Low-coherence interferometric dimensional measurement technique based on synchrosqueezed wavelet transform

This paper addresses the issue of reduced measurement stability in low-coherence measurement techniques when applied to glass-based dispersive media. A high-precision, low-coherence interferometric measurement method is proposed based on synchrosqueezed Wavelet Transform (SSWT). First, the Schott dispersion formula is used to analyze the impact of glass-based dispersive media on the phase of the interference spectrum. Wavelet transform is then employed to extract the chirp information of the interference spectrum, enabling the separation of optical path lengths for different wavenumbers. Building upon this, SSWT is introduced to enhance time-frequency resolution further, improving the measurement performance of the system. An experimental setup is constructed to validate the effectiveness of the proposed method. Compared to traditional methods, SSWT optimizes the distribution of wavelet coefficients, concentrating signal energy and significantly improving instantaneous frequency capture accuracy. Experimental results show that, in addition to effectively capturing chirp characteristics and reducing phase noise, SSWT achieves a 3-fold and 7-fold improvement in peak full-width at half-maximum compared to conventional Fourier Transform (FT) and Continuous Wavelet Transform (CWT), respectively, and a 9.1-fold and 17.1-fold improvement in standard deviation over 20 measurements, demonstrating superior noise resistance and measurement precision. In conclusion, the SSWT-based white-light interferometric measurement method provides a high-precision, reliable solution for dimensional measurements in industrial applications.