Fig. 3: Design and demonstration of the acoustic micrometer using spiral twist meta-atoms.

a A physical micrometer through spiral twist of a mechanical knob. b An acoustic micrometer designed by the spiral twist meta-atoms loaded with screw threads with a pitch of d, where an interference intensity is regarded as a displacement mark. c Interference intensity versus the spiral twist displacement for the acoustic micrometer (q = 4) with d = 3 mm, 10 mm and 16 mm, where the relevant results of experiments (red balls), the ideal theory (black solid curves), the coupled-mode theory (dot curves) involving the phase distortion and practical losses in meta-atoms, and the fitting results using Eq. (3) (dash dot curves) are respectively shown in each case. The stable region (shaded area ranging from 0 to π/8) in all cases is selected as the available measurement range for the acoustic micrometer. The error bars are the standard deviation of three measurements. d Scaling formula of the acoustic micrometer (q = 4 and d = 16 mm) using logarithmically fitting (solid curve) on experimental data (red balls), which is used for micron-scale displacement metrology. The error bars are the standard deviation of one hundred measurements.