Stepwise Fourier correction algorithm for enhancing the robustness of dispersion fringe sensing to tip/tilt errors

This work explores the performance of dispersion fringe sensing (DFS) in the presence of tip/tilt errors. A dispersion fringe model incorporating the effects of tip/tilt errors is proposed, revealing the significant impact on the quality of the dispersion fringes. The theoretical analysis shows that tip/tilt errors blur the dispersion fringes and introduce additional optical path difference. Importantly, a novel two-step algorithm, to our knowledge, is proposed to correct the detection results based on the Fourier transform. Numerical simulations demonstrate that the algorithm achieves high-precision piston sensing with an RMS error of about 0.005 µm. These promising results suggest that DFS can still be used for high-precision co-phase sensing despite inevitable tip/tilt errors.