Acoustic method for determination of the effective temperature and refractive index of air in accurate length interferometry

Abstract

An acoustic method for the measurement of the effective temperature and refractive index of air for precision length interferometry is described. The method can be used to improve the accuracy of interferometric length measurements outside the best laboratory conditions and also in industrial conditions. The method is based on the measurement of speed of 50-kHz ultrasound over the same distance measured with a laser interferometer. The measured speed of ultrasound is used to define the effective temperature or the refractive index of air along the laser beam path using the equations presented. The measured speed of sound, Cramer equation, dispersion correction, and Edlén equations are used in the fitting of new equations for the effective air temperature and refractive index of air as a function of speed of 50-kHz ultrasound. The standard uncertainties of the effective temperature and the refractive index of air equations are 15 mK and 1.7×10–8, respectively. The uncertainties of the effective temperature and refractive index of air measured with the test setup for distances of about 5 m are 25 mK and 2.6×10–8, respectively.