Refractive-index determination of solids from first- and second-order critical diffraction angles of periodic surface patterns

We present two approaches for measuring the refractive index of transparent solids in the visible spectral range based on diffraction gratings. Both require a small spot with a periodic pattern on the surface of the solid, collimated monochromatic light, and a rotation stage. We demonstrate the methods on a polydimethylsiloxane film (Sylgard® 184) and compare our data to those obtained with a standard Abbe refractometer at several wavelengths between 489 and 688 nm. The results of our approaches show good agreement with the refractometer data. Possible error sources are analyzed and discussed in detail; they include mainly the linewidth of the laser and/or the angular resolution of the rotation stage. With narrow-band light sources, an angular accuracy of ±0.025∘ results in an error of the refractive index of typically ±5 ⋅ 10−4. Information on the sample thickness is not required.