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Phase-shifting algorithm inside an optical cavity for absolute length measurement.

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    A new phase-shifting algorithm enhances optical cavity measurements by compensating for nonlinear phase errors. This method significantly reduces systematic errors in length and diameter measurements, improving precision.

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    Area of Science:

    • Optical physics
    • Metrology
    • Interferometry

    Background:

    • Phase-shifting interferometry (PSI) is crucial for precise measurements within optical cavities.
    • Conventional PSI algorithms struggle with spatially uniform phase errors from nonlinear phase modulation.
    • Existing methods often introduce systematic errors, like 1.5 nm for a 3% quadratic nonlinearity.

    Purpose of the Study:

    • To develop an error-compensating PSI algorithm for enhanced measurement accuracy.
    • To eliminate systematic errors caused by nonlinear phase modulation in optical cavity measurements.
    • To improve the precision of length and diameter measurements for cubic objects and spheres.

    Main Methods:

    • Proposed a novel error-compensating phase-shifting algorithm.
    • Introduced a modified discrete Fourier transform window within a 13-frame algorithm.
    • Extended sampling weight definitions to complex numbers to address dc errors.

    Main Results:

    • The new algorithm effectively eliminates spatially uniform phase errors.
    • Reduced systematic errors from 1.5 nm to less than 0.5 nm for a 3% quadratic nonlinearity.
    • Demonstrated improved accuracy in measuring cubic object lengths and metal sphere diameters.

    Conclusions:

    • The developed algorithm significantly enhances the precision of phase-shifting interferometry.
    • It offers a robust solution for compensating nonlinear phase modulation errors in optical measurements.
    • This advancement is vital for high-accuracy metrology applications.