Dimensionality-reduced iterative ellipse fitting algorithm for fiber-optic sinusoidal frequency modulation interferometer quadrature signal correction

•A computationally efficient dimensionality-reduced iterative ellipse fitting algorithm is proposed.•Real-time correction of the interferometer quadrature signals based on the fast ellipse fitting are realized.•This method supports interferometer to perform fast and accurate displacement measurement in extended range.•This method can be economically deployed with low sampling rate and sparing hardware resource. A computationally efficient ellipse fitting algorithm is introduced to address the quadrature signal distortions in fiber-optic sinusoidal frequency modulation interferometer (SFMI) when extending the measurement range. The disturbance effects are firstly eliminated with the established multiple error factor signal model for pre-correction. Then, the dimensionalities of the Lissajous ellipse equation formed by the pre-corrected quadrature signals are downscaled for fast iterative fitting. Finally, the fit ellipse parameters are used to real-time correct distortions in the quadrature signals, guarantying fast and accurate phase measurement in extended displacement range. Simulations and experiments verified that the proposed method could extend the measurement range of SFMI to 20 mm with nonlinear error of 0.8 nm and allowable measurement speed up to 1.55 m/s, and could be economically deployed with low sampling rate (30 MHz) and sparing hardware resource. These merits significantly enhance the performance of the SFMI and broaden its applications.