Broad Range and High Precision Self-Mixing Interferometer Based on Spectral Analysis With Multiple Reflections

Abstract

In this paper, a novel self-mixing interferometer is proposed with spectral analysis by multiple reflection technique. The relationship between the vibration amplitude, the dominant frequency, and the reflection time is deduced, which indicates that the theoretical minimum measurable vibration amplitude is <inline-formula> <tex-math notation= LaTeX >$0.21\\lambda $ </tex-math></inline-formula>/G(N,<inline-formula> <tex-math notation= LaTeX >$\\theta$ </tex-math></inline-formula>) and the precision is about <inline-formula> <tex-math notation= LaTeX >$0.08\\lambda $ </tex-math></inline-formula>/G(N,<inline-formula> <tex-math notation= LaTeX >$\\theta$ </tex-math></inline-formula>). The displacement sensitivity gain G(N,<inline-formula> <tex-math notation= LaTeX >$\\theta$ </tex-math></inline-formula>) increases with the reflection time. Theoretical analysis results show that the proposed method for vibration measurement has the advantages of high precision and broad measurement range, especially for the measurement of amplitude much smaller than <inline-formula> <tex-math notation= LaTeX >$\\lambda $ </tex-math></inline-formula>/2. The validity of the method is tested by several experiments with different amplitudes and reflection times. An amplitude of 75 nm has been proved to be measurable and the absolute error is 5.43 nm, which is within the theoretical error range. The proposed method plays an important role in high precision and nanoscale measurement.