Method on double-pass acousto-optic frequency shifter in absolute distance measurement using Fabry-Pérot interferometry

In order to realize nanometer-scale absolute distance measurements based on Fabry-Pérot interferometry for long-range displacement measurement of the moving coil in Joule balance, the acousto-optic frequency shifter (AOFS) in double-pass configuration is presented, and a tunable frequency difference in a range of 200 MHz is achieved. The focus length of the lens is determined by analyzing the relationship of the tradeoff between the AOFS modulation bandwidth and its diffraction efficiencies; the beam spot of the first-order diffraction beam is guaranteed by accurately positioning the focused beam according to the distribution of the zero-order diffraction beam spot. The experimental single-pass and double-pass peak diffraction efficiency of the AOFS are 79.54% and 61.41%, respectively; the tunable frequency difference of 440-640 MHz, which is twice the single-pass modulation bandwidth output of 220-320 MHz, is obtained by the beat note between the incident beam and the first-order diffraction beam of the double-pass AOFS, and has a good signal-to-noise ratio. Theoretical analysis shows that a folded Fabry-Pérot cavity length displacement of about 53 mm can be measured through the tunable frequency difference achieved by means of double-pass AOFS.