A Multi-Stage Algorithm of Fringe Map Reconstruction for Fiber-End Surface Analysis and Non-Phase-Shifting Interferometry

Interferometers are essential tools for quality control of optical surfaces. While interferometric techniques like phase-shifting interferometry offer high accuracy, they involve complex setups, require stringent calibration, and are sensitive to phase shift errors, noise, and surface inhomogeneities. In this research, we introduce an alternative algorithm that integrates Moving Average and Fast Fourier Transform (MAFFT) techniques with Polynomial Fitting. The proposed method achieves results comparable to a Zygo interferometer under standard conditions, with an error margin under 2%. It also maintains measurement stability in noisy environments and in the presence of significant local inhomogeneities, operating in real-time to enable wavefront measurements at 30 Hz. We have validated the algorithm through simulations assessing noise-induced errors and through experimental comparisons with a Zygo interferometer.