Conjugate complex function coupling strategy of interferometric field: Synthetic-wavelength interferometric fringe extraction in simultaneous dual-wavelength interferometry. (May 2023)

• Record Type: Journal Article
• Authors: Cheng, Jinlong; Chen, Guibin; Xu, LiPing; Cheng, Ju; Zuo, Fen; Yang, Zhongming; Gao, Zhishan; Yuan, Qun
• Is Part Of: Optics and lasers in engineering. Volume 164(2023)
• Publication Date: 2023-05
• Subjects: Interferometry -- Phase measurement -- Dual-wavelength -- Fourier transform techniques; Lasers in engineering -- Periodicals; Optical measurements -- Periodicals; Optics -- Periodicals; Lasers en ingénierie -- Périodiques; Mesures optiques -- Périodiques; Optique -- Périodiques; 621.36605
• DOI: 10.1016/j.optlaseng.2023.107495
• Languages: English
• ISSNs: 0143-8166

Abstract

Highlights: The CCFC method could extract the synthetic-wavelength interferogram from moiré fringe patterns in simultaneous dual-wavelength interferometry without the introduction of other wavelength interferometric information. Coupled by the multiplication for the conjugate complex functions, only the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. The half-band filter in used in CCFC method is appropriate for the different spectral width or carrier spatial frequency. The necessary introduced linear carrier in CCFC method is merely about 0.0947 times of the carrier in the traditional spatial domain fourier transform demodulation theory numerically. The introduced carrier is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes in CCFC method. Abstract: Simultaneous dual-wavelength interferometry (SDWI) supplies a better solution to extend the measurement range of traditional single-wavelength interferometry with higher efficiency. To decompose the needed longer beat-frequency synthetic-wavelength ( λ S ) information from the generated moiré fringe pattern in SDWI, a conjugate complex function coupling strategy (CCFC) of interferometric field is proposed in this study. By the Fourier transform and the half-band filter in one side of the spectrum, the positive half spectrum is obtained. The inverse Fourier transform and conjugate operation are performed on the half spectrums to obtain the two conjugate complex functions of the interferometric field. Coupled by the multiplication for the conjugate complex functions, the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. And if the SDWI is implemented with the π/2 phase shift at λ S, the obtained phase-shift interferogram for λ S could be demodulated by the conventional phase-shift algorithm. Compared with other spatial-domain Fourier transform demodulation theory, the half-band filter used in CCFC method is appropriate for the different spectral width and carrier spatial frequency. The necessary introduced linear carrier is merely about 0.0947 times of the carrier in the former numerically. And it is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes. The feasibility and applicability of the CCFC method are verified using simulation and experimental results.