A novel micro-vibration reconstruction method based on inverse Hilbert transform is presented. By inversing either side of the SMI signal after Hilbert transform, micro-vibration can be reconstructed quickly and conveniently. In the paper, the principle of inverse Hilbert transform algorithm is studied. And, the effectiveness of the method is verified through simulated signals, and several experiments are carried out, including the self-mixing signal affected by speckle effect. The experimental results show that the external cavity phase can be rapidly extracted by inverse Hilbert transform algorithm, and the relative error is no more than 7%.

中文翻译：

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基于逆希尔伯特变换的激光自混合干涉测量微振动测量

提出了一种基于希尔伯特逆变换的微振动重构新方法。通过希尔伯特变换后反转SMI信号的任一侧，可以快速方便地重建微振动。本文研究了逆希尔伯特变换算法的原理。并且，通过仿真信号验证了该方法的有效性，并进行了多次实验，包括受斑点效应影响的自混合信号。实验结果表明，利用逆希尔伯特逆变换算法可以快速提取外腔相位，相对误差不超过7％。