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    Area of Science:

    • Optics and Photonics
    • Interferometry
    • Metrology

    Background:

    • Sinusoidal phase modulating interferometers (SPMI) often suffer from nonlinearity due to phase modulation depth errors, carrier phase delay, and imperfect low-pass filters.
    • The arctangent approach for phase generated carrier (PGC-Arctan) demodulation is sensitive to these nonlinearities, impacting measurement accuracy.
    • Accurate real-time evaluation and reduction of these nonlinearities are crucial for high-precision interferometric measurements.

    Purpose of the Study:

    • To propose and validate a modified EOM-based SPMI system for real-time normalization of quadrature components in PGC-Arctan demodulation.
    • To introduce a fixed-phase-difference detection method for real-time evaluation of periodic nonlinearity in PGC demodulation.
    • To demonstrate the effectiveness of the proposed real-time normalization technique in reducing nonlinear errors and enabling nanometer displacement measurements.

    Main Methods:

    • A modified EOM-based SPMI was developed, incorporating a monitor and a probe interferometer sharing a reference corner cube.
    • Periodic interference signals were generated using a slowly moving stage for real-time normalization of quadrature components.
    • A fixed-phase-difference detection method using two photodetectors at a quarter-fringe interval was employed to evaluate nonlinear errors.

    Main Results:

    • The real-time normalization technique successfully reduced the nonlinear error in phase demodulation to less than ± 1°.
    • The fixed-phase-difference detection method effectively evaluated periodic nonlinearities in real time.
    • Nanometer-level displacement measurements were achieved, demonstrating the practical utility of the proposed method.

    Conclusions:

    • The modified EOM-based SPMI with real-time normalization effectively mitigates nonlinear errors in PGC-Arctan demodulation.
    • The fixed-phase-difference detection method provides a reliable means for real-time nonlinearity assessment.
    • The proposed approach significantly enhances the accuracy and precision of interferometric displacement measurements.