–1.66) are higher than typical lead glasses (1.55–1.57).
- The Bonetti and Salvagno model (1983) is the most accurate for historical enamels with errors < 0.04 units.
- PbO and B2O3 are key compounds influencing refractive index, while metallic elements increase it further.

## Abstract

The refractive index is an important parameter for the restoration of historical cultural heritage and for non-destructive optical techniques. In this study, different mathematical models for lead glasses were assessed in order to analyze their feasibility to calculate the theoretical refractive index of the historical enamels in stained-glass windows. The models selected were those specifically developed for lead glasses: the Appen method (1949), the Fanderlik and Skrivan model (1972), and the Bonetti and Salvagno method (1983). The results of the mathematical methods were compared with the real values analyzed via ellipsometry. The historical enamels were determined on non-prepared samples, taking into account the Cauchy model in order to avoid damaging the historical pieces. We show that the measured refractive indices of the historical enamels (1.59–1.66) are higher than the values of the lead glasses in the literature (1.55–1.57). The PbO and B2O3 were the compounds that most influenced the value of the refractive index; nevertheless, the presence of metallic elements increased their value compared to pure lead glasses. In addition, the presence of a thin layer of grisaille on the historical enamels and the formation of alteration layers could also modify the real value of the refractive index. As far as theoretical calculations are concerned, the mathematical model of Bonetti and Salvagno (1983) seems to be the most accurate model for this material, with errors < 0.04 units. None of the three models work for glasses with >60% PbO, which is not common in cultural heritage.