Sur Amit, Joshi K D, Sharma Archana, Kaushik T C
Applied Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India.
Homi Bhabha National Institute, Mumbai 400094, India.
Rev Sci Instrum. 2020 Jan 1;91(1):015001. doi: 10.1063/1.5092252.
Instantaneous frequency extraction of a highly nonstationary optical interferometric fringe signal using continuous wavelet transform with Morlet wavelet often fails in the neighborhood of the null phase gradient. The present work reports that the optimal selection of the central frequency and time variance of the Morlet wavelet reduces the spread of wavelet energy to its adjacent bins, and the reassignment technique further sharpens the energy density and enhances accuracy of the extracted instantaneous frequency of the fringe signal. The developed algorithm is applied to a sinusoidal frequency-modulated fringe signal for which the mean square error percentage in normalized instantaneous frequency is determined to be 0.0032 Hz, which is significantly less than 0.0507 Hz obtained with a conventional continuous wavelet transform. Results are also compared with the existing phase stepping technique and found to be more accurate and free from any ripple like nonlinear error for sinusoidal fringe signals. The proposed technique is applied to a fringe signal obtained with a Michelson interferometer, generating displacement profiles that show advantages over those produced by the phase stepping technique. The applicability of the proposed technique is further extended to an arbitrary phase signal.
使用具有Morlet小波的连续小波变换来提取高度非平稳光学干涉条纹信号的瞬时频率，在零相位梯度附近常常会失败。目前的工作表明，Morlet小波中心频率和时间方差的最优选择可减少小波能量向其相邻频段的扩散，而重分配技术进一步锐化了能量密度，并提高了提取的条纹信号瞬时频率的准确性。所开发的算法应用于正弦调频条纹信号，其归一化瞬时频率的均方误差百分比确定为0.0032 Hz，这明显小于采用传统连续小波变换所获得的0.0507 Hz。结果还与现有的相移技术进行了比较，发现对于正弦条纹信号，该算法更准确且不存在任何类似纹波的非线性误差。所提出的技术应用于用迈克尔逊干涉仪获得的条纹信号，生成的位移轮廓显示出优于相移技术所产生的轮廓的优势。所提出技术的适用性进一步扩展到任意相位信号。
