Picometer measurements of strain coefficients by quadrature interferometry and lock-in amplification

Abstract

Modulated strain displacements were measured with a quadrature Michelson–Morley interferometer employing polarization optics and two lock-in amplifiers to filter noise and thermal drift. The advantages of the technique, its limitations, and estimates on the accuracy are discussed, including an algorithm to correct for non-ideal components and non-linear effects. Instructions for the construction and setup of the quadrature interferometer are provided. To test the interferometer, the dynamic converse piezoelectric effect was used, and by modulating the electric field across the sample, the d14 strain coefficient for x-cut quartz was determined to be 0.66±0.04 pC/N, which is within 1.5 standard deviations of the accepted standard. The measurements had a standard deviation of 4.1 pm, resulting in standard errors as low as 5 fm/V after fitting.