Ultraprecise Measurement of Thermal Expansion Coefficients — Recent Progress

Abstract

A technique has been developed for measurement of small displacements. The method relies on multiple beam optical interference, with the sample used as a Fabry‐Perot etalon spacer. Extreme precision is made possible by monitoring in the electrical domain the thermally induced changes in optical interference. The method is as follows: A frequency stable laser is used to probe the resonances of a Fabry‐Perot etalon whose mirrors are optically contacted to the ends of the sample. The incident beam is electro‐optically modulated to impress sidebands on it which can be moved in frequency until one coincides with a Fabry‐Perot transmission peak. When the sample temperature is changed an amount ΔT the subsequent length change ΔL causes the Fabry‐Perot resonances to shift an amount $\mathrm{\Delta \nu \hspace{0.17em}=\hspace{0.17em}(\nu /}\mathrm{L}\mathrm{)\Delta }\mathrm{L}$ . This change in modulation frequency is related to the thermal expansion coefficient $\text{α\hspace{0.17em}≡\hspace{0.17em}(1/Δ}\mathrm{T}\mathrm{)\hspace{0.17em}(\Delta }\mathrm{L}/\mathrm{L}\text{)\hspace{0.17em}=\hspace{0.17em}(1/Δ}\mathrm{T}\mathrm{)(\Delta \nu /\nu )}$ . For small values of α the precision of measurement is limited by the laser's frequency stability, which is approximately one part in 10⁹. Measurements have been made in the temperature range 0 – 300°C. A proposal is outlined for increasing the laser's stability and hence the precision of measurement by at least 3 orders of magnitude. Applications for such high precision are discussed.