A general auto-shift minimal-step phase-shifting algorithm for arbitrary cavity length

• Published in: Optics and lasers in engineering Vol. 149; p. 106791
• Main Authors: Chang, Lin, He, Tingting, Yu, Yingjie
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2022
• Subjects: Interferometry; Phase demodulation; Phase-shifting by wavelength-tuning; Wavefront reconstruction; Window function; Wavefront reconstruction; Phase-shifting by wavelength-tuning; Window function; Phase demodulation; Interferometry
• ISSN: 0143-8166
• DOI: 10.1016/j.optlaseng.2021.106791

•The innovation and practical significance of this manuscript are as follows:•compared with the existing multi-surface phase-shifting algorithms, the proposed algorithm can realize the measurement in arbitrary cavity lengths of the measured plate.•through a set of interferograms, the phase information of the front surface, rear surface, and thickness variation signal can be obtained simultaneously.•by the proposed pre-matching technique, the optimal phase-shifting value and the minimum frames of the captured interferograms can be auto-shifted to realize the measurements at arbitrary cavity lengths.•the weighting operation in phase demodulation can be achieved by matrix operation using the data of all pixels in the interferogram. So the complex point-by-point calculation is avoided.•the frequencies of the interferometric signals are estimated by the corresponding optical path differences. By this method, the measurement costs can be further reduced. Phase demodulation by wavelength-tuning phase-shifting interferometry is increasingly significant for precision metrology of engineering surfaces. However, the existing multi-surface measurement algorithms can only be applied to the case that the cavity length of the measured plate is a certain multiple of its optical thickness. For flexible muti-surface interferometry, we present a general auto-shift minimal-step phase-shifting algorithm (AMPA) for arbitrary cavity lengths. To achieve this, as a basis, the in-depth analysis of the residual error of the phase demodulation algorithm under each combination of the cavity coefficient M and the phase division number N is performed. By this method, the residual error of the phase demodulation algorithm can be controlled by adjusting N for each M. And due to a wise selection of the Blackman-Harris window function, the satisfactory abilities of harmonic error suppression and phase extraction can be provided. The performance of the developed algorithm is studied under various factors, and its superiority over traditional algorithms is verified. Based on the Zernike polynomials, the numerical simulation indicates the maximum error of reconstructed wavefronts is less than 2 × 10−5λ0. Experimental studies on a rectangular plate and a circular plate using a Fizeau wavelength-tuning interferometer further imply that our algorithm is valid and reliable. Meanwhile, a comparative analysis of the reconstructed surface shapes using the developed AMPA and the classical 36-step and 6N-5 algorithms is performed based on the introduced height evaluation parameters. The comparative results show that the maximum errors of the arithmetic mean height Sa and the root mean square height Sq are 6.8 nm and 6.5 nm, respectively. And other height parameters also support the validity of the proposed algorithm.