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

Abstract 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.