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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Precision Engineering

    Background:

    • Phase-shifting interferometry (PSI) algorithms are designed to correct for phase shift increment errors and harmonic distortions.
    • A significant, yet often overlooked, error source in PSI is the synergistic effect of these two imperfections.
    • This combined error significantly impacts the accuracy of phase estimation in Fizeau interference signals.

    Purpose of the Study:

    • To derive an analytical formula for quantifying the combined errors of phase shift tuning and harmonic distortions in PSI.
    • To identify the characteristics of an optimal PSI algorithm that minimizes these combined errors.
    • To establish realistic error bounds for sub-nanometer metrology in Fizeau cavities.

    Main Methods:

    • Development of a novel analytical formula to evaluate the combined impact of phase shift detuning and harmonic distortions.
    • Analysis of Fizeau interference signals, considering multiple reflections.
    • Comparison of advanced PSI algorithms and two-beam calculations.

    Main Results:

    • Phase shift tuning errors amplify the sensitivity to higher-order harmonics in Fizeau signals.
    • Multiple reflections drastically increase the error contribution of detuning, by orders of magnitude compared to two-beam models.
    • A practical limit of 30% tuning error is identified for sub-nm metrology in a 4%-4% Fizeau cavity.

    Conclusions:

    • The combination of phase shift errors and harmonic distortions is a critical error source in PSI.
    • Advanced PSI algorithms are susceptible to these combined errors, especially in multi-reflection environments.
    • For high-precision measurements in spherical cavities, wavelength tuning or iterative solvers accommodating unknown phase shifts are recommended over traditional mechanical phase shifting.